Pressure and Temperature Sensitive Paints (Experimental Fluid Mechanics)

Experimental Fluid Mechanics R.J. Adrian · M. Gharib · W. Merzkirch D. Rockwell · J.H. Whitelaw

T. Liu J.P. Sullivan

Pressure and Temperature Sensitive Paints

Tianshu Liu NASA Langley Research Center MS 493, Hampton, VA 23681-0001 USA Prof. John P. Sullivan Purdue University School of Aeronautics and Astronautics 315 N. Grant St. Grissom Hall West Lafayette, IN 47907-2023 USA

ISBN 3-540-22241-3

Springer Berlin Heidelberg New York

Library of Congress Control Number: 2004109333 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in other ways, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable to prosecution under German Copyright Law. Springer is a part of Springer Science+Business Media springeronline.com

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Series Editors Prof. R.J. Adrian University of Illinois at Urbana-Champaign Dept. of Theoretical and Applied Mechanics 216 Talbot Laboratory 104 South Wright Street Urbana, IL 61801 USA Prof. M. Gharib California Institute of Technology Graduate Aeronautical Laboratories 1200 E. California Blvd. MC 205-45 Pasadena, CA 91125 USA Prof. Dr. W. Merzkirch Universit¨ at Essen Lehrstuhl f¨ ur Str¨ omungslehre Sch¨ utzenbahn 70 45141 Essen Germany Prof. Dr. D. Rockwell Lehigh University Dept. of Mechanical Engineering and Mechanics Packard Lab. 19 Memorial Drive West Bethlehem, PA 18015-3085 USA Prof. J.H. Whitelaw Imperial College Dept. of Mechanical Engineering Exhibition Road London SW7 2BX UK

Preface

The aim of this book is to provide a systematic description of pressure and temperature sensitive paints (PSP and TSP) developed since the 1980s for aerodynamics/fluid mechanics and heat transfer experiments. PSP is the first global optical technique that is able to give non-contact, quantitative surface pressure visualization for complex aerodynamic flows and provide tremendous information on flow structures that cannot be easily obtained using conventional pressure sensors. TSP is a valuable addition to other global temperature measurement techniques such as thermographic phosphors, thermochromic liquid crystals and infrared thermography. This book mainly covers research made in the United States, Japan, Germany, France, Great Britain and Canada. Excellent work on PSP in Russia has been described in the book “Luminescent Pressure Sensors in Aerodynamic Experiments” by V. E. Mosharov, V. N. Radchenko and S. D. Fonov of the Central Aerohydrodynamic Institute (TsAGI). We are truly grateful to our colleagues in the field of PSP and TSP for kindly providing their paper drafts, offering comments, and allowing us to use their published results. Without their helps, this book cannot be completed. Especially, we would like to thank the following individuals and organizations: T. Amer, K. Asai, J. H. Bell, T. J. Bencic, O. C. Brown, G. Buck, A. W. Burner, S. Burns, B. Campbell, B. F. Carroll, L. N. Cattafesta, J. Crafton, R. C. Crites, G. Dale, R. H. Engler, R. G. Erausquin, W. Goad, L. G. Goss, J. W. Gregory, M. Gounterman, M. Guille, M. Hamner, J. M. Holmes, C. Y. Huang, J. P. Hubner, J. Ingram, H. Ji, R. Johnston, J. D. Jordan, M. Kameda, M. Kammeyer, J. T. Kegelman, N. Lachendro, J. Lepicovsky, Y. Le Sant, X. Lu, Y. Mebarki, R. D. Mehta, K. Nakakita, C. Obara, D. M. Oglesby, T. G. Popernack, W. M. Ruyten, H. Sakaue, E. T. Schairer, K. S. Schanze, M. E. Sellers, Y. Shimbo, K. Teduka, S. D. Torgerson, B. T. Upchurch, A. N. Watkins. NASA, ONR, AFOSR, Boeing, Raytheon, Japanese NAL.

Table of Contents

1.

2.

3.

4.

5.

Introduction .................................................................................................... 1 1.1. Pressure Sensitive Paint ....................................................................... 2 1.2. Temperature Sensitive Paint ................................................................ 8 1.3. Historical Remarks ............................................................................ 11 Basic Photophysics....................................................................................... 15 2.1. Kinetics of Luminescence.................................................................. 15 2.2. Models for Conventional Pressure Sensitive Paint ............................ 18 2.3. Models for Porous Pressure Sensitive Paint ...................................... 24 2.3.1. Collision-Controlled Model .................................................... 26 2.3.2. Adsorption-Controlled Model................................................. 27 2.4. Thermal Quenching ........................................................................... 31 Physical Properties of Paints ........................................................................ 33 3.1. Calibration ......................................................................................... 33 3.2. Typical Pressure Sensitive Paints ...................................................... 34 3.3. Typical Temperature Sensitive Paints................................................ 45 3.4. Cryogenic Paints................................................................................ 50 3.5. Multi-Luminophore Paints................................................................. 54 3.6. ‘Ideal’ Pressure Sensitive Paint ......................................................... 56 3.7. Desirable Properties of Paints............................................................ 58 Radiative Energy Transport and Intensity-Based Methods .......................... 61 4.1. Radiometric Notation......................................................................... 61 4.2. Excitation Light ................................................................................. 62 4.3. Luminescent Emission and Photodetector Response......................... 65 4.4. Intensity-Based Measurement Systems ............................................. 69 4.4.1. CCD Camera System .............................................................. 70 4.4.2. Laser Scanning System ........................................................... 74 4.5. Basic Data Processing........................................................................ 75 Image and Data Analysis Techniques........................................................... 81 5.1. Geometric Calibration of Camera...................................................... 82 5.1.1. Collinearity Equations............................................................. 82 5.1.2. Direct Linear Transformation ................................................. 85 5.1.3. Optimization Method .............................................................. 87 5.2. Radiometric Calibration of Camera ................................................... 92 5.3. Correction for Self-Illumination ........................................................ 95 5.4. Image Registration........................................................................... 102 5.5. Conversion to Pressure .................................................................... 105 5.6. Pressure Correction for Extrapolation to Low-Speed Data.............. 107 5.7. Generation of Deformed Surface Grid............................................. 112

X

6.

7.

8.

Table of Contents

Lifetime-Based Methods ............................................................................ 115 6.1. Response of Luminescence to Time-Varying Excitation Light ....... 116 6.1.1. First-Order Model ................................................................. 116 6.1.2. Higher-Order Model ............................................................. 118 6.2. Lifetime Measurement Techniques.................................................. 118 6.2.1. Pulse Method ........................................................................ 118 6.2.2. Phase Method........................................................................ 119 6.2.3. Amplitude Demodulation Method ........................................ 121 6.2.4. Gated Intensity Ratio Method ............................................... 123 6.3. Fluorescence Lifetime Imaging ....................................................... 128 6.3.1. Intensified CCD Camera ....................................................... 128 6.3.2. Internally Gated CCD Camera .............................................. 130 6.4. Lifetime Experiments ...................................................................... 131 Uncertainty ................................................................................................. 137 7.1. Pressure Uncertainty of Intensity-Based Methods........................... 137 7.1.1. System Modeling .................................................................. 137 7.1.2. Error Propagation, Sensitivity and Total Uncertainty ........... 138 7.1.3. Photodetector Noise and Limiting Pressure Resolution........ 141 7.1.4. Errors Induced by Model Deformation ................................. 144 7.1.5. Temperature Effect ............................................................... 145 7.1.6. Calibration Errors.................................................................. 145 7.1.7. Temporal Variations in Luminescence and Illumination ...... 146 7.1.8. Spectral Variability and Filter Leakage ................................ 146 7.1.9. Pressure Mapping Errors....................................................... 146 7.1.10. Paint Intrusiveness ................................................................ 147 7.1.11. Other Error Sources and Limitations .................................... 148 7.1.12. Allowable Upper Bounds of Elemental Errors...................... 149 7.1.13. Uncertainties of Integrated Forces and Moments.................. 150 7.2. Pressure Uncertainty Analysis for Subsonic Airfoil Flows ............. 151 7.3. In-Situ Calibration Uncertainty ....................................................... 156 7.3.1. Experiments .......................................................................... 156 7.3.2. Simulation ............................................................................. 159 7.4. Pressure Uncertainty of Lifetime-Based Methods ........................... 163 7.4.1. Phase Method........................................................................ 163 7.4.2. Amplitude Demodulation Method ........................................ 164 7.4.3. Gated Intensity Ratio Method ............................................... 166 7.5. Uncertainty of Temperature Sensitive Paint .................................... 169 7.5.1. Error Propagation and Limiting Temperature Resolution..... 169 7.5.2. Elemental Error Sources ....................................................... 170 Time Response ........................................................................................... 175 8.1. Time Response of Conventional Pressure Sensitive Paint............... 175 8.1.1. Solutions of Diffusion Equation............................................ 175 8.1.2. Pressure Response and Optimum Thickness......................... 178 8.2. Time Response of Porous Pressure Sensitive Paint ......................... 182 8.2.1. Deviation from the Square-Law............................................ 182 8.2.2. Effective Diffusivity ............................................................. 183 8.2.3. Diffusion Timescale.............................................................. 186

Table of Contents

XI

8.3. 8.4.

Measurements of Pressure Time Response...................................... 187 Time Response of Temperature Sensitive Paint .............................. 194 8.4.1. Pulse Laser Heating on Thin Metal Film .............................. 195 8.4.2. Step-Like Jet Impingement Cooling ..................................... 198 9. Applications of Pressure Sensitive Paint .................................................... 201 9.1. Low-Speed Flows ............................................................................ 201 9.1.1. Airfoil Flows ......................................................................... 201 9.1.2. Delta Wings, Swept Wings and Car Models......................... 207 9.1.3. Impingement Jet.................................................................... 214 9.2. Subsonic, Transonic and Supersonic Wind Tunnels........................ 215 9.2.1. Aircraft Model in Transonic Flow ........................................ 215 9.2.2. Supercritical Wing at Cruising Speed ................................... 221 9.2.3. Transonic Wing-Body Model ............................................... 223 9.2.4. Laser Scanning Pressure Measurement on Transonic Wing . 225 9.2.5. Boundary Layer Control in Supersonic Inlets....................... 226 9.3. Hypersonic and Shock Wind Tunnels.............................................. 230 9.3.1. Expansion and Compression Corners ................................... 230 9.3.2. Moving Shock Impinging to Cylinder Normal to Wall......... 236 9.4. Cryogenic Wind Tunnels ................................................................. 237 9.5. Rotating Machinery ......................................................................... 242 9.5.1. Laser Scanning Measurements.............................................. 242 9.5.2. CCD Camera Measurements................................................. 247 9.6. Impinging Jets.................................................................................. 249 9.7. Flight Tests ...................................................................................... 256 9.8. Micronozzle ..................................................................................... 260 10. Applications of Temperature Sensitive Paint ............................................. 263 10.1. Hypersonic Flows .......................................................................... 263 10.2. Boundary-Layer Transition Detection ........................................... 270 10.3. Impinging Jet Heat Transfer .......................................................... 275 10.4. Shock/Boundary-Layer Interaction ................................................ 280 10.5. Laser Spot Heating and Heat Transfer Measurements ................... 282 10.6. Hot-Film Surface Temperature in Shear Flow ............................... 289 References .................................................................................................. 293 Appendix A. Calibration Apparatus ........................................................... 313 Appendix B. Recipes of Typical Pressure and Temperature Sensitive Paints................................................. 317 Appendix C. Vendors ................................................................................. 319 Color Plates ................................................................................................ 321 Index........................................................................................................... 327

1. Introduction

Quantitative measurements of surface pressure and temperature in wind tunnel and flight testing are essential to understanding of the aerodynamic performance and heat transfer characteristics of flight vehicles. Pressure data are required to determine the distribution of aerodynamic loads for the design of a flight vehicle, while temperature data are used to estimate heat transfer on the surface of the vehicle. Pressure and temperature measurements provide critical information on important flow phenomena such as shock, flow separation and boundary-layer transition. In addition, accurate pressure and temperature data play a key role in validation and verification of computational fluid dynamics (CFD) codes. Traditionally, surface pressure is measured by utilizing a pressure tap or orifice at a location of interest connected through a small tube to a pressure transducer (Barlow et al. 1999). Hundreds of pressure taps are needed to obtain an acceptable pressure field on a complex aircraft model. Manufacturing, tubing and preparing such a model for wind tunnel testing is very labor-intensive and costly. For thin models such as supersonic transports, military aircraft and small fan blades, installation of a large number of pressure taps is impossible. Furthermore, pressure measurements at discrete taps ultimately limit the spatial resolution of measurements such that some details of a complex flow field cannot be revealed. Similarly, a surface temperature field is traditionally measured using temperature sensors such as thermocouples and resistance thermometers distributed at discrete locations (Moffat 1990). Since the 1980s, new optical sensors for measuring surface pressure and temperature have been developed based on the quenching mechanisms of luminescence. These luminescent molecule sensors are called pressure sensitive paint (PSP) and temperature sensitive paint (TSP). Compared with conventional techniques, they offer a unique capability for non-contact, full-field measurements of surface pressure and temperature on a complex aerodynamic model with a much higher spatial resolution and a lower cost. Therefore, they provide a powerful tool for experimental aerodynamicists to gain a deeper understanding of rich physical phenomena in complex flows around flight vehicles. Both PSP and TSP use luminescent molecules as probes that are incorporated into a suitable polymer coating on an aerodynamic model surface. In general, the luminophore and polymer binder in PSP and TSP can be dissolved in a solvent; the resulting paint can be applied to a surface using a sprayer or brush. After the solvent evaporates, a solid polymer coating in which the luminescent molecules are immobilized remains on the surface. When a light of a proper wavelength illuminates the paint, the luminescent molecules are excited and the luminescent

2

1. Introduction

light of a longer wavelength is emitted from the excited molecules. Figure 1.1 shows a schematic of a generic luminescent paint layer emitting radiation under excitation by an incident light. Detector (CCD, PMT, PD)

Excitation light (UV, laser, LED)

Optical Filter

Calibrated output for pressure & temperature

Emission

Luminescent molecule Binder (polymer, porous solid)

Fig. 1.1. Schematic of a luminescent paint (PSP or TSP) on a surface

The luminescent emission from a paint layer can be affected by certain physical processes. The main photophysical process in PSP is oxygen quenching that causes a decrease of the luminescent intensity as the partial pressure of oxygen or air pressure increases. The polymer binder for PSP is oxygen permeable, which allows oxygen molecules to interact with the luminescent molecules in the binder. For certain fast-responding PSP, a mixture of the luminophore and solvent is directly applied to a porous solid surface. In fact, PSP is an oxygen-sensitive sensor. By contrast, the major mechanism in TSP is thermal quenching that reduces the luminescent intensity as temperature increases. TSP is not sensitive to air pressure since the polymer binder used for TSP is oxygen impermeable, while due to the thermal quenching PSP is intrinsically temperature-sensitive. After PSP and TSP are appropriately calibrated, pressure and temperature can be remotely measured by detecting the luminescent emission. PSP and TSP are companion techniques because they not only utilize luminescent molecules as probes, but also use the same measurement systems and similar data processing methods.

1.1. Pressure Sensitive Paint The basic concepts of pressure sensitive paint (PSP) are simple. After a photon of radiation with a certain frequency is absorbed to excite the luminophore from the ground electronic state to the excited electronic state, the excited electron returns

1.1. Pressure Sensitive Paint

3

to the unexcited ground state through radiative and radiationless processes. The radiative emission is called luminescence (a general term for both fluorescence and phosphorescence). The excited state can be deactivated by interaction of the excited luminophore molecules with oxygen molecules in a radiationless process; that is, oxygen molecules quench the luminescent emission. According to Henry’s law, the concentration of oxygen in a PSP polymer is proportional to the partial pressure of oxygen in gas above the polymer. For air, pressure is proportional to the oxygen partial pressure. So, for higher air pressure, more oxygen molecules exist in the PSP layer and as a result more luminescent molecules are quenched. Hence, the luminescent intensity is a decreasing function of air pressure. The relationship between the luminescent intensity and oxygen concentration can be described by the Stern-Volmer relation. For experimental aerodynamicists, a convenient form of the Stern-Volmer relation between the luminescent intensity I and air pressure p is

I ref I

= A+ B

p p ref

,

(1.1)

where I ref and p ref are the luminescent intensity and air pressure at a reference condition, respectively. The Stern-Volmer coefficients A and B, which are temperature-dependent due to the thermal quenching, are experimentally determined by calibration. Theoretically speaking, the intensity ratio I ref / I can eliminate the effects of non-uniform illumination, uneven coating and nonhomogenous luminophore concentration in PSP. In typical tests in a wind tunnel, I ref is taken when the tunnel is turned off and hence it is often called the wind-off intensity (or image); likewise, I is called the wind-on intensity (or image). Figures 1.2 and 1.3 show, respectively, the luminescent intensity as a function of pressure at the ambient temperature and the corresponding Stern-Volmer plots for three PSPs: Ru(ph2-phen) in GE RTV 118, Pyrene in GE RTV 118 and PtOEP in GP 197. A measurement system for PSP or TSP is generally composed of paint, illumination light, photodetector, and data acquisition/processing unit. Figure 1.4 shows a generic CCD camera system for both PSP and TSP. Many light sources are available for illuminating PSP/TSP, including lasers, ultraviolet (UV) lamps, xenon lamps, and light-emitting-diode (LED) arrays. Scientific-grade chargecoupled device (CCD) cameras are often used as detectors because of their good linear response, high dynamic range and low noise. Other commonly-used photodetectors are photomultiplier tubes (PMT) and photodiodes (PD). A generic laser-scanning system, as shown in Fig. 1.5, typically uses a laser with a computer-controlled scanning mirror as an illumination source and a PMT as a detector along with a lock-in amplifier for both intensity and phase measurements. Optical filters are used in both systems to separate the luminescent emission from the excitation light.

4

1. Introduction

7 Ru(ph2-phen) in GE RTV 118 Pyrene in GE RTV 118 PtOEP in GP 197

6 5

I/Iref

4 3 2 1 0 0.0

0.2

0.4

0.6

0.8

1.0

p/pref Fig. 1.2. The luminescent intensity as a function of pressure for three PSPs at the ambient temperature, where pref is the ambient pressure and Iref is the luminescence intensity at the ambient conditions. 1.0

0.8

Iref/I

0.6

0.4

Ru(ph2-phen) in GE RTV 118

0.2

Pyrene in GE RTV 118 PtOEP in GP 197

0.0 0.0

0.2

0.4

0.6

0.8

1.0

p/pref Fig. 1.3. The Stern-Volmer plots for three PSPs at the ambient temperature, where pref is the ambient pressure and Iref is the luminescence intensity at the ambient conditions.

1.1. Pressure Sensitive Paint

5

Fig. 1.4. Generic CCD camera system for PSP and TSP

Once PSP is calibrated, in principle, pressure can be directly calculated from the luminescent intensity using the Stern-Volmer relation. Nevertheless, practical data processing is more elaborate in order to suppress the error sources and improve the measurement accuracy of PSP. For an intensity-based CCD camera system, the wind-on image often does not align with the wind-off reference image due to aeroelastic deformation of a model in wind tunnel testing. Therefore, the image registration technique must be used to re-align the wind-on image to the wind-off image before taking a ratio between those images. Also, since the SternVolmer coefficients A and B are temperature-dependent, temperature correction is certainly required since the temperature effect of PSP is the most dominant error source in PSP measurements. In wind tunnel testing, the temperature effect of PSP is to a great extent compensated by the in-situ calibration procedure that directly correlates the luminescent intensity to pressure tap data obtained at welldistributed locations on a model during tests. To further reduce the measurement uncertainty, additional data processing procedures are applied, including image

6

1. Introduction

summation, dark-current correction, flat-field correction, illumination compensation, and self-illumination correction. After a pressure image is obtained, to make pressure data more useful to aircraft design engineers, data in the image plane should be mapped onto a model surface grid in the 3D object space. Therefore, geometric camera calibration and image resection are necessary to establish the relationship between the image plane and the 3D object space. Besides the intensity-ratio method for a single-luminophore PSP, lifetime measurement systems and multi-luminophore PSP systems have also been developed. Theoretically speaking, the luminescent lifetime is independent of the luminophore concentration, illumination level and coating thickness. Hence, the lifetime method does not require the reference intensity (or image) and it is ideally immune from the troublesome ratioing process in the intensity-ratio method for a deformed model. Similarly, one of the purposes of developing the multipleluminophore PSP system is to eliminate the need of the wind-off reference image and reduce the error associated with model deformation. Another goal of using the multiple-luminophore PSP system is to compensate the temperature effect of PSP.

Computer

Laser Modulator

Lock-in Amplifier

PMT

2D Scanner

Laser Beam

Luminescence

Painted Model

Fig. 1.5. Generic laser scanning lifetime system for PSP and TSP

1.1. Pressure Sensitive Paint

7

Most PSP measurements have been conducted in high subsonic, transonic and supersonic flows on various aerodynamic models in both large production wind tunnels and small research wind tunnels. PSP is particularly effective in a range of Mach numbers from 0.3 to 3.0. Figure 1.6 shows a typical PSP-derived pressure field on the F-16C model at Mach 0.9 and the angle-of-attack of 4 degrees, which was obtained by Sellers and his colleagues (Sellers 1998a, 1998b, 2000; Sellers and Brill 1994) at the Arnold Engineering Development Center (AEDC). For PSP measurements in large wind tunnels, the accuracy of PSP is typically 0.02-0.03 in the pressure coefficient, while in well-controlled experiments the absolute pressure accuracy of 1 mbar (0.0145 psi) can be achieved. In short-duration hypersonic tunnels (Mach 6-10), measurements require very fast time response of PSP and minimization of the temperature effect of PSP. Binder-free, porous anodized aluminum (AA) PSP has been used in hypersonic flows and rotating machinery since it has a very short response time of 30–100 µs in comparison with a timescale of about 0.5 s for a conventional polymer-based PSP. Furthermore, because AA-PSP is a part of an aluminum model, an increase of the surface temperature in a short duration is relatively small due to the high thermal conductivity of aluminum. Since a porous PSP usually exhibits the pressure sensitivity at cryogenic temperatures, AA-PSP and polymerbased porous PSP have been used for pressure measurements in cryogenic wind tunnels where the oxygen concentration is extremely low and the total temperature is as low as 90 K.

Fig. 1.6. PSP image for the F-16C model at Mach 0.9 and the angle-of-attack of 4 degrees. From Sellers (2000)

8

1. Introduction

PSP measurements in low-speed flows are difficult since a very small change in pressure must be resolved and the major error sources must be minimized to obtain acceptable quantitative pressure results. Some low-speed PSP measurements were conducted on delta wings where upper surface pressure exhibited a relatively large change induced by the leading-edge vortices. In addition, experiments were conducted on airfoils, car models and impinging jets at speeds as low as 20 m/s. The pressure resolution of PSP in low-speed flows is ultimately limited by the photon shot noise of a CCD camera. Instead of pushing PSP instrumentation to the limit in low-speed flows, the pressure-correction method was proposed to recover the incompressible pressure coefficient from PSP results obtained in subsonic flows at suitably higher Mach numbers by removing the compressibility effect. Since PSP is a non-contact technique, it is particularly suitable to pressure measurements on high-speed rotating blades in rotating machinery where conventional techniques are difficult to use. Both CCD camera and laser scanning systems have been used for PSP measurements on rotating blades in turbine engines and helicopters. Impinging jets were used in some studies as a canonical flow for testing the performance of PSP systems. Flight test is a challenging area where PSP has showed its advantages as a non-contact, optical pressure measurement technique. The pressure distributions on wings and parts of aircrafts have been measured using film-based camera systems in early in-flight experiments and a laser scanning system in recent flight tests.

1.2. Temperature Sensitive Paint Temperature sensitive paint (TSP) is a polymer-based paint in which the temperature-sensitive luminescent molecules are immobilized. The quantum efficiency of luminescence decreases with increasing temperature; this effect associated with temperature is thermal quenching that serves as the major working mechanism for TSP. Over a certain temperature range, a relation between the luminescent intensity I and absolute temperature T can be written in the Arrhenius form

ln

E §1 I( T ) 1 = nr ¨ − ¨ I ( Tref ) R © T Tref

· ¸, ¸ ¹

(1.2)

where Enr is the activation energy for the non-radiative process, R is the universal gas constant, and Tref is a reference temperature in Kelvin. Figures 1.7 and 1.8 show, respectively, the temperature dependencies of the luminescent intensity and the Arrhenius plots for three TSPs: Ru(bpy) in Shellac, Rodamine-B in dope and EuTTA in dope. The procedure for applying TSP to a surface is basically the same as that for PSP. Not only does TSP use the same measurement systems shown in Figs. 1.4 and 1.5, but also most data processing methods for TSP are similar to those for PSP. Ideally, TSP can be used in tandem with PSP to correct

1.2. Temperature Sensitive Paint

9

the temperature effect of PSP and simultaneously obtain the temperature and pressure distributions. Compared to conventional temperature sensors, TSP is a global measurement technique that is able to obtain the surface temperature distribution with reasonable accuracy at a much higher spatial resolution. o A family of TSPs has been developed, covering a temperature range of –196 C o o to 200 C. The accuracy of TSP is typically 0.2-0.8 C. TSP has been used in various aerodynamic experiments to measure the temperature and heat transfer distributions. In hypersonic wind tunnel tests, TSP not only visualized flow transition patterns, but also provided quantitative heat transfer data calculated based on quasi-steady and transient heat transfer models. Figure 1.9 shows a windward-side heat transfer image of the lower half of the waverider model at Mach 10 at 0.57 s after the wind tunnel started to run (Liu et al. 1995b), where the 2 gray intensity bar denotes heat flux in kW/m . TSP is an effective technique for visualizing boundary-layer transition from laminar to turbulent flow. Due to a significant difference in convection heat transfer between the laminar and turbulent flow regimes, TSP can visualize a surface temperature change across the transition line. In low-speed wind tunnel tests, a model is typically heated or cooled to increase the temperature difference. However, in high-speed flows, friction heating often produces a sufficient temperature difference for TSP transition visualization. Cryogenic TSPs have been used to detect boundary-layer transition on airfoils in cryogenic wind tunnels over a range of the total temperatures from 90 K to 150 K. Complemented with other techniques, TSP has been used to study the relationship between heat transfer and flow structures in an acoustically excited impinging jet. The mapping capability of TSP allows quantitative visualization of the impingement heat transfer fields controlled (enhanced or suppressed) by acoustical excitation. The heat transfer fields in complex separated flows induced by shock/boundary-layer interactions have also been studied using TSP. A novel heat transfer measurement technique has been developed, which combines a laser scanning TSP and a laser spot heating units into a single non-intrusive system. An infrared laser was used to generate local heat flux and convection heat transfer was determined based on a transient heat transfer model from the surface temperature response measured using TSP. This system was applied to quantitative heat transfer measurements in complex flows on a 75-degree swept delta wing and around an intersection of a strut and a wall. Through an optical magnification system, TSP can achieve a very high spatial resolution over the surface of a small object like MEMS devices. TSP has been used to measure the surface temperature field of a miniature flush-mounted hotfilm sensor in a flat-plate turbulent boundary layer.

1. Introduction

1.5

EuTTA-dope

I(T)/I(Tr)

Ru(bpy)-Shellac

1.0

0.5 Rhodamine-B-dope

0.0 0

20

40

60

80

T (deg. C)

Fig. 1.7. Temperature dependencies of the luminescent intensity for three TSPs

0.5 0.0

ln[I(T)/I(Tr)]

10

Ru(bpy)-Shellac

-0.5 -1.0

Rodamine-B-dope

-1.5 EuTTA-dope

-2.0 -2.5 -0.6

-0.4

-0.2 3

0.0 -1

(1/T - 1/Tr )10 ( K )

Fig. 1.8. The Arrhenius plots for three TSPs

0.2

1.3. Historical Remarks

11

Fig. 1.9. Heat transfer image obtained using TSP on the windward side of the waverider at Mach 10. From Liu et al. (1995b)

1.3. Historical Remarks The working principles of PSP are based on the oxygen quenching of luminescence that was first discovered by H. Kautsky and H. Hirsch (1935). The quenching effect of luminescence by oxygen was used to detect small quantities of oxygen in medical applications (Gewehr and Delpy 1993) and analytical chemistry (Lakowicz 1991, 1999) before experimental aerodynamicists realized its utility as an optical sensor for measuring air pressure on a surface. J. Peterson and V. Fitzgerald (1980) demonstrated a surface flow visualization technique based on the oxygen quenching of dye fluorescence and revealed the possibility of using oxygen sensors for surface pressure measurements. Pioneering studies of applying oxygen sensors to aerodynamic experiments were initiated independently by scientists at the Central Aero-Hydrodynamic Institute (TsAGI) in Russia and the University of Washington in collaboration with the Boeing Company and the NASA Ames Research Center in the United States. The conceptual transformation from oxygen concentration measurement to surface pressure measurement was really a critical step for aerodynamic applications of PSP, signifying a paradigm shift from conventional point-based pressure measurement to global pressure mapping. G. Pervushin and L. Nevsky (1981) of TsAGI, inspired by the work of I. Zakharov et al. (1964, 1974) on oxygen measurement, suggested the use of the oxygen quenching phenomenon for pressure measurements in aerodynamic experiments. The first PSP measurements at TsAGI were conducted at Mach 3 on a sphere, a half-cone and a flat plate with an upright block that were coated with a long-lifetime luminescent paint excited by a flash lamp. Their PSP was acriflavine or beta-aminoanthraquinone in a matrix consisting of silichrome, starch, sugar and polyvinylpyrrolidone. A photographic film camera was used for imaging the luminescent intensity field. The results obtained in these tests were in reasonable agreement with the known theoretical solution and pressure tap data (Ardasheva et al. 1982, 1985). Another TsAGI group consisting of A. Orlov, V.

12

1. Introduction

Mosharov, S. Fonov and V. Radchenko started their research in 1983 to improve the accuracy of PSP by measuring the lifetime (the decay time). In their first tests on a cone-cylinder model at Mach 2.5 and 3.0, they used a photomultiplier tube as a detector and a pulsed Argon laser mechanically scanned over a surface to excite a newly developed PSP (Radchenko 1985). Unfortunately, they found that the lifetime measurements suffered from very strong temperature sensitivity (about o 7%/ C) and a very long lifetime (about several minuets) of their first PSP. As a result, their effort has been exclusively focused on the development of intensitybased techniques since 1985. At TsAGI, a number of proprietary PSP formulations have been developed and applied to various subsonic, transonic, supersonic, shock, dynamic tunnels, and rotating machinery (Bukov et al. 1992, 1993; Troyanovsky et al. 1993; Mosharov et al. 1997). The imaging devices used at TsAGI covered a range of photographic film cameras, TV cameras, scientific grade CCD cameras and photomultiplier tubes with laser scanning systems. In the later 1980s, TsAGI marketed its PSP technology through the Italian firm INTECO and issued a one-page advertisement in the magazine ‘Aviation Week & Space Technology’ in February 12, 1990. Interestingly, scientists in the Western World were not aware of Russia’s work on PSP until reading the advertisement. Then, TsAGI’s PSP system was demonstrated in several wind tunnel tests at the Boeing Company in 1990 and Deutsche Forschungsanstalt fur Luft- und Raumfahrt (DLR) in Germany in 1991, which attracted widespread attention of researchers in the aerospace community (Volan and Alati 1991). PSP was independently developed by a group of chemists led by M. Gouterman and J. Callis at the University of Washington (UW) in the late 1980s (Gouterman et al. 1990; Kavandi et al. 1990). The chemists at UW were initially interested in use of porphyrin compounds as an oxygen sensor for biomedical applications. After stimulating discussions with experimental aerodynamicists J. Crowder of the Boeing Company and B. McLachlan of NASA Ames, Gouterman and Callis understood the important implication of oxygen sensors in aerodynamic testing and started to develop a luminescent coating applied to surface for pressure measurements. Their classical PSP used platinum-octaethylporphorin (PtOEP) as a luminescent probe molecule in a proprietary commercial polymer mixture called GP-197 made by the Genesee Company. In 1989, using PtOEP in GP-197, M. Gouterman and J. Kavandi conducted PSP measurements on a NACA 0012 airfoil model (3-in chord and 9-in span) in the 25×25 cm wind tunnel at NASA Ames Fluid Dynamics Laboratory. The model was spray coated with a commercial white epoxy Krylon base-coat and then sprayed with PtOEP in GP-197. An UV lamp was used for excitation, and an analog camera interfaced to an IBM-AT computer with an 8-bit frame grabber for image acquisition. The model was set at o the angle-of-attack of 5 and the Mach numbers ranged from 0.3 to 0.66. Their data showed very favorable agreement with pressure tap data, clearly indicating the formation of a shock on the upper surface of the model as the Mach number increases (Kavandi et al. 1990; McLachlan et al. 1993a). More importantly, this work established the basic procedures for intensity-based PSP measurements such as image ratioing and in-situ calibration. Following the tests at NASA Ames, Kavandi demonstrated the same PSP system in the Boeing Transonic Wind

1.3. Historical Remarks

13

Tunnel on various commercial airplane models, which was briefly discussed by Crowder (1990). Several proprietary paint formulations have been developed at UW, and successfully applied to wind tunnel testing at the Boeing Company and NASA Ames (McLachlan et al. 1993a, 1993b, 1995; McLachlan and Bell 1995; Bell and McLachlan 1993, 1996; Gouterman 1997). Excellent work on PSP was also made at the former McDonnell Douglas (MD, now the Boeing Company at St. Louis) (Morris et al. 1993a, 1993b; Morris 1995; Morris and Donovan 1994; Donovan et al. 1993; Dowgwillo et al. 1994, 1996; Crites 1993; Crites and Benne 1995). MD PSPs were mainly based on Ruthenium compounds that were successfully used in subsonic, transonic and supersonic flows for a generic wing-body model, a full-span ramp, F-15 model, and a converging-diverging nozzle. Other major PSP research groups in the United States include NASA Langley, NASA Glenn, Arnold Engineering Development Center (AEDC), United States Air Force Wright-Patterson Laboratory, Purdue University, and University of Florida. European researchers in DLR (Germany), British Aerospace (BAe, UK), British Defense Evaluation and Research Agency (DERA, UK), and Office National d’Etudes et de Recherches Aerospatiales (ONERA, France) have been active in the field of PSP (Engler et al. 1991, 1992; Engler and Klein 1997a, 1997b; Engler 1995; Davies et al. 1995; Lyonnet et al. 1997). In Japan, the National Aerospace Laboratory (NAL), in collaboration with Purdue and a number of Japanese universities, developed cryogenic and fastresponding PSPs (Asai 1999; Asai et al. 2001, 2003). More and more research institutions all over the world are becoming interested in developing PSP technology because of its obvious advantages over conventional techniques. Brown (2000) gave a historical review with personal notes and recollections from some pioneers on early PSP development. Before the advent of polymer-based luminescent TSPs, thermographic phosphors and thermochromic liquid crystals have been used for measuring the surface temperature distributions in heat transfer and aerothermodynamic experiments. Thermographic phosphors are usually applied to a surface in the form of insoluble powder or crystal in contrast to polymer-based luminescent TSPs although both techniques utilize the temperature dependence of luminescence. A family of thermographic phosphors can cover a temperature range from room temperature (293 K) to 1600 K, which overlaps with the temperature range of polymer-based TSPs from cryogenic temperature (about 100 K) to 423 K. In this sense, thermographic phosphors and polymer-based luminescent TSPs are complementary to cover a broader range from cryogenic to high temperatures. L. Bradley (1953) explored aerodynamic application of thermographic phosphors mixed with binders and ceramic materials to measure surface temperature. Then, thermographic phosphors were used for temperature measurements in high-speed wind tunnels (Czysz and Dixon 1969; Buck 1988, 1989, 1991; Merski 1998, 1999), gas turbine engines (Noel et al. 1985, 1986, 1987; Tobin et al. 1990; Alaruri et al. 1995), and fiber-optic thermometry systems (Wickersheim and Sun 1985). Allison and Gillies (1997) gave a comprehensive review on thermographic phosphors. Thermochromic liquid crystals applied to a black surface selectively reflect light and hue varies depending on the temperature

14

1. Introduction

of the surface, which allows measurement of the surface temperature in a o relatively narrow range from 25 to 45 C. After E. Klein (1968) used liquid crystals in aerodynamic testing, this technique for global temperature measurement has been used in turbine machinery (Jones and Hippensteele 1988; Hippensteele and Russell 1988; Ireland and Jones 1986), hypersonic tunnels (Babinsky and Edwards 1996), and turbulent flows (Smith et al. 2000). Polymer-based TSPs are relatively new compared to thermographic phosphors and thermochromic liquid crystals. P. Kolodner and A. Tyson (1982, 1983a, 1983b) of the Bell Laboratory used a Europium-based TSP in a polymer binder to measure the surface temperature distribution of an operating integrated circuit. A family of TSPs have been developed at Purdue University and used in low-speed, supersonic and hypersonic aerodynamic experiments (Campbell et al. 1992, 1994; Campbell 1994; Liu et al. 1992b, 1994a, 1994b, 1995a, 1995b, 1996, 1997a, o 1997b). Two typical TSPs are EuTTA in model airplane dope (-20 to 100 C) and o o Ru(bpy) in Shellac (0 to 90 C). Several cryogenic TSPs (-175 to 0 C) were first discovered at Purdue University (Campbell et al. 1994) and used for transition detection in cryogenic flows (Asai et al. 1997c; Popernack et al. 1997). Further development of cryogenic TSPs was made at Purdue (Eransquin 1998a, 1998b), NAL in Japan (Asai et al. 1997c; Asai and Sullivan 1998) and NASA Langley. TSP formulations were also studied at the University of Washington (Gallery 1993) and one of the paints was used for boundary-layer transition detection at NASA Ames (McLachlan et al. 1993b). PSP and TSP have become an active and growing interdisciplinary research area, offering the promise of quantitative pressure and temperature mapping on the one hand and giving new technical challenges on the other hand. Useful reviews were given by Crites (1993), McLachlan and Bell (1995a), Crites and Benne (1995), Liu et al. (1997b), Mosharov et al. (1997), Bell et al. (2001), and Sullivan (2001). This book provides a systematic and detailed description of all the technical aspects of PSP and TSP, including basic photophysics, paint formulations and their physical properties, radiative energy transport, measurement methods and systems, uncertainty, time response, image and data analysis techniques, and various applications in aerodynamics and fluid mechanics.

2. Basic Photophysics

2.1. Kinetics of Luminescence Pressure sensitive paint (PSP) and temperature sensitive paint (TSP) are, respectively, based on the oxygen and thermal quenching processes of luminescence which are reversible processes in molecular photoluminescence. The general principles of luminescence are described in detail by Rebek (1987), Becker (1969) and Parker (1968). The different energy levels and photophysical processes of luminescence for a simple luminophore can be clearly described by the Jablonski energy-level diagram shown in Fig. 2.1. The lowest horizontal line represents the ground-state energy of the molecule, which is normally a singlet state denoted by S0. The upper lines are energy levels for the vibrational states of excited electronic states. The successive excited singlet and triplet states are denoted by S1 and S2, and T1, respectively. As is normally the case, the energy of the first excited triplet state T1 is lower than the energy of the corresponding singlet state S1. A photon of radiation is absorbed to excite the luminophore from the ground electronic state to excited electronic states ( S 0 → S 1 and S 0 → S 2 ). The excitation process is symbolically expressed as S 0 + !ν → S 1 , where ! is the Plank constant and ν is the frequency of the excitation light. Each electronic state has different vibrational states, and each vibrational state has different rotational states. The excited electron returns to the unexcited ground state by a combination of radiative and radiationless processes. Emission occurs through the radiative processes called luminescence. The radiation transition from the lowest excited singlet state to the ground state is called fluorescence, which is expressed as S 1 → S 0 + !ν f . Fluorescence is a spin-allowed radiative transition between two states of the same multiplicity. The radiative transition from the triplet state to the ground state is called phosphorescence ( T1 → S 0 + !ν p ), which is a spinforbidden radiative transition between two states of different multiplicity. The lowest excited triplet state, T1, is formed through a radiationless transition from S1 by intersystem crossing ( S 1 → T1 ). Since phosphorescence is a forbidden transition, the phosphorescent lifetime is typically longer than the fluorescent lifetime. Luminescence is a general term for both fluorescence and phosphorescence.

16

2. Basic Photophysics

Singlet Excited States Internal Conversion

Triplet Excited State

Vibrational Relaxation

S2

Interstystem Crossing S1

Energy

T1

Adsorption

Fluorescence

Internal and External Conversion

Phosphorescence

So Ground State Vibrational Relaxation

Fig. 2.1. Jablonsky energy-level diagram

Radiationless deactivation processes mainly include internal conversion (IC), intersystem crossing (ISC) and external conversion (EC). The internal conversion (IC) is a spin-allowed radiationless transition between two states of the same multiplicity ( S 2 → S 1 , S 1 → S 0 ). Typically, this process is expressed as

S 1 → S 0 + ∆ , where ∆ denotes heat released. IC appears to be particularly efficient when two electronic energy levels are sufficiently close. The intersystem crossing (ISC) is a spin-forbidden radiationless transition between two states of the different multiplicity, which are expressed as S 1 → T1 + ∆ and T1 → S 0 + ∆ . Phosphorescence depends to a large extent on the population of the triplet state ( T1 ) from the excited singlet state ( S 1 ) by the intersystem crossing. In addition, deactivation of an excited electronic state may involve interaction and energy transfer between the excited molecules and the environment like solutes, which are called external conversion (EC). The excited singlet and triplet states can be deactivated by interaction of the excited molecules with the components of a system. These bimolecular processes are quenching processes, including collisional quenching (diffusion or nondiffusion controlled), concentration quenching, oxygen quenching, and energy transfer quenching. The oxygen quenching of luminescence is the major photophysical mechanism for PSP. Due to the oxygen quenching, air pressure on

2.1. Kinetics of Luminescence

17

an aerodynamic model surface is related to the luminescent intensity by the SternVolmer equation that will be further discussed. The quantum efficiency of luminescence in most molecules decreases with increasing temperature because the increased frequency of collisions at elevated temperatures improves the possibility for deactivation by the external conversion. This effect associated with temperature is the thermal quenching, which is the major photophysical mechanism for TSP. The population of the excited singlet states ( S 1 ) and triplet states ( T1 ) at any given time depends on the competition among different photophysical processes listed in Table 2.1. The singlet state population [ S 1 ] and triplet state population

[ T1 ] are described by the following first-order kinetic model d [ S1 ] = I a − ( k f + k ic + k isc( s1 −t1 ) + k q( s ) [ Q ])[ S 1 ] dt d [ T1 ] = k isc ( s1 −t1 ) [ S 1 ] − ( k p + k isc( t1 − s0 ) + k q( t ) [ Q ])[ T1 ] dt

,

(2.1)

where I a is the light absorption rate of generating the excited singlet states, [ Q ] is the population of the quencher Q, k f and k p are, respectively, the rate constants for fluorescence and phosphorescence, k isc( s1 −t1 ) and k isc( t1 − s0 ) are, respectively, the rate constants for the intersystem crossings S 1 → T1 and

T1 → S 0 , k ic is the rate constant for the internal conversion, and k q( s ) and k q( t ) are the rate constants for the quenching in the singlet states and triplet states, respectively. The light absorption rate I a = k s 1 [ S 0 ] is proportional to the population [ S 0 ] in the ground state and the rate constant of excitation k s 1 . After a pulse excitation, the times required for the populations in the excited singlet state and triplet state to decay to 1/e of the initial value are, respectively,

τ f = 1 / ( k f + k ic + k isc( s1 −t1 ) + k q ( s ) [ Q ])

τ p = 1 / ( k p + k isc( t1 − s0 ) + k q( t ) [ Q ]) .

(2.2)

The time constants τ f and τ p are defined as the fluorescent and phosphorescent lifetimes, respectively. Usually, the lifetime of a specific photophysical process is defined as the reciprocal of the corresponding rate constant. Typical values of the lifetimes for different photophysical processes are listed in Table 2.1. When the intersystem crossing from T1 back to S 1 ( T1 → S 1 + ∆ ) is included in the kinetic model, extra terms k isc ( t1 − s1 ) [ T1 ]

and − k isc( t1 − s1 ) [ T1 ]

should be added,

respectively, to the right-hand sides of Eq. (2.1) for [ S 1 ] and [ T1 ] , where

k isc( t1 − s1 ) is the rate constant for the intersystem crossing T1 → S 1 . In this case,

18

2. Basic Photophysics

the kinetic model becomes a coupled system of equations (Mosharov et al. 1997; Bell et al. 2001). Since S 1 is a higher energy state than T1 , this intersystem crossing is thermally activated and therefore the rate constant for the process T1 → S 1 is temperature-dependent. Table 2.1. Photophysical processes involving electronically excited states Step

Process

Rate

Lifetime (s)

Excitation

S 0 + !ν → S 1

k s1 [ S0 ]

10 −15

Fluorescence (F)

S 1 → S 0 + !ν f

k f [ S1 ]

10 −11 − 10 −6

Internal Conversion (IC)

S1 → S 0 + ∆

k ic [ S 1 ]

10 −14 − 10 −11

Intersystem Crossing (ISC)

S 1 → T1 + ∆

k isc( s1 −t1 ) [ S 1 ]

10 −11 − 10 −8

Phosphorescence (P)

T1 → S 0 + !ν p

k p [ T1 ]

10 −3 − 10 2

Intersystem Crossing (ISC)

T1 → S 0 + ∆

k isc( t1 − s0 ) [ T1 ]

2.2. Models for Conventional Pressure Sensitive Paint From a standpoint of engineering application, it is unnecessary to analyze all the intermediate photophysical processes and their interactions. Therefore, a lumped model for luminescence (fluorescence and phosphorescence) is given here by considering the main processes: excitation, luminescent radiation, non-radiative deactivation, and quenching. The luminophore is excited by a photon from a ground state L0 to an excited state L* , i.e., L0 + !ν → L* . The excited state L* returns to the ground state L0 by either a radiative process (emission) or a radiationless process (deactivation). In the radiative process, the luminescent kr L0 + !ν l , where k r is the rate emission releases energy of !ν l , that is L* → constant for the radiation process and ν l is the frequency of the luminescent emission. In the deactivation process, L* returns to L0 by releasing heat, which k nr is expressed as L*  → L0 + ∆ , where k nr is the rate constant for the combined effect of all the non-radiative processes. If temperature around a luminophore molecule increases, the deactivation rate increases, reducing the radiative process from L* . Thus, the rate constant k nr for the non-radiative processes is temperature-dependent. The quenching process by a quencher Q is expressed as kq L* + Q → L0 + Q* , where k q is the rate constant of the quenching process

2.2. Models for Conventional Pressure Sensitive Paint

19

and Q* denotes the excited quencher. The molecular oxygen O2 in the ground state is an efficient quencher for both the excited singlet and triplet states. The molecular oxygen is excited to O2* once it quenches luminescence, i.e.,

L* + O2 → L0 + O2* . By combining the rates of emission, deactivation and quenching processes, the rate of change of the population of the excited state [ L* ] is given by the first-order equation d [ L* ] = I a − ( k r + k nr + k q [ Q ])[ L* ] . dt

(2.3)

The rate of excitation is I a = k s 1 [ L0 ] , where [ L0 ] is the population in the ground state and k s 1 is the rate constant for excitation.

At a steady state

d [ L* ] / dt = 0 , without quenching ( [ Q ] = 0 ), we have * I a = ( k r + k nr )[ L ] .

(2.4)

The amount of luminophore molecules in a given excited state is described by the quantum yield of luminescence defined by

Φ=

rate of luminescence . rate of excitation

(2.5)

The quantum yield Φ for the luminescent emission from L* with the quencher Q is expressed by [ *] I kr , (2.6) Φ = kr L = = k r + k nr + k q [ Q ] I a Ia where I is the luminescent intensity. The quantum yield without quenching is

[ *] Φ0 = k r L = Ia

I kr = 0 k r + k nr I a

,

(2.7)

where I 0 is the luminescent intensity without quenching. Dividing Φ 0 by Φ , we obtain the well-known Stern-Volmer relation

Φ0 I 0 kq = = 1+ [ Q ] = 1 + k qτ 0 [ Q ] , Φ I k r + k nr where τ 0 = 1 /( k r + k nr ) is the luminescent lifetime without quenching. luminescent lifetime with the quencher is

τ =

1 + + k r k nr k q [ Q ]

.

(2.8) The

(2.9)

20

2. Basic Photophysics

Thus, Eq. (2.8) can be written as

Φ0 / Φ = τ 0 / τ .

(2.10)

When the quencher is oxygen, the Stern-Volmer equation is

I0 τ 0 = = 1 + k qτ 0 [ O2 ] . τ I

(2.11)

In general, the rate constants k nr and k q for the non-radiative and quenching processes are temperature-dependent. The temperature dependency of k nr can be decomposed into a temperature-independent term and a temperature-dependent term modeled by the Arrhenius relation (Bennett and McCartin 1966; Song and Fayer 1991), i.e., E nr ), (2.12) k nr = k nr 0 + k nr 1 exp( − RT where k nr 0 = k nr ( T = 0 ) and k nr 1 are the rate constants for the temperatureindependent and temperature-dependent processes, respectively, Enr is the activation energy for the non-radiative process, R is the universal gas constant, and T is the absolute temperature in Kelvin. The temperature dependency of the rate constant k q for the quenching process is related to oxygen diffusion in a homogenous polymer layer used for a conventional PSP. According to the Smoluchowski relation, the rate constant k q for the oxygen quenching can be described by k q = 4π R AB N 0 D (2.13) where R AB is an interaction distance between the luminophore and oxygen molecules, and N 0 is the Avogadro's number. The diffusivity D has the temperature dependency modeled by the Arrhenius relation D = D0 exp( −

ED ), RT

(2.14)

where E D is the activation energy for the oxygen diffusion process. Therefore, from Eq. (2.9), the reciprocal of the luminescent lifetime is

1

τ

= k r + k nr 0 + k nr 1 exp( −

E nr E ) + 4πR AB N 0 D0 exp( − D ) [ O2 ] polymer RT RT

(2.15)

According to Henry's law, the oxygen population [ O2 ] polymer in a polymer binder is proportional to the partial pressure of oxygen pO2 or air pressure p , i.e.,

[ O2 ] polymer = S pO2 = S φ O2 p

(2.16)

2.2. Models for Conventional Pressure Sensitive Paint

21

where S is the oxygen solubility in a polymer binder layer and φ O2 is the mole fraction of oxygen in the testing gas. The mole fraction of oxygen φ O2 is 21% in the atmosphere, but it varies depending on testing facilities. For example, φ O2 is -4 only a few ppm (1ppm = 10 %) in a cryogenic wind tunnel where the working gas is nitrogen. Defining the permeability P0 = SD0 , from Eq. (2.15), we have

1

τ

= ka + K p ,

(2.17)

where the coefficients k a and K are defined as

k a = k r + k nr 0 + k nr 1 exp( −

E E nr ) and K = 4πR AB N 0 P0 exp( − D )φ O2 . (2.18) RT RT

In aerodynamic applications, it is difficult to obtain the zero-oxygen condition since the working gas in most wind tunnels is air containing 21% oxygen. Thus, instead of using the zero-oxygen condition, we usually utilize the zero-speed (wind-off) condition as a reference. Taking a luminescent intensity ratio between the wind-off and wind-on conditions, we obtain the Stern-Volmer equation suitable to aerodynamic applications

I ref I

=

τ ref p . = A polymer ( T ) + B polymer ( T ) τ p ref

(2.19)

The Stern-Volmer coefficients in Eq. (2.19) are

A polymer = A polymer ,ref

K ka , and B polymer = B polymer , ref , k aref K ref

(2.20)

where the reference coefficients are defined as

A polymer , ref =

1 + K ref

p ref 1 and B polymer , ref = . p ref / k aref k aref / K ref + p ref

(2.21)

The subscript ‘polymer’ specifically denotes a conventional polymer-based PSP; it will be seen that porous PSPs have somewhat different forms of the SternVolmer coefficients. Eq. (2.19) indicates that a ratio between the luminescent intensities in the wind-on and wind-off conditions is required to determine air pressure. This intensity-ratio method is commonly employed in PSP and TSP measurements. Using the expressions for k a and K , we can write A polymer and B polymer as a function of temperature ª 1 + ξ exp( − E nr RT ) º » A polymer = A polymer , ref « «¬ 1 + ξ exp( − E nr R T ref ) »¼

22

2. Basic Photophysics

ª E D B polymer = B polymer , ref exp «− «¬ R T ref

·º § Tref ¨ − 1¸ » , ¸» ¨ T ¹¼ ©

(2.22)

where the factor ξ is defined as ξ = k nr 1 /( k r + k nr 0 ) . For ( T − Tref ) / Tref << 1 , the linearized expressions for A polymer and B polymer are

ª E nr A polymer = A polymer , ref «1 + η R T ref «¬ ª ED B polymer = B polymer , ref «1 + R T ref «¬

§ T − Tref ¨ ¨ T ref ©

§ T − Tref ¨ ¨ T ref ©

·º ¸» ¸» ¹¼

·º ¸» , ¸» ¹¼

(2.23)

where the factor η is

η=

ξ exp( − E nr RTref ) . 1 + ξ exp( − E nr R T ref )

(2.24)

Clearly, the Stern-Volmer coefficients A polymer and B polymer satisfy the following constraint A polymer ( Tref ) + B polymer ( Tref ) = 1 . (2.25) Eq. (2.23) indicates that the Stern-Volmer coefficient B polymer depends on the activity energy E D for the oxygen diffusion process; this implies that the temperature sensitivity of PSP is mainly related to the oxygen diffusion. Indeed, experiments conducted by Gewehr and Delpy (1993) and Schanze et al. (1997) for two different oxygen sensors showed that the temperature dependency of the oxygen diffusivity in a polymer dominated the temperature effect of PSP. This finding has an important implication in the design of low-temperature-sensitive PSP formulations; the low-temperature-sensitive PSP should have a polymer binder with the low activation energy for oxygen diffusion. In another special case where E D ≈ E nr and η ≈ 1 over a certain range of temperature, the coefficients A polymer ( T ) and B polymer ( T ) have the same temperature dependency; thus a ratio between A polymer ( T ) and B polymer ( T ) becomes temperature independent. PSP satisfying the above conditions is so-called ‘ideal’ PSP (see Section 3.6). This paint is advantageous for correcting the temperature effect since the Stern-Volmer relation becomes temperature independent when the intensity ratio scaled by a single temperature-dependent factor is used as a similarity variable. In many PSP measurements, the linear Stern-Volmer relation Eq. (2.19) is sufficiently accurate in a certain range of pressure. However, over an extended range of the partial pressure of oxygen or air pressure, the non-linear Stern-

2.2. Models for Conventional Pressure Sensitive Paint

23

Volmer behavior becomes appreciable for microheterogeneous PSPs (Carraway et al. 1991a; Xu et al. 1994; Hartmann et al. 1995). The main physical mechanisms behind the non-linear Stern-Volmer characteristics are associated with microheterogeneity of the environment of a probe molecule and deviation from Henry’s law. Solid-state matrices like polymers may provide numerous different kinds of environments for a probe molecule, resulting in the non-exponential decay or multiple-exponential decay of luminescence. In some cases, a double exponential model is sufficient for the decay; thus the oxygen quenching of luminescence in microheterogeneous systems is described by a two-component model −1

º I0 ª f 01 f 02 =« + » , I ¬ 1 + K SV 1 [ O 2 ] 1 + K SV 2 [ O 2 ] ¼ where

f 01 and

(2.26)

f 02 are the fractional intensity contributions of the two

components in the absence of oxygen ( f 01 + f 02 = 1 ), K SV 1 and K SV 2 are the Stern-Volmer constants of the two components. Furthermore, for the probe molecule incorporated into a polymer, dual sorption mechanisms are considered and thus the oxygen concentration is related to the applied partial pressure by adsorption isotherm. These mechanisms are responsible for a slight deviation of the actual concentration from that given by Henry’s law. The analytical form of dual sorption in a polymer is obtained by adding the Langmuir isotherm to Henry’s law, i.e., b pO2 , (2.27) [ O2 ] polymer = S pO2 + C' 1 + b pO2 where C' is the Langmuir gas capacity due to adsorption and b is the Langumir affinity coefficient. Based on the dual sorption model Eq. (2.27), Hubner and Carroll (1997) suggested an extended form of the Stern-Volmer relation

I ref I

= A+ B

D ( p / p ref ) p +C . p ref 1 + D ( p / p ref )

(2.28)

Eq. (2.28) was able to give a good fit to experimental data for some PSPs. From a standpoint of aerodynamic applications, an empirical form of the non-linear SternVolmer relation is usually given by a polynomial 2

§ p · p ¸ +. = A( T ) + B( T ) + C( T ) ¨ ¨ p ref ¸ I p ref © ¹

I ref

(2.29)

24

2. Basic Photophysics

2.3. Models for Porous Pressure Sensitive Paint In the preceding section, the photophysical models for a conventional polymer PSP are discussed. Nevertheless, according to the work of Sakaue (1999), the photophysical models for a porous PSP or open PSP system are different. In general, pores in a porous PSP are macroscopic, which are much larger than the size of an oxygen molecule. Figure 2.2 shows schematically a comparison of a conventional polymer PSP with a porous PSP. In a conventional polymer PSP, as shown in Fig. 2.2(a), the oxygen molecules in the working gas permeate into a polymer binder layer and quench the luminescence. In contrast, as illustrated in Fig. 2.2(b), a porous PSP has a much larger open surface to which the luminophore molecules are directly applied; the oxygen molecules can directly quench the luminescence without having to permeate into a binder layer. Therefore, the use of a porous material as a binder for PSP offers two advantages. First, a porous PSP can achieve a very fast time response (in the order of microseconds) for unsteady PSP measurements; secondly, it makes PSP measurements possible at cryogenic temperatures at which oxygen diffusion is prevented through a conventional homogeneous polymer. Oxygen Molecules

Oxygen Permeation Incident Light

Luminescence Polymer Layer

(a)

Luminophore

Model

Incident Light

Luminescence Oxygen Molecules

Porous Material Surface

(b)

Luminophore

Model Surface

Oxygen Quenching

Fig. 2.2. Schematic of (a) conventional polymer PSP and (b) porous PSP. From Sakaue (1999)

2.3. Models for Porous Pressure Sensitive Paint

25

The oxygen quenching process in a porous PSP is different from that in a conventional polymer PSP. Figures 2.3(a) and (b) illustrate two scenarios of the oxygen quenching in a porous PSP; in both cases, a luminophore molecule is adsorbed on a porous surface opened to the working gas. In Fig. 2.3(a), a gaseous oxygen molecule collides to a luminophore molecule, resulting in the oxygen quenching; in this case, the oxygen quenching process is controlled by a collision between the gaseous oxygen molecule and luminophore molecule adsorbed on the surface. In other case, as illustrated in Fig. 2.3(b), an adsorbed oxygen molecule can cause quenching by diffusing to a luminophore molecule and hence the oxygen quenching process is related to adsorption and diffusion of the oxygen molecule into the luminophore molecule. Wolfgang and Gafney (1983) studied the oxygen quenching of tris(2,2'-bipyridyl)ruthenium (Ru(bpy)) on a porous Vycor glass and reported that Ru(bpy) was quenched by either a gaseous oxygen molecule colliding to the adsorbed Ru(bpy) or an adsorbed oxygen molecule.

gaseous oxygen

adsorbed oxygen

collision porous surface

porous surface

surface diffusion

oxygen quenching (b): Adsorption Controlled Model quencher: adsorbed oxygen process: adsorption/surface diffusion

luminophore

(a): Collision Controlled Model quencher: gaseous oxygen process: collision

Fig. 2.3. Oxygen quenching mechanisms for porous PSP: (a) Collision controlled model; (b) Adsorption controlled model. From Sakaue (1999)

Two photophysical models were developed by Sakaue (1999) to describe the oxygen quenching on a porous surface by considering the Eley-Rideal (ER) mechanism and Langmuir-Hinshelwood (LH) mechanism. The ER mechanism is a target annihilation reaction between a gaseous oxygen molecule and an adsorbed luminophore molecule; it is a collision-controlled reaction (Samuel et al. 1992). The LH mechanism, which is adsorption/surface-diffusion-controlled, is a reaction between an adsorbed oxygen molecule and an adsorbed luminophore molecule (Hinshelwood 1940). Samuel et al. (1992) studied the oxygen quenching of Ru(bpy) on a porous silica surface over a temperature range of 88-353 K and reported that at low temperatures the oxygen quenching was diffusion-controlled (the LH type). As temperature increased, the reaction remained the LH type in nature, but it was increasingly influenced by the target annihilation reaction (the

26

2. Basic Photophysics

ER type). At higher temperatures, the reaction was no longer the LH type, which was dominated by the ER type reaction. In these cases, the rate constant kq for the oxygen quenching and the oxygen concentration [O2] were described in a different manner from that for a conventional polymer binder. 2.3.1. Collision-Controlled Model When the rate constant kq for the oxygen quenching and the oxygen concentration [O2] are considered in a collision-controlled reaction, the Stern-Volmer relation is called the collision-controlled model to distinguish from the diffusion-controlled relation (or adsorption-controlled model). The rate of collision of the oxygen * molecules on a porous surface is [ O2 ] c* / 4 , where c is the average speed of the molecules. According to the theory of ideal gas, one knows

[ O2 ] =

N 0 pO2 RT

and c* =

8RT

(2.30)

π Mm

where pO2 is the partial pressure of oxygen, T is the absolute temperature in Kelvin, Mm is the molar mass, R is the universal gas constant, and N0 is the Avogadro's number. The rate of the oxygen quenching is modeled by a product of an effective contact area σeff and the collision rate

k q [ O2 ] =

σ eff [ O2 ] c * 4

=

σ eff N 0 p O2 2π M m RT

=

σ eff N 0 φ O2 p 2π M m RT

.

(2.31)

Hence, the rate of the oxygen quenching is proportional to the partial pressure of oxygen or air pressure, but is inversely proportional to the square root of temperature. The Stern-Volmer relation for the luminescent lifetime then becomes σ eff N 0 φ O2 1 = ka + p (2.32) τ 2π M m RT For aerodynamic applications, the Stern-Volmer relation for the collisioncontrolled quenching process can be written as

p I ref = Acollision ( T ) + B collision ( T ) . I p ref

(2.33)

In Eq. (2.33), the Stern-Volmer coefficients are

Acollision = Acollision, ref

T ref k a and , B collision = B collision ,ref T k aref

(2.34)

2.3. Models for Porous Pressure Sensitive Paint

27

where the coefficients at the reference conditions are defined as

Acollision , ref = 1 /( 1 + ζ ) , B collision , ref = ζ /( 1 + ζ ) ,

ζ =

σ eff N 0φ O2 p ref k aref

2π M m R Tref

.

(2.35)

Although Eq. (2.33) has the same form as that for a conventional polymer binder, the Stern-Volmer coefficients Acollision and Bcollision have different physical meanings. The coefficient Bcollision has weaker temperature dependency that is inversely proportional to the square root of temperature. In contrast, the temperature dependency of Acollision has the same form as that for a conventional polymer binder; linearization of Eq. (2.34) at T = Tref leads to ª E nr Acollision = Acollision , ref «1 + R T ref «¬

§ T − Tref ¨ ¨ T ref ©

·º ¸» . ¸» ¹¼

(2.36)

2.3.2. Adsorption-Controlled Model Besides the collision-controlled quenching, an adsorbed oxygen molecule on a porous surface can also quench the luminescence; if this is the dominant mechanism, the oxygen quenching is controlled by adsorption and surface diffusion of the adsorbed oxygen on the porous surface. The oxygen concentration on a porous surface, [O2]ads, can be described by the fractional coverage of oxygen on the porous surface

θ=

[ O2 ] ads [ O2 ] adsM

,

(2.37)

where [O2]adsM is the maximum oxygen concentration on the porous surface. The Stern-Volmer equation is then written as

I0 = 1 + τ k q 0 [ O2 ] adsM θ , I

(2.38)

and accordingly the convenient form of the Stern-Volmer relation for aerodynamic applications is θ I ref = A( T ) + B( T ) , (2.39) I θ ref where

A=

k q [ O2 ] adsM θ ref ka and B = . k a + k qref [ O2 ] adsM θ ref k a + k qref [ O2 ] adsM θ ref

(2.40)

28

2. Basic Photophysics

The rate constant kq for the oxygen quenching, which is surface-diffusioncontrolled, can be described by (Freeman and Doll 1983) 0 k q = 2πR AB λ B D = k q exp( − E sdiff / RT ) ,

(2.41)

where RAB is the relative distance between an adsorbed oxygen and an adsorbed luminophore, and D is the diffusivity and the parameter λΒ is a ratio of the modified first-order and second-order Bessel functions of the second kind. Basically, kq is temperature-dependent due to the Arrhenius relation D = D0 exp( − E sdiff / RT ) . To describe θ, either the Langmuir isotherm or the Freundlich isotherm can be used (Carraway et al. 1991b). The Langmuir isotherm relates θ to the partial pressure of oxygen pO2 in the working gas by

θ=

b p O2 1 + b p O2

.

(2.42)

The factor b in Eq. (2.42) is a function of temperature (Butt 1980)

σ eff

b= kd

2π M m RT

exp( − E ads / RT ) = b0

exp( − E ads / RT ) T

,

(2.43)

where kd is the desorption rate constant per unit surface area and Eads is the heat of adsorption. Since the oxygen concentration is [ O2 ] = b pO2 , Eq. (2.38) becomes

b pO2 1 + bref pO2 ref I ref = ALangmuir + B Langmuir I 1 + b p O2 bref pO2 ref

.

(2.44)

Eq. (2.44) is the adsorption-controlled model derived from the Langmuir isotherm; for [ O2 ] = b pO2 << [ O2 ] adsM , it can be approximated by

pO2 I ref = ALangmuir ( T ) + B Langmuir ( T ) I pO2 ref

,

(2.45)

.

(2.46)

where the Stern-Volmer coefficients are

ALangmuir =

B Langmuir =

ka + [ O k a k qref 2 ] adsM b ref p O2 ref k q [ O2 ] adsM b pO2 ref k a + k qref [ O2 ] adsM bref pO2 ref

The coefficient ALangmuir has the same temperature dependency as that for a conventional polymer PSP and that in the collision-controlled model, i.e.,

2.3. Models for Porous Pressure Sensitive Paint

ALangmuir = ALangmuir , ref

ka k aref

,

29

(2.47)

and the linearized form for ALangmuir is

ª E nr ALangmuir = ALangmuir , ref «1 + R T ref «¬

§ T − T ref ¨ ¨ T ref ©

·º ¸» . ¸» ¹¼

(2.48)

Hence, Eq. (2.48) indicates that ALangmuir is related to the temperature dependency of the non-radiative processes of the luminophore. On the other hand, BLangmuir has the following temperature dependency ª − E l § T ref ·º kq b T ref ¨ ¸» , (2.49) = B Langmuir , ref exp « − 1 B Langmuir = B Langmuir , ref ¨ ¸ T k qref b ref «¬ R T ref © T ¹»¼ where E l = E sdiff + E ads . Rewriting Eq. (2.49) in an exponential form yields

ª El B Langmuir = B Langmuir , ref exp «− «¬ R T ref

· 1 § T ref § T ref ¨¨ − 1¸¸ + ln¨¨ ¹ 2 © T © T

·º ¸¸» , ¹»¼

(2.50)

and furthermore, linearization of Eq. (2.50) at T = Tref gives

ª EL B Langmuir = B Langmuir , ref «1 + R T ref «¬

§ T − T ref ¨ ¨ T ref ©

·º ¸» , ¸» ¹¼

(2.51)

where E L = El − R Tref / 2 = E sdiff + E ads − R Tref / 2 . Clearly, the temperature dependency of the coefficient BLangmuir, Eq. (2.51), is associated with both surface diffusion and adsorption; but it has the similar form to Eq. (2.23) for a conventional polymer layer. The reference Stern-Volmer coefficients ALangmuir , ref and B Langmuir , ref

(their lengthy expressions are not given here) satisfy the

constraint ALangmuir , ref + B Langmuir , ref = 1 . The Freundlich isotherm can serve as another model for surface adsorption

θ = bF ( p O2 )γ

(2.52)

where the coefficient and exponent are

bF =

b0 T

γ

exp( − E ads / RT ) and γ =

RT E adsM

.

(2.53)

The exponent γ is an empirical parameter that is temperature-dependent. For a known γref at a known reference temperature Tref, EadsM is given by

30

2. Basic Photophysics

E adsM =

R T ref

.

γ ref

(2.54)

Substituting Eqs. (2.52), (2.53) and (2.54) into Eq. (2.39), we obtain the non-linear Stern-Volmer equation

§ pO I ref 2 = AFreundlich ( T ) + B Freundlich ( T ) ¨ ¨ p O ref I © 2

· ¸ ¸ ¹

γ

(2.55)

where

AFreundlich =

B Freundlich =

ka γ ref

k a + k qref [ O2 ] absM b Fref ( pO2 ref ) k q [ O2 ] absM b F ( pO2 ref )

γ ref γ ref

k a + k qref [ O2 ] absM b Fref ( pO2 ref )

.

(2.56)

The coefficient AFreundlich has the same temperature dependency as that in other models ka , (2.57) AFreundlich = AFreundlich , ref k aref and the linearized form for AFreundlich is

ª E nr AFreundlich = AFreundlich , ref «1 + R T ref «¬

§ T − T ref ¨ ¨ T ref ©

·º ¸» . ¸» ¹¼

(2.58)

.

(2.59)

The coefficient BFreundlich has the temperature dependency

B Freundlich = B Freundlich , ref

γ k q b F ( pO2 ref ) γ ref

k qref b Fref ( pO2 ref )

Substituting Eqs. (2.41) and (2.53) into (2.59) yields

B Freundlich = B Freundlich , ref

( T ref ) Tγ

( p O2 ref )γ

γ ref

( pO2 ref )

γ ref

ª −Ef exp « «¬ R T ref

§ T ref ·º ¨ ¸» , − 1 ¨ T ¸ © ¹ »¼

(2.60)

where E f = E sdiff + E ads . When an approximation γref ≈ γ is used for a small temperature change, the expression for B Freundlich becomes

B Freundlich

§ T ref = B Freundlich , ref ¨¨ © T

· ¸ ¸ ¹

γ ref

ª −Ef exp « ¬« R T ref

§ T ref ·º ¨ ¸ ¨ T − 1¸ » , © ¹»¼

(2.61)

2.4. Thermal Quenching

31

which is similar to BLangmuir. After rewriting all the terms in Eq. (2.61) in an exponential form, linearization at T = Tref yields ª EF B Freundlich = B Freundlich , ref «1 + R T ref «¬

§ T − Tref ¨ ¨ T ref ©

·º ¸» , ¸» ¹¼

(2.62)

where

E F = − E sdiff − E ads + γ ref R T ref

ª §p «ln¨ O2 ref « ¨¨ T ref «¬ ©

· ¸− ¸¸ ¹

º 1» . 2» »¼

(2.63)

Similar to the Langmuir-type model, the coefficient BFreundlich has the temperature dependency associated with surface diffusion and adsorption. However, the photophysical model Eq. (2.55) describes the non-linear behavior of the SternVolmer plot for a porous PSP.

2.4. Thermal Quenching For TSP where the paint layer is not oxygen-permeable such that no oxygen quenching occurs, from Eq. (2.8), the quantum yield of luminescence is simply given by kr I = Φ = . (2.64) Ia k r + k rn The temperature dependency of the non-radiative processes k nr can be decomposed into a temperature-independent term and a temperature-dependent term modeled by the Arrhenius relation (Bennett and McCartin 1966; Song and Fayer 1991; Schanze et al. 1997) E nr ), (2.65) k nr = k nr 0 + k nr 1 exp( − RT where k nr 0 = k nr ( T = 0 ) and k nr 1 are the rate constants for the temperatureindependent and temperature-dependent processes, respectively, Enr is the activation energy for the non-radiative process, R is the universal gas constant, and T is the absolute temperature in Kelvin. From Eqs. (2.64) and (2.65), we have ln

I ( T )[ I ( 0 ) − I ( Tref )] I ( Tref )[ I ( 0 ) − I ( T )]

=

E nr R

§1 ¨ − 1 ¨ T Tref ©

· ¸, ¸ ¹

(2.66)

where I ( 0 ) = I ( T = 0 ) is the luminescent intensity at the absolute zero temperature.

For | I ( T ) − I ( Tref ) | / I ( 0 ) << 1 and I ( T )I ( Tref ) /[ I ( 0 )] 2 << 1

32

2. Basic Photophysics

over a certain temperature range, a relation between the luminescent intensity and temperature can be approximately written in the Arrhenius form ln

E §1 I( T ) 1 = nr ¨ − I ( Tref ) R ¨© T Tref

· ¸. ¸ ¹

(2.67)

Theoretically speaking, the Arrhenius plot of ln[ I ( T ) / I ( Tref )] versus 1/T gives a straight line of the slope Enr/R. Experimental results indeed indicate that the simple Arrhenius relation Eq. (2.67) is able to fit data over a certain temperature range. However, for some TSPs, experimental data may not fully obey the simple Arrhenius relation over a wider range of temperature. Thus, as an alternative, an empirical functional relation between the luminescent intensity and temperature is I( T ) = f ( T / Tref ) , (2.68) I ( Tref ) where f ( T / Tref ) could be a polynomial, exponential or other function to fit experimental data over a working temperature range. Either Eq. (2.67) or Eq. (2.68) can serve as an operational form of the calibration relation for TSP in practical applications.

3. Physical Properties of Paints

3.1. Calibration In order to quantitatively measure air pressure with PSP, the relationship between the luminescence signal (intensity, lifetime or phase) and air pressure should be experimentally determined by calibration. Apparatus for calibration of PSP over a temperature range of 90-423 K are described in Appendix A. A generic calibration set-up consists of a pressure chamber, excitation light source and photodetector. A PSP sample is placed in the pressure chamber where pressure can be adjusted from vacuum to high pressures. The surface temperature of the PSP sample is controlled using a heating/cooling device and measured using a temperature sensor. The PSP sample is excited by an illumination source (e.g. UV lamp, LED array or laser) through a window of the pressure chamber. The luminescent emission from the paint sample, after filtered by a band-pass optical filter, is measured using a photodetector (e.g. photodiode, PMT or CCD camera), and the photodetector output is acquired with a PC over a range of pressures and temperatures. Therefore, the correspondence between the luminescence signal and pressure, which is usually described by the Stern-Volmer equation, is established over a range of temperatures. Typical calibration results for a number of PSP formulations based on Platinum Porphrins, Ruthenium complexes and Perlene/Pyrene are given in the following sections. The calibration set-up for PSP can be used for TSP calibration when the surface temperature of a paint sample varies while pressure in the chamber is kept constant. Calibration data for TSP are typically presented as an Arrhenius plot over a certain temperature range; typical calibration results for TSP formulations are given in Sections 3.3 and 3.4. The most common calibrations for PSP and TSP are based on measurements of the luminescent intensity as a function of pressure and/or temperature. As discussed before, however, the luminescent lifetime (or phase) is also a function of pressure and/or temperature. In a lifetime calibration apparatus, a pulsed (or modulated) excitation light source is used, and after an exciting pulse light ceases the exponential decay of the luminescent intensity is measured using a fastresponding photodetector and recorded with a PC or an oscilloscope. The luminescent lifetime can be determined by fitting data with a single exponential function or multiple-exponential function for certain paints over a range of pressures and temperatures. Early instrument for measuring the luminescent

34

3. Physical Properties of Paints

lifetime was described by Brody (1957) and Bennett (1960), and the current state of luminescent lifetime measurement systems in photochemistry and medical applications was comprehensively reviewed by Lakowicz (1991, 1999). The Stern-Volmer relations between the lifetime and oxygen partial pressure (or concentration) for oxygen sensitive luminescent materials were determined by Gewehr and Delpy (1993), Gord et al. (1995), Sacksteder et al. (1993), Xu et al. (1994), and Papkovsky (1995). Lifetime calibration results for TSPs and thermographic phosphors were also reported by Sholes and Small (1980), Grattan et al. (1987), Bugos (1989), Noel et al. (1985), and Lakowicz (1999). A more detailed discussion on the lifetime and phase methods is given in Chapter 6.

3.2. Typical Pressure Sensitive Paints A typical PSP is prepared by dissolving a luminescent dye and a polymer binder in a solvent; the order of mixing the components and the relative concentration of the components may change the characteristics of the paint. Chlorinated organic solvents such as dichloromethane and trichloroethane have been used for making PSP. The selection of a polymer binder for PSP is important, which should be based on a balanced consideration of its oxygen permeability, temperature effect, humidity effect, adhesion, mechanical stability, photodegradation, and other required properties. Silicone rubbers, GP-197, silica gel and sol-gel-derived coatings have been used as binders for PSPs and oxygen sensors (Wan 1993; Gallery 1993; Xu et al. 1994; MacCraith et al. 1995; Jordan et al. 1999a, 1999b). Other polymers and porous materials that are potentially useful for PSP can be found in the literature of polymers (Krevelen 1976; Mulder 1991; Fried 1995; Robinson and Perlmutter 1994). The permeability, solubility and diffusion coefficients of a polymer binder are related to the pressure sensitivity and time response of PSP. Furthermore, the behavior of PSP depends on interaction between a probe molecule and its surrounding polymer. The microenvironment of the probe molecule in the polymer binder can significantly affect the luminescence and quenching behavior (Hartmann et al. 1995; Meier et al. 1995; Xu et al. 1994; Lu and Winnik 2001; Lu et al. 2001). Also, it was observed that a basecoat might affect the behavior of PSP (Coyle et al. 1995). A useful review on quenching of luminescence by oxygen in polymer films was given by Lu and Winnik (2000), stressing on luminescent materials and polymers. Table 3.1 lists some PSP formulations along with their spectroscopic properties and the Stern-Volmer coefficients. In Table 3.1, the Stern-Volmer coefficients A( T ) and B( T ) are the coefficients in the linear relation

I ref / I = A( T ) + B( T ) p / pref at the room temperature of about 20 C, where the o

reference pressure p ref is the ambient pressure of 1 atm. For certain PSPs that do not completely obey the linear Stern-Volmer relation, the coefficients A( T ) and

B( T ) are estimated by fitting data over a finite linear range. The results are collected from the theses and papers by Wan (1993), Burns (1995), Baron et al.

3.2. Typical Pressure Sensitive Paints

35

(1993), Kavandi et al. (1990), and McLachlan et al. (1993a, 1995), which documented the absorption spectra, emission spectra, and Stern-Volmer plots of oxygen-sensing luminophores and supporting polymer matrices. Table 3.1 also include a number of proprietary PSPs developed by TsAGI (Troyanovsky et al. 1993; Bukov et al. 1993), the former McDonnell Douglas (now Boeing at St. Louis) (Morris et al. 1993a, 1993b; Morris 1995), the University of Washington/NASA Ames (McLachlan and Bell 1995) and NASA Langley (Oglesby and Jordan 2000). Some PSP formulations of the former McDonnell Douglas have been patented (Schwab and Levy 1994). Generally speaking, a good PSP has the Stern-Volmer coefficient B( T ) larger than 0.5, indicating acceptable pressure sensitivity for quantitative measurements (Oglesby et al. 1995a). Table 3.1. Pressure sensitive paints Luminophore

Binder

Excitation Emission Stern-Volmer wavelength wavelength coefficients A B (nm) (nm)

H2TSPP H2(Me2N)TFPP H2TCPP H2TNMPP H2TTMAPP Perylene dibutyrate Perylene dye PtTFPP

silica gel silica gel silica gel silica gel silica gel silica gel silica gel silica gel DuPont Chrom. Polystyrene FEM

400 400 410 420 410 457 480, 530 390

PtTFPP PtTFPP PtOEP Pyrene Ru(bpy) Ru(ph2-phen) [Ru(ph2-phen)3] 2+

FIB GP-197 silica gel GE RTV 118 silica gel silica gel GE RTV118 GP-134/silica

650, 709 650 709 661, 714 653, 710 520 550, 570 650

390

650

390 366, 543

650 650

360-390 337, 457 337, 457

470 600 600

337

620

NASA-Ames PSP McDonnell Douglas PSP TsAGI LPSL2

blue 320-350

425-550

0.58 0.43 0.40 0.43 0.40 0.33 0.47 0.27 0.50 0.29 0.17

0.42 0.56 0.61 0.60 0.60 0.67 0.53 0.72 0.52 0.69 0.83

0.13 0.32 0.12 0.12 0.33 0.17 0.27 0.22

0.87 0.70 0.88 0.88 0.68 0.84 0.75 0.78

0.38

0.62

0.18

0.82

0.25

0.75

Lifetime Temp. at room coeff. (%/0C) temp. (micro s) ~0 ~0 0.013 50

4.5 0.35 -2.1 -1.8 -4.3 -1.4

50

-1.0 -1.7 -~0

3 4.7 0.3

-1.3 -0.78 -1.5

-0.3

Reference

Purchase source

Wan (1993) Wan (1993) Wan (1993) Wan (1993) Wan (1993) Burns (1995) Wan (1993) Wan (1993), Burns (1995)

Porphyrin Porphyrin Porphyrin Aldrich Aldrich Pylam Aldrich Porphyrin

Burns (1995)

NASA Langley ISSI Porphyrin

Burns (1995) Burns (1995)

Aldrich GFS Chem.

Xu et al. (1994) McLachlan and Bell (1995) Dowgwillo et al. (1994) Bukov et al. (1993)

NASA Ames McDonnell Douglas TsAGI

Three families of luminescent dyes, Platinum Porphyrins, Ruthenium Polypyridyls and Pyrene derivatives, have been commonly used for making PSP. Recipes of three PSP formulations are given in Appendix B. The Platinum Porphyrin compounds, which can be excited by either an UV light or a green light, emit red luminescence. They are very sensitive to oxygen, but they often have a long lifetime and low luminescent intensity at the atmospheric pressure. The Ruthenium compounds also emit red luminescence when excited by either an UV light or a blue light. They are very photo-stable, but are difficult to incorporate into polymer systems. The Pyrene derivatives, which are UV excited, emit blue

36

3. Physical Properties of Paints

luminescence. The Pyrene derivatives have weak temperature sensitivity; however, they suffer from photodegradation and sublimation. Figure 3.1 shows the chemical structure, and absorption and emission spectra for platinum meso-tetra(pentafluorophenyl)porphine (PtTFPP). Figures 3.2 and 3.3 show the Stern-Volmer plots and temperature dependencies for two PtTFPP PSP formulations: PtTFPP in the FIB polymer (poly-heptafluoro-n-butyl methacrylate-co-hexafluorisopropyl methacrylate) developed by the University of Washington (Gouterman and Carlson 1999) and PtTFPP in the FEM polymer (poly-tifluoro-ethylmethacrylate-co-isobutylmethacrylate) developed by NASA Langley (Oglesby and Jordan 2000). In these figures, the lower temperature sensitivity of PSP at vacuum represents the intrinsic temperature dependency of the luminophore, while the higher temperature sensitivity of PSP at the atmospheric pressure indicates an additional temperature effect on the oxygen diffusion in the polymer. F

F F

F

F

F

F

F N

F N F

Pt

F N F

N

F

F F F

(a)

F

F F

F

(b) Fig. 3.1. (a) Chemical structure of PtTFPP, (b) absorption and emission spectra of PtTFPP. From Puklin et al. (2000)

3.2. Typical Pressure Sensitive Paints

37

1 .4

1 .3

2 4 .4 o 3 4 .7 o 4 5 .7 o 5 5 .3 o

1 .2 1 .1 1 .0

C C C C

I

ref

/I

0 .9 0 .8 0 .7 0 .6 0 .5 0 .4

I ref = I a t 1 4 . 7 0 p si a a i r a t 2 4 . 4 o C

0 .3 0 .2 0 .1 0 .0 0 .0

0 .1

0 .2

0 .3

0 .4

0 .5

0 .6

0 .7

0.8

0 .9

1.0

1 .1

P /P r e f

(a)

Relative Emission Intensity

1 .0 -0.46%/ o C

vacuum 0 .9

-1.00%/ o C

0 .8

1 atm

0 .7 20

30

40

T e m p e ra tu re ( o C )

50

60

(b) Fig. 3.2. (a) The Stern-Volmer plots, and (b) temperature dependency for PtTFPP in the FIB Polymer. From Oglesby and Jordan (2000)

38

3. Physical Properties of Paints 1 .5 1 .4

25.1o 35.6o 45.5o 55.6o

1 .3 1 .2 1 .1

C C C C

1 .0

Iref /I

0 .9 0 .8 0 .7 0 .6 0 .5 0 .4

I r e f = I a t 1 4 . 7 0 p si a a i r a t 2 5 . 1 o C

0 .3 0 .2 0 .1 0 .0 0.0

0 .1

0.2

0 .3

0 .4

0 .5

0 .6

0 .7

0 .8

0.9

1 .0

1 .1

P /P r e f

(a) 1.0 Relative Emission Intensity

vacuum -0.64%/o C

0.9 1 atm

0.8 -1.4%/o C

0.7 20

30

40

50

Temperature (o C )

(b) Fig. 3.3. (a) The Stern-Volmer plots, and (b) temperature dependency for PtTFPP in the FEM polymer (NASA Langley). From Oglesby and Jordan (2000)

3.2. Typical Pressure Sensitive Paints

39

2.2

85

FIB FEM SOLGEL UNICOAT PAR

2.0

80

1.8

75 ST (%/deg)

SP (%/bar)

1.6

70 65

1.4 1.2 1.0

60

FIB FEM SOLGEL UNICOAT PAR

55

0.8 0.6 0.4

50 10

15

20

25 T (deg. C)

30

35

40

0.0

0.5

1.0

1.5

2.0

2.5

p/pref

Fig. 3.4. Pressure sensitivity (SP) and temperature sensitivity (ST) for PtTFPP in five different polymer binders, where Pref = 1 bar and Tref = 10°C. From Mebarki and Le Sant (2001)

In order to examine the effect of a polymer binder on the properties of PSP, Mebarki and Le Sant (2001) calibrated five PSP formulations that used the same porphyrin molecule, PtTFPP, with different polymer binders. Two formulations, the PAR PSP from the Institute for Aerospace Research (IAR) of NRC in Canada (Mebarki 2000) and the FEM PSP from NASA Langley (Oglesby and Upchurch 1999), are not commercially available. Other paints, the FIB PSP originally developed by the University of Washington (Gouterman and Carlson 1999), solgel PSP (Jordan et al. 1999a, 1999b) and the Uni-Coat PSP (Mebarki 2000), were commercially produced by Innovative Scientific Solutions Inc. (ISSI). Except for the Uni-Coat PSP that did not require a primer layer, the commercial FIB and solgel PSP formulations were supplied with their respective primers. To simplify the application procedures and solve adhesion problems, the FIB active layer was applied on the top of the Tristar (DHMS C4.01TY3) white epoxy primer that was also used as a screen layer for both the FEM PSP and PAR PSP. It was found that the primer had no effect on the pressure or temperature sensitivity of the active layer. However, the polymer binder (or permeable matrix) in which the porphyrin molecule was immobilized affected both the pressure and temperature sensitivities of the paint. To evaluate the performance of PSP, the pressure sensitivity and temperature sensitivity are defined as SP = ∆( I ref / I ) / ∆P (in % per bar) and

ST = −∆( I / I ref ) / ∆T (in % per degree), respectively. The pressure sensitivity was calculated in a pressure range of 0.15-2 bars and the temperature sensitivity was determined in a temperature range of 10-35°C. Figure 3.4 shows the pressure sensitivity SP as a function of temperature and the temperature sensitivity ST as a function of pressure. The pressure sensitivity SP varied from 55% to nearly

40

3. Physical Properties of Paints

80% per bar, depending on the polymer binder used and temperature as well. The FIB PSP formulation had nearly constant pressure sensitivity over a temperature range of 10-40°C. The Uni-Coat and sol-gel PSP formulations had a similar linear dependency of the pressure sensitivity SP on temperature; the temperature sensitivity ST ranges from 0.6% to 1.6% per degree. The temperature sensitivity was somewhat affected by pressure for all the PSP formulations except the FIB PSP. The FIB PSP also has the lowest temperature sensitivity among them. Figure 3.5 shows the chemical structure, and absorption and emission spectra of Bathophen Ruthenium Chloride (Ru(ph2-phen) or Ru(dpp)). Ruthenium-based oxygen sensors have been studied extensively by analytical chemists (Bacon and Demas 1987; Carraway et al. 1991a, 1991b; Sacksteder et al. 1993; Xu et al. 1994; Klimant and Wolfbeis 1995). The Ruthenium-based PSP formulations have been developed and used for wind tunnel testing by the former McDonnell Douglas (now Boeing at St. Louis) (Schwab and Levy 1994). Figure 3.6 shows the SternVolmer plots for Ru(dpp) in GE RTV 118 added with silica gel particles at different temperatures; Figure 3.7 shows the luminescent lifetime as a function of o pressure for Ru(dpp) in GE RTV 118 at 22 C.

N

N

Ru2+ N

N N

N

Intensity (arbitrary units)

(a)

Absorption

200

300

400

Luminescence

500

600

700

800

900

Wavelength (nm)

(b) Fig. 3.5. (a) Chemical structure, and (b) Absorption and emission spectra of Ru(ph2-phen) or Ru(dpp)

3.2. Typical Pressure Sensitive Paints

41

1.0 243K 253K 258K 263K 268K 273K 283K 293K linear fit

0.9

0.8

Iref/I

0.7

0.6

0.5

0.4

0.3 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

P/Pref

Fig. 3.6. The Stern-Volmer plots for Ru(ph2-phen) or Ru(dpp) in GE RTV 110 added with silica gel particles, where the reference pressure pref is 14.5 psi and reference temperature is 293 K. From Lachendro (2000) 5

1.4 Ru(ph2-phen) in GE RTV 118

4

1.2

3

0.8 0.6

2

τref/τ

Lifetime τ (µs)

1.0

0.4

τ τref/τ

1

0.2

0

0.0 0

200

400

600

800

P (mmHg)

Fig. 3.7. Lifetime-pressure relation for Ru(ph2-phen) in GE RTV 118 at 22 C, where τref is the lifetime at the ambient pressure (1 atm). From Liu et al. (1997b) o

Figure 3.8 shows the chemical structure and absorption and emission spectra of Pyrene. The Pyrene-based PSP formulations were developed by TsAGI/OPTROD in Russia (Fonov et al. 1998). One of them was the binary paint (B1 PSP) in which a pressure-insensitive reference component was added to correct the excitation light variations on a surface in performing a ratio between the wind-on and wind-off images. Figure 3.9 shows the Stern-Volmer plots at different temperatures for Pyrene complex in GE RTV 118. Obviously, this Pyrene-based

42

3. Physical Properties of Paints o

PSP exhibits weak temperature dependency over a temperature range of 17-40 C. Note that Perylene and its derivatives like Green Gold (perylene dibutylate) were also used as a luminescent dye for PSP. Besides TsAGI, ONERA in France and DLR in Germany developed Pyrene-based PSP formulations as well (Engler et al. 2001a). The PyGd PSP formulation developed by ONERA contained Pyrene as a pressure-sensitive dye and a gadolinium oxysulfide as a reference component. Figure 3.10 shows the emission spectrum of the PyGd PSP excited at 325 nm. The two components in the paint absorbed an ultraviolet excitation light and emitted at sufficiently different wavelengths such that the emissions from the two components can be separated using optical filters. Figure 3.11 shows the SternVolmer plots at the ambient temperature for three Pyrene-based PSP formulations: PyGd, B1 and PdGd. Because the temperature sensitivity of the reference component was similar to that of the Pyrene dye in the PyGd PSP, the temperature effect can be compensated by taking a ratio between the luminescent intensities from the pressure-sensitive component (Pyrene) and reference component. As a result, the PyGd PSP displayed very low temperature sensitivity of 0.05%/K. A number of ‘Göttingen Dyes’ (GD) were developed by DLR and the University of Göttingen, and three stable Pyrene-based paints, GD145, GD146 and GD147, were tested in wind tunnels (Engler and Klein 1997b). Figure 3.12 shows the pressure sensitivities of the Göttingen PSP formulations. A shortcoming of Pyrene-based paints is that sublimation may occur when temperature is greater than 40oC.

(a)

Emission

(b) Wavelength (nm)

Fig. 3.8. (a) Chemical structure of Pyrene, and (b) absorption and emission spectra of Pyrene. From Mebarki (2001)

3.2. Typical Pressure Sensitive Paints

43

intensity (A.U)

Fig. 3.9. The Stern-Volmer plots for Pyrene in GE RTV 118, where the excitation source is filtered at 334±5 nm and the luminescent emission is filtered at >450 nm. The reference conditions are Tref = 17°C and Pref = 1bar. Sublimation of Pyrene occurs initially at 40°C, o resulting in an intensity decrease and thus a different curve at 50 C. From Mebarki (2001)

vacuum

Pref=1bar

300

400

500

600 λ (nm)

Fig. 3.10. Emission spectra of a binary Pyrene-based PSP (PyGd) at 1 bar and vacuum. From Engler et al. (2001a)

44

3. Physical Properties of Paints 1.02 1 0.98

Iref/I

0.96 0.94 0.92 0.9 PyGd

0.88

PdGd 0.86 0.84 0.82

B1 0.84

0.86

0.88

0.9

0.92

0.94

0.96

0.98

1

1.02

P/Pref

Fig. 3.11. The Stern-Volmer plots for three Pyrene-based PSP formulations (PyGd, PdGd, and B1) used at ONERA. From Engler et al. (2001a)

Fig. 3.12. The Stern-Volmer plots for the Göttingen Pyrene-based PSP formulations (GD 145, GD 146, and GD 147). From Engler et al. (2001a)

3.3. Typical Temperature Sensitive Paints

45

3.3. Typical Temperature Sensitive Paints Like PSP, TSP is prepared by dissolving a luminescent dye and a binder in a solvent. Many commercially available resins and epoxies can serve as polymer binders for TSP if they are not oxygen permeable and do not degrade the activity of the probe luminophore molecule. Table 3.2 lists some TSP formulations as well as the spectroscopic properties, temperature sensitivities and useful temperature measurement ranges. Data are collected from Campbell (1993) and Gallery (1993) and other sources. For a comparison between different TSP formulations, the maximum logarithmic slope max{ d [ln( I / I ref )] / dT } is used as an indicator of the temperature sensitivity for TSP over a certain temperature range, where I ref is the reference luminescence intensity. Here, the logarithmic slope is used since it is independent of the reference intensity that is different in various sources. Two proprietary TSP formulations and two high-temperature thermographic phosphors are also included in Table 3.2 for comparison. Figure 3.13 shows typical temperature dependencies of the luminescent intensity for a number of TSP formulations. Some of them have been used to measure the temperature and heat transfer fields in various applications (Kolodner and Tyson 1982, 1983a, 1983b; Romano et al. 1989; Campbell et al. 1993, 1994; Liu et al. 1995a, 1995b, 1996; Hamner et al. 1994; Asai et al. 1996, 1997c). Table 3.2. Temperature sensitive paints Luminophore

Binder

Coumanin CuOEP

PMMA GP-197

EuTTA Perylene Perylenedicarboximide Pyronin B Pyronin Y Rhodamine B Ru(bpy) Ru(bpy)/Zeolite

Dope Dope PMMA PMMA Dope Dope Shellac Poly Vinyl Alcohol GP-197 Poly Vinyl Alcohol

Ru(trpy) Ru(trpy)/Zeolite La2O2S:Eu Y 2O3:Eu NASA-Ames (Univ. of Washington) TSP McDonnell Douglas TSP

Excitation Emission Useful wavelength wavelength temperature range (nm) (nm) (degree C) UV 20 to 100 480-515 -180 to 20

Max. log slope (%/0C) -0.4 -2.9

Lifetime at room temp. (micro s)

350 330-450 480-515 460-580 460-580 460-590 320, 452 320, 452

612 430-580

-3.9 -1.9 -0.7 -4.6 -5.5 -1.8 -0.93 -4.1

500 0.005

550-590 588 588

-20 to 80 0 to 100 50 to 100 50 to 100 0 to 100 0 to 80 0 to 90 -20 to 80

310, 475 310, 475

620 620

-170 to -50 -1.34 -180 to 80 -1.8

337 266

537 611

100 to 200 -3.5 510 to 1000 -1.88

UV 340-500

>500

0 to 50

-3.9

-5 to 90

-2.7

0.004 5

100 1400

Reference

Purchase source

Campbell (1993) Campbell et al. (1994) Liu (1996) Campbell (1994) Campbell (1993) Campbell (1993) Campbell (1993) Sullivan (1991) Liu (1996) Campbell et al. (1994)

Purdue Purdue

Campbell (1993) Campbell et al. (1994)

Purdue Purdue

Noel et al. (1985) Alaruri et al. (1995) McLachlan et al (1993b) Cattafesta and Moore (1995)

Kodak Aldrich Aldrich Aldrich Aldrich Aldrich GFS Chem. GFS Chem.

Allison Eng. Univ. of Washington McDonnell Douglas

46

3. Physical Properties of Paints 1.2 1.0

I/Iref

0.8 8

5

0.6

7 6

0.4

4

0.2 1

2

3

0.0 -150

-100

-50

0

50

100

150

T (deg. C)

Fig. 3.13. Temperature dependencies of the luminescence intensity for TSP formulations: (1) Ru(trpy) in Ethanol/Methanol, (2) Ru(trpy)(phtrpy) in GP-197, (3) Ru(VH127) in GP197, (4) Ru(trpy) in DuPont ChromaClear, (5) Ru(trpy)/Zeolite in GP-197, (6) EuTTA in dope, (7) Ru(bpy) in DuPont ChromaClear, (8) Perylenedicarboximide in Sucrose o Octaacetate. (Tref = -150 C). From Liu et al. (1997b)

Two typical TSP formulations are Ru(bpy) in an automobile clear coat (DuPont ChromaClear) binder and EuTTA in model airplane dope (see Appendix B); both are easy to prepare and use. Figure 3.14(a) shows the chemical structure of tris(2,2’-bipyridyl) ruthenium or Ru(bpy) and Figure 3.14(b) shows the absorption and emission spectra of Ru(bpy) that are similar to those of Ru(dpp) for PSP. Ru(bpy) can be excited by a UV lamp, nitrogen laser, argon laser, doubled YAG laser or blue LED array. Since the Stokes shift is large (the emission peak at about 620 nm), the excitation light can be easily separated from the luminescent emission using an optical filter. An automobile urethane clear coat, which is usually used as a top coat on most automobiles, is used as a polymer binder for Ru(bpy); particularly, DuPont ChromaClear 7500S is used, but other brands should work as well. The advantage of this binder is that it is oxygen impermeable, readily available, and easy to spray although some pressure sensitivity was observed at very high pressures and temperatures. Figure 3.13 shows the temperature dependency of the luminescent intensity for Ru(bpy) in DuPont ChromaClear along with other TSP formulations. Ru(bpy) can also mixed with a Shellac binder; the Ru(bpy)-Shellac TSP is similar to Ru(bpy) in DuPont ChromaClear in terms of the temperature sensitivity. It is also easy to apply. Figures 3.15 and 3.16 show, respectively, the Arrhenius plot and lifetime for the Ru(bpy)-Shellac TSP compared with the EuTTA-dope TSP.

3.3. Typical Temperature Sensitive Paints

N

N N

2+

N

Ru N

47

N

Intensity (arb. units)

(a)

Absorption

200

300

(b)

400

Emission

500

600

700

800

900

Wavelength (nm)

Fig. 3.14. (a) Chemical structure of Ru(bpy), and (b) absorption and emission spectra of Ru(bpy) 1

ln[I(T)/I(Tref)]

0

-1

-2

EuTTA-dope Ru(bpy)-Shellac

-3 -0.8

-0.6

-0.4

-0.2

0.0 3

0.2

0.4

-1

(1/T - 1/Tref)10 (K )

Fig. 3.15. The Arrhenius plots for two TSP formulations: EuTTA-dope TSP and Ru(bpy)Shellac TSP, where Tref = 293 K. From Liu et al. (1997b)

3. Physical Properties of Paints

Lifetime of Ru(bpy)-Shellac (µs)

7

2.5 Ru(bpy)-Shellac EuTTA-dope

6

2.0

5 1.5

4 1.0

3

0.5

2 1

Lifetime of EuTTA-dope (ms)

48

0.0

0

20

40

60

80

Temperature (degree C)

Fig. 3.16. Lifetime-temperature relations for two Ru(bpy)-Shellac TSP and EuTTA-dope TSP. From Liu et al. (1997b) S O F F

O

F

F

F

F

Eu O

O

O

S F

Intensity (arb. units)

(a)

O

Absorption

300

(b)

F F

350

400

450

S

Emission

500

550

600

650

700

Wavelength (nm)

Fig. 3.17. (a) Chemical structure of EuTTA, (b) absorption and emission spectra of EuTTA

3.3. Typical Temperature Sensitive Paints

49

Another good TSP is based on Europium (III) Thenoyltrifluoroacetonate or EuTTA whose structure and the absorption and emission spectra are shown in Fig. 3.17. Obviously, a UV lamp or a nitrogen laser can be used for excitation. EuTTA has a high quantum yield and a large Stokes shift (the emission peak at about 620 nm). The binder used with this luminphore is a clear model airplane dope that, like DuPont ChromaClear and Shellac, is readily available, easy to spray, and oxygen impermeable. Figures 3.15 and 3.16 show, respectively, the Arrhenius plot and lifetime for the EuTTA-dope TSP along with those for the Ru(bpy)-Shellac TSP. Thermographic phosphors and thermochromic liquid crystals are also temperature sensitive coatings for measuring the surface temperature distributions. Similar to polymer-based TSPs, thermographic phosphors utilize the thermal quenching of the luminescent emission from ceramic materials that are doped or activated with rare-earth elements (Allison and Gillies 1997). However, they are usually in the form of insoluble powders or crystals in contrast to a polymer-based TSP where luminescent molecules are immobilized in a polymer matrix. The luminescent intensity (or lifetime) of thermographic phosphor and polymer-based TSP follows the same functional relation I ∝ [ 1 + a0 exp( − a1 / T )] −1 . Figure 3.18 shows the measurement envelops of thermographic phosphors and polymerbased luminescent TSPs. A family of thermographic phosphors can cover a temperature range of 273-1600 K, which overlaps with the temperature range of the polymer-based TSP family from 90 to 423 K. Hence, a combination of thermographic phosphors and polymer-based luminescent TSPs can cover a very broad range from cryogenic to high temperatures. The measurement systems (intensity- and lifetime-based systems) for thermographic phosphors are essentially the same as those for polymer-based luminescent TSPs. The emission spectrum of certain phosphor has multiple distinct lines that have very different temperature sensitivities. Thus, an emission-intensity ratio between the temperature-sensitive and -insensitive lines can eliminate the effect of nonuniform illumination on a surface. Note that certain emission lines of certain phosphors are also temperature sensitive in cryogenic conditions. Thermochromic liquid crystals selectively reflect light depending on the surface temperature, and hence the dominant wavelength or hue of the reflected light varies monotonically with temperature over a relatively narrow temperature range of about 32-42oC (Smith et al. 2000). For comparison, Figure 3.18 plots the normalized hue of a typical thermochromic liquid crystal as a function of temperature; the temperature sensitivity of the thermochromic liquid crystal is high over a narrow temperature range.

50

3. Physical Properties of Paints

Normalized Luminescent Intensity or Hue

1.4 Measurement Envelop of TSPs Measurement Envelop of Phosphors Typical Calibration Curve for Liquid Crystal

1.2 1 0.8 0.6 0.4 0.2 0

0

200

400

600

800 1000 1200 Temperature (Kelvin)

1400

1600

1800

Fig. 3.18. Measurement envelops for polymer-based TSPs and thermographic phosphors along with a typical normalized calibration curve of thermochromic liquid crystal

3.4. Cryogenic Paints A challenging problem is application of PSP in cryogenic wind tunnels like the NASA Langley National Transonic Facility (NTF) and European Transonic Wind Tunnel Facility (ETW). Porous materials were usually used as binders for PSP at cryogenic temperatures. Porous material has a large exposure surface area where the probe luminophore can be directly applied and luminescence can be directly quenched by oxygen. The use of porous materials as binders allows PSP measurements at cryogenic temperatures and achieves fast time response as well (in the order of microseconds). Various porous materials were investigated as binders for PSP, including a thin layer chromatography (TLC) plate (Baron et al. 1993), hydrothermal coating (Bacsa and Gratzel 1996), sol-gel (MacCraith et al. 1995; Jordan et al. 1999a, 1999b), tape-casting (Scroggin 1999), anodized aluminum (Asai 1997a), anodized titanium and porous paper filter (Erausquin 1998; Erauquin et al. 1998). Aluminum can be anodized to create a thin aluminum oxide layer on the surface through an electrochemical process. Anodized aluminum (AA) is highly porous with 10-100 nm micropores uniformly distributed on the surface. AA-PSP is made by adsorbing the luminophore into the pores on the AA surface (Asai 1997a). Figure 3.19 shows the Stern-Volmer plot for an AA-PSP, Ru(dpp) on anodized aluminum, compared with a conventional polymer-based PSP (Ru(dpp) in RTV) at cryogenic temperatures. This AA-PSP still exhibits good sensitivity to oxygen even at 100 K, whereas the conventional PSP loses its sensitivity to oxygen at 150 K. Upchurch et al. (1998) and Asai et al. (2000, 2002) developed a polymer-based cryogenic PSP that used highly porous Poly(TMSP) as a binder.

3.4. Cryogenic Paints

51

To compare the two cryogenic PSP formulations, Figure 3.20 shows the SternVolmer plots for the Poly(TMSP)-based PSP and AA-PSP that use Ru(dpp) as a luminescent dye; both PSPs exhibit the non-linear behavior in the Stern-Volmer plot. 2.0

AA-PSP (pO ref=14Pa, T=100K) 2

Iref/I

1.5

1.0

0.5

conventional PSP (pO ref=14Pa, T=150K) 2

0.0 0.0

0.5

1.0

1.5

p /p O2

2.0

2.5

3.0

3.5

O2ref

Fig. 3.19. The Stern-Volmer plots for a porous AA-PSP and a conventional PSP with silicone rubber as a binder at cryogenic temperatures. Both PSP formulations uses Ru(ph2phen) as a probe luminophore. From Sakaue (1999)

1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0

É ÉÑÉÑ ÉÑ É É Ñ T=100K ÉÉ Ñ É ÉÉ Ñ ÉÉ Ñ É ÉÉ ÑÑ ÉÉ Ñ Ñ ÉÉ ÑÑÑ É ÑÑÑ É ÑÑ Ñ poly(TMSP) Ñ ÉÑÑ É anodized É ÑÑ 0

200 400 600 800 1000 oxygen concentration, ppm

Fig. 3.20. Comparison of Poly(TMSP) PSP with anodized aluminum (AA) PSP at 100 K, where excitation is at 400±50 nm and emission is at 650±50 nm. From Asai et al. (2000)

A family of the luminescent molecules Ru(trpy) (see Fig. 3.21 for the chemical structure) has been studied for making cryogenic TSP formulations since it is found that these compounds are temperature sensitive at cryogenic temperatures (Campbell 1994; Erausquin 1998; Iijima et al. 2003). They have very intense emission at low temperatures, but they are nearly fully quenched at the room temperature. The absorption and emission spectra of the family of Ru(trpy) are

52

3. Physical Properties of Paints

very similar to those of Ru(dpp) and Ru(bpy). The Ru(trpy) compounds, which can be excited by either a UV light or blue light, emit red luminescence. Various [Ru(trpy)2] molecules with different ligands were synthesized (Erausquin 1998). The dynamics of the metal-to-ligand bond, as well as the electron donating or accepting characteristics of the ligand, has a significant effect on the temperature sensitivity of a luminescent molecule. Thus, this would enable synthesis of a molecule specifically designed to respond with high sensitivity over a certain range of cryogenic temperatures. DuPont ChromaClear (CC) is selected as a binder for cryogenic TSP due to its low oxygen diffusivity and good surface adhesion at cryogenic temperatures (Erausquin 1998). Figure 3.22 shows a comparison of several synthesized [Ru(trpy)2] compounds in the polymers CC and GP-197. In general, interaction between a polymer binder and a luminescent molecule can affect the mobility of the metal-to-ligand bonds, changing the temperature dependency of the paint. Figure 3.23 shows the temperature dependencies for [Ru(trpy)(phtrpy)](PF6)2 in two different polymer binders CC and GP-197. Other Ruthenium compounds have a good response at cryogenic temperatures as well, as shown in Table 3.3 that summarizes the temperature sensitivities and useful temperature ranges for cryogenic TSP formulations calibrated by Erausquin (1998).

N

N N

Ru

N

Fig. 3.21. Chemical structure of Ru(trpy)

I(T) / Iref(T)

1.6 1.4

[Ru(trpy)2] in CC [Ru(trpy)(phtrpy)](PF6)2

1.2

[Ru(ppd-trpy)2](TFPB)2 in CC

1.0

[Ru(trpy)(VH-127)](PF6)2 in GP-197

0.8 0.6 0.4 0.2 0.0

-200

-150

-100

-50

0

50

Temperature (oC)

Fig. 3.22. Comparison of Ru(trpy)-based cryogenic TSP formulations, where CC denotes DuPont ChromaClear. From Erausquin (1998)

3.4. Cryogenic Paints

53

1.6 GP-197 Chromaclear

1.4

I(T) / Iref(T)

1.2 1.0 0.8 0.6 0.4 0.2 0.0 -200

-150

-100

-50

0

50

Temperature (oC)

Fig. 3.23. Temperature calibration for cryogenic TSPs: [Ru(trpy)(phtrpy)](PF6)2 in GP-197 and DuPont ChromaClear. From Erausquin (1998) Table 3.3. Cryogenic temperature sensitive paints

Paint

Useful temp.

Temp. sensi. coeff.

range ( C)

∆(I/Iref)/∆T

[Rh(bzq)2Cl]2 in CC

-175 to -130

-0.0191

[Rh(bzq)2(phen)](PF6) in CC

-100 to –50

-0.0107

[Ru(trpy)] in CC

-175 to –85

-0.0112

o

[Ru(trpy)(4'-C6F5-trpy)](NO3)2 in CC

-175 to –50

-0.0081

[Ru(trpy)(4'-Cl-trpy)](Cl2) in CC

-175 to –50

-0.0106

[Ru(trpy)(4'-NC-trpy)](NO3)2 in CC

-150 to –50

-0.0078

[Ru(phtrpy)(Cltrpy)](NO3)2 in CC

-175 to –50

-0.0093

[Ru(trpy)(4'-TfO-trpy)](NO3)2 in CC

-175 to –50

-0.0101

[Ru(trpy)(MeStrpy)](NO3)2 in CC

-175 to –75

-0.0105

[Ru(trpy)(phtrpy)](PF6)2 in GP-197

-175 to –50

-0.0114

[Ru(trpy)(phtrpy)](PF6)2 in CC

-150 to –100

-0.0142

[Ru(trpy)(ppd-trpy)](TFPB)2 in CC

-175 to –50

-0.0097

[Ru(trpy)(phyphen)](TFPB)2 in CC

-175 to –50

-0.0090

[Ru(trpy)(SO2Me-trpy)](PF6)2 in CC

-175 to –75

-0.0104

[Ru(trpy2)](TFPB)2 in CC

-170 to –75

-0.0114

[Ru(ppd-trpy)2](TFPB)2 in CC

-175 to –75

-0.0149

[Ru(trpy)(Vh127)](PF6)2 in GP-197

-175 to –75

-0.0154

54

3. Physical Properties of Paints

3.5. Multiple-Luminophore Paints The intensity-based method for PSP and TSP requires a ratio between the wind-on and wind-off images of a painted model. When a model moves in a nonhomogenous illumination filed during a test, the image-ratio method inevitably causes inaccuracy in determining pressure and temperature. A multipleluminophore paint is designed to eliminate the need for a wind-off reference image. Generally, a two-luminophore PSP consists of a pressure-sensitive luminophore and a pressure-insensitive reference luminophore; similarly, a twoluminophore TSP combines a temperature-sensitive luminophore with a temperature-insensitive reference luminophore. The probe and reference luminophores can be excited by the same illumination light. Ideally, there is no overlap between the emission spectra of the probe and reference luminophores such that the luminescent emissions from the two components can be completely separated using optical filters. Theoretically, a ratio I λ1 / I λ2 between the probe and reference images could able to eliminate the effects of spatial non-uniform illumination, paint thickness and luminophore concentration, where I λ1 and I λ2 are the luminescent intensities at the emission wavelengths λ1 and λ 2 , respectively. However, McLean (1998) pointed out that since two luminophores cannot be perfectly mixed, the simple two-color intensity ratio I λ1 / I λ2 cannot completely compensate the effect of non-homogenous dye concentration. In this case, a ratio of ratios ( I λ1 / I λ2 ) /( I λ1 / I λ2 )0 should be used to correct the effects of non-homogenous dye concentration and paint thickness variation, where the subscript 0 denotes the wind-off condition. Besides the above combinations of luminophores, a temperature-sensitive luminophore, which cannot be quenched by oxygen, can be combined with an oxygen-sensitive luminophore. This two-luminophore temperature/pressure paint can be used for correcting the temperature effect of PSP. In particular, when the temperature dependencies of the two luminophores are close, a two-color intensity ratio between the two luminophores exhibits a very weak temperature dependency (Engler et al. 2001a). Figure 3.24 shows a ratio of ratios of a two-luminophore PSP (PtTFPP in FIB with a proprietary reference luminophore) as a function of pressure at different temperatures (Crafton et al. 2002). Clearly, the data at different temperatures overlap, and a ratio of ratios of this PSP is almost o temperature insensitive in a range of 5-45 C. Furthermore, a multipleluminophore PSP can be developed to correct the temperature effect as well as the effect of non-uniform illumination simultaneously.

3.5. Multiple-Luminophore Paints

55

1.5

Ro/R

1.2 0.9

5C 15 C 25 C 35 C 45 C

0.6 0.3 0 0

0.3

0.6

0.9

1.2

1.5

P/Po

Fig. 3.24. Ratio of ratios of a two-luminophore PSP (PtTFPP in FIB with a reference luminophore) as a function of pressure at different temperatures, where R = I λ1 / I λ2 and

R0 = ( I λ1 / I λ2 )0 are the two-color intensity ratios between the probe and reference luminophores at the run and reference conditions, respectively. From Crafton et al. (2002)

Oglesby et al. (1995b) used PtOEP or PtTFPP as a pressure probe luminophore and Fluorol Green Gold 084 (3,9-perylenedicarboxylic acid, bis(2methylpropyl)ester) as a reference luminophore in the GP-197 polymer. Harris and Gouterman (1995, 1998) used PtTFPP as a pressure-sensitive luminophore 2+ and incorporated a solid-state phosphor BaMg2Al16O27:Eu (BaMgAl) as a reference luminophore in an Acrylic copolymer. Since BaMgAl is insoluble, the reference luminophore was not uniformly distributed and therefore the paint suffers from the effect of the uneven layer thickness. TsAGI/OPTROD developed the proprietary two-luminophore PSP formulations, LPS B1 and LPS B12 (Bukov, et al. 1997; Lyonnet, et al. 1997). Three pressure sensitive paints with an internal temperature sensitive luminophore were also tested by Oglesby et al. (1996), where EuTTA, MgOEP and Ru(bpy) were used as temperature-sensitive reference luminophores. Hradil et al. (2002) used Ru(dpp) as a pressure probe molecule and manganese-activated magnesium fluorogermanate (MFG) as a thermographic phosphor. The preliminary results showed that two-luminophore PSPs indeed enabled point-by-point correction for the temperature effect of PSP. Buck (1988, 1989, 1991) used a blue-green Radelin thermographic phosphor for aerothermodynamic testing that intrinsically exhibited two narrow-band emission peaks at 450 nm and 520 nm. It was found that a ratio of the blue to green emission intensity was a function of temperature, but independent of the UV illumination intensity. Another two-color phosphor system used a green-red mixture of rare-earth and Radelin phosphors for a broader range of temperatures. Buck (1988, 1989) gives a detailed description of the multiple-color phosphor thermography system developed at NASA Langley.

56

3. Physical Properties of Paints

3.6. ‘Ideal’ Pressure Sensitive Paint A perfect PSP should be completely temperature independent. According to Eq. (2.23), a temperature insensitive PSP should have such small activity energy E D for the oxygen diffusion process that the Stern-Volmer coefficient B polymer is a weak function of temperature over a certain range of temperature. However, since the excited-state decay rates of a luminophore are intrinsically temperature dependent, it is unlikely to develop an absolutely temperature-insensitive PSP whose the Stern-Volmer coefficients A polymer and B polymer are constants. Instead, researchers seek a so-called ‘ideal’ PSP exhibiting invariant temperature dependency at different pressures over a certain range of temperatures (Puklin et al. 1998; Coyle et al. 1999; Bencic 1999; Ji et al. 2000). Note that the term ‘ideal PSP’ does not accurately describe the invariant property of this special paint. Nevertheless, since this term has been used in the PSP community, we adopt it here and discuss its true meaning below. Consider the Stern-Volmer relation in the following form

I0(T ) = 1 + K SV ( T ) p , I ( p ,T )

(3.1)

where I 0 ( T ) = I ( p = 0 ,T ) is the luminescent intensity at zero pressure (vacuum) and K SV ( T ) is related to the coefficients A polymer ( T ) and B polymer ( T ) by

K SV ( T ) = [ B polymer ( T ) / A polymer ( T )] / p ref .

(3.2)

If the coefficients A polymer ( T ) and B polymer ( T ) have the same temperature dependency, the Stern-Volmer coefficient K SV ( T ) becomes temperature independent. According to Eq. (2.23), this situation may occur under the conditions E D ≈ E nr and η ≈ 1 over a certain range of temperatures. Therefore, for an ‘ideal’ PSP, the Stern-Volmer coefficient K SV ( T ) in Eq. (3.1), rather than the coefficients A polymer ( T ) and B polymer ( T ) , is temperature independent. Consequently, the Stern-Volmer relation in the form for aerodynamic application can be written as I ref p , (3.3) g( T ) = A polymer , ref + B polymer , ref I p ref where the function g ( T ) is defined as

ª ED g ( T ) = «1 + R T ref «¬

§ T − Tref ¨ ¨ T ref ©

·º ¸» ¸» ¹¼

−1

ª E nr = «1 + R T ref «¬

§ T − Tref ¨ ¨ T ref ©

·º ¸» ¸» ¹¼

−1

(3.4)

3.6. ‘Ideal’ Pressure Sensitive Paint

57

and the coefficients A polymer , ref and B polymer , ref are temperature independent given the reference conditions. For an ‘ideal’ PSP, the Stern-Volmer relation Eq. (3.3) enjoys such similarity that it is invariant at different temperatures for the variable g( T )I ref / I . The temperature effect of PSP is concentrated in a single scaling factor g ( T ) ; this similarity simplifies the temperature correction procedure for PSP. Ji et al. (2000) developed a bichromophic molecule Ru-Pyrene for an ‘ideal’ PSP, which, as shown in Fig. 3.25, consisted of a covalently linked assembly of a Ruthenium (II) polypyridyl complex and Pyrene. They also synthesized the MPP acrylate polymer binder for Ru-Pyrene. Figure 3.26(a) shows the Stern-Volmer plots for the Ru-pyrene/MPP PSP at pressures ranging from 0.005 to 1 atm and o temperatures from 25 to 55 C. The Stern-Volmer plots at different temperatures are collapsed onto a single curve. Figure 3.26(b) illustrates the temperature dependency of the Ru-Pyrene/MPP PSP at 0.005, 0.14, 0.55 and 1 atm, indicating that the temperature dependency of this PSP is independent of pressure.

Fig. 3.25. Chemical structure of Ru-pyrene. From Ji et al. (2000)

Fig. 3.26. (a) The Stern-Volmer plots for Ru-pyrene/MPP PSP at eight pressures ranging o from 0.005 to 1 atm and four temperatures from 25 to 55 C; (b) the temperature dependency of Ru-pyrene/MPP PSP at pressures of 0.005, 0.14, 0.55 and 1 atm. From Ji et al. (2000)

58

3. Physical Properties of Paints

3.7. Desirable Properties of Paints As pointed out before, PSP or TSP is prepared by dissolving a luminescent dye and a polymer binder in a solvent solution; the resulting mixture is then applied on a surface by spraying, brushing or dipping. After the solvent evaporates, a thin coating of the paint remains on the surface, in which the luminescent molecules are immobilized in the polymer matrix. The polymer binder is an important ingredient of the paint adhering to the surface of interest. In some cases, the polymer matrix is only a passive anchor; in other cases, the polymer may significantly affect the photophysical behavior of the paint through complicated interaction between the luminescent molecule and the macromolecule of the polymer. Since how the polymer affects the photophysical processes in the paint is not well understood, it is basically a trial and error process to find an optimal combination of a luminophore and a polymer. A good paint (PSP or TSP) for aerodynamic applications should have certain required physical and chemical properties. The following discussion is focused on the required properties of PSP while some requirements are generally applicable to TSP. A general strategy for the development of improved PSP formulations was proposed by Benne et al. (2002).

Pressure Response The Stern-Volmer coefficients of PSP should be chosen to match the pressure range on a tested article and the performance requirements of a photodetector (e.g. CCD camera) used in particular measurements. A large Stern-Volmer coefficient B( T ) generally indicates a good pressure response. However, for aerodynamic experiments at high pressures, a large Stern-Volmer coefficient B( T ) of PSP may cause unwanted severe oxygen quenching in the ambient reference conditions, considerably reducing the luminescent emission from the paint and therefore the signal-to-noise ratio (SNR) of a photodetector.

Luminescent Output The luminescent emission of a luminophore is characterized by the quantum yield (or efficiency); it is generally desirable to have as high a luminescent output as possible to maximize the SNR of a photodetector. The luminescent intensity is proportional to the concentration of the probe molecules over a certain range. However, it cannot be increased indefinitely by increasing the dye concentration; if the concentration is too high, self-quenching of luminescence occurs. Similarly, the luminescent intensity is no longer linearly proportional to the excitation light intensity at a very high excitation level, and eventually it saturates when the excitation light intensity increases further. Paint Stability Ideally, the luminescent intensity of PSP should not change with time under excitation. Usually, the luminescent intensity decreases with time due to photodegradation of a luminophore (Egami and Asai 2002). A decrease in the luminescent intensity could also be due to the presence of certain chemicals other than oxygen that can quench the luminescence. The polymer binder undergoes

3.7. Desirable Properties of Paints

59

aging, which can change its characteristics with respect to the oxygen solubility and diffusivity. As a result, the Stern-Volmer coefficients of PSP may be altered.

Response Time The response time of PSP is mainly determined by oxygen diffusion through a paint layer when the luminescent lifetime is much shorter than the diffusion timescale. The high porosity of the paint will increase the time response. The need for fast time response depends on a particular application; a short response time of PSP is required for unsteady aerodynamic measurements. For steady-state measurements, however, the use of a fast-responding PSP does not necessarily offer an advantage. For a highly oxygen-permeable PSP with a short response time, the Stern-Volmer coefficient B( T ) is usually large, and thus weak luminescence of PSP in the ambient conditions may lead to a low SNR. Temperature Sensitivity A good PSP should have a weak temperature effect. The temperature sensitivity arises from two sources: the intrinsic temperature dependency of a luminophore and the temperature dependency of the solubility and diffusivity of oxygen in a polymer matrix. The latter is a major contributor to the temperature sensitivity of PSP. Physical Characteristics The physical properties of a polymer binder, such as adhesion, hardness, coating smoothness and thickness, should be considered prior to a test. Adhesion should be strong enough to sustain skin friction on a surface particularly in high-speed flows, which is related to surface tension, solvent softening and chemical bonding. Hardness primarily depends on the type of polymers, the molecular weight and the degree of cross-linking. For example, silicone rubbers (or RTVs) are generally soft, whereas Acrylates and methacrylates are generally hard. Smoothness depends primarily on paint itself and application techniques; for most paints uniform leveling of the paint is essential to a smooth finish. The coating thickness is very dependent on application techniques for both the basecoat and PSP topcoat. It is generally desirable to minimize the coating roughness and thickness to avoid any effect on the aerodynamic characteristics of a model. Typically, the maximum rms roughness of a coating should be less than 0.25 µm, and the coating thickness ranges from 20 to 40 µm. Chemical Characteristics Toxicity of paint is a major concern of safety; toxic solvents such as chlorinated solvents should be avoided. Painter must be protected against contact with paint spray through the use of fresh air breathing equipment and adequate ventilation. The paint must be easily sprayed, leveled, and cured to give the specified physical characteristics of coating under different environmental conditions in wind tunnels. The solvent evaporation rate must be controlled under different conditions of temperature and humidity. Since the wind tunnel time is expensive, application of the paint should be as fast as possible. The curing temperature must o be reasonable (less than 100 C); if the curing temperature is too high, it is difficult to achieve uniform curing over different metal materials. In addition, paint removal and reapplication on a model is a practical issue in wind tunnel testing.

60

3. Physical Properties of Paints

Some paints, particularly those designed for good and robust adhesion, are difficult to remove and generally require an aggressive paint stripper like methylene chloride. This introduces problems with toxicity and insuring adequate ventilation.

4. Radiative Energy Transport and Intensity-Based Methods

4.1. Radiometric Notation Luminescent radiation from a luminescent paint (PSP or TSP) on a surface involves two major transport processes of radiative energy. The first process is absorption of an excitation light through a paint layer and the second process is luminescent radiation that is an absorbing-emitting process in the paint layer. These processes can be described by the transport equations of radiative energy (Modest 1993; Pomraning 1973). The luminescent intensity emitted from a paint layer in plane geometry can be analytically determined by solving the transport equations. Thus, the corresponding photodetector output can be derived for an analysis of measurement system performance and uncertainty. Before doing a detailed analysis, it is necessary to discuss the radiometric notation. In the literature of PSP and TSP, the term ‘luminescent intensity’ or ‘fluorescent intensity’, which is usually denoted by the capital English letter ‘I’, has been widely used. In a strict radiometric sense, the luminescent intensity I is the luminescent radiance defined as the radiant energy flux (power) per unit solid angle and per unit projected area of an elemental surface of PSP or TSP (units: watt-m-2-sr-1 or J-s-1-m-2-sr-1). Z Incident light

θ

Emission

Y

φ

X

Fig. 4.1. Incident excitation light and luminescent emission in a local polar coordinate system

62

4. Radiative Energy Transport and Intensity-Based Methods

The radiance is a function of both position and direction, which is graphically represented by a cone of a solid angle element in radiometry as shown in Fig. 4.1. The direction of the radiance (incident or emitting radiance) is given by the polar angle ș (measured from the surface normal) and the azimuthal angle φ (measured between an arbitrary axis on the surface and the elemental solid angle on the surface) in a local coordinate system. In radiometry, the radiance is conventionally denoted by the captical English letter ‘L’. The term ‘intensity’ is sometimes confusing because its definition is different in a number of different -1 disciplines. In radiometry, the radiant intensity (units: watt-sr ), denoted by the letter ‘I’, is the radiant flux per unit solid angle, which is different from the radiance (McCluney 1994; Wolfe 1998). However, in the literature of radiative heat transfer, the radiative intensity, denoted by the same letter ‘I’, is essentially equivalent to the radiance in radiometry (Modest 1993). In order to avoid confusion in notation, we specifically define the luminescent intensity ‘I’ as the luminescent radiance from PSP or TSP, which is consistent with the notation and terminology commonly used in the literature of PSP and TSP. In a general case, we still use the traditional radiometric notation ‘L’ to denote the radiance in other radiometric measurements and modeling. The spectral radiance such as I Ȝ and

L Ȝ at a wavelength λ (units: watt-m -sr -nm ) is usually denoted by a subscript -2

-1

-1

λ ; the radiance I (or L) is the integration of the spectral radiance I Ȝ (or L Ȝ ) over a certain range of the radiation wavelengths. Since the radiation from a luminescent molecule is isotropic, a plausible assumption is that the luminescent radiance from PSP or TSP is independent of the azimuthal angle φ . Under this assumption, an analysis of transport of the luminescent radiative energy in PSP or TSP is considerably simplified. The following analysis is given for PSP, but it is also valid for TSP that is treated as a special case of PSP when the oxygen quenching vanishes.

4.2. Excitation Light We consider a PSP layer with a thickness h on a wall, as shown in Fig. 4.2. Suppose that PSP is not a scattering medium and scattering exists only at the wall surface. When an incident excitation light beam with a wavelength λ1 enters the layer, without scattering and other sources for the excitation energy, the incident light is attenuated due to absorption through the PSP medium. In plane geometry where the luminescent intensity (radiance) is independent of the azimuthal angle, the intensity of the incident excitation light with λ1 can be described by

µ

d I Ȝ−1 dz

+ ȕ Ȝ1 I Ȝ−1 = 0 ,

(4.1)

4.2. Excitation Light

63

where I Ȝ−1 is the incident excitation light intensity, µ = cos ș is the cosine of the polar angle ș , and ȕ Ȝ 1 is the extinction coefficient of the PSP medium for the incident excitation light with λ1.

The extinction coefficient ȕ Ȝ1 = İ Ȝ1 c is a

product of the molar absorptivity İ Ȝ1 and luminescent molecule concentration c . Again, note that the spectral intensity is defined as radiative energy transferred per -2 unit time, solid angle, spectral variable and area normal to the ray (units: watt-m -1 -1 sr -nm ). The superscript ‘-‘ in I Ȝ−1 indicates the negative direction in which the light enters the layer. The incident angle ș ranges from ʌ / 2 to 3 ʌ /2 ( −1 ≤ µ ≤ 0 ) (see Fig. 4.2). Incident excitation light q 0

Luminescence

Z

θ

Air PSP

h

+

Ιλ2

+

Ιλ 2 θ

θ

−

Ιλ 2

−

Ιλ1

+

Ιλ1

θ

O

Wall Reflected/scattered luminescent light

Reflected/scattered excitation light

Fig. 4.2. Radiative energy transports in a luminescent paint layer

For the collimated excitation light, the boundary value for Eq. (4.1) is the component penetrating into the PSP layer,

I Ȝ−1 (z = h) = ( 1 − ȡ Ȝap1 ) q0 E Ȝ 1 (Ȝ 1 ) į(µ − µ ex ) ,

(4.2)

where q0 and E Ȝ 1 (Ȝ 1 ) are the radiative flux and spectrum of the incident excitation light, respectively, ȡ Ȝap1 is the reflectivity of the air-PSP interface, µex is the cosine of the incident angle of the excitation light, and į(µ ) is the Dirac-delta function. The solution to Eq. (4.1) is

I Ȝ−1 = ( 1 − ȡ Ȝap1 ) q0 E Ȝ 1 (Ȝ 1 ) į(µ − µex ) exp [( ȕ Ȝ 1 / µ)(h − z)] . ( −1 ≤ µ ≤ 0 )

(4.3)

This relation describes a decay of the incident excitation light intensity through the layer. The incident excitation light flux at the wall integrated over the ranges of ș from either ʌ to ʌ / 2 or ʌ to 3 ʌ /2 is

64

4. Radiative Energy Transport and Intensity-Based Methods

q Ȝ−1 ( z = 0 ) = −

³

0 −1

I Ȝ−1 (z = 0) µ dµ ≅ C d ( 1 − ȡ Ȝap1 ) q 0 E Ȝ 1 (Ȝ 1 ),

(4.4)

where C d is the coefficient representing the directional effect of the excitation light, that is, C d = − µ ex exp( ȕ Ȝ 1 h / µ ex ) . ( −1 ≤ µ ex ≤ 0 ) (4.5) When the incident excitation light impinges on the wall, the light reflects and re-enters into the layer. Without a scattering source inside PSP, the intensity of the reflected and scattered light from the wall is described by

µ

d I Ȝ+1 dz

+ ȕ Ȝ1 I Ȝ+1 = 0 ,

(4.6)

where I Ȝ+1 is the excitation light intensity in the positive direction emanating from the wall. As shown in Fig. 4.2, the range of µ is 0 ≤ µ ≤ 1 ( 0 ≤ ș ≤ ʌ /2 and −ʌ / 2 ≤ ș ≤ 0 ) for the outgoing reflected and scattered excitation light. The superscript ‘+’ indicates the outgoing direction from the wall. For the wall that reflects diffusely, the boundary condition for Eq. (4.6) is

I Ȝ+1 (z = 0) = ȡ Ȝwp1 q Ȝ−1 ( z = 0 ) = C d ȡ Ȝwp1 ( 1 − ȡ Ȝap1 ) q0 E Ȝ 1 (Ȝ 1 ),

(4.7)

where ȡ Ȝwp1 is the reflectivity of the wall-PSP interface for the excitation light. The solution to Eq. (4.6) is (0 ≤ µ ≤ 1 )

I Ȝ+1 = C d ȡ Ȝwp1 ( 1 − ȡ Ȝap1 ) q0 E Ȝ 1 (Ȝ 1 ) exp ( − ȕ Ȝ 1 z / µ).

(4.8)

At a point inside the PSP layer, the net excitation light flux is contributed by the incident and scattering light rays from all the possible directions. The net flux is calculated by adding the incident flux (integrated over ș = ʌ to ʌ /2 and

ș = ʌ to 3ʌ /2 ) and scattering flux (integrated over ș = 0 to − ʌ /2 ). Hence, the net excitation light flux is ( q Ȝ 1 )net = − 2

³

0 −1

I Ȝ−1 µ dµ − 2

³

0 1

ș = 0 to ʌ /2

I Ȝ+1 µ dµ

and

(4.9)

≅ C d ( 1 − ȡ ) q0 E Ȝ 1 (Ȝ 1 )[ exp ( − ȕ Ȝ 1 z /µex ) + ȡ exp ( −3 ȕ Ȝ 1 z / 2)] . ap Ȝ1

wp Ȝ1

Note that the derivation of Eq. (4.9) uses an approximation of the exponential integral of third order, E 3 (x) ≅ (1/2) exp ( −3 x / 2) .

4.3. Luminescent Emission and Photodetector Response

65

4.3. Luminescent Emission and Photodetector Response After the luminescent molecules in PSP absorb the energy from the excitation light with a wavelength λ1, they emit luminescence with a longer wavelength λ2 due to the Stokes shift. Luminescent radiative transfer in PSP is an absorbingemitting process; the luminescent light rays from the luminescent molecules radiate in both the inward and outward directions. For the luminescent emission toward the wall, the luminescent intensity I Ȝ−2 can be described by

µ

d I Ȝ−2 dz

+ ȕ Ȝ2 I Ȝ−2 = S Ȝ2 (z) ,

( −1 ≤ µ ≤ 0 )

(4.10)

where S Ȝ2 (z) is the luminescent source term and the extinction coefficient

ȕ Ȝ2 = İ Ȝ2 c is a product of the molar absorptivity İ Ȝ2 and luminescent molecule concentration c .

S Ȝ2 (z) is assumed to be

The luminescent source term

proportional to the extinction coefficient for the excitation light, the quantum yield, and the net excitation light flux filtered over a spectral range of absorption. Therefore, a model for the luminescent source term is expressed as

S Ȝ 2 (z) = Φ ( p, T ) E Ȝ 2 ( Ȝ 2 )

³

∞ 0

(q Ȝ 1 )net ȕ Ȝ 1 Ft 1 ( Ȝ 1 ) dȜ 1 ,

(4.11)

where Φ ( p, T ) is the luminescent quantum yield that depends on air pressure (p) and temperature (T), E Ȝ 2 (Ȝ 2 ) is the luminescent emission spectrum, and

Ft 1 ( Ȝ1 ) is a filter function describing the optical filter used to insure the excitation light within the absorption spectrum of the luminescent molecules. With the boundary condition I Ȝ−2 (z = h) = 0 , the solution to Eq. (4.10) is § ȕȜ2 z · 1 ª ¸ « I Ȝ−2 = exp ¨ − ¨ ¸µ« µ © ¹ ¬

³

z 0

§ ȕȜ2 z · ¸ dz − S Ȝ2 ( z ) exp ¨ ¨ µ ¸ © ¹

³

h 0

§ ȕȜ2 z · ¸ dz S Ȝ2 ( z ) exp ¨ ¨ µ ¸ © ¹

( −1 ≤ µ ≤ 0 )

º ». » ¼

(4.12)

The incoming luminescent flux toward the wall at the surface (integrated over ș = ʌ to ʌ /2 and ș = ʌ to 3ʌ /2 ) is

q Ȝ−2 ( z = 0 ) = − 2 where

³

0 −1

I Ȝ−2 (z = 0) µ dµ ,

(4.13)

66

4. Radiative Energy Transport and Intensity-Based Methods

I Ȝ−2 ( z = 0 ) = −

1 µ

³

h 0

S Ȝ2 ( z ) exp (

ȕȜ2 z µ

)dz .

We consider the luminescent emission in the outward direction and assume that the scattering occurs only at the wall. The outgoing luminescent intensity I Ȝ+2 can be described by

µ

d I Ȝ+2 dz

+ ȕ Ȝ2 I Ȝ+2 = S Ȝ2 (z) .

(0 ≤ µ ≤ 1)

(4.14)

Similar to the boundary condition for the scattering excitation light, a fraction of the incoming luminescent flux q Ȝ− 2 ( z = 0 ) is reflected diffusely from the wall. Thus, the boundary condition for Eq. (4.14) is

I Ȝ+2 (z = 0) = ȡ Ȝwp2 q Ȝ−2 ( z = 0 ) = − 2 ȡ Ȝwp2

³

0 −1

I Ȝ−2 (z = 0) µ dµ ,

(4.15)

where ȡ Ȝwp2 is the reflectivity of the wall-PSP interface for the luminescent light. The solution to Eq. (4.14) with the boundary condition Eq. (4.15) is

§ ȕȜ2 z · ª 1 ¸« I Ȝ+2 = exp ¨ − ¨ ¸«µ µ © ¹¬

³

º § ȕȜ2 z · ¸ dz + I + ( z = 0 )» . S Ȝ2 ( z ) exp¨ Ȝ2 ¨ µ ¸ 0 » © ¹ ¼ z

( −1 ≤ µ ≤ 0 )

(4.16)

At this stage, the outgoing luminescent intensity I Ȝ+2 can be readily calculated by substituting the source term Eq. (4.11) into Eq. (4.16). In general, I Ȝ+2 has a nonlinear distribution across the PSP layer, which is composed of the exponentials of ȕ Ȝ 1 z and ȕ Ȝ2 z . For simplicity of algebra, we consider an asymptotic but important case ʊ an optically thin PSP layer. When the PSP layer is optically thin ( ȕ Ȝ 1 h , ȕ Ȝ 2 h , ȕ Ȝ 1 z and ȕ Ȝ2 z <<1), the asymptotic expression for I Ȝ+2 is simply

I Ȝ+2 ( z ) = Φ ( p, T ) q0 E Ȝ 2 (Ȝ 2 )K 1 (ȕ Ȝ 1 / µ)( z + 2 ȡ Ȝwp2 h µ) , ( −1 ≤ µ ≤ 0 ) where

K 1 = ȕ Ȝ−11

³

∞ 0

ȕ Ȝ 1 E Ȝ 1 (Ȝ 1 ) C d ( 1 − ȡ Ȝap1 )( 1 + ȡ Ȝwp1 )Ft 1 ( Ȝ1 ) dȜ1 .

(4.17)

4.3. Luminescent Emission and Photodetector Response

67

Eq. (4.17) indicates that for an optically thin PSP layer the outgoing luminescent intensity is proportional to the extinction coefficient (a product of the molar absorptivity and luminescent molecule concentration), paint layer thickness, quantum yield of the luminescent molecules, and incident excitation light flux. The term K 1 represents the combined effect of the optical filter, excitation light scattering and direction of the incident excitation light. The outgoing luminescent intensity averaged over the layer is

< I Ȝ+2 > = h −1

³

h 0

I Ȝ+2 (z) dz = h Φ ( p, T ) q0 E Ȝ 2 (Ȝ 2 )K 1 (ȕ Ȝ 1 / µ) M(µ ),

(4.18)

where M ( µ ) = 0.5 + 2 ȡ Ȝwp2 µ. The outgoing luminescent energy flow rate Q Ȝ+2 (radiant flux) on an area element A s of the PSP paint surface collected by a detector is

Q Ȝ+2 = A s

³

ȍ

< I Ȝ+2 > cos ș dȍ = ȕ Ȝ 1 h Φ ( p, T ) q0 E Ȝ 2 (Ȝ 2 ) K 1 < M > A s ȍ

, (4.19)

where Q Ȝ+2 is equivalent to the spectral radiant flux in radiometry (watt-nm ), ȍ -1

is a collecting solid angle of the detector, and the extinction coefficient ȕ Ȝ1 = İ Ȝ1 c is a product of the molar absorptivity İ Ȝ1 and luminescent molecule concentration c . The coefficient < M > represents the effect of reflection and scattering of the luminescent light at the wall, which is defined as

< M > = ȍ −1

³

ȍ

M(µ ) dȍ = 0.5 + ȡ Ȝwp2 ( µ1 + µ 2 ) ,

where µ1 = cos ș1 and µ 2 = cos ș 2 are the cosines of two polar angles in the solid angle ȍ . Imaging system aperture area, A0 = ʌ D2 /4

Source area

Image of source area AI

As

R1

R2

Fig. 4.3. Schematic of an imaging system

68

4. Radiative Energy Transport and Intensity-Based Methods

The response of a photodetector to the luminescent emission can be derived based on a model of an optical system (Holst 1998). Consider an optical system located at a distance R1 from a luminescent source area, as shown in Fig. 4.3. The collecting solid angle with which the lens is seen from the source can be approximated by ȍ ≈ A 0 / R12 , where A0 = ʌ D 2 /4 is the imaging system entrance aperture area, and D is the effective diameter of the aperture. Using Eq. (4.19) and additional relations A s / R12 = A I / R22 and 1 / R1 + 1 / R2 = 1 / fl , we obtain the radiative energy flux onto the detector (QȜ 2 )det =

ʌ AI Top Tatm ȕ Ȝ h Φ ( p, T ) q0 E Ȝ 2 (Ȝ 2 ) K 1 < M > , 4 F 2 (1 + M op )2 1

(4.20)

where F = fl / D is the f-number, M op = R2 / R1 is the optical magnification, fl is the system’s effective focal length, AI is the image area, and Top and Tatm are the system’s optical transmittance and atmospheric transmittance, respectively. The output of the detector is

V =G

³

∞

0

Rq (Ȝ 2 ) (Q Ȝ 2 )det Ft 2 ( Ȝ2 )dȜ2 ,

(4.21)

where Rq (Ȝ 2 ) is the detector’s quantum efficiency, G is the system’s gain, and

Ft 2 ( Ȝ2 ) is a filter function describing the optical filter for the luminescent emission. The dimension of V/G is [V/G] = J/s. Substitution of Eq. (4.20) into Eq. (4.21) yields V =G

AI ʌ ȕ Ȝ h Φ ( p, T ) q0 K 1 K 2 , 4 F 2 (1 + M op ) 2 1

(4.22)

where

K2 =

³

∞

0

Top Tatm E Ȝ 2 (Ȝ 2 )< M > Rq (Ȝ 2 ) Ft 2 ( Ȝ2 )dȜ2 .

The term K 2 represents the combined effect of the optical filter, luminescent light scattering, and system response to the luminescent light. The above analysis is made based on an assumption that the radiation source is on the optical axis. In general, the off-axis effect is taken into account by multiplying a factor cos 4 θ p in the right-hand side of Eq. (4.22), where θ p is the angle between the optical axis and light ray through the optical center (McCluney 1994). Eq. (4.19) gives the directional dependency of the luminescent radiant flux

Q Ȝ+2 ∝ 1 + 2 ρ λwp2 [cos( θ − ∆θ / 2 ) + cos( θ + ∆θ / 2 )] ,

(4.23)

4.4. Intensity-Based Measurement Systems

69

where ∆θ = θ 2 − θ 1 is the difference between two polar angles in the solid angle ȍ . Clearly, the luminescent radiant flux contains a constant irradiance term and a Lambertian term that is proportional to the cosine of the polar angle θ . Le Sant (2001b) measured the directional dependency of the luminescent emission of the OPTROD’s B1 PSP composed of a derived Pyrene dye and a reference component. Figure 4.4 shows the normalized luminescent intensity as a function of the viewing polar angle for the B1 paint and the B1 paint with talc compared with the theoretical distribution Eq. (4.23) with ρ λwp2 = 0.5 and ∆θ = 4 degrees. The experimental directional dependency remains nearly constant for both paints o until the viewing polar angle is larger than 60 . The theoretical distribution for a non-scattering paint fails to predict the flatness of the experimental directional distributions of the luminescent emission. This is because the simplified theoretical analysis does not consider scattering particles (e.g. talc and solid reference component particles) re-directing and re-distributing both the excitation light and luminescent light inside the paints. A more complete analysis of the radiative energy transport in a luminescent paint with scattering particles requires a numerical solution of an integro-differential equation (Modest 1993).

Normalized Luminescent Intensity

1.2

1.0

0.8

0.6

Theory B1 PSP without talc B1 PSP with talc

0.4

0.2 -100

-80

-60

-40

-20

0

20

40

60

80

100

Polar Angle (degree)

Fig. 4.4. Directional dependency of the luminescent emission from the B1 paint and B1 paint with talc, compared with the theoretical directional distribution for a non-scattering paint. Experimental data for the B1 paints are from Le Sant (2001b)

4.4. Intensity-Based Measurement Systems The photodetector output V responding to the luminescent emission, Eq. (4.22), is re-written as V = Ȇ c Ȇ f ȕ Ȝ1 h q0 Φ ( p, T ) . (4.24)

70

4. Radiative Energy Transport and Intensity-Based Methods

The parameters Ȇ c and Ȇ f

are Ȇ c = ( ʌ / 4) G AI [ F 2 (1 + M op ) 2 ] −1 and

Ȇ f = K 1 K 2 , which are related to the imaging system (camera) performance and filter parameters, respectively. The quantum yield Φ ( p, T ) is described by

Φ ( p,T) = k r /( k r + k nr + k q S φO2 p ) , where kr is the radiative rate constant, knr is the radiationless deactivation rate constant, kq is the quenching rate constant, p is air pressure, S is the solubility of oxygen, and φ O2 is the volume fraction of oxygen in air. In PSP applications, the intensity-ratio method is commonly used to eliminate the effects of spatial variations in illumination, paint thickness, and molecule concentration. Without any model deformation, air pressure p is related to a ratio between the wind-off and wind-on outputs by the Stern-Volmer relation

Vref V

= A( T ) + B( T )

p . p ref

(4.25)

The essential elements of a measurement system for PSP and TSP include illumination sources, optical filters, photodetectors and data acquisition/processing units. In terms of the detectors and illumination sources used, measurement systems can be generally categorized into CCD camera system and laser scanning system with a single-sensor detector. Since each system has advantages over the other, researchers can choose one most suitable to meet the requirements for their specific experiments.

4.4.1. CCD Camera System A CCD camera system is most commonly used for PSP and TSP measurements in wind tunnel tests. Figure 1.4 shows a schematic of a CCD camera system. The luminescent paint (PSP or TSP) is applied to a model surface, which is excited to luminesce by an illumination source such as UV lamp, LED array or laser. The luminescent emission is filtered optically to eliminate the illuminating light before projecting onto a CCD sensor. Images (wind-on and wind-off images) are digitized and transferred to a computer for data processing. In order to correct the dark current in a CCD camera, a dark current image is acquired when no light is incident on the camera. A ratio between the wind-on and wind-off images is taken after the dark current image is subtracted from both images, resulting in a luminescent intensity ratio image. Then, using the calibration relation for the paint, the distribution of the surface pressure or temperature is computed from the intensity ratio image. Scientific grade cooled CCD digital cameras are ideal imaging sensors for PSP and TSP, which can provide a high intensity resolution (12 to 16 bits) and high spatial resolution (typically 512×512, 1024×1024, up to 2048×2048 pixels). Because a scientific grade CCD camera exhibits a good linear response and a high signal-to-noise ratio (SNR) up to 60 dB, it is particularly suitable to quantitative measurement of the luminescent emission (LaBelle and Garvey 1995). The major

4.4. Intensity-Based Measurement Systems

71

disadvantages of a scientific grade CCD camera are its high cost and a very slow frame rate. Less expensive consumer grade CCD video cameras were used in early PSP and TSP measurements (Kavandi et al. 1990; Engler et al. 1991; McLachlan et al. 1992); the intensity resolution of a CCD video camera is typically 8 bits with a conventional frame grabber. When there is a large pressure variation over a model surface, a consumer grade video CCD camera can be used as an alternative to give acceptable quantitative results after the camera is carefully calibrated to correct the non-linearity of the radiometric response function of the camera (see Chapter 5). The low SNR of a video camera can be improved by averaging a sequence of images to reduce the random noise. In addition, film-based camera systems were occasionally used in special PSP measurements like flight tests (Abbitt et al. 1996). The performance of a CCD array is characterized by the responsivity, charge well capacity and noise. From these quantities, the minimum signal, maximum signal, signal-to-noise ratio and dynamic range can be estimated (Holst 1998; Janesick 1995). These performance parameters are critical for quantitative radiometric measurements of the luminescent emission, which can be estimated based on the camera model and noise models (Holst 1998). Here, the most relevant concepts are briefly discussed. The responsivity, the efficiency of generating electrons by a photon, is determined by the spectral quantum efficiency Rq ( λ ) of a detector. The full-well capacity specifies the number of photoelectrons that a pixel can hold before charge begins to spill out, thus reducing the response linearity. The maximum signal is proportional to the fullwell capacity. Normally, the well size is approximately proportional to the pixel size. Therefore, in a fixed CCD area, increasing the effective pixel size to enhance the SNR may reduce the spatial resolution. The dynamic range, defined as the maximum signal (or the full-well capacity) divided by the rms readout noise (or noise floor), loosely describes the camera’s ability to measure both low and high light levels. The minimum signal is limited by the camera noises, including the photon shot noise, dark current, reset noise, amplifier noise, quantization noise, and fixed pattern noise. The photon shot noise is associated with the discrete nature of photoelectrons obeying the Poisson statistics in which the variance is equal to the mean. The dark current is due to thermally generated electrons, which can be reduced to a very low level by cooling a CCD device. The reset noise is associated with resetting the sense node capacitor that is temperature-dependent. The amplifier noise contains two components: 1/f noise and white noise; the array manufacturer usually provides this value and calls it the readout noise, noise equivalent electrons, or noise floor. By careful optimization of the camera electronics, the readout noise or noise floor can be reduced to as low as 4-6 electrons. The quantization noise results from the analog-to-digital conversion. The fixed pattern noise (the pixel-to-pixel variation) is due to differences in pixel responsivity, which is called the scene noise, pixel noise, or pixel nonuniformity as well.

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4. Radiative Energy Transport and Intensity-Based Methods

Noise Electrons (rms)

10000

Total Noise

1000

100 Noise Floor 10

Fixed Pattern Noise Photon Shot Noise

1 10

100

1000

10000

100000

Photoelectrons

Fig. 4.5. Noise curves of CCD for the noise floor = 50e and non-uniformity U = 0.25%

Although various noise sources exist, for many applications, it is sufficient to consider the photon shot noise, noise floor, and fixed pattern noise due to pixel nonuniformity. Thus, according to the Poisson statistics, the total system noise < nsys > is given by 2 < nsys > = < nshot > + < n 2floor > + < n 2pattern > = n pe + < n 2floor > + ( Un pe )2

, (4.26)

2 > , < n 2floor > and < n 2pattern > are the variances of the photon shot where < nshot

noise, noise floor and pattern noise, respectively, n pe is the number of collected photoelectrons, and U is the pixel nonuniformity. Accordingly, the signal-to-noise ratio (SNR) is

SNR = n pe / n pe + < n 2floor > + ( Un pe ) 2

.

(4.27)

Figure 4.5 shows the total noise, photon shot noise, noise floor (readout noise), and fixed pattern noise of a CCD as a function of the number of photoelectrons for < n 2floor > 1 / 2 = 50e and U = 0.25%. For a very low photon flux, the noise floor dominates. As the incident light flux increases, the photon shot noise dominates. At a very high level of the incident light flux, the noise may be dominated by the fixed pattern noise. When the photon shot noise dominates, the SNR asymptotically approaches to

SNR = n pe , and the dynamic range is

( n pe )max / < n floor > , where ( n pe )max is the full-well capacity. The dark current only affects those applications where the SNR is low. In most applications of PSP

4.4. Intensity-Based Measurement Systems

73

and TSP, the pressure and temperature resolutions are limited by the photon shot noise. Table 4.1, which is adapted from Crites (1993), lists the performance parameters of some CCD sensors. Table 4.1. Characteristics of CCD Sensors CCD

TH7883PM

TH7895B

TH896A

TK512CB

Pixel array

384×586

512×512

1024×1024

512×512

1024×1024

1024×1024

Full well (e)

180000

290000

350000

700000

450000

256000

o

TK1024F

TK1024B

Temperature ( C)

-45

-45

-40

-40

-40

-40

Dark current (e)

8

8

25

4

3

6

Readout Noise (e)

12

6

6

10

9

9

Quantum efficiency

40%

40%

40%

80%

35%

80%

Peak wavelength (nm)

700

670

670

650

670

650

The selection of an appropriate illumination source depends on the absorption spectrum of a luminescent paint and optical access of a specific facility. An illumination source must provide a sufficiently large number of photons in the wavelength band of absorption without saturating the luminescence and causing serious photodegradation. It is desirable for a source to generate a reasonably uniform illumination field over a surface such that the measurement uncertainty associated with model deformation can be reduced. A continuous illumination source should be stable and a flash source should be repeatable. A variety of illumination sources are commercially available. Pulsed and continuous-wave lasers with fiber-optic delivery systems were used in wind tunnel tests (Morris et al. 1993a, 1993b; Crites 1993; Bukov et al. 1992; Volan and Alati. 1991; Engler et al. 1991, 1992; Lyonnet et al. 1997). Lasers have obvious advantages in terms of providing narrow band intense illumination. Very stable blue LED arrays were developed for illuminating paints (Dale et al. 1999). LED arrays are attractive as an illumination source since they are light in weight and they produce little heat; they can be suitably distributed to form a fairly uniform illumination field. In addition, they can be easily controlled to generate either continuous or modulated illumination. Other light sources reported in the literature of PSP and TSP include xenon arc lamps with blue filters (McLachlan et al. 1993a), incandescent tungsten/halogen lamps with blue filters (Morris et al. 1993a; Dowgwillo et al. 1994) and fluorescent UV lamps (Liu et al. 1995a, 1995b). The spectral characteristics of illumination sources can be found in The Photonics Design and Applications Handbook (1999). Crites (1993) discussed some available light sources from a viewpoint of PSP application. Optical filters are used to separate the luminescent emission from the excitation light, or separate the luminescent emissions from different luminophores. There are two kinds of filters: interference filters and color glass filters. Interference filters select a band of light through a process of constructive and destructive interference. They consist of a substrate onto which chemical layers are vacuum deposited in such a fashion that the transmission of certain wavelengths is

74

4. Radiative Energy Transport and Intensity-Based Methods

enhanced, while other wavelengths are either reflected or absorbed. Band-pass interference filters only transmit light in a spectral band; the peak wavelength and spectral width can be tightly controlled. Edge interference filters only transmit light above (long pass) or below (short pass) a certain wavelength. Color glass filters are used for applications that do not need precise control over wavelengths and transmission intensities. The ratio of transmission to blocking is a key filter characteristic. All filters are sensitive to the angle of incidence of the incoming light. For interference filters, the peak transmission wavelength decreases as the angle of incidence deviates from the normal, while the bandwidth and transmission characteristics generally remain unchanged. For color glass filters, an increase of the incident angle increases the transmission path, reducing the transmission efficiency. 4.4.2. Laser Scanning System A generic laser scanning system for PSP and TSP is shown in Fig. 1.5. A lowpower laser beam is focused to a small point and scanned over a model surface using a computer-controlled mirror to excite the paint on a model. The luminescent emission is detected using a low-noise photodetector (e.g. PMT); the photodetector signal is digitized with a high-resolution A/D converter in a PC and processed to calculate pressure or temperature based on the calibration relation for the paint. When the laser beam is modulated, a lock-in amplifier can be used to reduce the noise. Furthermore, the phase angle between the modulated excitation light and responding luminescence can be obtained using a lock-in amplifier for phase-based PSP and TSP measurements. The laser can be scanned continuously or in steps; it is synchronized to data acquisition such that the position of the laser spot on the model is known. In order to compensate for a laser power drift, the laser power variation is monitored using a photodiode. The laser scanning systems for PSP and TSP measurements were discussed by Hamner et al. (1994), Burns (1995), Torgerson et al (1996), and Torgerson (1997). Compared to a CCD camera system, a laser scanning system offers certain advantages. Since a low-noise PMT is used to measure the luminescent emission, before an analog output from the PMT is digitized, standard SNR enhancement techniques are available to improve the measurement accuracy. Amplification and band-limited filtering can be used to improve the SNR. The signal is then digitized with a high-resolution A/D converter (12 to 24 bits). Additional noise reduction can be accomplished using a lock-in amplifier when the laser beam is modulated. The laser scanning system is able to provide uniform illumination over a surface by scanning a single laser spot. The laser power is easily monitored and correction for the laser power drift can be made for each measurement point. The laser scanning system can be used for PSP and TSP measurements in a facility where optical access is so limited that a CCD camera system is difficult to use.

4.5. Basic Data Processing

75

4.5. Basic Data Processing The most basic processing procedure in the intensity-based method for PSP and TSP is taking a ratio between the wind-on image and the wind-off reference image to correct the effects of non-homogenous illumination, uneven paint thickness and non-uniform luminophore concentration. However, this ratioing procedure is complicated by model deformation induced by aerodynamic loads, which results in misalignment between the wind-on and wind-off images. Therefore, additional correction procedures are required to eliminate (or reduce) the error sources associated with model deformation, the temperature effect of PSP, selfillumination, and camera noises (dark current and fixed pattern noise). Figure 4.6 shows a generic data processing flowchart for intensity-based measurements of PSP and TSP with a CCD camera. A laser scanning system has similar data processing procedures for intensity-based measurements. The windon and wind-off images are acquired using a CCD camera. Usually, a sequence of acquired images is averaged to reduce the random noise like the photon shot noise. The dark current image and ambient lighting image are subtracted from data images to eliminate the dark current noise of the CCD camera and the contribution from the ambient light. The dark current image is usually acquired when the camera shutter is closed. In a wind tunnel environment, there is always weak ambient light that may cause a bias error in data images. The ambient lighting image is acquired when the shutter is open while all controllable light sources are turned off. The integration time for the dark current image and ambient lighting image should be the same as that for data images. The data images are then divided by the flat-field image to correct the fixed pattern noise. At a very high signal level, this correction is necessary since the fixed pattern noise may surpass the photon shot noise. Ideally, the flat-field image is acquired from a uniformly illuminated scene. A simple but less accurate approach is use of several diffuse scattering glasses mounted in the front of the lens of the camera to generate an approximately uniform illumination field. When a uniform illumination field cannot be achieved, a more complex noise-model-based approach can be used to obtain the fixed pattern noise field for a CCD camera (Healey and Kondepudy 1994). Normally, a scientific grade CCD camera has a good linear response of the camera output to the incident irradiance of light. However, conventional CCD video cameras often exhibit a non-linear response to the incident light intensity; in this case, a video camera should be radiometrically calibrated to correct the non-linearity. A simple but useful radiometric camera calibration technique is described in Chapter 5.

76

4. Radiative Energy Transport and Intensity-Based Methods

Wind-On Image

Wind-Off Image

Correction for Dark Current, Ambient Light & Fixed Pattern Noise

Correction for Non-Linearity of Response of Detector Registered & Corrected Wind-On Image

Corrected Wind-Off Image

Image Registration

Ratio Image

Self-Illumination Correction

PSP/TSP Image

PSP/TSP Calibration

PSP/TSP Data on 3D Grid

Image Resection

Forces & Moments/Heat Transfer

Fig. 4.6. Generic data processing flowchart for intensity-based PSP and TSP measurements

In this stage, even though the noise-corrected wind-on and wind-off images are obtained, we cannot yet calculate a ratio of the wind-off image over the wind-on image, Vref / V , for conversion to a pressure or temperature image. This is because the wind-on image may not align with the wind-off image due to model deformation produced by aerodynamic loads. A ratio between those non-aligned images can lead to a considerable error in calculation of pressure or temperature using a calibration relation. Also, some distinct flow features such as shock, boundary layer transition and flow separation could be smeared. In order to correct the non-alignment problem, the image registration technique should be used to match the wind-on image to the wind-off image (Bell and McLachlan 1993, 1996; Donovan et al. 1993). The image registration technique is based on a mathematical transformation ( x' , y' )  ( x , y ) , which empirically maps the deformed wind-on image coordinate ( x' , y' ) onto the reference wind-off image coordinate ( x , y ) . For a small deformation, an image registration transformation is well described by polynomials m

( x, y ) = (

¦

i , j =0

m

a ij x' i y' j ,

¦ b x' ij

i

y' j ) .

(4.28)

i , j =0

Geometrically, the constant terms, linear terms, non-linear terms in Eq. (4.28) represent translation, rotation and scaling, and higher-order deformation of a

4.5. Basic Data Processing

77

model in the image plane, respectively. In measurements of PSP and TSP, black fiducial targets are placed in the locations on a model where deformation is appreciable. The displacement of these marks in the image plane represents perspective projection of real model deformation in the 3D object space. From the corresponding centroids of the targets in the wind-on and wind-off images, the polynomial coefficients aij and bij in Eq. (4.28) can be determined using least-squares method. More targets will increase the statistical redundancy and improve the precision of least-squares estimation. For most wind tunnel tests, a second-order polynomial transformation (m = 2) is found to be sufficient. As a pure geometric correction method, however, the image registration technique fails to take into account a variation in illumination level on a model due to model movement in a non-homogenous illumination field. An estimate of this error requires the knowledge of the illumination field and the movement of the model relative to the light sources. Bell and McLachlan (1993, 1996) gave an analysis on this error in a simplified circumstance and found that this error was small if the illumination light field was nearly homogenous and model movement was small. Experiments showed that the image registration technique considerably improved the quality of PSP and TSP images (McLachlan and Bell 1995). Weaver et al. (1999) utilized spatial anomalies (dots formed from aerosol mists in spraying) in a basecoat and calculated a pixel shift vector field of a model using a spatial correlation technique similar to that used in particle image velocimetry (PIV). Based on the shift vector field, the wind-on image was registered. Le Sant et al. (1997) described an automatic scheme for target recognition and image alignment. A detailed discussion on the image registration technique is given in Chapter 5. After a ratio of the wind-off image over the registered wind-on image is taken, a pressure or temperature image can be obtained using the calibration relation (the Stern-Volmer relation for PSP or the Arrhenius relation for TSP). Compared to relatively straightforward conversion of an intensity ratio image to a temperature image, conversion to a pressure image is more difficult since the intensity ratio image of PSP is a function of not only pressure, but also temperature. The temperature effect of PSP often has a dominant contribution to the total uncertainty of PSP measurements if it is not corrected. When the Stern-Volmer coefficients A( T ) and B( T ) are determined in a priori laboratory PSP calibration and the temperature field on the surface are known, the pressure field can be, in principle, calculated from a ratio image. The need of temperature correction provoked the development of multiple-luminophore PSP and tandem use of PSP with TSP. The surface temperature distribution can be measured using TSP and infrared (IR) cameras. Also, the temperature field can be given by theoretical and numerical solutions to the motion and energy equations of flows. Unfortunately, experiments have shown that the use of a priori laboratory PSP calibration with a correction for the temperature effect still leads to a systematic error in the derived pressure distribution due to certain uncontrollable factors in wind tunnel environment. To correct this systematic error, pressure tap data at a number of locations are used to correlate the intensity ratio values to the pressure tap data; this procedure is referred to as in-situ calibration of PSP. In the worst

78

4. Radiative Energy Transport and Intensity-Based Methods

case where A( T ) and B( T ) are not known and the surface temperature field is not given, in-situ calibration is still able to give a pressure field. However, the accuracy of interpretation of PSP data between the pressure taps is not guaranteed especially when the gradients of the pressure and temperature fields between the taps are large. Obviously, the selection of the locations of the pressure taps is critical to assure the accuracy of in-situ calibration. The pressure tap data at the discrete locations for in-situ calibration should reasonably cover the pressure distribution on the surface. The in-situ calibration uncertainty of PSP is discussed in Chapter 7. PSP and TSP data in images have to be mapped onto a surface grid of a model in the 3D object space since the pressure and temperature fields on the surface grid are more useful for engineers and researchers. Further, this mapping is necessary for extraction of aerodynamic loads and heat transfer and for comparison with CFD results. In the literature of PSP and TSP, this mapping procedure is often called image resection. Note that the meaning of resection in the PSP and TSP literature is somewhat broader and looser than the strict one in photogrammetry. From the standpoint of photogrammetry, a key of this procedure is geometric camera calibration by solving the perspective collinearity equations to determine the camera interior and exterior orientation parameters, and lens distortion parameters. Once these parameters in the collinearity equations relating the 3D object space to the image plane are known, PSP and TSP data in images can be mapped onto a given surface grid in the 3D object space. A detailed discussion on analytical photogrammetric techniques is given in Chapter 5. In most PSP and TSP measurements conducted so far, data in images are mapped onto a rigid CFD or CAD surface grid of a model. However, when a model experiences a significant aeroelastic deformation in wind tunnel tests, mapping onto a rigid grid misrepresents the true pressure and temperature fields. Therefore, a deformed surface grid of a model should be generated for PSP and TSP mapping. Liu et al. (1999) discussed generation of a deformed surface grid based on videogrammetric model deformation measurements conducted along with PSP/TSP measurements (see Chapter 5). Finally, the integrated aerodynamic forces and moments can be calculated from the pressure distribution on the surface. For example, the lift is given by FL = ¦ p i ( n • l L ∆S )i , where n is the unit normal vector of a panel on the surface, ∆S is the area of the panel, and l L is the unit vector of the lift. Similarly, the integrated quantities of heat transfer can be obtained from the surface temperature fields based on appropriate heat transfer models. The self-illumination correction is implemented after the luminescent intensity data are mapped on a surface grid in the 3D object space. The socalled self-illumination is a phenomenon that the luminescent emission from one part of a model surface illuminates another surface, thus increasing the observed luminescent intensity of the receiving surface and producing an additional error in calculation of pressure and temperature. This distorting effect often occurs on the surfaces of neighboring components such as wind/body junctures and concave surfaces. The self-illumination depends on the surface geometry, the luminescent field, and the reflecting properties of a paint layer. Assuming that a

4.5. Basic Data Processing

79

paint surface is Lambertian, Ruyten (1997a, 1997b, 2001a) developed an analytical model and a numerical scheme for correcting the self-illumination effect. The self-illumination correction scheme is discussed in Chapter 5. One of the original purposes of developing two-luminophore PSPs is to simplify the data processing for PSP. The dependency of a two-color intensity ratio I λ1 / I λ2 on pressure p and temperature T is generally expressed as

I λ1 / I λ2 = f ( p , T ) , where I λ1 and I λ2 are the luminescent intensities at the emission wavelengths λ1 and λ 2 , respectively. Ideally, a two-color intensity ratio can eliminate the effect of spatially non-uniform illumination on a surface. However, since two luminophores cannot be perfectly mixed, the simple twocolor intensity ratio I λ1 / I λ2 cannot completely compensate the effect of nonhomogenous dye concentration. In this case, a ratio of ratios ( I λ1 / I λ2 ) /( I λ1 / I λ2 )0 should be used to correct the effects of non-homogenous dye concentration and paint thickness variation, where the subscript 0 denotes the wind-off condition (McLean 1998). Since the wind-off images are required, the ratio-of-ratios method still needs image registration. The ratio-of-ratios approach was also applied to non-pressure-sensitive reference targets to compensate the effect of non-homogenous illumination on a moving model (Subramanian et al. 2002).

5. Image and Data Analysis Techniques

This Chapter describes image and data analysis techniques used in various processing steps for PSP and TSP. For quantitative PSP and TSP measurements, cameras should be geometrically calibrated to establish the accurate relationship between the image plane and the 3D object space and map data in images onto a surface grid in the object space. Analytical camera calibration techniques, especially the Direct Linear Transformation (DLT) and the optimization calibration method, are discussed. Since PSP and TSP are based on radiometric measurements, an ideal camera should have a linear response to the luminescent radiance. For a camera having a non-linear response, radiometric camera calibration is required to determine the radiometric response function of the camera for correcting the image intensity before taking a ratio between the wind-on and wind-off images. A simple but effective technique is described here for radiometric camera calibration. The self-illumination of PSP and TSP may cause a significant error near a conjuncture of surfaces when a strong exchange of the radiative energy occurs between neighboring surfaces. The numerical methods for correcting the selfillumination are generally described and the errors associated with the selfillumination are estimated for a typical case. The self-illumination correction is usually made on a surface grid in the object space since it highly depends on the surface geometry. A standard procedure in the intensity-based method for PSP and TSP is to take a ratio between the wind-on and wind-off images to eliminate the effects of non-homogenous illumination intensity, dye concentration, and paint thickness. However, since a model deforms due to aerodynamic loads, the wind-on image does not align with the wind-off image. The image registration technique based on a mathematical transformation between the wind-on and wind-off images is described to re-align these images. A crucial step for PSP is to accurately convert the luminescent intensity to pressure; cautious use of the calibration relations with a correction of the temperature effect of PSP is discussed. PSP measurements in low-speed flows are particularly difficult since a very small pressure change has to be sufficiently resolved by PSP. The pressure-correction method is described as an alternative to extrapolate the incompressible pressure coefficient from PSP measurements at suitably higher Mach numbers by removing the compressibility effect. The final processing step for PSP and TSP is to map results in images onto a model surface grid in the object space. When a model has a large deformation produced by aerodynamic loads, a deformed surface grid should be generated for more accurate PSP and TSP mapping. A methodology for generating a deformed wing grid is proposed based on

82

5. Image and Data Analysis Techniques

videogrammetric aeroelastic deformation simultaneously with PSP and TSP measurements.

measurements

conducted

5.1. Geometric Calibration of Camera

5.1.1. Collinearity Equations After the results of pressure and temperature are extracted from images of PSP and TSP, it is necessary to map the data onto a surface grid in the 3D object space (or physical space) to make the results more useful for design engineers and researchers. The collinearity equations in photogrammetry provide the perspective relationship between the 3D coordinates in the object space and corresponding 2D coordinates in the image plane (Wong 1980; McGlone 1989; Mikhail et al. 2001; Cooper and Robson 2001; Liu 2002). A key problem in quantitative image-based measurements is camera calibration to determine the camera interior and exterior orientation parameters, and lens distortion parameters in the collinearity equations. Simpler resection methods have often been used in PSP and TSP systems to determine the camera exterior orientation parameters under an assumption that the interior orientation and lens distortion parameters are known (Donovan et al. 1993; Le Sant and Merienne 1995). The standard Direct Linear Transformation (DLT) was also used to obtain the interior orientation parameters in addition to the exterior orientation parameters (Bell and McLachlan 1993, 1996). An optimization method for comprehensive camera calibration was developed by Liu et al. (2000), which can determine the exterior orientation, interior orientation and lens distortion parameters (as well as the pixel aspect ratio of a CCD array) from a single image of a 3D target field. The optimization method, combined with the DLT, allows automatic camera calibration without an initial guess of the orientation parameters; this feature particularly facilitates PSP and TSP measurements in wind tunnels. Besides the DLT, a closed-form resection solution given by Zeng and Wang (1992) is also useful for initial estimation of the exterior orientation parameters of a camera based on three known targets. Figure 5.1 illustrates the perspective relationship between the 3D coordinates ( X, Y, Z ) in the object space and the corresponding 2D coordinates (x, y) in the image plane. The lens of a camera is modeled by a single point known as the perspective center, the location of which in the object space is ( X c ,Yc ,Z c ) . Likewise, the orientation of the camera is characterized by three Euler orientation angles. The orientation angles and location of the perspective center are referred to in photogrammetry as the exterior orientation parameters. On the other hand, the relationship between the perspective center and the image coordinate system is defined by the camera interior orientation parameters, namely, the camera principal distance c and the photogrammetric principal-point location ( x p ,y p ) .

5.1. Geometric Calibration of Camera

83

The principal distance, which equals the camera focal length for a camera focused at infinity, is the perpendicular distance from the perspective center to the image plane, whereas the photogrammetric principal-point is where a perpendicular line from the perspective center intersects the image plane. Due to lens distortion, however, perturbation to the imaging process leads to departure from collinearity that can be represented by the shifts dx and dy of the image point from its ‘ideal’ position on the image plane. The shifts dx and dy are modeled and characterized by the lens distortion parameters. Z

Y Object point X

O Object space

y Perturbed image point

Model Perspective center c

dy

Principal point

dx yp

x

xp Ideal image point Image plane

Fig. 5.1. Camera imaging process and the interior orientation parameters

The perspective relationship is described by the collinearity equations

x − x p + d x =− c

m11 ( X − X c ) + m12 ( Y − Yc ) + m13 ( Z − Z c ) U = −c W m31 ( X − X c ) + m32 ( Y − Yc ) + m33 ( Z − Z c )

, y − y p + d y =− c

(5.1)

m21 ( X − X c ) + m22 ( Y − Yc ) + m23 ( Z − Z c ) V = −c W m31 ( X − X c ) + m32 ( Y − Yc ) + m33 ( Z − Z c )

where mij (i, j = 1, 2, 3) are the elements of the rotation matrix that are functions of the Euler orientation angles ( ω ,φ ,κ ) ,

84

5. Image and Data Analysis Techniques

m11 = cos φ cos κ m12 = sin ω sin φ cos κ + cos ω sin κ m13 = − cos ω sin φ cos κ + sin ω sin κ m21 = − cos φ sin κ m22 = − sin ω sin φ sin κ + cos ω cos κ

(5.2)

m23 = cos ω sin φ sin κ + sin ω cos κ m31 = sin φ m32 = − sin ω cos φ m33 = cos ω cos φ . The orientation angles ( ω ,φ ,κ ) are essentially the pitch, yaw, and roll angles of a camera in an established coordinate system. The terms dx and dy are the image coordinate shifts induced by lens distortion, which can be modeled by a sum of the radial distortion and decentering distortion (Fraser 1992; Fryer1989)

d x=d xr + d xd and d y =d y r + d y d ,

(5.3)

where

d x r = K 1 ( x' − x p ) r 2 + K 2 ( x' − x p ) r 4 , d y r = K 1 ( y' − y p ) r 2 + K 2 ( y' − y p ) r 4 , d x d = P1 [ r 2 + 2( x' − x p ) 2 ] + 2 P2 ( x' − x p )( y' − y p ) ,

(5.4)

d y d = P2 [ r 2 + 2( y' − y p ) 2 ] + 2 P1 ( x' − x p )( y' − y p ) , r 2 = ( x' − x p ) 2 + ( y' − y p )2 . Here, K1 and K2 are the radial distortion parameters, P1 and P2 are the decentering distortion parameters, and x’ and y’ are the undistorted coordinates in the image plane. When lens distortion is small, the unknown undistorted coordinates can be approximated by the known distorted coordinates, i.e., x' ≈ x and y' ≈ y . For large lens distortion, an iterative procedure can be employed to determine the appropriate undistorted coordinates to improve the accuracy of estimation. The following iterative relations can be used: ( x' )0 = x and ( y' )0 = y ,

( x' )k +1 = x + d x [( x' ) k ,( y' )k ] and ( y' )k +1 = y + d y [( x' ) k ,( y' ) k ] , where the superscripted iteration index is k = 0 , 1, 2  . The collinearity equations Eq. (5.1) contain a set of the camera parameters to be determined by camera calibration; the parameter sets ( ω ,φ ,κ , X c ,Yc , Z c ) , (c, x p , y p ) , and (K 1 , K 2 , P1 , P2 ) in Eq. (5.1) are the exterior orientation, interior orientation, and lens distortion parameters of a camera, respectively. Analytical camera calibration techniques have been used to solve the collinearity equations

5.1. Geometric Calibration of Camera

85

with the lens distortion model for the camera exterior and interior parameters (Rüther 1989; Tsai 1987). Since Eq. (5.1) is non-linear, iterative methods of leastsquares estimation have been used as a standard technique for the solution of the collinearity equations in photogrammetry (Wong 1980; McGlone 1989). However, direct recovery of the interior orientation parameters is often impeded by inversion of a nearly singular normal-equation-matrix in least-squares estimation. The singularity of the normal-equation-matrix mainly results from strong correlation between the exterior and interior orientation parameters. In order to reduce the correlation between these parameters and enhance the determinability of (c, x p , y p ) , Fraser (1992) suggested the use of multiple camera stations, varying image scales, different camera roll angles and a well-distributed target field in three dimensions. These schemes for selecting suitable calibration geometry improve the properties of the normal equation matrix. In general, iterative least-squares methods require a good initial guess to obtain a convergent solution. Mathematically, the singularity problem can be treated using the singular value decomposition that produces the best solution in a least-squares sense. Also, the Levenberg-Marquardt method can stay away to some extent from zero pivots (Marquardt 1963). Nevertheless, multiple-station, multiple-image methods for camera calibration are not easy to use in a wind tunnel environment where only a limited number of windows are available for cameras and the positions of cameras are fixed. Thus, it is highly desirable for PSP and TSP to have a single-image, easy-to-use calibration method devoid of the singularity problem and an initial guess. In the computer vision community, Tsai’s two-step method is particularly popular. Instead of directly solving the standard collinearity equations Eq. (5.1), Tsai (1987) used a radial alignment constraint to obtain a linear least-squares solution for a subset of the calibration parameters, whereas the rest of the parameters including the radial distortion parameter are estimated by an iterative scheme. Tsai’s method is fast, but less accurate than the standard photogrammetric methods. In addition, the radial alignment constraint prevents this method from incorporating a more general model of lens distortion. Here, we first discuss the DLT that can automatically provide initial values of the camera parameters and then describe an optimization method for more comprehensive calibration of a camera. 5.1.2. Direct Linear Transformation The Direct Linear Transformation (DLT), originally proposed by Abdel-Aziz and Karara (1971), can be very useful to determine approximate values of the camera parameters. Rearranging the terms in the collinearity equations leads to the DLT equations L1 X + L2 Y + L3 Z + L4 − ( x+ d x )( L9 X + L10 Y + L11 Z + 1 ) = 0 . (5.5) L5 X + L6 Y + L7 Z + L8 − ( y + d y )( L9 X + L10 Y + L11 Z + 1 ) = 0

86

5. Image and Data Analysis Techniques

The DLT parameters L1 ,  L11 are related to the camera exterior and interior orientation parameters ( ω ,φ ,κ , X c ,Yc , Z c ) and (c, x p , y p ) (McGlone 1989). Unlike the standard collinearity equations Eq. (5.1), Eq. (5.5) is linear for the DLT parameters when the lens distortion terms dx and dy are neglected. In fact, the DLT is a linear treatment of what is essentially a non-linear problem at the cost of introducing two additional parameters. The matrix form of the linear DLT equations for M targets is L = ( L1 ,  L11 )T , B L = C , where

C = ( x1 , y1 ,  x M , y M )T , and B is the 2M×11 configuration matrix that can be directly obtained from Eq. (5.5). A least-squares solution for L is formally given by L = (B T B) −1 B T C without using an initial guess. The camera parameters can be extracted from the DLT parameters from the following expressions

x p = ( L1 L9 + L2 L10 + L3 L11 )L2 , y p = ( L5 L9 + L6 L10 + L7 L11 )L2 , c = ( L21 + L22 + L23 )L2 − x 2p

,

φ = sin −1 ( L9 L ) , ω = tan −1 ( − L10 / L11 ) , κ = cos −1 ( m11 / cos( φ )) , m11 = L( x p L9 − L1 ) / c , L = − ( L29 + L210 + L211 )−1 / 2 ,

§ Xc · § L1 ¨ ¸ ¨ ¨ Yc ¸ = − ¨ L5 ¨ ¸ ¨ © Zc ¹ © L9

L2 L6 L10

L3 · § L4 · ¸¨ ¸ L7 ¸ ¨ L8 ¸ . ¸¨ L11 ¹ © 1 ¸¹

Because of its simplicity, the DLT is widely used in both non-topographic photogrammetry and computer vision. When dx and dy cannot be ignored, however, iterative solution methods are still needed and the DLT loses its simplicity. In general, the DLT can be used to obtain fairly good values of the exterior orientation parameter and the principal distance, although it gives a poor estimate for the principal-point location (x p ,y p ) (Cattafesta and Moore 1996). Therefore, the DLT is valuable since it can provide initial approximations for more accurate methods like the optimization method discussed below for comprehensive camera calibration.

5.1. Geometric Calibration of Camera

87

5.1.3. Optimization Method In order to develop a simple and robust method for comprehensive camera calibration, the singularity problem must be dealt with to solve the collinearity equations. Liu et al. (2000) proposed an optimization method based on the following insight. Strong correlation between the interior and exterior orientation parameters leads to the singularity of the normal-equation-matrix in least-squares estimation for a complete set of the camera parameters. Therefore, to eliminate the singularity, least-squares estimation is used for the exterior orientation parameters only, while the interior orientation and lens distortion parameters are calculated separately using an optimization scheme. This optimization method contains two separate, but interacting procedures: resection for the exterior orientation parameters and optimization for the interior orientation and lens distortion parameters. When the image coordinates (x, y) are given in pixels, we express the collinearity equations Eq. (5.1) as

f 1 = S h x n − x p + d x + cU / W = 0 f 2 = S v y n − y p + d y + cV / W = 0

,

(5.6)

where Sh and Sv are the horizontal and vertical pixel spacings (mm/pixel) of a CCD array, respectively. In general, the vertical pixel spacing is fixed and known for a CCD camera, but the effective horizontal spacing may be variable. Thus, an additional parameter, the pixel-spacing-aspect-ratio S h / S v , is introduced. We define Ȇ ex = ( Ȧ, ij, ț, X c , Yc , Z c )T for the exterior orientation parameters and

Ȇ in = (c, x p , y p , K 1 , K 2 , P1 , P2 , S h / S v )T for the interior orientation and lens distortion parameters in addition to the pixel-spacing-aspect-ratio. For given values of Ȇ in , and a set of known points (targets) pn =(x n ,y n )T and Pn =(X n ,Yn ,Z n )T , a solution for Ȇ ex in Eq. (5.6) can be found using an iterative least-squares method, referred to as resection in photogrammetry. The linearized collinearity equations for targets (n = 1, 2, , M) are written as V = ǹ ( ǻȆ ex ) − l , where ǻȆ ex is the correction term for the exterior orientation parameters, V is the 2M×1 residual vector, A is the 2M×6 configuration matrix, and l is the 2M×1 observation vector. The configuration matrix A and observation vector l in the linearized collinearity equations are § (∂ f 1 / ∂ Ȇ ex )1 · § ( f 1 )1 · ¨ ¸ ¨ ¸ ¨ (∂ f 2 / ∂ Ȇ ex )1 ¸ ¨ ( f 2 )1 ¸ ¨ ¸ ¨ ¸  (5.7) A=¨ ¸ and l = − ¨  ¸ , ¨ (∂ f 1 / ∂ Ȇ ex ) ¸ ¨ ( f 1 )M ¸ M ¨ ¸ ¨ ¸ ¨( f2 ) ¸ ¨ (∂ f 2 / ∂ Ȇ ex ) ¸ M ¹ M ¹ © ©

88

5. Image and Data Analysis Techniques

where

the

operator

∂ /∂ Ȇ ex

is

defined

as

( ∂ /∂ Ȧ,∂ /∂ ij,∂ /∂ ț, ∂ /∂ X c , ∂ /∂Yc , ∂ /∂ Z c ) and the subscript denotes a target. The components of the vectors ∂ f 1 / ∂ Ȇ ex and ∂ f 2 / ∂ Ȇ ex are

∂ f1 U c = { m12 ( Z − Z c ) − m13 ( Y − Yc ) − [ m32 ( Z − Z c ) − m33 ( Y − Yc )]} , ∂Ȧ W W ∂ f1 c U = [ −cos ț W − (cos ț U − sin ț V)] , ∂ij W W ∂ f 1 cV = W ∂ț

,

∂ f1 U c = ( −m11 + m31 ) , ∂Xc W W ∂ f1 U c = ( −m12 + m32 ) , ∂Yc W W ∂ f1 U c = ( −m13 + m33 ) , ∂Zc W W ∂ f2 V c = { m22 ( Z − Z c ) − m23 ( Y − Yc ) − [ m32 ( Z − Z c ) − m33 ( Y − Yc )]} , ∂Ȧ W W ∂ f2 c V = [sin ț W − (cos ț U − sin ț V)] , ∂ij W W ∂ f2 cU =− W ∂ț

,

∂ f2 V c = ( −m 21 + m31 ) , ∂Xc W W ∂ f2 V c = ( −m22 + m32 ) , ∂Yc W W ∂ f2 V c = ( −m23 + m33 ) . ∂Zc W W A least-squares solution to minimize the residuals V for the correction term is ǻȆ ex =(AT A) −1 AT l . In general, the 6 × 6 normal-equation-matrix ( AT A ) can be inverted without any singularity problem since the interior orientation and lens

5.1. Geometric Calibration of Camera

89

distortion parameters are not included in least-squares estimation. To obtain such Ȇ ex that the correction term ǻȆ ex becomes zero, the Newton-Raphson iterative method is used for solving the non-linear equation (AT A) −1 AT l = 0 for Ȇ ex . This approach converges over a considerable range of the initial values of Ȇ ex . Therefore, for given Ȇ in , the corresponding exterior orientation parameter Ȇ ex can be obtained, which are symbolically expressed as Ȇ ex = RESECTION( Ȇ in ) . At this stage, the exterior orientation parameters Ȇ ex are not necessarily correct unless the given interior orientation and lens distortion parameters Ȇ in are accurate. Obviously, an extra condition is needed to obtain correct Ȇ in and the determination of Ȇ in is coupled with the resection for Ȇ ex . An optimization scheme to obtain the correct Ȇ in is described as follows. We notice that the correct values of Ȇ in are intrinsic constants for a camera/lens system, and they are independent of the target locations p n = (x n ,y n )T in the image plane and Pn = (X n ,Yn ,Z n )T in the object space. Mathematically, Ȇ in is an invariant under a transformation ( p n ,Pn )  ( p m ,Pm ) ( m≠n ). Therefore, for the correct values of Ȇ in , the parameters (c, x p , y p ) are invariant under the transformation ( p n ,Pn )  ( p m ,Pm ) ( m≠n ). In other words, for the correct values of Ȇ in , the standard deviation of (c, x p , y p ) calculated over all the targets from the collinearity equations should be zero, i.e., M

std(x p ) = [ ¦ ( x p − < x p > ) 2 /( M − 1 ) ] 1/2 = 0 , where std denotes the standard n =1

deviation and < > denotes the mean value. Furthermore, since std ( x p ) ≥ 0 is always valid, the correct Ȇ in must correspond to the global minimum point of the function std ( x p ) . Hence, the determination of the correct Ȇ in becomes an optimization problem to seek such values of Ȇ in that the objective function

std ( x p ) is minimized, i.e., std ( x p ) → min . To solve this multiple-dimensional optimization problem, the sequential golden section search technique is used because of its robustness and simplicity. Since (c, x p , y p ) are estimated from Eq. (5.1) for given Ȇ ex , the optimization scheme for Ȇ in is coupled with the resection scheme for Ȇ ex . Other appropriate objective functions can also be used; an obvious choice is the root-mean-square (rms) deviation of the calculated object space coordinates of all the targets from the measured ones. In fact, it is found that std ( x p ) or std ( y p ) is equivalent to this rms deviation in the optimization problem. The quantities std ( x p ) and std ( y p ) for optimization have a simple topological structure near the global minimum point, exhibiting a single ‘valley’ structure in the parametric space (Liu et al. 2000). Generally, the topological

90

5. Image and Data Analysis Techniques

structure of std ( x p ) or std ( y p ) depends on three-dimensionality of a target field; stronger three-dimensionality of the target field produces a steeper ‘valley’ in topology, leading to faster convergence. The topological structure of std ( x p ) or std ( y p ) can also be affected by random disturbances on the targets. Larger noise in images leads to a slower convergence rate and produces a larger error in optimization computations. Although the simple ‘valley’ topological structure allows convergence of optimization computation over a considerable range of the initial values, appropriate initial values are still required to obtain a converged solution. The DLT can provide such initial values for the exterior orientation parameters ( Ȧ, ij, ț , X c , Yc , Z c ) and the principal distance c . Combined with the DLT, the optimization method allows rapid and comprehensive automatic camera calibration to obtain a total of 14 camera parameters from a single image without requiring a guess of the initial values.

Fig. 5.2. Step target plate for camera calibration

The optimization method was used for calibrating a Hitachi CCD camera with a Sony zoom lens (12.5 to 75 mm focal length) and an 8 mm Cosmicar television. As shown in Fig. 5.2, a three-step target plate with a 2-in step height provided a 3D target field for camera calibration, on which 54 circular retro-reflective targets of a 0.5-in diameter spaced out 2 inches apart are placed. Figure 5.3 shows the principal distance given by the optimization method versus zoom setting for the Sony zoom lens. Figures 5.4 and 5.5 show, respectively, the principal-point location and radial distortion coefficient K1 as a function of the principal distance for the Sony zoom lens. The results given by the optimization method are in reasonable agreement with measurements for the same lens using optical equipment in laboratory (Burner 1995). The optimization method was also used to calibrate the same Hitachi CCD camera with an 8 mm Cosmicar television lens. Table 5.1 lists the calibration results given by the optimization method compared well with those obtained using optical equipment. In order to determine accurately the interior orientation parameters, a target field should fill up an image for camera calibration. In large wind tunnels, however, a camera is often located far from a model such that the target field looks small in the image plane. In this case, a two-step approach is suggested that determines the interior and exterior orientation parameters separately. First, placing a target plate near a camera to produce a sufficiently large target field in the image plane, we can determine accurately the interior orientation parameters

5.1. Geometric Calibration of Camera

91

using the optimization method. Next, assuming that the determined interior orientation parameters are fixed for locked camera setting, we obtain the exterior orientation parameters using a resection scheme from the target field in a given wind-tunnel coordinate system. 90

Principal distance c (mm)

80

Optimization algorithm Linear fit

70 60 50 40 30 20 10 10

20

30

40

50

60

70

80

Zoom setting (mm)

Fig. 5.3. Principal distance vs. zoom setting for a Sony zoom lens. From Liu et al. (2000) 2 Optimization algorithm

xp or yp (mm)

Laser illumination technique

1

yp 0

xp -1 10

20

30

40

50

60

70

80

90

c (mm)

Fig. 5.4. Principal-point location as a function of the principal distance for a Sony zoom lens connected to a Hitachi camera. From Liu et al. (2000)

92

5. Image and Data Analysis Techniques 0.0010 Optimization algorithm Burner (1995)

0.0005

K1 (mm-2)

0.0000

-0.0005

-0.0010

-0.0015

-0.0020 10

20

30

40

50

60

70

80

90

c (mm)

Fig. 5.5. The radial distortion coefficient as a function of the principal distance for a Sony zoom lens connected to a Hitachi camera. From Liu et al. (2000)

Table 5.1. Calibration for Hitachi CCD camera with 8 mm Cosmicar TV lens Interior orientation

c (mm) xp (mm)

yp (mm)

Sh /Sv

K1 (mm-2)

K2 (mm-4)

Optimization

8.133

0.2014

0.99238

0.0026

3.3×10

Optical techniques

8.137

-0.156 -0.168

0.2010

0.99244

0.0027

P2 (mm-1)

-5

1.8×10-4

3×10-5

-5

-4

7×10-5

4.5×10

P1 (mm-1)

1.7×10

5.2. Radiometric Calibration of Camera Since PSP and TSP are based on radiometric measurements, a CCD camera used for measurements should have a good linear response of the electrical output to the scene radiance. However, there are many stages of image acquisition that may introduce non-linearity; for example, video cameras often include some form of ‘gamma’ mapping. When the radiometric response function of a camera is known, the non-linearity can be corrected. Here, a simple algorithm is described to determine the radiometric response function of a camera from a scene image taken in different exposures. First, we define I ( x ) as a linear radiometric response to the scene radiance and m [ I ( x )] as the measurement of I ( x ) by camera electronic circuitry that may produce a non-linear electrical output. Actually, the measurement m [ I ( x )] is the brightness or gray level of an image, where x is the image coordinates. The non-dimensional response function relating I ( x ) to m [ I ( x )] is defined by

5.2. Radiometric Calibration of Camera

I ( x ) / I max = f [ ξ ( x )] ,

93

(5.8)

where ξ ( x ) = m[ I ( x )] / m( I max ) is the non-dimensional measurement of I ( x ) normalized by the maximum value and I max corresponds to the maximum

radiance in the scene. Recovery of f (ξ ) is the task of the radiometric calibration of a camera. Two images of a scene are taken in two different exposures. According to the camera formula (Holst 1998), I ( x ) is proportional to the integration time t INT and inversely proportional to the square of the f-number F. Thus, we have the following functional equation for f (ξ ) ,

f (ξ 1 ) / f ( ξ 2 ) = R12 ,

(5.9)

where the subscripts 1 and 2 denote the image 1 and image 2, and the factor R12 is defined as I ( t / F 2 )1 . (5.10) R12 = max 2 INT I max 1 ( t INT / F 2 )2 Since m( I max ) corresponds to I max , the boundary condition for

f (ξ = 1) = 1 . We assume that f (ξ ) can be expanded as f (ξ ) =

f (ξ ) is

N

¦ c φ (ξ ) , n

(5.11)

n

n =0

where the base functions φ n ( ξ ) are the Chebyshev functions although other orthogonal functions and non-orthogonal functions like polynomials can also be used. Substitution of Eq. (5.11) to Eq. (5.9) leads to the following equations for the coefficients c n N

¦ c [φ ( ξ n

n

1

) − R12 φ n ( ξ 2 )] = 0 ,

n =0 N

¦ c φ (1) = 1 .

(5.12)

n n

n =0

For selected M pixels in a scene image, Eq. (5.12) constitutes a system of M+1 equations for the N+1 unknowns c n ( M ≥ N ). For a given R12 , a least-squares solution for c n can be found. In practice, since the factor R12 is not exactly known a priori, we use an approximate value of R12

R12 ≈

m( I max 2 ) ( t INT / F 2 )1 m( I max 1 ) ( t INT / F 2 )2

.

An iteration scheme can be used to give an improved value of R12 . Figure 5.6 shows two images taken by a Cannon digital still camera (EOS D30) at two

94

5. Image and Data Analysis Techniques

different f-numbers of F = 4.0 and F = 5.6, where Ansel Adams’ photograph of Mirror Lake of Yosemite was used as a test scene providing a broad range of the gray levels for radiometric calibration. Figure 5.7 shows the radiometric response function of the camera retrieved from the two images, where six terms of the Chebyshev functions in Eq. (5.11) were used. The response function of the Cannon digital still camera exhibits a non-linear behavior; it is also different for the red, green and blue (RGB) color channels.

(a)

(b)

Fig. 5.6. Two images of Mirror Lake of Yosemite (Ansel Adams 1935) taken by a Cannon digital still camera (EOS D30) at different F-numbers (a) F = 4.0 and (b) F = 5.6 for radiometric calibration of the camera

Camera Response Function, I/Imax

1.0

R G B

0.8

0.6

0.4

0.2

0.0 0.0

0.2

0.4

0.6

0.8

1.0

m(I)/m(Imax)

Fig. 5.7. Response functions of a Cannon digital still camera (EOS D30) for the R, G, and B color channels obtained from radiometric calibration

5.3. Correction for Self-Illumination

95

5.3. Correction for Self-Illumination The self-illumination of PSP and TSP results from the luminescent contribution to a point on a surface from all visible neighboring points; it becomes appreciable near a conjuncture of two surfaces and on a concave surface (Ruyten 1997a, 1997b, 2001a; Ruyten and Fisher 2001; Le Sant 2001b). Although the selfillumination can be to certain extent suppressed by taking a ratio between a windon image and a wind-off image, it cannot be eliminated without considering an exchange of the radiative energy between neighboring surfaces, which may produce an error in data reduction of PSP and TSP. Therefore, we need to know how much the radiative energy leaves from an area element and travels toward another element. The geometric relations for this inter-surface process are known as view factors, configuration factors, shape factors, or angle factors (Modest 1993). We consider diffuse surfaces that absorb and emit diffusely, and also reflect the radiative energy diffusely. The view factor dFdA i − dA j between two infinitesimal surface elements dAi and dA j , as shown in Fig. 5.8, is defined as a ratio between the diffuse energy leaving dAi directly toward and intercepted by

dA j and the total diffuse energy leaving dAi , which is expressed as dFdA i − dA j =

cos θ i cos θ j

π | X ij |

2

dA j =

( ni • X ij )( n j • X ij )

π | X ij |4

dA j ,

(5.13)

where n i (or n j ) is the unit normal vector of dAi (or dA j ), X ij is the position vector directing from dAi toward dA j , and θ i (or θ j ) is the angle between the position vector X ij and the normal n i (or n j ). The view factors leaving dAi directly toward the total surface A j or leaving A j toward dAi , or leaving A j toward Ai can be similarly defined by integrating dFdA i − dA j (Modest 1993). The law of reciprocity dAi dFdA i −dA j = dA j dFdA j −dA i is valid for these view factors. The view factor is a function of the geometric parameters. Methods for evaluating the view factors were discussed by Modest (1993) and a large collection of the view factors for simple geometric configurations was complied by Howell (1982). For partially specular surfaces, the determination of the view factors is more complicated since the bidirectional reflectance distribution function (BRDF) of the paint must be known (Nicodemus et al. 1977; Asmail 1991).

96

5. Image and Data Analysis Techniques

Xj nj

θj dAj

Xij

ni θi

Xi

dAi

Fig. 5.8. Radiative exchange between two surface elements

The self-illumination correction is applied to an image intensity (or brightness intensity) field denoted by I in this sub-section after it is mapped onto a model surface grid in the object space. Because the image intensity is proportional to the luminescent energy flow rate, the image intensity I i at an area element dAi is a sum of the local intrinsic intensity I i( 0 ) and an integration of the contributions from all the neighboring elements, i.e., N

I i = I i( 0 ) + ρ λwp2

¦I j =1

j

dFdA j − dAi dA j

,

(5.14)

where ρ λwp2 is the reflectivity of the wall-paint interface at the luminescent wavelength. In simulations, given a set of the intrinsic intensities I i( 0 ) , the image intensity I i affected by the self-illumination can be obtained using a simple iteration scheme N

I i( n+1 ) = I i( 0 ) + ρ λwp2

¦I j =1

(n) j

dFdA j −dA i dA j

.

(5.15)

The more efficient Gauss-Seidel iteration scheme was used by Ruyten and Fisher (2001). In measurements, since the image intensity I i is known in PSP and TSP images, an explicit relation is used to correct the self-illumination and recover the intrinsic intensity I i( 0 ) , i.e., N

I i( 0 ) = I i − ρ λwp2

¦I j =1

j

dFdA j −dA i dA j

.

(5.16)

5.3. Correction for Self-Illumination

97

The steps for correcting the self-illumination are: (1) measuring the reflectivity ρ λwp2 ; (2) defining a surface grid consisting of N surface elements dAi ; (3) evaluating the view factors dFdA j −dA i ; (4) mapping the image intensity I i onto the surface grid; (5) calculating the intrinsic (corrected) intensity I i( 0 ) using Eq. (5.16); and (6) calculating a ratio of the intrinsic (self-illumination-corrected) intensities and converting it to pressure or temperature. Ruyten and Fisher (2001) conducted a numerical simulation of correcting the self-illumination for a PSP test of the Alpha jet and found that the error associated with the self-illumination in PSP measurements could reach several percents of actual pressure.

plate 2

plate 1 dA1

α

Fig. 5.9. Wedge-shaped conjunction of two plates

Here, we consider a simple but representative geometric configuration, a wedge-shaped conjunction of two infinitely large plates, as shown in Fig. 5.9; this case allows an analytical estimate of the error induced by the self-illumination. The image intensity at a location on the plate 1 is

I 1 = I 1( 0 ) + ρ λwp2

³I

2

dFdA2 −dA1 dA2 .

(5.17)

plate 2

Assuming that the image intensity at the plate 2 is homogenous, by integrating the view factor for this configuration (Modest 1993), we obtain the image intensity at the plate1 affected by the plate 2

I 1 ≈ I 1( 0 ) + ε 1 I 2 ,

(5.18)

where the parameter ε 1 = ρ λwp2 ( 1 + cos α ) / 2 represents the combined effect of the angle α between the plates and reflectivity. Clearly, the self-illumination decreases from the maximum value at α = 0 o to zero at α = 180 o . A reciprocal relation gives the image intensity at the plate 2

98

5. Image and Data Analysis Techniques

I 2 ≈ I 2( 0 ) + ε 1 I 1 .

(5.19)

When the parameter ε 1 is small, the image intensity ratio at the plate 1 is 0) I 1 ref / I 1 ≈ ( I 1( ref / I 1( 0 ) ) ( 1 + ε 1 ε 2 ) .

(5.20)

0) − I 2( 0 ) / I 1( 0 ) reflects the difference of the relative The parameter ε 2 = I 2( 0ref) / I 1( ref influence of the plate 2 on the pate 1 between the wind-off reference and wind-on conditions. Using the Stern-Volmer relation for PSP, we obtain an estimate for the pressure error associated with the self-illumination for the wedge configuration

§ A p( 0 ) | p − p( 0 ) | ≈ ε1 | ε 2 | ¨ + (0 ) (0 ) ¨ B p ref p ref ©

· ¸, ¸ ¹

(5.21)

(0 ) are, where A and B are the Stern-Volmer coefficients, and p ( 0 ) and p ref respectively, the intrinsic PSP-derived pressures in the wind-on and wind-off reference conditions that are not affected by the self-illumination. Similarly, using the Arrhenius relation for TSP, we have an estimate for the temperature error associated with the self-illumination for the wedge configuration

|T − T (0 ) | R ≈ ε1 | ε2 | E nr T (0 )

,

(5.22)

where R is the universal gas constant, E nr is the activity energy of TSP, and

T ( 0 ) is the intrinsic TSP-derived temperature that is not affected by the selfillumination. The above discussion is based on an assumption that the luminescent paint surface is a diffuse surface or Lambertian surface. Nevertheless, a real paint surface is neither Lambertian nor specular. To characterize reflection on a general surface, the bidirectional reflectance distribution function (BRDF) was introduced by Nicodemus et al. (1977). As shown in Fig. 5.10, the incident radiance is generally a function of the incident direction defined by the incident polar angle and azimuthal angle ( θ i ,φ i ) , i.e., Li = Li ( θ i ,φ i ) .

(5.23)

The reflection radiance Lr ( θ i ,φ i ;θ r ,φ r ) is quantitatively characterized by the BRDF

f r ( θ i ,φ i ;θ r ,φ r ) = dLr ( θ i ,φ i ;θ r ,φ r ) / dEi ( θ i ,φ i ) .

(5.24)

where ( θ r ,φ r ) defines the direction of reflection and the infinitesimal incident irradiance dE i ( θ i ,φ i ) over a solid angle element dω i is

5.3. Correction for Self-Illumination

dEi ( θ i ,φ i ) = Li ( θ i ,φ i ) cosθ i dω i .

99

(5.25)

-1

The BRDF has a unit of steradian . Here, the conventional radiometric notations L and E are used for radiance and irradiance, which are also applicable to the luminescent emission. The BRDF depends on a surface roughness distribution. For a perfectly diffuse surface where the reflection radiance is isotropic, i.e., Lr = const . , the BRDF is

f r = 1 / π (Horn and Sjoberg 1979). For a general surface, the BRDF can be derived based on either the wave equation for electromagnetic waves or geometrical optics models (Beckmann and Spizzichino 1963; Torrance and Sparrow 1967; Nayar et al. 1991). Asmail (1991) gave a bibliographical review on the BRDF. From a viewpoint of application, empirical expressions for the scattered radiance from a rough surface are very useful due to their simplicity (Cook and Torrance 1981; Haussecker 1999). An empirical model for a single light source is Lr ( X ) = ρ a E a ( X ) + ρ d Els ( X )( N T Ls ) + ρ s Els ( X ) p( R T V ) ,

(5.26)

where the first, second and third terms are, respectively, the contributions from the ambient reflection, diffuse reflection, and specular reflection. In Eq. (5.26), ρ a ,

ρ d , and ρ s , are the empirical reflection coefficients for the ambient reflection, diffuse reflection, and specular reflection. As shown in Fig. 5.10, the vectors N , Ls , R , and V are, respectively, the unit normal vector of a surface, the unit vector directing the light source from the surface, the unit main directional vector of the specular reflection, and the unit viewing vector. E a ( X ) and Els ( X ) are the irradiances for the ambient environment and light sources, respectively. The function p( R T V ) is the directional distribution of the specular reflection, describing the spreading of scattered light. Phong (1975) gave a power function p( R T V ) = ( R T V )n . In general, the main directional vector of the specular reflection, R , is a function of the incident direction of light − Ls . Although there are certain theories for predicting the specular direction R (Torrance and Sparrow 1967), R is not known for a general surface. The unknowns in Eq. (5.26), such as R , the reflection coefficients, and the parameters in p( R T V ) , have to be determined experimentally by calibration. Le Sant (2001b) measured the BRDF for the B1 PSP paint with talc using a BRDF calibration rig. As illustrated in Fig. 5.11, the BRDF calibration rig included a lamp for illumination and a spectrometer to measure the reflected light from a sample. The lamp emitted white light, enabling the calibration of the o o BRDF in the visible range; the lamp moved from 0 at the vertical position to 60 . o o The zenith (or polar) angle of the spectrometer moved from 0 to 60 and the o o o azimuth angle moved from 0 to 180 , where 180 was in the opposite direction of the emission. Figure 5.12 shows the measured BRDF for the B1 paint, which was nearly Lambertian when the zenith (or polar) angle of illumination was 10°, while specular reflection occurred when the zenith angle increased further. The

100

5. Image and Data Analysis Techniques

maximum value was always achieved in the specular direction. The low value obtained at the azimuth angle of 0° was incorrect since the spectrometer was in the front of the lamp and thus the PSP sample was no longer illuminated. The measured BRDF showed a superposition of diffuse reflection and specular reflection. A specular peak was observed at the zenith angle of 60° as well as a secondary peak at the azimuth angle of 90°. The value of the diffuse reflection factor depended on the zenith angle of illumination. Le Sant (2001b) was able achieve a good fit to the measured BRDF using the modified Phong model (Phong 1975), as shown in Fig. 5.13, and the modeled BRDF captured the main features of the measured BRDF except the secondary specular peaks.

LI

θE

V

N

R

θH

φH

Fig. 5.10. Vectors of incident, reflecting, and viewing directions zenith (spectrometer) zenith (illumination)

0°

180° 90°

90°

azimuth 0°

Fig. 5.11. The zenith (or polar) and azimuth angles in the BRDF calibration rig. From Le Sant (2001b)

5.3. Correction for Self-Illumination BRDF

BRDF

0.4

0.4

0.2

0.2

0.2

0.1

0.1

0.1 60

0

60

0

180

zenith

20

zenith

20

azimuth

zenith

80

20

0

0

40

0.6

50

0.4

60

0.4

0.2

0.2

60

0

0.1 60

0

180

10

180

40

160 140

zenith

zenith

azimuth

10

40

160

azimuth

80

10

40 20

20 0

0

0

azimuth

60

40

20

120 100

20

80 60

140

30

120 100

20

180

40

160 140

30

120 100 80

0

50

50

60

0.4

0.3

0.1

50

20

0.5

0.3

0.1 60

BRDF 0.5

0.3

30

0

0.6

BRDF 0.5

40

azimuth

40 20 0

0.6

0

80 60

10

40 20 0

BRDF

zenith

120 100

azimuth

60 10

40

160 140

30

120 100

20 0

180

40

160 140

30

80 60

10

180

40

160 140 120 100

0

50

50

50

30

0.4

0.3

0.3

0.3

40

0.5

30

0.5

20

0.5

60

0.6

0.6

0.6

BRDF

10

101

0

0

Fig. 5.12. The measured BRDF of the B1 paint at the illumination zenith angles of 10, 20, 30, 40, 50 and 60 degrees. From Le Sant (2001b)

BRDF

BRDF

10

20

0.5

0.4

30

0.5

0.4

0.2

0.1

0.1 60

0

60

0

180

zenith

80

20

zenith

80

0.4

0 160 140

30

120 100

20

80 60

10

azimuth

180

0.2

0.1 60

0

50 40

160

180

0.1 60

0

50 180

40

160

140

30

zenith

120 100

20

80 60

10

40

40 20

0.4

0.3

0.2

0.2

40

60

0.4

0.5

0.3

0.1

50

0.6

BRDF 0.5

0.3

60

0

0.6

50

0.5

azimuth

40 20 0

BRDF

40

0

80 60

10

0

0.6

0

20

40 20 0

0

BRDF

zenith

120 100

azimuth

60 10

40 20 0

160 140

30

120 100

azimuth

60 10

180

40

160 140

30

120 100

20

180

40

160 140

30

0

50

50

50 40

0.4

0.3

0.2

0.2

0.1

zenith

0.5

0.3

0.3

60

0.6

0.6

0.6

BRDF

140

30

zenith

120 100

20

80

azimuth

60 10

0

azimuth

40

20 0

20 0

0

Fig. 5.13. The modeled BRDF of the B1 paint at the illumination zenith angles of 10, 20, 30, 40, 50 and 60 degrees using the modified Phong model. From Le Sant (2001b)

Le Sant (2001b) also studied the self-illumination in a corner to validate a correction algorithm. The corner was painted with a Pyrene-based paint providing an image significantly affected by the self-illumination near the junction of the two plates, as shown in Fig. 5.14. Then, the left plate was covered with a black sheet, removing the effect of the self-illumination on the right plate, as shown in

102

5. Image and Data Analysis Techniques

the right image in Fig. 5.14. Figure 5.15 shows results before and after correcting the self-illumination based on the diffuse surface model and the Phong model. The self-illumination correction was effective; the self-illumination effect was reduced to 15% from about 40% near the junction. This paint behaved mostly like a diffuse paint such that the Phong model did not exhibit a significant improvement. Although the Phong model might improve the accuracy of correction for a surface with strong specular reflection, the computation time for the Phong model was much longer than that for the diffuse surface model.

Fig. 5.14. Self-illumination in a corner coated with PSP. From Le Sant (2001b) 0.16

with SI effect

0.15 0.14 0.13

diffuse model

0.12 0.11

Phong model

0.10 0

10

20

30

without SI 40 X (mm) 50

Fig. 5.15. Self-illumination correction using the diffuse and Phong models. From Le Sant (2001b)

5.4. Image Registration The intensity-based method for PSP and TSP requires a ratio between the wind-on and wind-off images of a painted model. Since a model deforms due to aerodynamic loads, the wind-on image does not align with the wind-off image; therefore these images have to be re-aligned before taking a ratio between the images. The image registration technique, developed by Bell and McLachlan (1993, 1996) and Donovan et al. (1993), is based on an ad-hoc transformation that

5.4. Image Registration

103

maps the deformed wind-on image coordinates ( xon , yon ) onto the reference wind-off image coordinates ( xoff , yoff ) . In order to register the images, some black fiducial targets are placed on a model. When the correspondence between the targets in the wind-off and wind-on images is established, a transformation between the wind-off and wind-on image coordinates of the targets can be expressed as x off = aij φ i ( x on )φ j ( y on ) . (5.27) y off = bij φ i ( xon )φ j ( y on )

¦ ¦

The base functions φ i ( ξ ) are either the orthogonal functions like the Chebyshev functions or the non-orthogonal power functions φ i ( x ) = x i used by Bell and McLachlan (1993, 1996) and Donovan et al. (1993). Given the image coordinates of the targets placed on a model, the unknown coefficients aij and bij can be determined using least-squares method to match the targets between the wind-on and wind-off images. For image warping, one can also use a 2D perspective transform (Jähne 1999)

x off =

a 11 x on + a 12 y on + a 13 a 31 x on + a 32 y on + 1

. (5.28) a 21 x on + a 22 y on + a 23 y off = a 31 x on + a 32 y on + 1 Although the perspective transform is non-linear, it can be reduced to a linear transform using the homogeneous coordinates. The perspective transform is collinear that maps a line into another line and a rectangle into a quadrilateral. Therefore, Eq. (5.28) is more restricted than Eq. (5.27) for PSP and TSP applications. Before the image registration technique is applied, the targets must be identified and their centroid locations in images must be determined. The target centroid ( xc , y c ) is defined as

¦¦ x I ( x , y ) / ¦¦ I ( x , y ) , = ¦¦ y I ( x , y ) / ¦¦ I ( x , y )

xc =

i

i

i

i

i

yc

i

i

i

i

i

(5.29)

where I ( xi , y i ) is the gray level on an image. When a target contains only a few pixels and the target contrast is not high, the centroid calculation using the definition Eq. (5.29) may not be accurate. Another method for determining the target location is to maximize the correlation between a template f ( x , y ) and the target scene I ( x , y ) (Rosenfeld and Kak 1982). The correlation coefficient C fI is defined as

104

5. Image and Data Analysis Techniques

C fI =

³³ f ( x + x , y + y )I ( x , y )dxdy ³³ f ( x , y )dxdy ³³ I ( x , y )dxdy 0

2

0

.

(5.30)

2

For the continuous functions f ( x , y ) and I ( x , y ) , one can determine the location

( x0 , y0 ) of the target by maximizing C fI . However, it is found that for small targets in images, sub-pixel misalignment between the template and the scene can significantly reduce the value of C fI even when the scene contains a perfect replica of the template. To enhance the robustness of a localization scheme, Ruyten (2001b) proposed an augmented template f ( x , y ) = f 0 ( x , y ) + f x ∆ x + f y ∆ y , where f 0 ( x , y ) represented a conventional template and f x and f y are the partial derivatives of f ( x , y ) . The additional shift parameters ( ∆ x , ∆ y ) allowed more robust and accurate determination of the target locations. In PSP and TSP measurements, operators can manually select the targets and determine the correspondence between the wind-off and wind-on images. However, PSP and TSP measurements with multiple cameras in production wind tunnels may produce hundreds or thousands of images in a given test; thus, image registration becomes very labor-intensive and time-consuming. It is non-trivial to automatically establish the point-correspondence between images taken by cameras at different viewing angles and positions. This problem is generally related to the epipolar geometry in which a point on an image corresponds to a line on another image (Faugeras 1993). Ruyten (1999) discussed the methodologies for automatic image registration including searching targets, labeling targets and rejecting false targets. Unlike ad-hoc techniques, the searching technique based on photogrammetric mapping is more rigorous. Once cameras are calibrated and the position and attitude of a tested model are approximately given by other techniques (such as accelerators and videogrammetric techniques), the targets in the images can be found using photogrammetric mapping from the 3D object space to the image plane (see Section 5.1). The aforementioned methods of using a single transformation for the whole image is a global approach for image registration. A local approach proposed by Shanmugasundaram and Samareh-Abolhassani (1995) divides an image domain into triangles connecting a set of targets based on the Delaunay triangulation (de Berg et al. 1998). For a triangle defined by the vertex vectors R1 , R2 and R2 , a point in the plane of the triangle can be described by a vector u1 R1 + u 2 R2 + u 3 R3 , where (u 1 , u 2 , u 3 ) are referred to as the parametric (barocentric) coordinates and a constraint u1 + u 2 + u 3 = 1 is imposed. When a wind-on pixel is identified inside a triangle and its parametric coordinates is given, the corresponding wind-off pixel can be determined by using the same parametric coordinates in the vertex vectors of the corresponding triangle in the wind-off image. Finally, the image intensity at that pixel is mapped from the wind-on

5.5. Conversion to Pressure

105

image to the wind-off image. This approach is basically a linear interpolation assuming that the relative position of a point inside a triangle to the vertices is invariant under a transformation from the wind-on image to the wind-off image. Weaver et al. (1999) proposed a so-called Quantum Pixel Energy Distribution (QPED) algorithm that utilizes local surface features to calculate a pixel shift vector using a spatial correlation method. The local surface features could be targets, pressure taps, and dots formed from aerosol mists in spraying on a basecoat. Similar to particle image velocimetry (PIV), the QPED algorithm can give a field of the displacement vectors when the registration marks or features are dense enough. Based on the shift vector field, the wind-on image can be registered. Although the QPED algorithm is computationally intensive, it can provide the local displacement vectors at certain locations to complement the global image registration techniques. A comparative study of different image registration techniques was made by Venkatakrishnan (2003).

5.5. Conversion to Pressure In PSP measurements, conversion of the luminescent intensity to pressure is complicated by the temperature effect of PSP especially when the surface temperature distribution is not known. Empirically, a priori calibration relation between air pressure and the relative luminescent intensity is expressed by a polynomial 2

§ I ref · I ref p ¸ . = C1 ( T ) + C2 ( T ) + C3 ( T ) ¨¨ ¸ pref I © I ¹

(5.31)

The experimentally determined coefficients C1 , C2 and C3 in Eq. (5.31) can be expressed as a polynomial function of temperature. If a distribution of the surface temperature is not given and the thermal conditions in a priori laboratory calibrations are different from those in wind tunnel tests, a priori relation Eq. (5.31) cannot be directly applied to conversion to pressure. To deal with this problem, a short-cut approach is in-situ PSP calibration that directly correlates the luminescent intensity to pressure data from taps distributed on a model surface. In this case, the constant coefficients C1 , C2 and C3 in Eq. (5.31) are determined using least-squares method to achieve the best fit to the pressure tap data over a certain range of pressures. Through in-situ calibration, the effect of a non-uniform surface temperature distribution is actually absorbed into a precision error of leastsquares estimation. When the temperature effect of PSP overwhelms a change of the luminescent intensity produced by pressure, in-situ calibration has a large precision error. In addition, when the pressure tap data do not cover the full range of pressure on a surface, in-situ PSP conversion may lead to a large bias error in data extrapolation outside the calibration range of pressures.

106

5. Image and Data Analysis Techniques

A hybrid method between in-situ and a priori methods is the so-called K-fit method originally suggested by M. Morris and recapitulated by Woodmansee and Dutton (1998). Eq. (5.31) is re-written as 2 ª § I off · § I off · º p ¸ + C3 ( T ) ¨ K I ¸ », = K P «C1 ( T ) + C2 ( T )¨¨ K I ¨ « poff I ¸¹ I ¸¹ » © © ¬ ¼

(5.32)

where I off = I ( poff ,Toff ) is the luminescent intensity in the wind-off conditions, and K I = I ref / I off and K P = pref / poff are called the K-factors. The reference conditions under which a priori calibration is made in a laboratory are generally different from the wind-off conditions in a wind tunnel. While the factor K P = pref / poff is known, the factor K I = I ref / I off is generally not known and has to be determined since illumination conditions and photodetectors used in laboratory may be different from those in wind tunnel. Given the coefficients C1 ,

C2 and C3 at a known temperature on an isothermal surface, K I can be determined using a single data point from pressure taps. When the surface temperature data near a number of pressure taps are provided by other techniques like TSP and IR camera, a more accurate value of K I can be obtained using leastsquares method with larger statistical redundancy. In the worst case where the surface temperature distribution is totally unknown, assuming an average temperature over the surface, we still able to estimate K I by fitting the pressure tap data. Similar to in-situ calibration, the effect of a non-uniform temperature distribution is absorbed into a precision error of least-squares estimation for K I . Bencic (1999) used a similarity variable of the luminescent intensity to scale the temperature effect of certain PSP

I ref I

= g( T ) corr

I ref I

,

(5.33)

where g( T ) was a function of temperature to be determined by a priori calibration. Under this similarity transformation, the calibration curves for the paint at different temperatures collapsed onto a single curve with the temperatureindependent coefficients, i.e.,

I ref p = C1 + C2 pref I

corr

§ I ref + C3 ¨ ¨ I ©

2

· ¸ . ¸ corr ¹

(5.34)

In this case, instead of using a 2D calibration surface in the parametric space, only a single one-parameter relation Eq. (5.34) was used to convert the luminescent intensity ratio to pressure. Bencic (1999) found that this similarity was valid for a

5.6. Pressure Correction for Extrapolation to Low-Speed Data

107

Ruthenium-based PSP used at NASA Glenn. In fact, as pointed out in Section 3.6, this similarity is a property of the so-called ‘ideal’ PSP that obeys the following relations (Puklin et al. 1998; Coyle et al. 1999)

I ( p,T ) / I ( p,Tref ) = g( T ) , I ref ( pref ,Tref ) I ( p,Tref )

= g( T )

I ref ( pref ,Tref ) I ( p,T )

.

(5.35)

Puklin et al. (1998) found that PtTFPP in FIB polymer was an ‘ideal’ PSP over a certain range of temperatures. Note that this similarity (or invariance) is not the universal property of a general PSP.

5.6. Pressure Correction for Extrapolation to Low-Speed Data PSP is particularly effective in high subsonic, transonic and supersonic flow regimes. However, in low-speed flows where the Mach number is typically less than 0.3, PSP measurement is a challenging problem since a very small pressure change may not be sufficiently resolved by PSP. The major error sources, notably the temperature effect, image misalignment and CCD camera noise, must be minimized to obtain acceptable quantitative pressure results at low speeds. The resolution of PSP measurements is eventually limited by the photon shot noise of a CCD camera. Liu (2003) proposed a pressure-correction method as an alterative to extrapolate low-speed pressure data without directly attacking the intrinsic difficulty of PSP instrumentation for low-speed flows. This method is able to obtain the incompressible pressure coefficient from PSP measurements at suitably higher Mach numbers (typically Mach 0.3-0.6) by removing the compressibility effect. It is noticed that there is a significant difference between the responses of the absolute pressure p and the pressure coefficient C p to the freestream Mach number M ∞ .

The sensitivity of C p to the Mach number for M ∞2 << 1 is

estimated by

M ∞ dC p (5.36) ≈ M ∞2 . C p dM ∞ In contrast, the sensitivity of pressure to the Mach number is approximately M∞ d( p − p∞ ) S p − p∞ = ≈ 2. (5.37) ( p − p ∞ ) dM ∞ SC p =

For

M ∞2 << 1 ,

SC p

is much smaller than

S p − p∞ ; for

M ∞ = 0.3

and

dM ∞ / M ∞ = 10% , the relative change of the absolute pressure difference is d ( p − p∞ ) /( p − p∞ ) ≈ 20% , while the relative change of C p is only

108

5. Image and Data Analysis Techniques

dC p / C p ≈ 0.9% .

Clearly, PSP can take the advantage of the relative

insensitivity of C p to the Mach number to obtain the approximate incompressible pressure coefficient distribution at suitably higher Mach numbers. Furthermore, the compressibility effect can be corrected using the pressure-correction methods. Historically, the pressure-correction formulas were derived in order to extrapolate the pressure coefficient in subsonic compressible flows from the incompressible flow theory and low-speed pressure measurements. In contrast, for PSP applications, the pressure-correction formulas are used to transform the compressible C p to the corresponding incompressible C pinc . The theoretical foundation for pressure correction in 2D potential flows is well established. The linearized theory for subsonic compressible flows gives the Prandtl-Glauert rule (Anderson 1990)

C p = C pinc / 1 − M ∞2 . (5.38) The use of a hodograph solution of the non-linear potential equation gives the Karman-Tsien rule (Anderson 1990) C pinc Cp = . (5.39) ·C § 2 M pinc ¸ ¨ ∞ 1 − M ∞2 + ¨ ¨ 1 + 1 − M ∞2 ¸¸ 2 ¹ © For PSP measurements on 2D airfoils at suitably high Mach numbers, both the Prandtl-Glauert rule and Karman-Tsien rule can be used to recover the incompressible pressure coefficient. Bell and Hand (1998) used the PrandtlGlauert rule for the purpose of improving the image ratioing procedure of PSP to obtain a pseudo wind-off pressure coefficient at a suitably low velocity. For complex 3D viscous flows such as separated flows, however, a general pressurecorrection method is required. Liu (2003) developed an iterative pressure-correction method for 3D flows. For M ∞2 << 1 , a pressure field can be generally expressed as a power series of M ∞2 . The pressure-correction formula for a general surface Z = S ( X ,Y ) has a functional form composed of an incompressible term and a compressible correction term C p ≈ C pinc + M ∞2 F [ X ,Y , S ( X ,Y )] . (5.40) Eq. (5.40) is valid for not only potential flows, but also complex viscous flows over a 3D body. Because C pinc = C pinc [ X ,Y , S ( X ,Y )] is a function of X and Y, we can, in principle, eliminate X in the correction function F [ X ,Y , S ( X ,Y )] by using C pinc and Y. Therefore, since the correction function F [ X ,Y , S ( X ,Y )] is not specified yet, the equivalent form to Eq. (5.40) is C p ≈ C pinc + M ∞2 F ( C pinc ,Y ) . (5.41) Eq. (5.41) indicates that the pressure correction in 3D flows depends on not only C pinc , but also one space coordinate Y. Note that the functional form of Eq. (5.41) remains valid after the coordinate Y is switched to another coordinate X. When

5.6. Pressure Correction for Extrapolation to Low-Speed Data

109

C p does not change along the coordinate Y, Eq. (5.41) is naturally reduced to the method for 2D and axisymmetrical flows. polynomial function, Eq. (5.41) becomes

By writing F ( C pinc ,Y ) as a

N

¦ a (Y )C

C p ≈ C pinc + M ∞2

n

n pinc

.

(5.42)

n =0

When the distributions of C p and C pinc are known along an intersection between the plane Y = const . and the surface Z = S ( X ,Y ) , the coefficients a n ( Y ) can be determined using least-squares method. In wind tunnel measurements, pressure tap data in subsonic flow and the corresponding low-speed flow can be used to establish the relationship between C p and C pinc . However, this approach is not convenient for PSP measurements in wind tunnels since extra pressure tap data are required. Here, an iterative method is proposed to recover C pinc from C p data at two different subsonic Mach numbers M ∞1 and M ∞ 2 . The biggest advantage of this method is that C pinc can be directly obtained from two PSP images taken at

M ∞1 and M ∞ 2 without use of additional pressure tap data. Denote C p 1 and C p 2 as the pressure coefficients at M ∞1 and M ∞ 2 , respectively, and assume M ∞1 < M ∞ 2 . Given the distributions of C p 1 and C p 2 along an intersection between the plane Y = const . and surface Z = S ( X ,Y ) , we need to solve the following equations to recover C pinc and a n ( Y ) N

C p1 ≈ C pinc + M ∞2 1

¦ a ( Y )C n

n pinc

n =0 N

C p 2 ≈ C pinc + M ∞2 2

¦ a ( Y )C n

n pinc

.

(5.43)

n =0

An iteration scheme for solving Eq. (5.43) is described below. (1) Give the initial distribution C pinc( k ) = C p1 (k = 0) as a function of X along an intersection between Y = const . and Z = S ( X ,Y ) in the object space (a row or column in the image plane). Here, k is the iteration index number; (2) Determine the coefficients a n( k ) ( Y ) ( n = 0 ,1 N ) in the polynomial from a system of equations

( C p 2 − C pinc( k ) ) / M ∞2 2 =

N

n ¦ a n( k ) ( Y ) C pinc (k )

using

least-squares

n =0

method; (3) Substitute a n ( Y ) into C pinc( k +1 ) ≈ C p1 − M ∞2 1

N

n ¦ a n( k ) ( Y ) C pinc (k )

to

n =0

obtain the corrected value C pinc( k +1 ) ; (4) Go back to Step (2), replace C pinc( k ) by the corrected value

C pinc( k +1 )

and iterate until the converged results

110

5. Image and Data Analysis Techniques

C pinc = Lim C pinc( k ) and a n ( Y ) = Lim a n( k ) ( Y ) ( n = 0 ,1 N ) are obtained; (5) k →∞

k →∞

Output the final C pinc = C pinc [ X ,Y , S ( X ,Y )] and a n ( Y ) . After processing for a large set of intersections, we can recover the distribution of C pinc on the whole surface. Unlike the classical pressure-correction formulas for 2D flows, this iterative method is a non-local approach that has to be done along an intersection. The selection of the order N of the polynomial in Eq. (5.43) depends on the complexity of the Mach number effect on the pressure distribution along the intersection. For 2D flows and near-2D flows, N = 2 is sufficient; for more complex flows, the order of the polynomial could be higher. The number of available data points on an intersection eventually limits the order of the polynomial. For PSP, data processing is typically done in the image plane rather than in the object space. Therefore, for convenience, the pressure-correction method should be used in the image plane. The aforementioned analysis is made in an arbitrary object-space coordinate system ( X ,Y , Z ) or a general non-orthogonal curvilinear coordinate system on a surface. Since there is a one-to-one projection mapping between the image plane ( x , y ) and the surface Z = S ( X ,Y ) , the iterative pressure correction method can be directly applied to rows or columns in PSP images. There are limitation conditions for application of the iterative pressurecorrection method (actually for any pressure-correction method). First, the two Mach numbers M ∞1 and M ∞ 2 should be lower than the critical Mach number at which flow becomes sonic at certain point on a surface. Secondly, the pressurecorrection method relies on an assumption that the pressure distribution does not have a drastic change due to the Reynolds number effect as the Mach number increases from M ∞ = 0 to M ∞1 and M ∞ 2 . When the Reynolds number effect on pressure overwhelms the effect of the Mach number, the pressure-correction method cannot produce correct results because the flow pattern has been qualitatively changed. This situation may happen on a high-lift model under certain testing conditions in certain flow separation regions that are particularly sensitive to the Reynolds number effect. Fortunately, there is a large class of flows in which the Reynolds number does not significantly affect the surface pressure distribution, such as attached flows and certain separated flows whose separation and re-attachment lines are fixed. For these flows, the pressurecorrection method is applicable. The iterative pressure-correction method was validated for flows over a circular cylinder, sphere, prolate spheroid, transonic body and delta wing (Liu 2003). Figure 5.16 shows the incompressible C pinc distribution on a circular cylinder recovered by the iterative pressure-correction method along with the results obtained using the Prandtl-Glauert rule and Karman-Tsien rule. The iterative method produced excellent recovery of C pinc given by the incompressible solution of potential flow over a cylinder (Lighthill 1954). The Karman-Tsien rule also gave a good correction while the Prandtl-Glauert rule was not accurate in the low-

5.6. Pressure Correction for Extrapolation to Low-Speed Data

111

pressure region C p = [ −3,−2 ] . The iterative method used the C p distributions at

M ∞1 = 0.4 and M ∞ 2 = 0.6 . The order of polynomial was N = 2 and the solution for C pinc converged after 10 iterations. Both the Karman-Tsien rule and PrandtlGlauert rule used C p at M ∞ = 0.4 to recover C pinc . Figure 5.17 shows the pressure correction for a prolate spheroid of a fineness ratio of 6 at the angle of o attack of 5.6 and zero ellipsoidal coordinate (Matthews 1953). The iterative method used C p data at M ∞1 = 0.6 and M ∞ 2 = 0.8 . Even though these Mach numbers are quite high, the iterative method still produced good results since the Mach numbers were less than the critical Mach number of 0.904 in this case. To examine the capability of the iterative pressure-correction method for complex vortical separated flows, it was also used to recover C pinc on the upper surface of o

a 65 delta wing; the recovered C pinc distributions showed a correct trend as the Mach number increases. 2 Cpinc, Iterative method Cpinc, Karman-Tsien Cpinc, Prandtl-Glauert Incompressible solution

1

0

Cp

-1

-2

-3 Mach 0.4 -4

Mach 0.6

Cylinder

-5 0

1

2

3

theta (radian)

Fig. 5.16. Pressure correction for a circular cylinder to recover the incompressible pressure coefficient. From Liu (2003)

112

5. Image and Data Analysis Techniques 0.4

Prolate spheroid of fineness ratio 6

0.3

Cpinc, Iterative method Mach 0.0 Mach 0.6 Mach 0.8

Cp

0.2

0.1

AoA = 5.6 deg omega = 0 deg

0.0

-0.1

-0.2 0

10

20

30

40

50

Percent distance from nose

Fig. 5.17. Pressure correction for a prolate spheroid to recover the incompressible pressure coefficient. From Liu (2003)

5.7. Generation of Deformed Surface Grid For a more accurate representation of data, PSP and TSP results in images should be mapped onto a deformed surface grid of a model rather than a rigid surface grid when the model undergoes a large deformation in wind tunnel tests. Aeroelastic deformation data for a model can be obtained using videogrammetric model deformation (VMD) measurement technique (Burner and Liu 2001). Hence, PSP and TSP systems should be integrated with a VMD system for fusion of pressure and temperature data with deformation data (Bell and Burner 1998; Liu et al. 1999). There are two approaches for integration of PSP/TSP with VMD. The first approach uses PSP/TSP simultaneously with VMD as a separate and independent system, while VMD, that is operated under the PSP/TSP lighting and surface conditions, provides deformation data for generating a deformed surface grid. The advantage of this approach is that the structure of a PSP/TSP system is not changed and PSP/TSP operation suffers no interference from VMD operation in large production wind tunnels. In contrast, the second approach uses the same camera for both PSP/TSP and VMD measurements at the same time; VMD software is integrated as an additional part of the PSP/TSP software package. Instead of a nearly normal view of a camera for pure PSP/TSP application, the combined system requires an oblique viewing angle of a camera to achieve good position sensitivity for VMD measurements. Usually, VMD gives wing deformation characterized by the twist and bending of a wing. When the local translation and twist are measured by VMD at different spanwise locations of a wing, a transformation of translation and rotation can be used to generate a deformed surface grid of the wing. At a spanwise location Y,

5.7. Generation of Deformed Surface Grid

113

the deformed coordinate ( X ' ,Y ' , Z' ) on a wing surface grid is locally related to the non-deformed grid coordinate ( X ,Y , Z ) by

§ X' · § X · § T ( Y )· ¸ ¨ ¸ = R( Y )¨ ¸ + ¨ x ¨ Z' ¸ ¨ Z ¸ ¨ T ( Y )¸ . © ¹ © ¹ © z ¹

(5.44)

The translation vector at a spanwise location Y of the wing is (Tx , Tz ) and the rotational matrix is sin ștwist · § cos ștwist ¸, R(Y) = ¨¨ (5.45) ¸ © − sin ș twist cos ș twist ¹ where the twist ș twist is a function of the spanwise location Y. When the bending relative to the wingspan is small, the spanwise location does not change much, i.e., Y ' ≈ Y , and the wing airfoil section remains the same. For illustration, we consider a fictional wing with a NACA0012 airfoil section and assume that the spanwise distributions of twist and bending are given by ștwist = − 5(Y/b)3 ,

Tz = 0.08 b (Y/b)3 and Tx = 0 , where b is the semi-span of the wing. Figure 5.18 shows a deformed surface grid generated using a transformation of translation and rotation.

Deformed Wing

Wing

Fig. 5.18. Generation of a deformed surface grid of a wing based on videogrammetric deformation measurements. From Liu et al. (1999)

6. Lifetime-Based Methods

Compared with the widely used intensity-based method, the greatest advantage of the lifetime-based method is that a relation between the luminescent lifetime and pressure is not dependent on the illumination intensity. Therefore, the problem associated with non-uniform illumination in the intensity-based method becomes essentially irrelevant to the lifetime method. Theoretically speaking, lifetime measurement is also insensitive to luminophore concentration, paint thickness, photodegradation and paint contamination; thus a wind-off reference intensity image (or signal) is not required and the troubles associated with model deformation do not exist. The lifetime method for PSP and TSP can be applied to both a laser scanning system and an imaging system. Davies et al. (1995) developed a pulsed laser scanning system to directly determine the luminescent lifetime and used it to measure the pressure distributions on a cylinder in subsonic flows and on a wedge at Mach 2. Torgerson et al. (1996) developed a portable, modulated, two-dimensional laser scanning system that can simultaneously measure both the luminescent intensity and phase angle; this system was used to measure the surface pressure distributions in a low-speed impinging jet and on an airfoil in transonic flow. The system was further refined by Lachendro et al. (1998) and used to measure the pressure distributions on a wing of a Beechjet in flight tests. A fluorescent lifetime imaging (FLIM) system for PSP and TSP has become promising as solid-state imaging technology makes a rapid advance. The FLIM system, originally proposed by biochemists for oxygen detection in a small area (Szmacinski and Lakowicz 1995; Hartmann and Ziegler 1996), was used for PSP measurements in wind tunnels at DERA (Holmes 1998). DERA’s FLIM system comprised a phase-sensitive camera, modulated blue LED array, associated control hardware and computer. This Chapter discusses the response of the luminescent emission to a time-varying excitation light and describes the luminescent lifetime measurement techniques, including the pulse method, phase method, amplitude demodulation method and gated intensity ratio method. Although the discussion is focused on PSP, these techniques are generally applicable to TSP as well. Measurement uncertainty of the lifetime methods is discussed in Chapter 7. Similar analyses of the lifetime-based techniques were given by Goss et al. (2000) and Bell (2001).

116

6. Lifetime-Based Methods

6.1. Response of Luminescence to Time-Varying Excitation Light

6.1.1. First-Order Model The lifetime method for PSP and TSP is based on the response of luminescence to a time-varying excitation light. The response of the luminescent emission I from a paint to an excitation light E(t) can be described as a first-order system

dI / d t = − I / IJ + E( t) , where IJ is the luminescent lifetime. solution to Eq. (6.1) is

I (t) =

³

t 0

(6.1)

With the initial condition I(0) = 0 , a

exp[ − ( t − u ) / IJ ] E( u ) du .

(6.2)

For a pulse light E(t) = Am į(t) , the luminescent response is simply an exponential decay I (t) = Am exp( − t / IJ ) . (6.3) We consider a general periodic excitation light that is expressed as a Fourier series

§a E(t) = Am ¨ 0 + ¨ 2 ©

∞

¦[a n =1

n

· cos(n Ȧt ) + bn sin(n Ȧ t ) ] ¸ , ¸ ¹

(6.4)

where Ȧ = 2ʌ f is the circular frequency of the excitation light. Substitution of Eq. (6.4) into Eq. (6.2) yields the luminescent response after a short transient process ∞ § a a n cos(n Ȧt − ijn ) + bn sin(n Ȧ t − ijn ) ·¸ (6.5) I (t) = Am IJ ¨¨ 0 + ¸¸ . 2 2 2 ¨ 2 + 1 n Ȧ IJ n =1 © ¹

¦

Here, the phase angles ijn are related to the luminescent lifetime by

tan ijn = n Ȧ IJ .

(6.6)

In the simplest case where the sinusoidally modulated excitation light is E(t) = Am [ 1 + H sin( Ȧ t )] , the luminescent response Eq. (6.5) is reduced to

I (t) = Am IJ [ 1 + H M eff sin(Ȧt − ij) ] ,

(6.7)

6.1. Response of Luminescence to Time-Varying Excitation Light

117

where M eff = (1 + IJ 2 Ȧ 2 ) −1 / 2 is the effective amplitude modulation index, Am is the amplitude, and H is the modulation depth. The phase angle ij is related to the luminescent lifetime simply by

tan ij = Ȧ IJ .

(6.8)

Other waveforms of the excitation light include square and triangle. Figure 6.1 shows the luminescent response to typical periodic excitations with the square, sine and triangle waveforms for the non-dimensional lifetime of Ȧ IJ = ʌ /10 . 2 .5

E x c ita tio n L ig h t

Intensity

2 .0

L u m in e s c e n c e

1 .5

1 .0

0 .5

0 .0 0

2

4

6

8

10

12

10

12

10

12

ω t (ra d ia n )

(a) Square waveform 4 .0

E x c ita tio n L ig h t

3 .5

L u m in e s c e n c e

Intensity

3 .0 2 .5 2 .0 1 .5 1 .0 0 .5 0

2

4

6

8

ω t ( r a d ia n )

(b) Sine waveform 5

E x c ita tio n L ig h t

Intensity

4

L u m in e s c e n c e

3

2

1

0

0

2

4

6

8

ω t (ra d ia n )

(c) Triangle waveform Fig. 6.1. Response of luminescence to time-varying excitations of the square, sine and triangle waveforms for Ȧ IJ = ʌ /10

118

6. Lifetime-Based Methods

6.1.2. Higher-Order Model In a micro-heterogeneous polymer matrix, the multiple-exponential luminescent emission decay can be observed in contrast to the single-exponential decay in a homogeneous medium (Carraway et al. 1991a; Sacksteder et al. 1993; Xu et al. 1994). This is associated with the fact that the host matrix has domains that vary with respect to their interaction with the luminescent probe molecules; as a result, the excited molecules decay at different rates, depending on their environments. Consider a paint system consisting of a number of independently emitting species with different single-exponential lifetimes IJ i ( i = 1, 2, 3, ) and relative contributions. The multiple-exponential luminescent decay is described as I (t) = Į i exp( − t / IJ i ) , (6.9)

¦

where Į i is the weighting constant for the ith component. The luminescent lifetime of each component obeys the Stern-Volmer relation IJ 0 i / IJ i = 1 + K SV i p , (6.10) where K SV i is the Stern-Volmer coefficient for the ith component. Hence, a higher-order model is needed to describe the luminescent response of an inhomogeneous PSP to a time-varying excitation light. We consider a third-order model a 0 d 3 I / dt 3 + a 1 d 2 I / dt 2 + a 2 dI / dt + a 3 I = E( t ) . (6.11) With the initial conditions I ( 0 ) = I' ( 0 ) = I' ' ( 0 ) = 0 , a solution for (6.11) is

I (t) =

³

3

t

E( u ) 0

¦ Į exp[ − ( t − u ) / IJ i

i

] du .

(6.12)

i =1

The lifetimes IJ i are related to the weighting constants Į i through the roots of the characteristic equation a 0 s 3 + a 1 s 2 + a 2 s + a 3 = 0 . The weighted mean lifetime is usually expressed as < IJ > = ¦ Į i IJ i / ¦ Į i . A general model for the nonexponential decay of luminescence was discussed by Ruyten (2004) and Ruyten and Sellers (2004) considering the continuous decay rate spectrum and excitation response function.

6.2. Lifetime Measurement Techniques

6.2.1. Pulse Method Our goal is to measure the luminescent lifetime and to determine air pressure through the Stern-Volmer relation. A variety of methods can be used to extract the lifetime from the luminescent response to a time-varying excitation light. The pulse method is the most direct method widely used in photochemistry (Lakowicz

6.2. Lifetime Measurement Techniques

119

1991, 1999). After PSP is excited by a pulsed illumination light, the luminescent decay is measured using a fast-responding photodetector and acquired using a PC or an oscilloscope. The lifetime is calculated by fitting the time-resolved data with a single exponential function or a multiple-exponential function. This direct time-domain approach was used by Davies et al. (1995) for lifetime measurements of PSP. For certain PSP with multiple distinct lifetimes, the pulse method allows simultaneous determination of pressure and temperature if the lifetimes have sufficiently different Stern-Volmer coefficients as a function of temperature. In this case, given the lifetimes ( IJ i ), a system of equations for pressure and temperature are IJ i ref p , ( i = 1, 2,  N , N ≥ 2 ) (6.13) = Ai ( T ) + Bi ( T ) IJi p ref In principle, unknown pressure and temperature can be simultaneously determined by solving Eq. (6.13). 6.2.2. Phase Method The phase method is a frequency-domain technique that detects a phase shift of the luminescent signal with respect to the modulated excitation light (Torgerson et al. 1996; Torgerson 1997). Figure 6.2 shows the working principle of the phase method with a lock-in amplifier. For the sinusoidal excitation light E(t) = Am [ 1 + H sin( Ȧ t )] , the corresponding modulated luminescent signal from a photodetector is mixed with the in-phase and quadrature reference signals, i.e., sin( Ȧ t ) and cos( Ȧ t ) . Next, the use of a low-pass filter generates the DC components Vc = − Am IJ H M eff sin (ij ) and Vs = Am IJ H M eff cos (ij ) , which are related to the phase angle ij between the luminescent emission and excitation light. A ratio between these filtered signals yields a quantity tan ij = Ȧ IJ = − Vc / Vs that is uniquely related to the lifetime for a fixed modulation frequency. Therefore, pressure is given by § Ȧ IJ0 · −1 ¨ ¸ p = K SV (6.14) ¨ tan ij − 1¸ . © ¹ The sensitivity of the phase angle ij to pressure is defined as ω dϕ ∂τ . (6.15) Sp = = 2 dp 1 + ( ωτ ) ∂p The optimal modulation frequency to achieve the maximum sensitivity S p is (6.16) ȦIJ = 1 . It must be noted that the maximum sensitivity to pressure does not tell the whole story if the noise is not taken into account. Besides good sensitivity to pressure, the signal-to-noise ratio (SNR) should be also considered in order to select the optimal modulation frequency. At a higher frequency, the modulation amplitude

120

6. Lifetime-Based Methods

and DC components from PSP decrease, resulting in a lower SNR. Figure 6.3 is a Bode plot showing the response of a typical PSP, PtTFPP in polymer/ceramic composite, to the modulation frequency; the behavior of this PSP is very close to the first-order system. E(t) = A m [ 1 + H sin( Ȧ t )]

PSP

I (t) = A m IJ [ 1 + H M

cos( Ȧt)

Mixer

eff

sin( Ȧ t − ij) ]

Low-Pass Filter

V c = − Am IJ H M

sin( Ȧt)

Mixer

Low-Pass Filter

eff

sin( ij )

V s = Am IJ H M

eff

cos( ij )

Divider

tan( ij ) = Ȧ IJ = − V c / V s

Fig. 6.2. Block diagram of the phase method

3 0 -3 -6 -9 0.07psi 2.32psi 5.37psi 8.49psi 11.42psi 14.68psi

dB

-12 -15 -18 -21

3rd Order Fit

-24 -27 -30 -33 102

103

104

105

Freqeuncy(Hz)

Fig. 6.3. The Bode plot of PSP (PtTFPP in polymer/ceramic composite) at –30°C. From Lachendro (2000)

6.2. Lifetime Measurement Techniques

121

6.2.3. Amplitude Demodulation Method The amplitude demodulation method was used for fluorescent lifetime measurements of tagged biological specimens in a flow cytometer (Deka et al. 1994). For the sinusoidally modulated excitation light, the luminescent response is given by Eq. (6.7) and the effective amplitude modulation index is M eff = (1 + IJ 2 Ȧ 2 ) −1 / 2 . Clearly, for a fixed modulation frequency, the lifetime can be obtained from measurement of the effective modulation index. Combination of the Stern-Volmer relation Eq. (6.10) with M eff = (1 + IJ 2 Ȧ 2 ) −1 / 2 yields an expression for pressure as a function of the effective amplitude modulation index M eff

§ · ¸ 1 ¨ Ȧ IJ 0 M eff −1¸ . (6.17) p= ¨ 2 K SV ¨ 1 − M ¸ eff © ¹ To measure the effective amplitude modulation index M eff , Deka et al. (1994) used the following expression I ( t ) − I min ( t min ) , (5.18) M eff = H −1 max max I max ( t max ) + I min ( t min ) where t max and t min were the times at which the modulated oscillating luminescent signal went through the maximum intensity I max ( t max ) and minimum intensity

I min ( t min ) , respectively. Here, as illustrated in Fig. 6.4, a simpler scheme is proposed to determine M eff by calculating the time-averaged quantities of the modulated luminescent signal. Define the time-averaged oscillating luminescent signal 1 T < I > = Lim I ( t ) dt . (6.19) T →∞ 2T −T The mean and standard deviation of the luminescent intensity I(t) are

³

< I > = Am IJ and std ( I ) = < ( I − < I > )2 > 1 / 2 = Am IJ H M eff / 2 . Therefore, taking a ratio between these quantities, we obtain a simple formula for the effective amplitude modulation index M eff = (1 + IJ 2 Ȧ 2 ) −1 / 2 std ( I ) < E > std ( I ) . (6.20) = std ( E ) < I > It is emphasized that Eq. (6.20) is valid only for the sinusoidally modulated excitation light E(t) = Am [ 1 + H sin( Ȧ t )] . Instrumentation for utilizing this methodology is particularly simple since only the mean and standard deviation of the sinusoidal luminescent intensity and excitation light intensity are required. The optimal modulation frequency can be obtained by maximizing the sensitivity of M eff to pressure M eff = 2 H −1

122

6. Lifetime-Based Methods

2 Ȧ2 IJ ∂τ . 2 2 3/2 dp (1 + Ȧ IJ ) ∂p The optimal modulation frequency for the maximum sensitivity is Sp =

d ( M eff )

=

(6.21)

(Ȧ IJ)op = ( 1 + 7 ) / 3 ≈ 1.215 .

(6.22)

For a typical PSP, Ru(dpp) in GE RTV 118, having the lifetime IJ = 4.7 µs at the ambient conditions, the optimal modulation frequency is 41 kHz. Figure 6.5 shows the effective amplitude modulation index M eff as a function of the relative pressure p/p ref at different sinusoidal modulation frequencies for this PSP having Clearly, the selection of the the lifetime IJ = IJ ref / ( 0.17 + 0.84 p/p ref ) . modulation frequency affects the performance of the system.

E(t) = A m [ 1 + H sin( Ȧ t )]

PSP

I (t) = A m IJ [ 1 + H M eff sin( Ȧ t − ij) ]

std ( I ) = 2 A m IJ H M eff

< I > = Am IJ

Divider

M eff = ( 1 + IJ 2 Ȧ 2 )−1 / 2 =

2 H −1 std ( I ) / < I >

Fig. 6.4. Block diagram of the amplitude demodulation method

6.2. Lifetime Measurement Techniques

123

1.2

Modulation frequency = 5 kHz 1.0

24 kHz

Meff

0.8

0.6

50 kHz

0.4

100 kHz

0.2

0.0 0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

P/Pref

Fig. 6.5. The effective amplitude modulation index M eff as a function of relative pressure o

at different sinusoidal modulation frequencies for Ru(dpp) in GE RTV 118 for T = 20 C and pref = 1 atm

6.2.4. Gated Intensity Ratio Method The gated intensity ratio method, as illustrated in Fig. 6.6, gates the modulated luminescent signal by applying two gain functions over two different intervals, i.e.,

I1 =

³

I ( t ) G1 ( t ) dt and I 2 =

∆ T1

³

I ( t ) G 2 ( t ) dt ,

∆ T2

(6.23)

where the gain functions G1 ( t ) and G2 ( t ) are certain time-varying functions. A ratio between the gated intensity integrals, I 2 / I 1 , is a function of the luminescent lifetime for given modulation parameters. In the simplest case, the gain function is a top-hat function or a square function where G1 ( t ) = G2 ( t ) = 1 in the time intervals ǻ T1 and ǻ T2 and G1 ( t ) = G2 ( t ) = 0 elsewhere.

In this case, the

square waveform of G1 ( t ) and G2 ( t ) serves as an ‘on-off’ gating function. The functional form for the excitation light and gain function can be selected to meet the requirements for a specific test. Common combinations are a pulse excitation with a square gain function (pulse-square), a sine-waveform excitation with a square gain function (sine-square), a square-waveform excitation with a square gain function (square-square), and a sine-waveform excitation with a sinewaveform gain function (sine-sine) (Goss et al. 2000).

124

6. Lifetime-Based Methods

E(t, r )

PSP

I (t, r )

I2 =

³

∆ T2

I1 =

I ( t , r ) G 2 ( t ) dt

³

∆ T1

I ( t , r ) G 1 ( t ) dt

Divider

I 2 /I 1 = F ( IJ )

Fig. 6.6. Block diagram of the gated intensity method

The modulated luminescent intensity is integrated over a gate time interval from 0 to 1/2f (0 to π in Ȧ t ) and over a gate time interval from 1/2f to 1/f (π to

2π in Ȧ t ) relative to a modulated excitation light. For the Fourier-series-form of the modulated excitation light Eq. (6.4), a ratio between the two integrals is I 2 /I 1 =

³

1/f

³

I dt 1/2f

1/2f 0

Idt =

ʌ − D( ωτ ) , ʌ + D( ωτ )

(6.24)

where

D(Ȧ IJ) =

2 a0

∞

[1 + ( −1) n +1 ] (a n n Ȧ IJ + bn ) n( 1 + n 2Ȧ2 IJ 2 )

¦ n =1

.

Obviously, the ratio I 2 / I 1 is only a function of the non-dimensional lifetime Ȧ IJ and therefore is related to pressure when the modulation frequency is fixed. In particular, the gated intensity ratio for the sinusoidally modulated excitation light E(t) = Am [ 1 + H sin( Ȧ t )] has a simple form

I 2 /I 1 =

³

1/f

I dt 1/2f

³

1/2f 0

Idt =

ʌ (1 + Ȧ 2 IJ 2 ) − 2 H ʌ (1 + Ȧ 2 IJ 2 ) + 2 H

.

(6.25)

6.2. Lifetime Measurement Techniques

125

Figure 6.7 shows the gated intensity ratio I 2 / I 1 as a function of the nondimensional lifetime Ȧ IJ for the excitation light with the square, triangle, sine and cosine waveforms. Although the lifetime is always positive, Figure 6.7 plots the ratio I 2 / I 1 over a range of −6 ≤ Ȧ IJ ≤ 6 to exhibit the global behavior of I 2 / I 1 as a function of Ȧ IJ . The behavior of I 2 / I 1 depends on the waveform of the modulated excitation light. Figure 6.8 shows the gated intensity ratio I 2 / I 1 as a function of the relative pressure p/p ref at different modulation frequencies for a typical PSP, Ru(dpp) in GE RTV 118, when the sinusoidal excitation light has the modulation depth of H = 1.

2.4

triangle wave 2.0

cosine wave sine wave

I2/I1

1.6

1.2

0.8

0.4

square wave 0.0 -6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

ωτ (radian)

Fig. 6.7. The gated intensity ratio as a function of the non-dimensional luminescent lifetime

1.2 Modulation frequency = 200 kHz

1.0

100 kHz

I2/I1

0.8

0.6

50 kHz

0.4

25 kHz

0.2

5 kHz

0.0 0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

P/Pref

Fig. 6.8. The gated intensity ratio as a function of pressure at different modulation o frequencies for Ru(dpp) in GE RTV 118 (T = 20 C and Pref = 1 atm) when the modulated excitation is sinusoidal

126

6. Lifetime-Based Methods

For the sinusoidal excitation light, the non-dimensional modulation frequency and modulation depth can be selected to achieve the greatest sensitivity of the gated intensity ratio to pressure defined as

Sp =

d ( I 2 /I 1 ) 8ʌ Ȧ 2 IJ H ∂τ = dp [ʌ (1 + Ȧ 2 IJ 2 ) + 2 H] 2 ∂p

.

(6.26)

The optimal modulation frequency for the maximum sensitivity is

(Ȧ IJ)op =

3 ≈ 1.732 .

(6.27)

For Ru(dpp) in GE RTV 118 that has the lifetime of 4.7 µs at the ambient conditions, the optimal modulation frequency is 59 kHz. The appropriate modulation depth H can also be selected according to certain criteria for a balance between the pressure sensitivity and SNR. It is noted that the off-phase intensity I 2 = ( Am IJ / 2 f )[ 1 − ( 2 H / ʌ )(1 + Ȧ 2 IJ 2 )−1 ] decreases as H increases and the normalized off-phase intensity at the optimal modulation frequency is I 2 /(I 2 )H =0 = 1 − H / 2ʌ . Since the SNR is proportional to

[ I 2 /(I 2 )H =0 ] 1 / 2 = ( 1 − H / 2π )1 / 2 , the SNR is a decreasing function of H in a range of 0 ≤ H ≤ 1 . On the other hand, the normalized sensitivity S p at the optimal modulation frequency, which is proportional to H / ( 2π + H ) 2 , is an increasing function of H in a range of 0 ≤ H ≤ 1 . Therefore, the appropriate modulation depth H of about 0.5 is chosen to achieve both a high SNR and good pressure sensitivity. The gated intensity integrals I1 and I2 are taken over the intervals from 0 to 1/2f (0 to π in Ȧ t ) and 1/2f to 1/f (π to 2π in Ȧ t ). The time variable t in these integrals is relative to the modulated excitation light. The integration is carried out immediately after the measurement system receives a trigger signal that is synchronized with the modulated excitation light. The trigger signal can be provided by a photodiode sensing the excitation light or a driver for the modulator. In practice, however, the trigger signal may have a time delay relative to the excitation light. The time delay, although small, may significantly alter the relation between I 2 / I 1 and pressure especially when the modulation frequency is high. For the sinusoidally modulated excitation light E(t) = Am [ 1 + H sin( Ȧ t )] , if the trigger signal has a time delay ǻt , the gated intensity ratio is

I 2 /I 1 =

³

1/f + ǻt 1/2f + ǻt

I dt

³

1/2f + ǻt ǻt

Idt =

ʌ − 2 H cos(ij ) cos( ij − Ȧ ǻt) ʌ + 2 H cos(ij ) cos( ij − Ȧ ǻt)

,

(6.28)

where cos( ij) = 1 / 1 + ( Ȧ IJ)2 . For a typical PSP, Ru(dpp) in GE RTV 118, Figure 6.9 shows the relation between I 2 / I 1 and p/p ref for different phase shifts Ȧ ǻt , where the sinusoidal modulation frequency is 25 kHz and the modulation depth is H = 1. It is clear that the behavior of the relation is significantly affected

6.2. Lifetime Measurement Techniques

127

by the phase shifts Ȧ ǻt and the curve is even no longer monotonous when the phase shift is large. The similar change also occurs for the excitation light having other waveforms like the square waveform. This change due to the trigger signal delay was observed in experiments. 0.9 ω∆t = π/2

0.8 0.7

I2/I1

0.6 0.5 π/3 0.4 π/4 0.3

0

0.2 0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

P/Pref

Fig. 6.9. The gated intensity ratio I 2 / I 1 as a function of p/p ref at different phase shifts

Ȧ ǻt for Ru(dpp) in GE RTV 118 (T = 20oC and Pref = 1 atm), where the sinusoidal modulation frequency is 25 kHz and the modulation depth H is one

Furthermore, the gated intensity ratio method can be applied to the pulse excitation light; in this case, the luminescent intensity signal is I (t) = Am exp( − t / IJ ) . For two gating intervals [ t 0 , t 1 ] and [ t 2 , t 3 ] where

t 3 > t 2 > t 1 > t 0 is assumed, the gated intensity ratio is I 2 /I 1 =

³

t3 t2

I dt

³

t1 t0

Idt =

exp( − t 3 / IJ ) − exp( − t 2 / IJ ) . exp( − t 1 / IJ ) − exp( − t 0 / IJ )

(6.29)

For the given gating intervals, the ratio I 2 / I 1 is only related to the lifetime. This integration approach was used as an alternative to the time-resolved pulse approach, which was called the time-resolved multiple-gate method by Goss et al. (2000). Bell (2001) discussed an optimization problem of the gating parameters ( t 0 , t1 , t 2 , t 3 ) to achieve the maximum sensitivity in an ICCD camera system. In a limiting but representative case where the time t g divides the two gating intervals [ 0 , t g ] and [ t g , ∞ ] ( t 0 = 0 , t 3 → ∞ , t 1 = t 2 = t g ), we have

I 2 /I 1 =

exp( − t g / IJ ) 1 − exp( − t g / IJ )

.

(6.30)

128

6. Lifetime-Based Methods

Although the above methods utilize two gating intervals, three gating intervals can be similarly used and therefore two gated intensity ratios like I 1 / I 2 and I 1 / I 3 can be obtained. If the two gated intensity ratios have sufficiently different dependencies to pressure and temperature for certain PSP, the surface pressure and temperature distributions can be determined simultaneously from the gated intensity ratio images.

6.3. Fluorescence Lifetime Imaging

6.3.1. Intensified CCD Camera The structure of an intensified CCD (ICCD) system is illustrated in Fig. 6.10. After being impacted by a photon, the photocathode creates photoelectrons that are amplified by the micro channel plate (MCP); the amplified electrons are converted back into photons by a phosphor screen. These photons are relayed to a CCD by either a fiber-optic bundle or a relay lens; the CCD creates the photoelectrons that are measured. The biggest advantage of ICCD is its ability of gating that allows the luminescent lifetime imaging over a painted area. Electronic shutter action can be produced by pulsing the MCP voltage and the gain can be modulated by simply changing the voltage on the intensifier. Figure 6.11 illustrates the luminescent lifetime imaging method with an ICCD. Photo Cathode

Micro Channel Plate

A

Phosphor Screen

Fiber-Optic Taper

CCD

A

A

Fig. 6.10. Structure of ICCD and multiple photon-electron conversions in ICCD

< I > =

I (t, r )

Image Intensifier

I(t, r ) G (t)

1 T

INT

³

T INT

I ( t , r ) G ( t ) dt

0

CCD

G (t)

Fig. 6.11. Diagram of lifetime imaging with ICCD for modulated illumination

6.3. Fluorescence Lifetime Imaging

129

For the pulse excitation light, the gain function is typically a top-hat function or a square function. The luminescent signal is gated in two different intervals during an exponential decay of luminescence and the gated intensity ratio is related to the luminescent lifetime by Eq. (6.29). This approach was employed for PSP measurements by Goss et al. (2000), Bencic (2001), Bell (2001), Baker (2001), and Mitsuo et al. (2002). Another approach uses the sinusoidal excitation light combined with either the square gain function (Holmes 1998) or sinusoidal gain function (Lakowicz and Berndt 1991). Consider the sinusoidally modulated excitation light E(t) = Am [ 1 + H sin( Ȧ t )] and the corresponding luminescent signal from PSP is I (t) = Am IJ [ 1 + H M eff sin(Ȧt − ij) ] , where the effective amplitude modulation index is M eff = (1 + IJ 2 Ȧ 2 ) −1 / 2 = cos( ij ) . When the gain function has a square-waveform, the gated intensity ratio is given by Eq. (6.25). Instead of using the square function, Lakowicz and Berndt (1991) adopted the sinusoidal gain function for modulating the intensifier. When the MCP is sinusoidally modulated, the gain function of the detector is G(t) = G0 [ 1 + m D sin(Ȧt − ș D ) ] , where G0 is the intensifier gain without applying a modulating signal, m D is the gain modulation depth, and ș D is the detector phase angle relative to the modulated illumination light. The CCD collecting photons over an integration time actually serves as an integrator; thus, the signal output from the CCD is represented by a time-averaged intensity over an integration time TINT

=

1 TINT

³

TINT 0

I ( t , r ) G( t ) dt = Am IJ G0 [ 1 + 0.5 M eff m D cos( ij − ș D ) ] . (6.31)

To extract the phase angle or lifetime from the CCD output < I > , several values of < I > are obtained by changing the detector phase angle ș D . Therefore, a system of equations is given for eliminating Am and G0 . These equations can be solved using least-squares method to determine the phase angle ij that is related to the luminescent lifetime τ. In the simplest case where only two different detector phase angles ș D1 and ș D2 are chosen, a ratio between the two timeaveraged intensities at ș D1 and ș D2 is

< I > ( șD 2 ) / < I > ( șD1 ) =

1 + 0.5 m D cos( ij ) cos( ij − ș D 2 ) . 1 + 0.5 mD cos( ij ) cos( ij − ș D 1 )

(6.32)

Once the parameters m D , ș D1 , and ș D2 are given, the ratio in Eq. (6.32) is only related to the phase angle ij . Lakowicz and Berndt (1991) used three different detector phase angles to recover the luminescent lifetime. One shortcoming of the intensifier CCD camera is that the SNR may be reduced due to quantum losses and additive noise in the multiple-step photon-electron transfer processes.

130

6. Lifetime-Based Methods

6.3.2. Internally Gated CCD Camera An internally gated CCD camera is promising for luminescent lifetime imaging. Fisher et al. (1999) developed a phase-sensitive CCD camera system for twodimensional imaging of concentrations of radical species in reacting flows such as turbulent flames. They modified a commercial scientific-grade CCD camera to perform phase-sensitive imaging as well as to reduce the level of integrated background light. In fact, this internally gated CCD camera has the capability to selectively integrate the time-varying luminescent intensity either in-phase or outof-phase with respect to the modulated excitation light. A ratio between the outof-phase and in-phase images is related to the luminescent lifetime, and thus a pressure field can be obtained from a luminescent lifetime image. Modern CCD cameras available for industrial machine vision or scientific uses possess many of the features required to construct a phase-sensitive imaging system. Most notably, the feature commonly referred to as ‘electronic shuttering’ can be suitably modified to serve phase sensitive imaging or lifetime imaging. The CCD array architecture employed by cameras capable of performing electronic shuttering is referred to as an interline transfer array shown in Fig. 6.12. It consists of photodiodes separated by vertical transfer registers that are covered by an opaque metal shield that prevents direct entry of photoelectrons. Charge accumulated in the photosensors can be transferred either to the vertical registers or discarded in the substrate by supplying a high voltage to the Read Out Gate (ROG) or the Over Flow Drain (OFD) respectively. In order to perform phase-sensitive imaging, charge shifting and storage in the CCD must be synchronized with the light-source modulation signal. This requires appropriate modification of the camera controller logic, and of the camera head circuitry and logic. Based on the modulation waveform, a suitable control signal will be generated, which raises the ROG voltage and lowers the OFD voltage during the in-phase half of the cycle. The in-phase luminescent signal is thus integrated into the vertical register. In the out-of-phase half of the modulation cycle, the ROG and OFD voltages are reversed, thus dumping the out-of-phase light into the substrate. This process is repeated for a number of cycles until the full-well capacity of the vertical registers is utilized to maximize the SNR. Finally, after the desired integration time (or the number of cycles) the accumulated charge in the vertical registers can be read out through the horizontal register using conventional frame transfer techniques. The out-of-phase image can be similarly obtained, the only difference being the introduction of a 180o phase lag between the modulation signal and the control signal described above. As pointed out before, a ratio between the out-of-phase and in-phase intensity images, I 2 /I 1 , is a function of the phase angle or the luminescent lifetime; therefore, a pressure field can be obtained from the luminescent lifetime image.

6.4. Lifetime Experiments

131

Fig. 6.12. Interline transfer CCD architecture and charge flow

6.4. Lifetime Experiments Lachendro (2000) used a set-up shown in Fig. A2 in Appendix A for phase calibration of PSP and TSP formulations at temperatures lower than –30°C, which was capable of holding pressures down to 0.03 psi. In order to make phase calibrations, LED arrays were used as a modulated excitation source; a blue LED array was used for Ruthenium-based complexes and a green LED array for Porphyrin-based luminophores. Each array consisted of seven LEDs arranged in a hexagonal formation for more uniform illumination. The light from an LED array was passed through an appropriate interference filter to eliminate unwanted emission. A function generator was used to directly power and modulate the arrays; the TTL signal from the function generator was used as an external reference for a lock-in amplifier. After passing through a focusing lens, the luminescent response of PSP (or TSP) was detected using a PMT fitted with an interference filter centered at 620 nm and then was sampled by the lock-in amplifier. A PC was used to acquire calibration data from the lock-in amplifier. Figures 6.13-6.15 show phase calibration results for three PSP formulations: Ru(dpp) in a silicone polymer with silica gel, PtTFPP in a silicone polymer with silica gel, and PtTFPP in a porous polymer/ceramic(Al2O3) composite tape casting. Figures 6.16-6.18 show phase calibration results for three TSP formulations: PtTFPP, Ru(trpy)(C6F5-trpy)(NO3)2, and Ru(bipy)2(p-bipy)2 in DuPont ChromaClear.

132

6. Lifetime-Based Methods

0 -5

Phase Shift (Degrees)

-10 -15 -20

-30οC -20οC -15οC -10οC -5οC 0οC 10οC 20οC 3rd Order

-25 -30 -35 -40 -45 -50 0

1

2

3

4

5

6

7

8

9

10 11

12 13

14

15

Pressure (psia)

Fig. 6.13. Phase calibration for PSP, Ru(dpp) in RTV 110 with Silica Gel. Lachendro (2000)

From

0 -2

Phase Shift (Degrees)

-4 -6 -8 -10

-30οC -18οC -3οC 10οC 20οC 5th Order Fit

-12 -14 -16 -18 -20 -22 0

1

2

3

4

5

6

7

8

9

10 11

12

13 14 15

Pressure(psia)

Fig. 6.14. Phase calibration for PSP, PtTFPP in RTV 110 with Silica Gel. From Lachendro (2000)

6.4. Lifetime Experiments

4

-50οC -45οC -40οC -35οC -30οC -25οC -20οC ο -15 C -10οC -5οC 0οC 5οC 10οC 15οC 20οC 25οC

0 -4 Phase Shift (Degrees)

133

-8 -12 -16 -20 -24 -28 -32 -36 -40 -44 0

1

2

3

4

5

6 7 8 9 10 11 12 13 14 15 Pressure (psia)

Fig. 6.15. Phase calibrations for PSP, PtTFPP in a porous polymer/ceramic(Al2O3) composite tape casting. From Lachendro (2000)

0 -1 Phase Shift (degrees)

-2 -3 -4 -5 -6 -7 -8 -9 -10 -50 -45 -40 -35 -30 -25 -20 -15 -10 -5 Temperature (οC)

0

5

10 15 20

Fig. 6.16. Phase calibration for TSP, PtTFPP in DuPont ChromaClear. From Lachendro (2000)

134

6. Lifetime-Based Methods 0 -2 Phase Shift (degrees)

-4 -6 -8 -10 -12 -14 -16 -18 -20 -50 -45 -40 -35 -30 -25 -20 -15 -10 -5

0

5

10 15 20

ο

Temperature ( C)

Fig. 6.17. Phase calibration for TSP, Ru(trpy)(C6F5-trpy)(NO3)2 in DuPont ChromaClear. From Lachendro (2000)

2 0 Phase Shift (degrees)

-2 -4 -6 -8 -10 -12 -14 -16 -18 -50 -45 -40 -35 -30 -25 -20 -15 -10 -5

0

5 10 15 20 25

Temperature (oC)

Fig. 6.18. Phase calibration for TSP, Ru(bipy)2(p-bipy)2 in DuPont ChromaClear. From Lachendro (2000)

Goss et al. (2000) evaluated the lifetime techniques based on several different modulation/gating combinations such as the time-resolved multiple-gate method for the pulse excitation, sine-square method, and square-square method. The detectors used were ICCD, phase-sensitive interline-transfer CCD, and back-lit CCD with a liquid-crystal shutter. A xenon strobe light and a Nd:YAG laser were

6.4. Lifetime Experiments

135

used as a pulse light source, while a LED array was used for the sinusoidal and square-wave excitation. PSP tested was PtTFPP in a sol-gel binder. The gated intensity ratio was measured as a function of pressure using the detectors with different gating strategies. They found that the time-resolved multiple-gate method had greater sensitivity to pressure than other lifetime methods and the intensity-based (or radiometric) method. The square-square method had the second best sensitivity to pressure. Figure 6.19 shows calibration results of the gated intensity ratio for that PSP obtained with the ICCD employing the timeresolved multiple-gate method and square-square method. One of the problems with the ICCD was a high noise level of the system; the rms variation of the gated intensity ratio was as high as 3-5% even after binning. 1.8 1.6

Multiple-Gate Method Square-Square Method

Gated Intensity Ratio

1.4

PtTFPP-sol-gel PSP

1.2 1.0 0.8 0.6 0.4 0.2 0.0 0

20

40

60

80

100

Pressure (kPa)

Fig. 6.19. Calibration of the gated intensity ratio for PtTFPP-sol-gel PSP with ICCD using the time-resolved multiple-gate method and square-square method. From Goss et al. (2000)

Bell (2001) studied the time-resolved multiple-gate method for the pulse excitation to optimize the gating parameters. He found that the gated intensity ratio was not constant over a PSP-coated surface even at constant pressure and temperature, and the variation was 0.5-3% depending on homogeneity of the paint. This indicated that the lifetime was different at different locations even when pressure and temperature are uniformly invariant over a surface. Earlier, in laser-scanning PSP measurements, Torgerson et al. (1996) observed a variation of o about 0.5 in the phase angle (related to the lifetime) across a measurement domain in the flow-off case where pressure and temperature were constant. Similar to Bell’s observation on the gated intensity ratio, the spatial phase pattern was repeatable, dependent on the location. Hartmann et al. (1995) also observed similar results and attributed this phenomenon to microheterogeneity of the polymer environment. The small lifetime or phase variation may not significantly affect PSP measurements at higher Mach numbers, whereas it can introduce a

136

6. Lifetime-Based Methods

considerable error in low-speed PSP measurements. To correct this intrinsic spatial variation of the lifetime, Torgerson et al. (1996) and Bell (2001) used raw lifetime or phase distributions in the flow-off conditions as a reference, and took a ratio between the wind-on and reference lifetime images (signals). Unfortunately, this correction method defeats to certain degree the original purpose of using the lifetime method to eliminate the wind-off reference. Bencic (2001) compared the lifetime method with the intensity-based method for PSP measurements at high viewing polar angles and in a shadowed region, and found that the lifetime-based measurements achieved better results in these cases. Mitsuo et al. (2002) studied the luminescent decay of a PtTFPP-based PSP using a streak camera and found that the multiple-exponential decay of the paint was sensitively dependent on pressure and temperature. This characteristic allowed simultaneous determination of pressure and temperature from three gated intensities obtained by an ICCD camera since two ratios between the three gated intensities had sufficiently different dependencies on pressure and temperature. They selected the first and third gating intervals ǻ T1 = 0 − 0.8 µs and

ǻ T3 = 30 − 82.8 µs. The gated intensity I 1 in ǻ T1 was almost independent from both pressure and temperature, whereas the gated intensity I 3 in ǻ T3 was very sensitive to pressure and temperature. The second gating interval ǻ T2 = 12 − 19.4 µs was chosen based on minimization of the pressure error due to a small pertubation of the intensity ratio signal. Their calibration experiments showed that pressure could be well described by polynomials of the gated intensity ratios I 1 / I 2 and I 1 / I 3 with the temperature-dependent coefficients. Using the calibration relations, they were able to obtain simultaneously the surface pressure and temperature fields in a sonic impinging jet from the two gated intensity ratio images. Recent tests by Watkins et al. (2003) used a new internally gated interline transfer CCD camera to alleviate noise sources associated with ICCD.

7. Uncertainty

7.1. Pressure Uncertainty of Intensity-Based Methods

7.1.1. System Modeling Uncertainty analysis is highly desirable in order to establish PSP as a quantitative measurement technique. Based on the Stern-Volmer equation, Sajben (1993) investigated error sources contributing to the uncertainty of PSP, and found that the uncertainty strongly depended on flow conditions and the surface temperature significantly affected the final measurement results. Oglesby et al. (1995a) presented an analysis of an intrinsic limit of the Stern-Volmer relation to the achievable sensitivity and accuracy. Mendoza (1997a, 1997b) studied CCD camera noise and its effect on PSP measurements and suggested the limiting Mach number for quantitative PSP measurements. From a standpoint of system modeling, Liu et al. (2001a) gave a general and comprehensive uncertainty analysis for PSP. The following uncertainty analysis focuses on the intensity-ratio method widely used in PSP measurements. From Eq. (4.24), air pressure p can be generally expressed in terms of the system’s outputs and other variables Vref ( t, x ) p ref A(T) p ref − . (7.1) p = U1 V( t' , x' ) B(T) B(T) The factor U1 in Eq. (7.1) is

U1 =

Ȇ c Ȇ f h( x' ) c( x' ) q0 ( t' , X' ) , Ȇ c ref Ȇ f ref href ( x ) c ref ( x ) q0 ref ( t, X )

where x = (x, y)T and x' = (x' , y' )T are the coordinates in the wind-off and windon images, respectively, X = (X, Y, Z)T and X' = (X' ,Y' , Z' )T are the object space coordinates in the wind-off and wind-on cases, respectively, and t and t’ are the instants at which the wind-off and wind-on images are taken, respectively. Here, the paint thickness h and dye concentration c are expressed as a function of the image coordinate x rather than the object space coordinate X since the image

138

7. Uncertainty

registration error is more easily treated in the image plane. In fact, x and X are related through the perspective transformation (the collinearity equations). In order to separate complicated coupling between the temporal and spatial variations of these variables, some terms in Eq. (7.1) can be further decomposed when a small model deformation and a short time interval are considered. The wind-on image coordinates can be expressed as a superposition of the wind-off image coordinates and an image displacement vector ǻx , i.e., x' = x + ǻx . Similarly, the temporal decomposition is t' = t + ǻt , where ǻt is a time interval between the instants at which the wind-off and wind-on images are taken. If ǻx and ǻt are small, a ratio between the wind-off and wind-on images can be separated into two factors, Vref ( t, x )/V( t' , x' ) ≈ Dt (ǻt ) D x (ǻx )Vref ( t, x )/V( t, x ) , where

the

factors

Dt ( ǻt ) = 1 − ( ∂V / ∂ t )( ǻt)/V

and

D x (ǻx ) = 1 − ( ∇V ) • ( ǻx ) /V represent the effects of the temporal and spatial changes of the luminescent intensity, respectively. The temporal change of the luminescent intensity is mainly caused by photodegradation and sedimentation of dusts and oil droplets on a surface. The spatial intensity change is due to model deformation generated by aerodynamic loads. In the same fashion, the excitation light flux can be decomposed into q0 ( t' , X' )/q0 ref ( t, X ) ≈ Dq0 (ǻt ) q0 ( t, X' )/q0 ref ( t, X ) ,

where

the

factor

Dq0 ( ǻt ) = 1 + ( ∂ q0 / ∂ t )( ǻt) / q0 ref represents the temporal variation in the excitation light flux. The use of the above estimates yields the generalized Stern-Volmer relation Vref ( t, x ) p ref A(T) p ref − , (7.2) p = U2 V( t, x ) B(T) B(T) where U 2 = Dt (ǻt ) D x (ǻx ) Dq0 (ǻt )

Ȇ c Ȇ f h( x' ) c( x' ) q0 ( t, X' ) . Ȇ c ref Ȇ f ref href ( x ) c ref ( x ) q0 ref ( t, X )

Without any model motion ( x' = x and X' = X ) and temporal illumination fluctuation, the factor U2 is unity and then Eq. (7.2) recovers the generic SternVolmer relation. Eq. (7.2) is a general relation that includes the effects of model deformation, spectral variability, and temporal variations in both illumination and luminescence, which allows a more complete uncertainty analysis and a clearer understanding of how these variables contribute the total uncertainty in PSP measurements. 7.1.2. Error Propagation, Sensitivity and Total Uncertainty According to the general uncertainty analysis formalism (Ronen 1988; Bevington and Robinson 1992), the total uncertainty of pressure p is described by the error propagation equation

7.1. Pressure Uncertainty of Intensity-Based Methods M [ var( ȗ i ) var( ȗ j )] 1/2 var (p) = S S ȡ i j ij p2 ȗ iȗ j i, j = 1

¦

where between

ȡi j = cov( ȗ i ȗ j )/[ var( ȗ i ) var( ȗ j )] 1/2 the

variables

ȗi

and

,

139

(7.3)

is the correlation coefficient

ȗj,

var (ȗ i ) = < ǻȗ i > 2

and

cov (ȗ i ȗ j ) = < ǻȗ i ǻȗ j > are the variance and covariance, respectively, and the notation < > denotes the statistical ensemble average. Here, the variables {ȗ i , i = 1 M} denote a set of the parameters Dt (ǻt ) , D x (ǻx ) , Dq0 (ǻt ) , V , Vref , Ȇ c /Ȇ c ref , Ȇ f /Ȇ f ref , h / href , c / c ref , q0 /q0 ref , p ref , T , A, and B in Eq. (7.2). The sensitivity coefficients S i are defined as S i = ( ȗ i /p )( ∂ p / ∂ ȗ i ) . Eq. (7.3) becomes particularly simple when the cross-correlation coefficients between the variables vanish ( ȡi j = 0 , i ≠ j ). Table 7.1 lists the sensitivity coefficients, the elemental errors and their physical origins. Many sensitivity coefficients are proportional to a factor ϕ = 1 + [A(T) /B(T)] / (p / p ref ) . For Bath Ruth + silica-gel in GE RTV 118, Figure 7.1 shows the factor 1 + [A(T) /B(T)] / (p / p ref ) as a function of p / p ref for different temperatures, which is only slightly changed by temperature. The temperature sensitivity coefficient is S T = −T [B' (T) + A' (T) p ref /p]/ B ( T ) , where the prime denotes differentiation respect with temperature. Figure 7.2 shows the absolute value of S T as a function of p / p ref at different temperatures. After the elemental errors in Table 7.1 are evaluated, the total uncertainty in pressure can be readily calculated using Eq. (7.3). The major elemental error sources are discussed below.

140

7. Uncertainty

Table 7.1. Sensitivity coefficients, elemental errors, and total uncertainty of PSP Variable

Sensi. Coef.

ȗi

Elemental Variance

Physical Origin

var( ȗ i )

Si

1

D t (ǻt )

ij

[( ∂V / ∂ t )( ǻt)/V ] 2

2

D x (ǻx )

ij

[ (∂V/∂x ) ı x2 + (∂V /∂ y ) ı 2y ] V − 2

3

D q0 (ǻt )

[( ∂ q 0 / ∂ t )( ǻt)/q 0 ref ] 2

4 5 6

Vref V Ȇ c /Ȇ c ref

7

Ȇ f /Ȇ f ref

8

h / href

ij ij -ij ij ij ij

9

c / c ref

ij

−2 [ (∂ c /∂ x ) ı x2 + (∂ c /∂ y ) ı 2y ] c ref

10 q 0 /q 0 ref

ij

( q0 ref )−2 ( ∇q0 ) • ( ǻX )

11

1

var( p)

p ref

12 T 13 A 14 B 15 Pressure

mapping

2

2

Temporal variation in luminescence due to photodegradation and surface contamination Image registration errors for correcting luminescence variation due to model motion Temporal variation in illumination Photodetector noise

V ref G ! Ȟ B d

Photodetector noise

V G !Ȟ Bd

[ R2 /(R1 + R2 )] (ǻR1 /R1 ) 2

2

var(Ȇ f /Ȇ f ref ) −2 [ (∂ h /∂ x ) ı x2 + (∂ h /∂ y ) ı 2y ] href 2

2

2

2

2

ST

var( T) 1 − ij var( A) -1 var( B) 1 (∂ p/∂x )2 ı x2 + (∂p /∂y )2 ı 2y and ( ∇ p )surf • ( ǻX )surf

2

Change in camera performance parameters due to model motion Illumination spectral variability and filter spectral leakage Image registration errors for correcting thickness variation due to model motion Image registration errors for correcting concentration variation due to model motion Illumination variation on model surface due to model motion Error in measurement of reference pressure Temperature effect of PSP Paint calibration error Paint calibration error Errors in camera calibration and pressure mapping on a surface of a presumed rigid body M

Total Uncertainty in Pressure

var (p)/ p 2 =

¦S

2 i

var( ȗ i )/ ȗ i

2

i =1

Note: (1) ı x and ı y are the standard deviations of least-squares estimation in the image registration or camera calibration. (2) The factors for the sensitivity coefficient are defined as ij = 1 + [ A( T ) / B( T )]( p ref / p ) and S T = − [ T / B ( T )] [B' (T) + A' (T)(p ref / p ) ] .

7.1. Pressure Uncertainty of Intensity-Based Methods

141

3.0 T = 293 K T = 313 K T = 333 K

1 + (A(T)/B(T))(Pref/P)

2.5

2.0

1.5

1.0

0.5 0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

P/Pref

Fig. 7.1. The sensitivity factor 1 + [A(T) /B(T)] / (p / p ref ) as a function of p / p ref at different temperatures for Bath Ruth + silica-gel in GE RTV 118. From Liu et al. (2001a) 10 9

T = 293 K T = 313 K T = 333 K

|(dP/dT)(T/P)|

8 7 6 5 4 3 2 0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

P/Pref

Fig. 7.2. The temperature sensitivity coefficient as a function of p / p ref at different temperatures for Bath Ruth + silica-gel in GE RTV 118. From Liu et al. (2001a)

7.1.3. Photodetector Noise and Limiting Pressure Resolution The uncertainties in the outputs V and Vref from a photodetector (e.g. camera) are contributed from a number of noise sources in the detector such as the photon shot noise, dark current shot noise, amplifier noise, quantization noise, and pattern

142

7. Uncertainty

noise. When the dark current and pattern noise are subtracted and the noise floor is negligible, the detector is photon-shot-noise-limited. In this case, the signal-tonoise ratio (SNR) of the detector is SNR = ( V / G ! ȞBd )1 / 2 , where ! is the Planck’s constant, ν is the frequency, Bd is the electrical bandwidth of the detection electronics, G is the system’s gain, and V is the detector output. The uncertainties in the outputs are expressed by the variances var(V) = V G ! Ȟ Bd and

var(Vref ) = Vref G ! Ȟ Bd . In the photon-shot-noise-limited case in which the error propagation equation contains only two terms related to V and Vref , the pressure uncertainty is ǻ p §¨ G Bd ! Ȟ ·¸ = ¨ V ref ¸ p © ¹

1/ 2

ª A( T ) p ref «1 + B( T ) p «¬

ºª p º » » «1 + A( T ) + B( T ) p ref ¼» »¼ ¬«

1/ 2

,

(7.4)

which holds for both CCD cameras and non-imaging detectors. For a CCD camera, the first factor in the right-hand side of Eq. (7.4) can be simply expressed by the total number of photoelectrons collected over the integration time ( ∝ 1 / Bd ), n pe = V /( G ! ȞBd ) . When the full-well capacity of the CCD camera is achieved, we obtain the minimum pressure difference that PSP can measure from a single frame of image

( ǻp)min 1 = p (n pe ref )max

ª p º A(T) p ref º ª » «1 + » «1 + A(T) + B(T) p ref »¼ B(T) p »¼ ¬« ¬«

1/2

,

(7.5)

where (n pe ref )max is the full-well capacity of the camera in reference conditions. When N images are averaged, the limiting pressure difference (7.5) is further 1/2 reduced by a factor N . Eq. (7.5) provides an estimate for the noise-equivalent pressure resolution for a CCD camera. When (n pe ref )max is 500,000 electrons for a CCD camera and Bath Ruth + silica-gel in GE RTV 118 is used, the minimum pressure uncertainty ( ǻp)min / p is shown in Fig. 7.3 as a function of p / p ref for different temperatures, indicating that an increased temperature degrades the limiting pressure resolution.

Figure 7.4 shows

(n pe ref )max ( ǻp)min / p

as a

function of p / p ref for different values of the Stern-Volmer coefficient B(T) . Clearly, a larger B(T) leads to a smaller limiting pressure uncertainty ( ǻp)min / p . Figure 7.5 shows

(n pe ref )max ( ǻp)min / p

as a function of the Stern-Volmer

coefficient B(T) for different values of p / p ref . There is no optimal value of B in this case.

Minimum pressure uncertainty (%)

7.1. Pressure Uncertainty of Intensity-Based Methods

143

0.40

0.36

0.32 T = 333 K T = 313 K

0.28 T = 293 K 0.24

0.20 0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

P/Pref

Fig. 7.3. The minimum pressure uncertainty ( ǻp)min / p as a function of p / p ref at different temperatures for Bath Ruth + silica-gel in GE RTV 118. From Liu et al. (2001a)

7

(∆P)min/P [(npe ref)max]

1/2

6

5 B = 0.5 4 0.6 3

0.7 0.8

2

0.9

1 0.0

0.5

1.0

1.5

2.0

P/Pref

Fig. 7.4. The normalized minimum pressure uncertainty

(n pe ref )max ( ǻp)min / p as a

function of p / p ref for different values of the Stern-Volmer coefficient B(T) . From Liu et al. (2001a)

144

7. Uncertainty

20 P/Pref = 0.2

(∆P)min/P [(npe ref)max]

1/2

0.5 15

1.0

1.5

10

2.0 5

0.0

0.2

0.4

0.6

0.8

1.0

B

Fig. 7.5. The normalized minimum pressure uncertainty

(n pe ref )max ( ǻp)min / p as a

function of the Stern-Volmer coefficient B for different values of p / p ref . From Liu et al. (2001a)

7.1.4. Errors Induced by Model Deformation Model deformation generated by aerodynamic loads causes a displacement ǻx = x' − x of the wind-on image relative to the wind-off image. This displacement leads to the deviations of the quantities D x (ǻx ) , h / href , c / c ref , and q0 /q0 ref in Eq. (7.2) from unity because the distributions of the luminescent intensity, paint thickness, dye concentration and illumination level are not spatially homogeneous on a surface. After the image registration technique is applied to re-align the wind-on and wind-off images, the estimated variances of these quantities are var[Dx (ǻx )] ≈ W ( V ) / V 2 , var( h / href ) ≈ W ( h ) /( href )2 , and

var( c / c ref ) ≈ W ( c ) /( c ref ) 2 .

The

operator

W( • )

is defined

as

W( • ) = (∂ /∂ x ) ı + (∂ /∂ y ) ı , where ı x and ı y are the standard deviations of least-squares estimation for image registration. The uncertainty in q0 ( X )/q0 ref ( X' ) is caused by a change in the illumination intensity on a model surface after the model moves with respect to the light sources. When a point on the model surface travels along the displacement vector ǻX = X' − X in the object space, the variance of q0 /q0 ref is estimated by 2

2 x

2

2 y

2

var[q0 ( X ) / q0 ref ( X' )] ≈ ( q0 ref )−2 ( ∇q0 ) • ( ǻX ) . Consider a point light source

7.1. Pressure Uncertainty of Intensity-Based Methods

with unit strength that has a light flux distribution q0 ( X − X s ) = X − X s

145 −n

,

where n is an exponent (normally n = 2) and X − X s is the distance between the point X on the model surface and the light source location X s . Thus, the variance of q0 /q0 ref for a single point light source is var[q0 ( X ) / q0 ref ( X' )]

= n2 X − X s

−4

2

( X − X s ) • ( ǻX ) .

The variance for multiple point light

sources can be obtained based on the principle of superposition. In addition, model deformation leads to a small change in the distance between the model surface and the camera lens. The uncertainty in the camera performance parameters due to this change is var(Ȇ c /Ȇ c ref ) ≈ [ R2 /(R1 + R2 )] 2 (ǻR1 /R1 )2 , where R1 is the distance between the lens and model surface and R2 is the distance between the lens and sensor. For R1 >> R2 , this error is very small.

7.1.5. Temperature Effect Since the luminescent intensity of PSP is intrinsically temperature-dependent, a temperature change on a model during a wind tunnel run results in a significant bias error in PSP measurements if the temperature effect is not corrected. In addition, temperature influences the total uncertainty of PSP measurements through the sensitivity coefficients of the variables in the error propagation equation. Hence, the surface temperature on a model must be known in order to correct the temperature effect of PSP. In general, the surface temperature distribution can be measured experimentally using TSP or IR camera and determined numerically by solving the motion and energy equations of flows coupled with the heat conduction equation for a model. For a compressible boundary layer on an adiabatic wall, the adiabatic wall temperature Taw can be estimated using a simple relation Taw / T0 = [ 1 + r( γ - 1)M 2 / 2 ] [ 1 + ( γ - 1)M 2 / 2 ] −1 , where r is the recovery factor for the boundary layer, T0 is the total temperature, M is the local Mach number, and γ is the specific heat ratio.

7.1.6. Calibration Errors The uncertainties in determining the Stern-Volmer coefficients A(T) and B(T) are calibration errors. In a priori PSP calibration in a pressure chamber, the uncertainty is represented by the standard deviation of data collected in replication tests. Because tests in a pressure chamber are well controlled, a priori calibration results usually show a small precision error. However, a significant bias error is found when a priori calibration results are directly used for data reduction in wind tunnel tests due to unknown surface temperature distribution and uncontrollable

146

7. Uncertainty

testing environmental factors. In contrast, in-situ calibration utilizes pressure tap data over a model surface to determine the Stern-Volmer coefficients. Because in-situ calibration correlates the local luminescent intensity with the pressure tap data, it can reduce the bias errors associated with the temperature effect and other sources, achieving a better agreement with the pressure tap data. The in-situ calibration uncertainty, which is usually represented as a fitting error, will be specially discussed in Section 7.3. 7.1.7. Temporal Variations in Luminescence and Illumination For PSP measurements in steady flows, a temporal change in the luminescent intensity mainly results from photodegradation and sedimentation of dusts and oil droplets on a model surface. The photodegradation of PSP may occur when there is a considerable exposure of PSP to the strong excitation light between the windoff and wind-on measurements. Dusts and oil droplets in air sediment on a model surface during wind-tunnel runs; the resulting dust/oil layer absorbs both the excitation light and luminescent emission on the surface and thus causes a decrease of the luminescent intensity. The uncertainty in Dt (ǻt ) due to the photodegradation and sedimentation can be collectively characterized by the variance var[Dt ( ǻt )] ≈ [( ∂V / ∂ t )( ǻt)/V ] 2 . Similarly, the uncertainty in

Dq0 (ǻt ) , which is produced by an unstable excitation light source, is described by var[Dq0 ( ǻt )] ≈ [( ∂q 0 / ∂ t )( ǻt)/q 0 ref ] 2 .

7.1.8. Spectral Variability and Filter Leakage The uncertainty in Ȇ f /Ȇ f ref is mainly attributed to the spectral variability of illumination lights and spectral leaking of optical filters. Possolo and Maier (1998) observed the spectral variability between flashes of a xenon lamp; the uncertainties in the absolute pressure and pressure coefficient due to the flash spectral variability were 0.05 psi and 0.01, respectively. If optical filters are not selected appropriately, a small portion of photons from the excitation light and ambient light may reach a detector through the filters, producing an additional output to the luminescent signal. 7.1.9. Pressure Mapping Errors The uncertainty in pressure mapping is related to the data reduction procedure in which PSP data in images are mapped onto a surface grid of a model in the object space. It is contributed from the errors in camera resection/calibration and mapping onto a surface grid of a presumed rigid body. The camera resection/calibration error is represented by the standard deviations ı x and ı y of the calculated target coordinates from the measured target coordinates in the

7.1. Pressure Uncertainty of Intensity-Based Methods

147

image plane. Typically, a good camera resection/calibration method gives the standard deviation of about 0.04 pixels in the image plane. For a given PSP image, the pressure variance induced by the camera resection/calibration error is 2 2 var(p) ≈ (∂ p/∂ x ) ı x2 + (∂p /∂ y ) ı 2y . The pressure mapping onto a presumably non-deformed model surface grid leads to another deformation-related error because a model may undergo a considerable deformation generated by aerodynamic loads in wind tunnel tests. When a point on a model surface moves by ǻX = X' − X in the object space, the pressure variance induced by mapping onto a presumed rigid body grid without 2

correcting the model deformation is var(p ) = ( ∇ p )surf • ( ǻX )surf , where (∇ p )surf is the pressure gradient on the surface and ( ǻX )surf is the component of the displacement vector ǻX projected on the surface in the object space. To eliminate this error, a deformed surface grid should be generated for PSP mapping based on optical model deformation measurements under the same testing conditions (Liu et al. 1999).

7.1.10. Paint Intrusiveness A thin PSP coating may slightly modify the overall shape of a model and produces local surface roughness and topological patterns. These unwanted changes in model geometry may alter flows over a model and affect the integrated aerodynamic forces (Engler et al. 1991; Sellers 1998a). Hence, this paint intrusiveness to flow should be considered as an error source in PSP measurements. The effects of a paint coating on pressure and skin friction are directly associated with locally changed flow structures and propagation of the induced perturbations in flow; these local effects may collectively alter the integrated aerodynamic forces. When a local paint thickness variation is much smaller than the boundary layer displacement thickness, a thin coating does not alter the inviscid outer flow. Instead of directly altering the outer flow, a rough coating may indirectly result in a local pressure change by thickening the boundary layer; coating roughness may reduce the momentum of the boundary layer to cause early flow separation at certain positions. Therefore, the effective aerodynamic shape of a model is changed and as a result the pressure distribution on the model is modified; this effect is mostly appreciable near the trailing edge due to the substantial development of the boundary layer on the surface. Vanhoutte et al. (2000) observed an increment in the trailing edge pressure coefficient relative to the unpainted model, which was consistent with an increase in the boundary layer thickness at the trailing edge. For certain models such as high-lift models, a coating may change the gap between the main wing and slat or flap when the gap is small; thus, the pressure distribution on the model is locally influenced. In addition, a coating may influence laminar separation bubbles near the leading edge at low Reynolds numbers and high angles-of-attack. The perturbations induced by a rough coating near the leading edge may enhance

148

7. Uncertainty

mixing that entrains the high-momentum fluid from the outer flow into the separated region. The perturbations could be amplified by several hydrodynamic instability mechanisms such as the Kelvin-Helmholtz instability in the shear layer between the outer flow and separated region and the cross-flow instability near the attachment line on a swept wing. Consequently, the coating causes the laminar separation bubbles to be suppressed. Vanhoutte et al. (2000) reported this effect that led to a reduction in drag. Schairer et al. (1998a, 2002) observed that a rough coating on the slats slightly decreased the stall angle of a high-lift wing. Also, they found that the empirical criteria for ‘hydraulic smoothness’ and ‘admissible roughness’ based on 2D data by Schichting (1979) were not sufficient to provide a satisfactory explanation for their observation. Indeed, in 3D complex flows on the high-lift model, the effect of the coating on the cross-flow instability and its interactions with the boundary layer and other shear layers such wakes and jets are not well understood. Schairer et al. (1998a, 2002) and Mebarki et al. (1999) found that a rough coating moved a shock wave upstream and the pressure distribution was shifted near the shock location. This change might be caused by an interaction between the shock and the incoming boundary layer affected by the coating. In an attached flow at high Reynolds numbers, a rough coating increases skin friction by triggering premature laminar-turbulent transition and increasing the turbulent intensity in a turbulent boundary layer (Mebarki et al. 1999; Vanhoutte et al. 2000). An increase in drag due to a rough coating was observed in airfoil tests in high subsonic flows (Vanhoutte et al. 2000). In fact, premature transition by coating roughness has been often observed in TSP transition detection experiments (see Chapter 10). Amer et al. (2001, 2003) reported that a very smooth coating on the upper surface of a delta wing model at Mach 0.2 and a semi-span arrow-wing model at Mach 2.4 did not significantly change the drag coefficients of these models. Generally speaking, the effect of a coating on aerodynamic forces highly depends on flows over a specific model configuration; there is no universal conclusion on this effect.

7.1.11. Other Error Sources and Limitations Other error sources include the self-illumination and induction effect; there are limitations in the time response and spatial resolution of PSP. The selfillumination is a phenomenon that the luminescent emission from one part of a model surface reflects to another surface, thus distorting the observed luminescent intensity at a point by superposing all the rays reflected from other points. It often occurs on surfaces of neighbor components of a complex model (Ruyten 1997a, 1997b, 2001a; Le Sant 2001b). The self-illumination effect on calculation of pressure and temperature are discussed in Section 5.3. Another problem is the ‘induction effect’ observed as an increase in the luminescent emission during the first few minutes of illumination for certain paints; the photochemical process behind it was explained by Uibel et al. (1993) and Gouterman (1997). In PSP measurements in unsteady flows, the limiting time response of PSP, which is

7.1. Pressure Uncertainty of Intensity-Based Methods

149

mainly determined by oxygen diffusion process across a PSP layer (see Chapter 8), imposes an additional restriction on the accuracy of PSP measurements. The spatial resolution of PSP is limited by oxygen diffusion in the lateral direction along a paint surface. Considering a pressure jump across a point on a surface (a normal shock wave), Mosharov et al (1997) gave a solution of the diffusion equation describing a distribution of the oxygen concentration in a PSP layer near the pressure jump point. According to this solution, the limiting spatial resolution is about five times of the paint layer thickness. 7.1.12. Allowable Upper Bounds of Elemental Errors In the design of PSP experiments, we need to give the allowable upper bounds of the elemental errors for the required pressure accuracy. This is an optimization problem subject to certain constraints. In matrix notations, Eq. (7.3) is expressed as ı P2 = ı T A ı , where the notations are defined as ı P2 = var (p)/p 2 ,

A ij = S i S j ȡi j , and ı i = [ var( ȗ i ) ] 1/2 / ȗ i . For required pressure uncertainty ı P , we look for a vector ı up to maximize an objective function H = W T ı , where

W is the weighting vector. The vector ı up gives the upper bounds of the elemental errors for a given pressure uncertainty ı P . The use of the Lagrange multiplier method requires H = W T ı + Ȝ ( ı P2 − ı T A ı ) to be maximal, where λ is the Lagrange multiplier. The solution to this optimization problem gives the upper bounds A −1 W ı up = ıP . (7.6) ( W T A −1 W )1/2 For the uncorrelated variables with ȡi j = 0 (i ≠ j) , Eq. (7.6) reduces to −1/2

· § (ı i )up = S i− 2 Wi ı P ¨¨ S −k 2 Wk2 ¸¸ . (7.7) ¹ © k When the weighting factors Wi equal the absolute values of the sensitivity coefficients | S i | , the upper bounds can be expressed in a very simple form

¦

(ı i )up / ı P = N V−1 / 2 S i

−1

, ( i = 1, 2 , , N V )

(7.8)

where N V is the total number of the variables or the elemental error sources. The relation Eq. (7.8) clearly indicates that the allowable upper bounds of the elemental uncertainties are inversely proportional to the sensitivity coefficients and the square root of the total number of the elemental error sources. Figure 7.6 shows a distribution of the upper bounds of 15 variables for PSP Bath Ruth + silica-gel in GE RTV 118 at p / p ref = 0.8 and T = 293 K. Clearly, the allowable upper bound for temperature is much lower than others, and therefore the temperature effct of PSP must be tightly controlled to achieve the required pressure accuracy.

150

7. Uncertainty

1.8 1.6 1.4 1.2

1

Dt (ǻt )

9

c / c ref

2

Dx (ǻx )

10

q0 /q0 ref

3

Dq0 (ǻt )

11

Pref

12 13

T A

B

V Vref

4

(ı i )up

1.0

ıP

0.8

5

0.6

6

Ȇ c /Ȇ c ref

14

7

Ȇ f /Ȇ f ref

15 Pressure mapping

8

h / href

0.4 0.2 0.0 0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

Variable Index

Fig. 7.6. Allowable upper bounds of 15 variables for Bath Ruth + silica-gel in GE RTV 118 when p / p ref = 0.8 , and T = 293 K. From Liu et al. (2001a)

7.1.13. Uncertainties of Integrated Forces and Moments The uncertainties of the integrated aerodynamic forces and moments can be estimated based on their definitions. For example, the uncertainty in the lift is 1/ 2

∆FL / FL = FL−1 [ ∆ −1 L

≈F

³³ ( ¦¦ ( n • l

p( n • l L )dS ] 2 L

∆S )i ( n • l L ∆S ) j < ∆ p i ∆ p j >

)

,

(7.9)

1/ 2

where n is the unit normal vector of a surface panel, ∆S is the area of the surface panel, and l L is the unit vector of the lift. The correlation between the pressure differences at the panel ‘i’ and panel ‘j’ is simply modeled by < ∆ p i ∆ p j >= δ ij < ∆ pi >< ∆ p j > , where the Kronecker delta is δ ij = 1 for i = j and δ ij = 0 for i ≠ j . Thus, the uncertainty in the lift can be estimated

based on the PSP uncertainty at all the surface panels, i.e.,

§ ǻF L / F L ≈ ¨ ¨ ©

N

¦ (n•l i =1

L

2 i

2

2 PSP i

ǻS ) ( p i / FL ) ( ǻp / p )

· ¸ ¸ ¹

1/ 2

(7.10)

Similarly, the uncertainties in the pressure-induced drag and pichting moment are estimated by

7.2. Pressure Uncertainty Analysis for Subsonic Airfoil Flows

§ ǻFD / FD ≈ ¨ ¨ © § ǻM c / M c ≈ ¨ ¨ ©

N

¦ (n•l

D

2 i

2

2 PSP i

ǻS ) ( p i / FD ) ( ǻp / p )

i =1

· ¸ ¸ ¹

1/ 2

,

N

¦ [ n×( X − X

mc

2 i

151

2

2 PSP i

) ǻS ] ( p i / M c ) ( ǻp / p )

i =1

(7.11)

· ¸ ¸ ¹

1/ 2

, (7.12)

where l D is the unit vector of the drag and X mc is the assigned moment center.

7.2. Pressure Uncertainty Analysis for Subsonic Airfoil Flows PSP measurements on a Joukowsky airfoil in subsonic flows are simulated in order to illustrate how to estimate the elemental errors and the total uncertainty using the techniques described above. The airfoil and incompressible potential flows around it are generated using the Joukowsky transform; the pressure coefficients Cp on the airfoil in the corresponding subsonic compressible flows are obtained using the Karman-Tsien rule. Figure 7.7 shows typical distributions of the pressure coefficient and adiabatic wall temperature on a Joukowsky airfoil at o Mach 0.4 and AoA = 5 .

-8

-3

Cp Temperature -6

-2

-4

0

-2

Cp

-1

Taw - Tref (deg C)

AoA = 5 deg, Mach = 0.4

0

1

Joukowski Airfoil 2

2 0.0

0.2

0.4

0.6

0.8

1.0

x/c

Fig. 7.7. Typical distributions of the pressure coefficient and adiabatic wall temperature on o a Joukowsky airfoil at Mach 0.4, AoA = 5 , and Tref = 293 K

152

7. Uncertainty

Presumably, PSP, Bath Ruth + silica-gel in GE RTV 118, is used, which has the Stern-Volmer coefficients A(T) ≈ 0.13 [ 1 + 2.82( T − Tref ) / Tref ] and

B(T) ≈ 0.87 [ 1 + 4.32( T − Tref ) / Tref ] over a temperature range of 293-333 K. The uncertainties in a priori PSP calibration are ǻA/A = ǻB/B = 1% . We assume that the spatial changes of the paint thickness and dye concentration in the image plane are 0.5%/pixel and 0.1%/pixel, respectively. The rate of photodegradation of the paint is 0.5%/hour for a given excitation level and the exposure time of the paint is 60 seconds between the wind-off and wind-on images. The rate of reduction of the luminescent intensity due to dust/oil sedimentation on the surface is assumed to be 0.5%/hour. In an object-space coordinate system whose origin is located at the leading edge of the airfoil, four light sources for illuminating PSP are placed at the locations X s1 = ( − c , 3c ) , X s2 = ( 2c, 3c ) , X s3 = ( − c , − 3c ) , and Xs4 = ( 2c, − 3c ) , where c is the chord of the airfoil. For the light sources with unit strength, the illumination flux distributions on the upper and lower surfaces are, respectively,

(q0 )up = X up - X s1

−2

+ X up - X s2

−2

and (q0 )low = X low - X s3

−2

+ X low - X s4

−2

,

where X up and X low are the coordinates of the upper and lower surfaces of the airfoil, respectively. The temporal variation of irradiance of these lights is assumed to be 1%/hour. It is also assumed that the spectral leakage of optical filters for the lights and cameras is 0.3%. Two cameras, viewing the upper surface and lower surface respectively, are located at ( c/2, 4 c ) and ( c/2, − 4c ) . The pressure uncertainty associated with the photon shot noise can be estimated by using Eq. (7.5). Assume that the full-well capacity of ( n pe )max = 350,000 electrons of a CCD camera is utilized. The numbers of photoelectrons collected in a CCD camera are mainly proportional to the distribution of the illumination field on the model surface. Thus, the photoelectrons on the upper and lower surfaces are estimated by ( n pe )up = ( n pe )max ( q0 )up / max[( q0 )up ] and

( n pe )low = ( n pe )max ( q0 )low / max[( q0 )low ] . Combination of these estimates with Eq. (7.5) gives the shot-noise-generated pressure uncertainty distributions on the surfaces. Movement of the airfoil produced by aerodynamic loads is expressed by a superposition of a local rotation (twist) and translation. A transformation between the non-moved and moved surface coordinates X = ( X ,Y )T and X' = ( X ' ,Y ' )T is X' = R( θ twist ) X + T , where R( θ twist ) is the rotation matrix, θ twist is the local wing twist, and T is the translation vector.

Here, for θ twist = −1o and

T = ( 0.001c , 0.01 c )T , the uncertainty in q0 ( X )/q0 ref ( X' ) is estimated by 2

var[q0 ( X ) / q0 ref ( X' )] ≈ ( q0 ref )−2 ( ∇q0 ) • ( ǻX ) , where the displacement vector is ǻX = X' − X . The pressure variance associated with mapping PSP data onto a rigid body grid without correcting the model deformation is estimated by

7.2. Pressure Uncertainty Analysis for Subsonic Airfoil Flows

153

2

var(p ) = ( ∇ p )surf • ( ǻX )surf , where (∇ p )surf is the pressure gradient on the surface and ( ǻX)surf = ( X' − X)surf is the component of the displacement vector projected on the surface. To estimate the temperature effect of PSP, an adiabatic model is considered at which the wall temperature Taw is given by

Taw / T0 = [ 1 + r( γ - 1)M 2 / 2 ] [ 1 + ( γ - 1)M 2 / 2 ] −1 , where the recovery factor is r = 0.843 for a laminar boundary layer. Assuming that the reference temperature Tref equals to the total temperature T0 = 293 K, we can calculate a temperature difference ∆T = Taw − Tref between the wind-on and wind-off cases. The adiabatic wall is the most severe case for PSP measurements since the surface temperature on a metallic model is much lower than the adiabatic wall temperature due to heat conduction to the model. The total uncertainty in pressure is estimated by substituting all the estimated elemental errors into Eq. (7.3). Figure 7.8 shows the pressure uncertainty distributions on the upper and lower surfaces of the airfoil for different freestream Mach numbers. It is indicated that the temperature effect of PSP dominates the uncertainty of PSP measurements on an adiabatic wall. The uncertainty becomes larger and larger as the Mach number increases because the adiabatic wall temperature increases. The local pressure uncertainty on the upper surface is as high as 50% at one location for Mach 0.7, which is caused by a local surface o temperature change of about 6 C. In order to compare the PSP uncertainty with the pressure variation on the airfoil, a maximum relative pressure variation on the airfoil is defined as

max ǻp

surf

/ p∞ = 0.5 γ M ∞2 max ∆C p . Figure 7.9 shows the maximum relative

pressure variation

max ǻp

surf

/ p∞

along with the chord-averaged PSP

uncertainty < ( ǻp/p)PSP > aw on the adiabatic airfoil at the Mach numbers of 0.050.7. The uncertainty < ( ǻp/p)PSP > ∆T =0 without the temperature effect is also plotted in Fig. 7.10, which is mainly dominated by the a priori PSP calibration error ǻB/B = 1% in this case. The curves max ǻp surf / p∞ , < ( ǻp/p)PSP > aw and < ( ǻp/p)PSP > ∆T =0 intersect near Mach 0.1. When the PSP uncertainty exceeds the maximum pressure variation on the airfoil, the pressure distribution on the airfoil cannot be quantitatively measured by PSP. As shown in Fig. 7.9, because a temperature change on a non-adiabatic wall is smaller, the PSP uncertainty for a real wind tunnel model generally falls into the shadowed region confined by < ( ǻp/p)PSP > aw and < ( ǻp/p)PSP > ∆T =0 . The PSP uncertainty associated with the photon shot noise < ( ǻp/p)PSP > ShotNoise is also plotted in Fig. 7.9. The intersection between max ǻp

surf

/ p∞ and < ( ǻp/p)PSP > ShotNoise gives the limiting low Mach number

154

7. Uncertainty

( ~ 0.06 ) for PSP measurements in this case. The uncertainties in the lift ( FL ) and pitching moment ( M c ) are also calculated from the PSP uncertainty distribution on the surface. Figure 7.10 shows the uncertainties in the lift and pitching moment relative to the leading edge for the Joukowsky airfoil over a o range of the Mach numbers when the angle of attack is 4 . The uncertainties in the lift and moment decrease monotonously as the Mach number increases since the absolute values of the lift and moment rapidly increase with the Mach number.

0.6 Upper Surface

0.5

Uncertainty in P

M = 0.7 0.4 0.3 0.2 M = 0.5

0.1

M = 0.3 0.0

M = 0.1 0.0

0.2

0.4

0.6

0.8

1.0

x/c

(a) 0.06

Lower Surface

Uncertainty in P

0.05

M = 0.7

0.04

M = 0.5

0.03

0.02 M = 0.3 0.01

M = 0.1 0.0

(b)

0.2

0.4

0.6

0.8

1.0

x/c

Fig. 7.8. PSP uncertainty distributions for different freestream Mach numbers on (a) the upper surface and (b) lower surface of a Joukowsky airfoil. From Liu et al. (2001a)

7.2. Pressure Uncertainty Analysis for Subsonic Airfoil Flows

155

1

Relative Error or Variation

Upper Surface

< ( ǻP/P)PSP > aw max ǻP

surf

/ P∞

0.1

0.01

< ( ǻP/P)PSP > ∆T =0 < ( ǻP/P)PSP > ShotNoise 0.001 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Freestream Mach number

(a) 1

Relative Error or Variation

Lower Surface

max ǻP

0.1

surf

/ P∞

< ( ǻP/P)PSP > aw

0.01

< ( ǻP/P)PSP > ∆T =0 < ( ǻP/P)PSP > ShotNoise 0.001 0.0

(b)

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Freestream Mach number

Fig. 7.9. The maximum relative pressure change and chord-averaged PSP uncertainties as a function of the freestream Mach number on (a) the upper surface and (b) the lower surface of a Joukowsky airfoil. From Liu et al. (2001a)

156

7. Uncertainty

0.7 0.6

Lift Pitching Moment

Uncertainty

0.5 0.4 0.3 0.2 0.1 0.0 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Freestream Mach Number

Fig. 7.10. Uncertainties in the lift and pitching moment of a Joukowsky airfoil as a function of the freestream Mach number. From Liu et al. (2001a)

7.3. In-Situ Calibration Uncertainty

7.3.1. Experiments

As pointed out before, the use of a priori PSP calibration in large wind tunnels often leads to a considerable systematic error since the surface temperature distribution is not known and the illumination change on a surface due to model deformation cannot be corrected by the image registration technique. The systematic error is also related to uncontrollable environmental testing factors. Therefore, in actual PSP measurements, experimental aerodynamicists are forced to calibrate PSP in situ by fitting (or correlating) the luminescent intensity to pressure tap data at a number of suitably distributed locations. In a sense, in-situ PSP calibration eliminates the systematic error associated with the temperature effect and the illumination change by absorbing it into an overall fitting error. Kammeyer et al. (2002a, 2002b) assessed the accuracy of the Boeing production PSP system by statistical analysis of comparison between PSP and pressure transducers over a large numbers of data points. The Boeing PSP system is a typical intensity-based system that uses eight CCD (1024×1024 or 512×512) cameras for imaging, thirty lamps for illumination, and two IR cameras measuring the surface temperature for correcting the temperature effect of PSP. The test article was a 1/12th-scale model of a Cessna Citation that was instrumented with a total of 225 pressure taps. The tests were conducted in the DNW/NLR HST wind tunnel, a variable-density, closed circuit, continuous tunnel with slotted top and bottom test section walls (12% open). The test section was 6.56 ft wide and was

7.3. In-Situ Calibration Uncertainty

157

configured to be 5.25 ft high. The cameras and lamps were mounted in the floor and ceiling. A run consisted of a lift polar at each of several Mach numbers from 0.22 to 0.82. Two Reynolds numbers, 4.5 and 8.3 millions, were run. Fourteen o angles of attack were from –4 to 10 . Over 8300 visual images and over 2000 IR images were obtained for 676 test points. The wind-off reference images were acquired after the run when the fan had stopped in order to reduce the effect of the model temperature distribution. Figure 7.11 shows a typical pressure distribution on the model obtained by PSP.

Fig. 7.11. Typical pressure distribution obtained from PSP on a Cessna Citation model. From Kammeyer et al. (2002a)

In-situ PSP calibrations were performed by utilizing 78 of 225 pressure taps for each of the cameras. Figure 7.12 shows the variation of the in-situ calibration slope (i.e. the Stern-Volmer coefficient B) as a function of test point throughout the tests, where no temperature correction was applied. The variation does not show an overall trend; the repeating pattern mirrors the pattern of the test conditions, wherein sequential angles of attack were run for sequentially increasing Mach numbers. The mean value of the slope is close to one, which is approximately consistent with the paint characteristics given by a priori calibration. The scatter is attributed to a number of factors, including the nonhomogeneous temperature distributions, temperature differences between the wind-off and wind-on conditions, lamp intensity drift, and image registration error. The accuracy of the PSP system was directly assessed by comparing the pressure value measured by a transducer/tap combination with that obtained from PSP at the same tap location. After some problematic pressure data were excluded, 130,391 comparisons from 221 taps and 676 wind-on test points were used as an overall set of realizations for statistical analysis. The PSP data

158

7. Uncertainty

processing included in-situ calibration, but did not exercise the explicit temperature correction. When examining the comparisons, the 78 taps were used for in-situ calibration to provide residual comparisons, while other taps provided truly independent comparisons. Figure 7.13 shows a histogram for the over set of comparisons, where a Gaussian distribution with the same mean and standard deviation is superimposed for comparison. Clearly, the distribution is nonGaussian. A robust estimate of the 68% confidence level gives an estimate of the standard uncertainty of 0.29 psi, which corresponds to 0.0065 in Cp. Figure 7.14 shows the standard uncertainty as a function of the angle of attack for the right wing. The behavior of the dependency of the uncertainty on the angle of attack corresponds to wing deformation. This indicates that the error is associated with the movement of the model in the non-homogenous illumination field, which cannot be corrected by the image registration technique. Kammeyer et al. (2002a, 2002b) also studied temperature correction using the IR cameras. Two sets of PSP data obtained before and after temperature correction were used to assess the effectiveness of the temperature correction. Figure 7.14 shows the standard uncertainty after the temperature correction as a function of the angle of attack. The temperature correction was increasingly effective when the angle of attack o was larger than 2 ; it removed the spatial biases associated with the temperature distribution on the model. Overall, the standard uncertainty, priori to the temperature correction, was in the range 0.16-0.45 psi (0.04-0.1Cp); with the temperature correction, it was in the range 0.17-0.35 psi (0.04-0.09Cp). The significance of the work of Kammeyer et al. (2002a, 2002b) is that it identifies the functional dependency of in-situ PSP calibration uncertainty on the testing parameters such as the angle of attack and Mach number.

Fig. 7.12. Variation of PSP in-situ calibration slope throughout the tests on a Cessna Citation model. From Kammeyer et al. (2002a)

7.3. In-Situ Calibration Uncertainty

159

Fig. 7.13. Histogram of the overall set of PSP errors compared with a Gaussian distribution of the equivalent mean and standard deviation. From Kammeyer et al. (2002a)

Fig. 7.14. Standard uncertainty of PSP on the right wing of a Cessna Citation model as a function of the angle of attack. From Kammeyer et al. (2002a)

7.3.2. Simulation

Inspired by the experimental study of Kammeyer et al. (2002a, 2002b), Liu and Sullivan (2003) studied in-situ calibration uncertainty of PSP through a simulation of PSP measurements in subsonic Joukowsky airfoil flows. It is assumed that insitu calibration uncertainty is mainly attributed to the temperature effect of PSP and illumination change on a surface due to model deformation. The Joukowsky airfoil and subsonic flows around it are generated using the Joukowsky transform plus the Karman-Tsien rule as described in Section 7.2. An adiabatic model is

160

7. Uncertainty

considered that is coated with Bath Ruth + silica-gel in GE RTV 118. Four point light sources for illuminating PSP and two cameras for imaging are placed at the same locations as described in Section 7.2. The twist θ twist and bending T y of the airfoil are a function of the angle of attack (AoA or α ) for a given Mach number and Reynolds number. Based on previous wing deformation measurements (Burner and Liu 2001), the typical linear relations θ twist = −0.113α (deg) and T y = 0.022 α ( in ) are used over a certain range of AoA at a certain spanwise location of a wing. Thus, a change of the illumination radiance on the airfoil surface due to the deformation is estimated using a transformation of rotation and translation for the airfoil moving in the given illumination field. In simulation, the measured luminescent intensity (I) distribution of PSP in the wind-on case (deformation case) is generated by I I ref 0

§ I ref =¨ ¨ I ref 0 ©

·§ · ¸ ¨ A( T ) + B( T ) p ¸ ¸¨ p ref ¸¹ ¹©

−1

§ L = ¨¨ © L0

−1

·§ p ·¸ ¸ ¨ A( T ) + B( T ) , ¸¨ p ref ¸¹ ¹©

where I ref 0 and I ref are the reference luminescent intensities (without wind) on the non-deformed airfoil and deformed airfoil, respectively. It is assumed that I ref 0 and I ref are proportional to the corresponding illumination radiance levels L0 and L on the non-deformed airfoil and deformed airfoil, respectively. The surface temperature T is substituted by the adiabatic wall temperature distribution Taw , and the pressure distribution is given by the Joukowsky transform plus the Karman-Tsien rule for subsonic flows. Therefore, the resulting luminescent intensity distribution contains the effects of both the illumination change and temperature variation on the surface. Assuming that the wind-on image (I) is already re-aligned with the wind-off image I ref 0 on the non-deformed airfoil by the image registration technique, in-

situ PSP calibration is made to correlate I ref 0 / I to p / p ref using the SternVolmer relation based on 104 virtual pressure taps on each of the upper and lower surfaces. For a given AoA and Mach number, the histogram of in-situ calibration error ∆p / p ref = ( p − pin − situ ) / p ref is found to be a near-Gaussian distribution, where ∆p is a difference between the true pressure from the theoretical distribution and the pressure converted from the luminescent intensity using insitu calibration. The standard deviation (std) of the probability density function is dependent on AoA and Mach number. Figures 7.15 and 7.16 show the std of the in-situ calibration error as a function of AoA for Mach 0.4 and as a function of the o Mach number for AoA = 5 , respectively. Figures 7.15 and 7.16 also show the isolated effects of the temperature and illumination change on the std. The behavior of the calculated std as a function of AoA is very similar to the experimental results shown in Fig. 7.14. The concavity of the std as a function of AOA in Fig. 7.15 is mainly attributed to the movement of the airfoil.

7.3. In-Situ Calibration Uncertainty

161

Figure 7.17 shows the simulated histogram for an overall sample set of

∆p / p ref (a total of 10920 samples) over the whole range of AoA and Mach numbers, duplicating the experimental non-Gaussian distribution in Fig. 7.13 given by Kammeyer et al. (2002a, 2002b). The Gaussian distribution with the same std is also plotted in Fig. 7.17 as a reference. In fact, for a union of sample sets having near-Gaussian distributions with different the std values at different AoA and Mach numbers, the distribution becomes non-Gaussian because more and more samples accumulate near zero when forming a union of the sample sets. The probability density function of a union of the N sample sets should be given by a sum of the Gaussian distributions rather than the Gaussian distribution, i.e., N

N −1

¦ exp( − x

2

/ 2σ i2 ) / 2π σ i .

i =1

As shown in Fig. 7.17, this distribution correctly describes the simulated histogram. Note that we should not confuse this case with the central limit theorem that deals with a sum of independent random variables. Although the simulation is made for an airfoil section of a wing, the in-situ calibration error for a wing can be estimated by averaging the local results over the full wingspan; therefore, the behavior of the error for a wing should be similar to that for an airfoil. 0.012 Illumination change only with constant temperature Temperature effect only without illumination change Both temperature effect and illumination change

std[(p - pin-situ)/pref]

0.010

0.008

0.006

0.004

0.002

0.000

Mach = 0.4

-5

0

5

10

15

AoA (deg)

Fig. 7.15. In-situ PSP calibration error as a function of the angle-of-attack (AoA) for Mach 0.4 in Joukowsky airfoil flows. From Liu and Sullivan (2003)

162

7. Uncertainty 0.004 Illumination change only with constant temperature Temperature effect only without illumination change Both temperature effect and illumination change

std[(p - pin-situ)/pref]

0.003

0.002

0.001

0.000 AoA = 5 deg

0.25

0.30

0.35

0.40

0.45

0.50

0.55

0.60

0.65

Mach Number o

Fig. 7.16. In-situ PSP calibration error as a function of the Mach number for AoA = 5 in Joukowsky airfoil flows. From Liu and Sullivan (2003)

900 800

Sample Number

700

Sum of Gaussian Distributions

600 500 400

Gaussian Distribution

300 200 100 0 -0.01 -0.008 -0.006 -0.004 -0.002

0

0.002 0.004 0.006 0.008

0.01

∆p/pref

Fig. 7.17. Histogram of the overall set of in-situ PSP calibration errors in the whole ranges of AoA and Mach numbers in Joukowsky airfoil flows. From Liu and Sullivan (2003)

7.4. Pressure Uncertainty of Lifetime-Based Methods

163

7.4. Pressure Uncertainty of Lifetime-Based Methods

7.4.1. Phase Method

The phase method for PSP measurements, as described in Chapter 6, determines pressure by § · −1 ¨ Ȧ IJ 0 ¸ p = K SV (7.13) ¨ tan ij − 1¸ , © ¹ where tan ij = Ȧ IJ = − Vc / Vs is uniquely related to the lifetime for a fixed modulation frequency, and Vc = − Am IJ H M eff sin (ij ) and Vs = Am IJ H M eff cos (ij ) are the DC components from the low-pass filters. The error propagation equation gives the relative variance of pressure var( K SV ) var( IJ 0 ) var (p) var( T ) = S T2 + S K2 SV + S IJ20 2 2 2 2 p T K SV IJ0 . (7.14) 2 var( V s ) 2 var( Vc ) + S Vs + SVc Vs2 Vc2 The first term is the uncertainty related to temperature, the second is the uncertainty in PSP calibration, the third is the error in the given reference lifetime, and the last two terms are the uncertainties associated with the measurement system composed of a photodetector and lock-in amplifier. The sensitivity coefficients in Eq. (7.14) are T ∂p T ∂K SV 1 + K SV p T ∂τ 0 =− ST = + , p ∂T K SV ∂T K SV p τ 0 ∂T

S K SV =

K SV ∂p = −1 , p ∂K SV

S IJ0 =

IJ0 ∂ p = 1 + 1 /( K SV p ) , p ∂ IJ0

SVs =

Vs ∂ p = 1 + 1 /( K SV p ) , p ∂ Vs

SVc =

Vc ∂ p = − SVs . p ∂ Vc

Compared to the intensity-based method discussed in Chapter 4, many error sources associated with model deformation do not exist, which reflects the advantage of the lifetime-based method. When the photon shot noise of the detector dominates, the pressure uncertainty is mainly contributed by the last two terms in Eq. (7.14). In the photon-shot-noise-limited case, the uncertainties in the outputs of the detector and lock-in amplifier are var(Vs ) = | Vs |G ! Ȟ Bd and

164

7. Uncertainty

var(Vc ) = | Vc | G ! Ȟ Bd , where G is the system gain, Bd is the bandwidth of the system, and ! is the Planck’s constant. Therefore, the photon-shot-noise-limited pressure uncertainty is given by

∆p p

§ GBd !ν · ¸ ¸ © | Vs | ¹

= ¨¨

1/ 2

· § 1 + K SV p · § ¸ ¨1 + 1 ¸ ¨1 + ¨ K SV p ¸¹ ¨© ȦIJ 0 ¸¹ ©

1/ 2

.

(7.15)

The estimate Eq. (7.15) for the phase method is similar to Eq. (7.4) for the intensity-based CCD camera system. The behavior of the pressure uncertainty as a function of pressure and the Stern-Volmer coefficient B is similar to that shown in Figs. 7.4 and 7.5. 7.4.2. Amplitude Demodulation Method

When the amplitude demodulation method is used, as indicated in Chapter 6, pressure is given by · Ȧ IJ0 1 § ¨ p= − 1 ¸¸ , (7.16) 2 2 1/ 2 ¨ K SV © [ H ( Vmean / Vstd ) / 2 − 1 ] ¹ where Vmean and Vstd are the mean and standard deviation of the photodetector output, respectively. Thus, the error propagation equation gives the relative variance of pressure var( K SV ) var( IJ 0 ) var (p) var( T ) = S T2 + S K2 SV + S IJ20 2 2 2 2 p T K SV IJ0 . (7.17) var( Vmean ) var( Vstd ) 2 S + SV2mean + Vstd 2 Vmean Vstd2 The first term is the uncertainty related to temperature, the second is the uncertainty in PSP calibration, the third is the error in the given reference lifetime, and the last two terms are the uncertainties associated with the photodetector. The sensitivity coefficients in Eq. (7.17) are T ∂p T ∂K SV 1 + K SV p T ∂τ 0 =− + , ST = p ∂T K SV ∂T K SV p τ 0 ∂T

S K SV = S IJ0 =

IJ0 ∂ p = 1 + 1 /( K SV p ) , p ∂ IJ0

§ 1 + K SV p ( 1 + K SV p )3 Vmean ∂p = − ¨¨ + p ∂( Vmean ) K SV p( ȦIJ 0 ) 2 © K SV p V ∂p = std = − SVmean . p ∂( Vstd )

SVmean = SVstd

K SV ∂p = −1 , p ∂K SV

· ¸, ¸ ¹

7.4. Pressure Uncertainty of Lifetime-Based Methods

165

In the photon-shot-noise-limited case, the uncertainties in the detector outputs are var(Vmean ) = Vmean G ! Ȟ Bd and var(Vstd ) = Vstd G ! Ȟ Bd . Thus the photon-shotnoise-limited pressure uncertainty is

∆p p

§ GB d !ν · ¸ ¸ © V mean ¹

1/ 2

= ¨¨

ª 1 + K SV p ( 1 + K SV p ) 3 º + » « K SV p( ȦIJ 0 ) 2 ¼» ¬« K SV p

1/ 2 ­ ( ȦIJ 0 ) 2 º ½° 2ª ° × ®1 + » ¾ «1 + H «¬ ( 1 + K SV p ) 2 ¼» ° °¯ ¿

.

1/ 2

(7.18)

Figure 7.18(a) shows the normalized pressure uncertainty 1/ 2 (ǻp/p)( Vmean / G ! Ȟ Bd ) as a function of p/p ref at different values of the SternVolmer coefficient B for Ȧ IJ 0 = 10 and H = 1 . Here, for a fixed temperature

T = Tref ,

we

use

the

following

= ( B / A )( p / p ref ) and A + B = 1 .

relations

K SV p = K SV p ref ( p / p ref )

Figure 7.18(b) shows the normalized

pressure uncertainty (ǻp/p)( Vmean / G ! Ȟ Bd )1 / 2 as a function of B at different values of p/p ref for Ȧ IJ 0 = 10 and H = 1 . Interestingly, in this case, there is an B at which optimal value of the Stern-Volmer coefficient 1/ 2 (ǻp/p)( Vmean / G ! Ȟ Bd ) is minimal. The optimal value of the Stern-Volmer coefficient B varies between 0.7 and 0.9, depending on the value of pressure. 20

50 45

P/Pref= 0.2

10

(∆P/P)(Vmean/GBdhν)1/2

(∆P/P)(Vmean/GBdhν)1/2

40 15

B = 0.5 0.6 0.7 0.8 0.9

5

35

0.5

30 25 20

1.0

15

1.5

10

2.0

5 0

0 0.0

0.5

1.0

1.5

2.0

0.0

P/Pref

(a)

0.2

0.4

0.6

0.8

1.0

B

(b)

Fig. 7.18. The normalized pressure uncertainty (ǻp/p)( Vmean / G ! Ȟ Bd )1 / 2 in the amplitude demodulation method with Ȧ IJ 0 = 10 and H = 1 as a function of p/p ref for different values of the Stern-Volmer coefficient B, and a function of B for different values of p/p ref

166

7. Uncertainty

7.4.3. Gated Intensity Ratio Method

In the gated intensity ratio method for the sinusoidally modulated excitation light, pressure can be expressed as a function of the gated detector output ratio V2 / V1 −1 / 2

· Ȧ IJ 0 § 2 H 1 + V2 / V1 1 ¨ − 1 ¸¸ − . (7.19) p= ¨ K SV © ʌ 1 − V2 / V1 K SV ¹ Therefore, the error propagation equation is var( K SV ) var( IJ 0 ) var( V1 ) var( V2 ) var (p) var( T ) = S T2 + S K2 SV + S IJ20 + SV21 + SV22 2 2 2 p2 T2 K SV V V22 IJ0 1 (7.20) where the sensitivity coefficients are T ∂p T ∂K SV 1 + K SV p T ∂τ 0 , =− + ST = p ∂T K SV ∂T K SV p τ 0 ∂T S K SV =

K SV ∂p = −1 , p ∂K SV

S IJ0 =

IJ0 ∂ p = 1 + 1 /( K SV p ) , p ∂ IJ0

SV1 =

V1 ∂ p { π [1 + Ȧ 2 IJ 02 ( 1 + K SV p )−2 ] − 2 H }( 1 + K SV p )3 , = p ∂V1 2ʌ Ȧ 2 IJ 02 K SV p

V2 ∂ p = − SV1 . p ∂V2 In the photon-shot-noise-limited case, the uncertainties in the detector outputs are var(V1 ) = V1 G ! Ȟ Bd and var(V2 ) = V2 G ! Ȟ Bd . Thus, the photon-shot-noiselimited pressure uncertainty for the gated intensity ratio method is SV2 =

§ GB d !ν = ¨¨ p © V1

∆p

· ¸ ¸ ¹

1/ 2

2π { π [1 + Ȧ 2 IJ 02 ( 1 + K SV p ) − 2 ] − 2 H } 1 / 2 2ʌ Ȧ 2 IJ 02

[1 + Ȧ 2 IJ 02 ( 1 + K SV p ) − 2 ] 1 / 2 ( 1 + K SV p ) 3 × K SV p

.

(7.21)

Figure 7.19(a) shows the normalized pressure uncertainty (ǻp/p)( V1 / G ! Ȟ Bd )1 / 2 as a function of p/p ref at different values of the Stern-Volmer coefficient B for

Ȧ IJ 0 = 10 and H = 1 . Figure 7.19(b) shows the normalized pressure uncertainty

(ǻp/p)( Vmean / G ! Ȟ Bd )1 / 2 as a function of B at different values of p/p ref for Ȧ IJ 0 = 10 and H = 1 . Similar to the amplitude demodulation method, there is an optimal value of B (around 0.8) to achieve the minimal value of (ǻp/p)( Vmean / G ! Ȟ Bd )1 / 2 . In general, to reduce the noise, the gated intensity ratio method has to collect sufficient photons over a large number of cycles. For

7.4. Pressure Uncertainty of Lifetime-Based Methods

167

example, compared to a standard CCD camera system with an integration time of 1 second, a gated CCD camera with a modulation frequency of 50 kHz needs to accumulate photons over 100,000 cycles to achieve the equivalently small uncertainty. The accumulation of photons can be done automatically in a phase sensitive camera. 15

(∆P/P)(V1/GBdhν)1/2

(∆P/P)(V1/GBdhν)1/2

4

3

B = 0.5

2

10

P/Pref= 0.2

0.5 5

0.6

1.0 1.5 2.0

0.7 0.8 0.9

0

1 0.0

0.5

1.0

P/Pref

(a)

1.5

2.0

0.0

0.2

0.4

0.6

0.8

1.0

B

(b)

Fig. 7.19. The normalized pressure uncertainty ( ∆p/p)( V1 / G ! Ȟ Bd )1 / 2 for the gated intensity method using a sinusoid modulation with Ȧ IJ 0 = 10 and H = 1 as a function of

p/p ref for different values of the Stern-Volmer coefficient B, and a function of B for different values of p/p ref

When the gated intensity ratio method is applied to the pulse excitation light, pressure can be expressed as a function of the gated detector output ratio V2 / V1

p=

IJ0 V2 / V1 1 , − ln t g K SV 1 + V2 / V1 K SV

(7.22)

where the time t g divides the two gating intervals [ 0 , t g ] and [ t g , ∞ ] . Thus, we have the pressure uncertainty var( K SV ) var( IJ 0 ) var( V1 ) var( V2 ) var (p) var( T ) = S T2 + S K2 SV + S IJ20 + SV21 + SV22 2 2 2 2 2 p T K SV V1 V22 IJ0 (7.23) where the sensitivity coefficients are ∂τ 0 ∂K SV T ∂p T ª 1 + K SV p § ¨¨ K SV = 2 « −τ0 ST = p ∂T K SV p «¬ τ 0 ∂T ∂T ©

· ∂K SV ¸¸ + ∂T ¹

º », »¼

168

7. Uncertainty

S K SV =

K SV ∂p = −1 , p ∂K SV

S IJ0 =

IJ0 ∂ p = 1 + 1 /( K SV p ) , p ∂ IJ0

SV1 =

τ0 V1 ∂ p =− 1 − exp[ −( 1 + K SV p )( t g / τ 0 )] , p ∂V1 t g K SV p

SV2 =

V2 ∂ p = − SV1 . p ∂V2

{

}

In the photon-shot-noise-limited case, only the terms associated with V1 and

V2 remain in Eq. (7.23) and the uncertainties of the system outputs are var(V1 ) = V1 G ! Ȟ Bd and var(V2 ) = V2 G ! Ȟ Bd . The photon-shot-noise-limited pressure uncertainty for the time-resolved multiple-gate method is

§ GBd !ν = ¨¨ p © V1

∆p

· ¸ ¸ ¹

1/ 2

1

1 − exp[ − ( 1 + K SV p )( t g / τ 0 )]

K SV p ( t g / τ 0 ) exp[ − 0.5( 1 + K SV p )( t g / τ 0 )]

. (7.24)

The factor V1 / G ! Ȟ Bd equals to the number of photoelectrons collected in the first gating interval [ 0 , t g ] .

Figure 7.20(a) shows the normalized pressure

uncertainty (ǻp/p)( V1 / G ! Ȟ Bd )1 / 2 as a function of p/p ref at different values of the Stern-Volmer coefficient B for a fixed gating time t g /IJ 0 = 0.2 , where the relations K SV p = ( B / A )( p / p ref ) and A + B = 1 are imposed. Figure 7.20(b) shows the normalized pressure uncertainty (ǻp/p)( Vmean / G ! Ȟ Bd )1 / 2 as a function of B at different values of p/p ref for t g /IJ 0 = 0.2 . The optimal value of the Stern-Volmer coefficient B is about 0.8-0.9. For t g /IJ 0 < 0.5 , the pressure uncertainty ǻp/p remains small, but ǻp/p rapidly increases as t g /IJ 0 approaches one.

7.5. Uncertainty of Temperature Sensitive Paint

169

15

4

(∆P/P)(V1/GBdhν)1/2

(∆P/P)(V1/GBdhν)

1/2

P/Pref= 0.2

3 B = 0.5

0.6

2 0.7

10 0.5

1.0

5

1.5 2.0

0.8 0.9

1

0 0.0

0.5

1.0

1.5

2.0

0.0

0.2

0.4

P/Pref

0.6

0.8

1.0

B

(b)

(a)

Fig. 7.20. The normalized pressure uncertainty ( ∆p/p)( V1 / G ! Ȟ Bd )1 / 2 for the gated intensity method with a pulse excitation and t g /IJ 0 = 0.2 as (a) a function of p/p ref for different values of the Stern-Volmer coefficient B, and (b) a function of B for different values of p/p ref

7.5. Uncertainty of Temperature Sensitive Paint

7.5.1. Error Propagation and Limiting Temperature Resolution

In principle, the above uncertainty analysis for PSP can be adapted for TSP since many error sources of TSP are the same as those of PSP. For simplicity, instead of the general Arrhenius relation, we use an empirical relation between the luminescent intensity (or the photodetector output) and temperature T for a TSP uncertainty analysis (Cattafesta and Moore 1995; Cattafesta et al. 1998) T − Tref = K T ln( I ref / I ) = K T ln( U 2 V ref / V ) ,

(7.25)

where K T is a TSP calibration constant with a temperature unit and U 2 is the factor defined previously in Eq. (7.2) for the PSP uncertainty analysis. Without model deformation and temporal illumination variation, the factor U 2 equals to one. Eq. (7.25) can be used to fit TSP calibration data over a certain range of temperature. The error propagation equation for TSP is M var( ȗ i ) var( K T ) K T2 var (T) = + , (7.26) 2 2 (T − Tref ) (T − Tref ) i = 1 ȗ i2 K K2

¦

170

7. Uncertainty

where the variables {ȗ i , i = 1 M} denote a set of the parameters Dt (ǻt ) ,

D x (ǻx ) , Dq0 (ǻt ) , V , Vref , Ȇ c /Ȇ c ref , Ȇ f /Ȇ f ref , h / href , c / c ref , and q0 /q0 ref as defined in Section 7.1. The summation term in the right-hand side of Eq. (7.26) include the errors associated with model deformation, unstable illumination, photodegradation, filter leakage, and luminescent intensity measurements. The last term in Eq. (7.26) is the TSP calibration error. Similar to the uncertainty analysis for PSP, in the photon-shot-noise-limited case without any model deformation, we are able to obtain the minimum temperature difference that TSP can measure from a single frame of image ª § T − Tref ( ǻT)min = «1 + exp¨¨ (n pe ref )max «¬ © KT )max is the full-well capacity of a CCD KT

where (n pe ref

1/2

·º ¸» , (7.27) ¸» ¹¼ camera in the reference

conditions. The minimum resolvable temperature difference ( ǻT)min is inversely proportional to the square-root of the number of collected photoelectrons, and approximately proportional to the calibration constant K T . When (n pe ref )max is o

500,000 electrons, for a typical Ruthenium-based TSP having K T = 37.7 C, the minimum resolvable temperature difference ( ǻT)min is shown in Fig. 7.21 as a o

function of T at a reference temperature Tref = 20 C. When N images are averaged, the limiting temperature resolution given by Eq. (5.27) should be 1/2 divided by a factor N . 7.5.2. Elemental Error Sources

The elemental error sources of TSP have been discussed by Cattafesta et al. (1998) and Liu et al. (1995c). Table 7.2 lists the elemental error sources, sensitivity coefficients, and total uncertainty of TSP. The sensitivity coefficients for many variables are related to ij = KT /(T − Tref ) . The elemental errors in the variables Dt (ǻt ) , D x (ǻx ) , Dq0 (ǻt ) , V , Vref , Ȇ c /Ȇ c ref , Ȇ f /Ȇ f ref , h / href ,

c / c ref , and q0 /q0 ref can be estimated using the same expressions given in the uncertainty analysis for PSP, which represent the error sources associated with model deformation, unstable illumination, photodegradation, filter leakage, and luminescence measurements. The camera calibration error and temperature mapping error can be also estimated using the similar expressions to those for PSP, i.e., var(T) ≈ (∂T/∂ x ) ı x2 + (∂T /∂ y ) ı 2y and var(T ) = ( ∇T )surf • ( ǻX )surf , 2

2

2

where ı x and ı y are the standard deviations of least-squares estimation in image registration or camera calibration. In order to estimate the TSP calibration errors, the temperature dependency of TSP was repeatedly measured using a calibration set-up over days for several TSP formulations (Liu et al. 1995c). Temperature measured by TSP was compared to accurate temperature values measured by a

7.5. Uncertainty of Temperature Sensitive Paint

171

Minimum Temperature Difference (deg. C)

standard thermometer. Figure 7.22 shows histograms of the temperature calibration error for EuTTA-dope and Ru(bpy)-Shellac TSPs, which exhibit a near-Gaussian distribution. The standard deviation for EuTTA-dope TSP is about o o 0.8 C over a temperature range of 15-70 C. For Ru(bpy)-Shellac TSP, the o histogram has a broader error distribution having the deviation of about 2 C over a o temperature range of 20-100 C. The temperature hysteresis introduces an additional error source for TSP, which was reported in calibration experiments for a Rhodamine(B)-based coating (Romano et al. 1989). The temperature hysteresis is related to the polymer structural transformation from a hard and relatively brittle state to a soft and rubbery one when temperature exceeds the glass temperature of a polymer. Since the thermal quenching of luminescence in a brittle condition is different from that in a rubbery state, the temperature dependency is changed after it is heated beyond the glass temperature. To reduce the temperature hysteresis, TSP should be preheated to a certain temperature above the glass temperature before it is used as an optical temperature sensor for quantitative measurements. It was found that for both pre-heated EuTTA-dope and Ru(bpy)-Shellac paints the temperature hysteresis was minimized such that the temperature dependency remained almost unchanged in repeated tests over several days (Liu et al. 1995c).

0.18 0.16 0.14 0.12 0.10 0.08 0.06 0.04 -20

0

20

40

60

80

100

Temperature (deg. C)

Fig. 7.21. The minimum resolvable temperature difference as a function of temperature for o o a Ruthenium-based TSP for (n pe ref )max = 500,000e, K T = 37.7 C , and Tref = 20 C

172

7. Uncertainty 0.4

1.0 EuTTA - dope paint

Ru(bpy) - Shellac paint 0

Gaussian with σ = 0.8 C

0.3 Frequency

Frequency

0.8

0.6

0.4

Gaussian with σ = 2 0C

0.2

0.1

0.2 0.0

0.0 -4

-3

-2 -1 0 1 2 3 Temperature error (deg. C)

(a)

4

-10 -8 -6 -4 -2 0 2 4 6 Temperature Error (deg. C)

8 10

(b)

Fig. 7.22. Temperature calibration error distributions for (a) EuTTA-dope TSP and (b) Ru(bpy)-Shellac TSP, where σ is the standard deviation. From Liu et al. (1997b)

7.5. Uncertainty of Temperature Sensitive Paint

173

Table 7.2. Sensitivity coefficients, elemental errors, and total uncertainty of TSP Variable

Sensi. Coef.

ζi

Si

Elemental Variance

Physical Origin

var( ȗ i )

1

D t (ǻt )

ij

[( ∂V / ∂ t )( ǻt)/V ] 2

2

D x (ǻx )

ij

[ (∂V/∂x ) ı x2 + (∂V /∂ y ) ı 2y ] V − 2

3

D q0 (ǻt )

ij

[( ∂ q 0 / ∂ t )( ǻt)/q 0 ref ] 2

4

ij

V ref G ! Ȟ B d

Photodetector noise

5 6

Vref V Ȇ c /Ȇ c ref

-ij ij

V G !Ȟ Bd

Photodetector noise

[ R 2 /(R 1 + R 2 )] 2 (ǻR1 /R1 ) 2

7

Ȇ f /Ȇ f ref

ij

var(Ȇ f /Ȇ f ref )

8

h / href

ij

−2 [ (∂ h /∂ x ) ı x2 + (∂ h /∂ y ) ı 2y ] href

9

c / c ref

ij

−2 [ (∂ c /∂ x ) ı x2 + (∂ c /∂ y ) ı 2y ] c ref

10

q0 /q0 ref

ij

( q0 ref )−2 ( ∇q0 ) • ( ǻX )

11

KT

1

var( K T )

Change in camera performance parameters due to model motion Illumination spectral variability and filter spectral leakage Image registration errors for correcting thickness variation due to model motion Image registration errors for correcting concentration variation due to model motion Illumination variation on model surface due to model motion Paint calibration error

12

Temperature mapping

1

2

2

2

2

2

2

2

(∂T/∂x )2 ı x2 + (∂T /∂y )2 ı 2y and ( ∇T )surf • ( ǻX )surf

2

Temporal variation in luminescence due to photodegradation and surface contamination Image registration errors for correcting luminescence variation due to model motion Temporal variation in illumination

Errors in camera calibration and temperature mapping on a surface of a presumed rigid body M

Total Uncertainty in Temperature

var (T)/ (T - Tref ) 2 =

¦S

2 i

var( ȗ i )/ ȗ i

2

i =1

Note: (1) ı x and ı y are the standard deviations of least-squares estimation in the image registration or camera calibration. (2) The factor for the sensitivity coefficient is defined as ij = KT /(T − Tref ) .

8. Time Response

8.1. Time Response of Conventional Pressure Sensitive Paint

8.1.1. Solutions of Diffusion Equation The fast time response of PSP is required for measurements in unsteady flows, which is related to two characteristic timescales of PSP. One is the luminescent lifetime of PSP that represents an intrinsic physical limit for an achievable temporal resolution of PSP. Another is the timescale of oxygen diffusion across a PSP layer. Because the timescale of oxygen diffusion across a homogenous polymer layer is usually much larger than the luminescent lifetime, the time response of PSP is mainly determined by oxygen diffusion. In a thin homogenous polymer layer, when diffusion is Fickian, the oxygen concentration [O2] can be described by the one-dimension diffusion equation ∂ [O2 ] ∂ 2 [ O2 ] , (8.1) = Dm ∂t ∂z2 where Dm is the diffusivity of oxygen mass transfer, t is time, and z is the coordinate directing from the wall to the polymer layer. The boundary conditions at the solid wall and the air-paint interface for Eq. (8.1) are ∂ [O2 ] / ∂ z = 0 at z = 0 ,

[O2 ] = [O2 ]0 f ( t ) at z = h ,

(8.2)

where the non-dimensional function f ( t ) describes a temporal change of the oxygen concentration at the air-paint interface, [O2 ]0 is a constant concentration of oxygen, and h is the paint layer thickness. The initial condition for Eq. (8.1) is [O2 ] = [O2 ]0 f ( 0 ) at t = 0 . (8.3) Introducing the non-dimensional variables n(t' , z' ) = [O2 ] / [O2 ]0 − f ( 0 ) , z' = z / h , t' = tDm / h 2 , (8.4) we have the non-dimensional diffusion equation

176

8. Time Response

∂n ∂ 2 n = ∂ t' ∂ z' 2

,

(8.5)

with the boundary and initial conditions ∂n / ∂ z' = 0 at z = 0 , n = g( t' ) at z' = 1 , n = 0 at t = 0 ,

(8.6)

where the function g( t' ) is defined as g ( t' ) = f ( t' ) − f ( 0 ) that satisfies the initial condition g ( 0 ) = 0 . Applying the Laplace transform to Eq. (8.5) and the boundary and initial conditions Eq. (8.6), we obtain a general convolution-type solution for the normalized oxygen concentration n(t' , z' )

n( t' , z' ) =

³

t'

g t ( t' −u ) W ( u , z' ) du .

0

(8.7)

In Eq. (8.7), the function g t ( t ) = d g( t ) / dt = df ( t ) / dt is the differentiation of

g(t) with respect to t and the function W ( t , z ) is defined as W( t,z ) =

∞

¦

( −1 )k erfc(

1 + 2k − z 2 t

k =0

)+

∞

¦ ( −1 ) erfc( k

1 + 2k + z 2 t

k =0

).

(8.8)

The derivation of Eq. (8.7) uses the following expansion in negative exponentials

[ 1 + exp( −2 s )] −1 =

∞

¦ ( −1 )

n

exp( −2n s ) , where s is the complex variable of

n =0

the Laplace transform. In particular, for a step change of the oxygen concentration at the air-paint interface, after g t ( t ) = δ ( t ) is substituted into Eq. (8.7), the oxygen concentration distribution in a paint layer is simply n( t' , z' ) = W ( t' , z' ) , a classical solution given by Crank (1995) and Carslaw and Jaeger (2000). Instead of using the Laplace transform, Winslow et al. (2001) studied the solution of the diffusion equation using an approach of linear system dynamics. The special solutions for a step change and a sinusoidal change of oxygen were used for PSP dynamical analysis by a number of researchers (Winslow et al. 1996, 2001; Carroll et al. 1995, 1996; Mosharov et al. 1997; Fonov et al. 1998). The trigonometrical-series-type solution for a step change of oxygen given by Carroll et al. (1996) is

[O2 ]( t , z ) − [O2 ] min = 1− [O2 ] max − [O2 ] min

∞

¦ [ A cos( λ z ) exp( −λ D k

k

2 k

m

t )] ,

(8.9)

k =1

where Ak = −2( −1 )k /( hλk ) , λk = ( 2k − 1 )π /( 2h ) , [O2 ] max = [O2 ]( t , h ) , and

[O2 ] min = [O2 ]( 0 , z ) . Similarly, Winslow et al. (1996) used the trigonometricalseries-type solution for a sinusoidal change of oxygen

8.1. Time Response of Conventional Pressure Sensitive Paint

177

[O 2 ]( t , z ) − [O 2 ] 0 = [O2 ] 1

4

∞

π ¦ k =1

( 2k − 1 )π z ( −1 ) k − 1 cos[ ] sin( ω t − β k ) cos( β k ) ( 2k − 1 ) 2h

(8.10)

where

β k = tan −1 [

4 h 2ω ]. π 2 ( 2 k − 1 ) 2 Dm

The constants [O2 ]0 and [O2 ]1 are given in the initial and boundary conditions

[O2 ]( 0 , z ) = [O2 ]0 and [O2 ]( t , h ) = [O2 ]0 + [O2 ]1 sin( ω t ) . Mosharov et al. (1997) also presented the trigonometrical-series-type solution of the diffusion equation in a similar form to Eq. (8.9) for a step change at a surface. Note that they defined a coordinate system in such a way that the airpaint interface was at z = 0 and the wall was at z = h . For a sinusoidal change of oxygen [O2 ]( t ,0 ) = [O2 ]0 + [O2 ]1 sin( ω t ) at the air-paint interface, they gave a solution composed of two harmonic terms, i.e., [O2 ]( t , z ) = [O2 ]0 + [O2 ]1 [ X ( γ , z' ) sin( ω t ) + Y ( γ , z' ) cos( ω t )] ,

(8.11)

where γ = ( ω h 2 / Dm )1 / 2 is a non-dimensional frequency and z' = z / h is a nondimensional coordinate normal to the wall. The coefficients in Eq. (8.11) are X ( γ , z' ) = cosh[ 2 γ ( 1 − z' / 2 )] cos( γ z' /

2 ) + cos[ 2 γ ( 1 − z' / 2 )] cosh( γ z' /

2)

cosh( 2 γ ) + cos( 2 γ )

Y ( γ , z' ) = sinh[ 2 γ ( 1 − z' / 2 )] sin( γ z' / 2 ) + sin[ 2 γ ( 1 − z' / 2 )] sinh( γ z' / 2 )

.

cosh( 2 γ ) + cos( 2 γ ) (8.12) These trigonometrical-series-type solutions, which are often obtained using the method of separation of variables, should be equivalent to the general convolution-type solution Eq. (8.7) that is reduced in these special cases. The solutions of the diffusion equation give a classical square-law estimate for the diffusion timescale τdiff through a homogenous PSP layer,

τ diff ∝ h 2 / Dm .

(8.13)

The square-law estimate is actually a phenomenological manifestation of the statistical theory of the Brownian motion. Interestingly, this estimate is still valid even when the diffusivity of a homogeneous polymer is concentration-dependent. The 1D diffusion equation with the concentration-dependent diffusivity can be

178

8. Time Response

reduced to an ordinary differential equation by using the Boltzmann’s transformation ξ = z /( 2t 1 / 2 ) ; hence, the solution for the concentration distribution can be expressed by this similarity variable (Crank 1995). Clearly, the Boltzmann’s scaling indicates that the timescale for any point to reach a given concentration is proportional to the square of the distance (or thickness). Using the solution of the diffusion equation for a step change of pressure, Carroll et al. (1997) estimated the mass diffusivity Dm for oxygen in a typical silicon polymer binder and gave D m = 1.23 − 1.88 × 10 −9 m 2 /s over a temperature

range of 9.9-40.2 C. The values of D m = 3.55 × 10 −9 m 2 /s for the pure polymer o

Poly(dimethyl Siloxane) (PDMS) and D m = 1.2 × 10 −9 m 2 /s for PDMS with 10% fillers were also reported (Cox and Dunn 1986; Pualy 1989). For a 10 µm thick polymer layer having the diffusivity D m = 10 −10 − 10 −9 m 2 /s , the diffusion timescale is in the order of 0.1-1 s. Therefore, a conventional non-porous polymer PSP has slow time response, and it is not suitable to unsteady pressure measurements. 8.1.2. Pressure Response and Optimum Thickness

Schairer (2002) studied the pressure response of PSP based on the solution Eq. (8.11) of the diffusion equation given by Mosharov et al. (1997). In a simpler notation, the luminescent intensity integrated over a paint layer is expressed as

I(t) = C

³

h 0

exp( − β z ) dz , a + k [ O 2 ]( t , z )

(8.14)

where β is the extinction coefficient for the excitation light, C is a proportional constant, and a and k are the coefficients. In the quasi-steady case, the indicated pressure by PSP is p PSP ( t ) = [ I ref / I ( t ) − A ] / B , (8.15) where the Stern-Volmer coefficients are determined from steady-state calibration of PSP. As shown in Eq. (8.15) coupled with Eqs. (8.11), (8.12) and (8.14), the indicated pressure p PSP ( t ) is a non-linear function of the true pressure that sinusoidally varies with time, p( t ) = p0 + p1 sin( ω t ) , although the diffusion equation is linear. However, if the amplitude of the unsteady pressure is small compared to the mean pressure ( p1 << p0 ), the PSP response can be linearized and it is given by p PSP ( t ) = p0 PSP + p1PSP sin( ω t + φ ) , (8.16) = p0 + p1 [ α ( γ ) sin( ω t ) + β ( γ ) cos( ω t )] where

8.1. Time Response of Conventional Pressure Sensitive Paint

α( γ ) = β(γ ) =

δ ln( 10 ) 1 − 10

−δ

δ ln( 10 ) 1 − 10

−δ

³ ³

1 0 1 0

179

10 −δ η X ( γ ,η )dη 10 −δ η Y ( γ ,η )dη .

(8.17)

The quantity δ = β h /ln(10) represents the optical thickness of the paint layer. The unsteady amplitude ratio and phase shift are given by

p1PSP / p1 = α 2 + β 2

φ = tan −1 ( β / α ) .

(8.18)

Figure 8.1 shows the attenuated amplitude ratio p1 PSP / p1 at different frequencies for δ / h = 0.01 µm −1 and D m = 10 3 µm 2 /s . The paint thickness affects both the frequency response and the signal-to-noise ratio (SNR) of PSP. As the thickness increases, the luminescent signal from PSP and thus the SNR increase, whereas the frequency response of PSP decreases as a result of the attenuation of the unsteady amplitude ratio. Hence, there exists an optimum thickness that balances the two conflicting requirements to achieve both high frequency response and SNR. Considering the unsteady luminescent signal I ( t ) = I 0 + I 1 sin( ω t ) , Schairer (2002) introduced the unsteady signal amplitude

I 1 = I 0 α 2 + β 2 and then the unsteady SNR, SNR' = I 1 / I 0 = I 0 α 2 + β 2 . Figure 8.2 shows the normalized SNR' as a function of the relative thickness h / h(-1.25dB) , where h(-1.25dB) is the thickness that corresponds to 1.25dB ( p1 PSP / p1 = 0.866 ) attenuation of the unsteady amplitude ratio as illustrated in Fig. 8.1. Thus, an empirical estimate for the optimum thickness is hop / h(-1.25dB) ≈ 1 that corresponds to the maximum value of the normalized

SNR' . As shown in Fig. 8.3, the optimum thickness hop ≈ h(-1.25dB) decreases with the unsteady pressure frequency for a given diffusivity and relative optical thickness. Figure 8.3 indicates that the optimum thickness is less than 5 µm for D m < 16 × 10 3 µm 2 /s when the pressure frequency is 100 Hz. For such a thin paint layer, the absolute SNR ( ∝ I 0 ) is so low that accurate measurement of the luminescent emission becomes difficult. This indicates that a conventional polymer-based PSP is not suitable to unsteady measurements. When an unsteady pressure variation is no longer small, the non-linear effect of PSP response is appreciable, and the waveform of the PSP signal is distorted. In this case, recovery of the true unsteady pressure from the distorted signal is nontrivial. Assuming that the oxygen concentration is uniform across a thin paint layer, we substitute p PSP ( t ) ≡ p = [ O2 ] S −1φ O−21 into Eq. (8.15) and use the general solution Eq. (8.7) for [ O2 ] , where S is the oxygen solubility of the binder and φ O2 is the mole fraction of oxygen in air. Thus, at the air-paint

180

8. Time Response

interface ( z' = z / h = 1 ), we obtain a Voltera-type integral equation for the function g t ( t ) = d g( t ) / dt = df ( t ) / dt

º 1 ª I ref − A» − f ( 0 ) = « B p 0 ¬« I ( t ) ¼»

³

t' 0

g t ( t' −u )W ( u ,1 ) du ,

(8.19)

where p0 = [ O2 ] 0 S −1φ O−21 is the initial pressure amplitude. In principle, after Eq. (8.19) is solved for

f ( t ) , the unsteady pressure can be recovered, i.e.,

p( t ) = p0 f ( t ) . However, since the non-dimensional time variable t' = tDm / h 2 in Eq. (8.19) contains the diffusion timescale τ diff = h 2 / D m , recovery of the true unsteady pressure is affected by the local paint thickness unlike steady-state PSP measurements where the effect of the thickness is, at least theoretically speaking, eliminated by the intensity ratio procedure.

Fig. 8.1. The unsteady amplitude ratio as a function of the paint thickness for δ / h = 0.01 µm −1 and D m = 10 3 µm 2 /s . From Schairer (2002)

8.1. Time Response of Conventional Pressure Sensitive Paint

181

Fig. 8.2. The normalized SNR’ as a function of the relative paint thickness for δ / h = 0.01 µm −1 and D m = 10 3 µm 2 / s . From Schairer (2002)

Fig. 8.3. The optimum thickness as a function of the unsteady pressure frequency for δ / h = 0.01 µm −1 . From Schairer (2002)

182

8. Time Response

8.2. Time Response of Porous Pressure Sensitive Paint

8.2.1. Deviation from the Square-Law

Compared to a conventional homogeneous PSP, a porous PSP has a much shorter diffusion time ranging from 18 µs to 500 µs due to enlarged air-polymer interface (Sakaue and Sullivan 2001; Sakaue et al. 2002a). Interestingly, recent measurements of the response time for three polymers, GP197, GP197/BaSO4 mixture and Poly(TMSP), show that the classical square-law estimate Eq. (8.13) does not hold for a porous PSP (Teduka 2001; Asai et al. 2001). As shown in Fig. 8.4, measurements gave the power-law relations for the diffusion timescale τ diff ∝ h 1.83 for GP197, τ diff ∝ h 1.07 for GP197/BaSO4 mixture, and τ diff ∝ h 0.29 for Poly(TMSP) at 313.1 K. For a porous anodized aluminum (AA) surface, the power-law relation is τ diff ∝ h 0.573 (Sakaue 1999; Sakaue and Sullivan 2001). For the GP197 silicone polymer, the power-law exponent is close to 2 as predicted by the classical estimate for a homogenous polymer film. However, the power-law exponent for the porous materials GP197/BaSO4 mixture, Poly(TMSP), and AAPSP is significantly smaller than 2. In addition, Figure 8.5 shows that the powerlaw exponent for the polymer Poly(TMSP) linearly increases with temperature over a temperature range of 293.1-323.1 K. In order to understand the time response of a porous PSP, from a standpoint of phenomenology, Liu et al. (2001b) derived the expressions for the effective diffusivity and diffusion timescale of a porous layer.

τ diff ∝ h 1.83

Time constant, msec

1000 100

GP197

τ diff ∝ h 1.07

GP197/BaSO4

10

τ diff ∝ h 0.29

poly(TMSP)

1

τ diff ∝ h 0.573

0.1

AA-PSP

0.01 1

10

Thickness, micron

Fig. 8.4. The power-law relationship between the response time and coating thickness for three polymers GP197, GP197/BaSO4 mixture and Poly(TMSP) at 313.1 K, and AA surface at about 300K. Experimental data are from Teduka (2001), Asai et al. (2001), and Sakaue (1999)

8.2. Time Response of Porous Pressure Sensitive Paint

183

0.5

Power-law exponent

0.4

0.3

0.2

0.1

0.0 290

295

300

305

310

315

320

325

Temperature, K

Fig. 8.5. The exponent of the power-law relation between time-scale and coating thickness for the polymer Poly(TMSP) as a function of temperature. Experimental data are from Teduka (2001) and Asai et al. (2001)

8.2.2. Effective Diffusivity

Diffusion in a porous material can be considered as a diffusion problem in a twophase system made up of one disperse phase and one continuous polymer or other material. In PSP, the disperse phase is composed of numerous pores filled with air. Figure 8.6 shows a typical scanning electron microscopic (SEM) image of an anodized aluminum (AA) surface for PSP. Consider an element of a porous polymer layer of the length l, width l, and thickness h, as shown in Fig. 8.7. The coordinate z is normally directed to the polymer layer from the upper surface of the layer. First, we assume that many cylindrical (tube-like) pores are distributed and oriented in the z-direction in the element. The effective radius and depth of a pore are denoted by rpore and h pore , respectively. The radius of a pore is much larger than the size of a molecule of oxygen. In general, the depth of a pore is smaller than or equal to the layer thickness, i.e., h pore ≤ h . For simplicity of expression, the normal directional derivative of the oxygen concentration [O2 ] at the air-polymer interface is denoted by ∂ [O2 ] . (8.20) v n (z) = ∂n

184

8. Time Response 20nm ~ 100nm micropore

100 nm (a): SEM picture.

(b): Schematic.

Fig. 8.6. SEM image and schematic of an anodized aluminum (AA) surface. From Sakaue (1999) pore

l

l

h pore

O

h

z 2rpore

Fig. 8.7. Element of a porous binder layer

The effective diffusivity Dmeff of the porous polymer layer with many cylindrical pores is given by a balance equation between the mass transfer through the apparent homogenous upper surface and the total mass transfer across the airpolymer interface, i.e., 2 2 Dmeff l 2 v n ( 0 ) = Dm ( l 2 − N poreπ r pore )v n ( 0 ) + Dm N poreπ r pore v n ( h pore )

+ Dm N pore 2π rpore

³

h pore 0

,

v n ( z )dz

(8.21)

where N pore is the total number of the pores in the element and Dm is the diffusivity of the polymer continuum. The integral term in Eq. (8.21) is the total mass transfer across the peripheral surface of the pores in the element. Thus, the effective diffusivity Dmeff is given by 2 Dmeff / Dm = 1 + [ v n ( h pore ) / v n ( 0 ) − 1 ] N pore π r pore l −2

+ N pore 2π r pore l −2 v n−1 ( 0 )

³

h pore 0

v n ( z )dz

.

(8.22)

8.2. Time Response of Porous Pressure Sensitive Paint

185

In a simplified case where v n (z) = const . across the thin layer, Eq. (8.22) becomes −1 D meff / D m = 1 + 2 aV r pore h,

(8.23)

2 h pore l −2 h −1 is the volume fraction of the cylindrical pores where aV = N pore π r pore in the polymer layer. Eq. (8.23) indicates that an increase of the effective diffusivity is proportional to the volume fraction of the pores and a ratio between the polymer layer thickness and the radius of the pore. Eq. (8.23) for Dmeff is valid only for an ideal porous polymer layer with the straight cylindrical pores oriented normally. Nevertheless, this model can be generalized for real porous polymers where topology of the pores is often highly complicated. For more realistic modeling, the topological structure of a pore is considered as a highly convoluted and folded tube in a polymer layer while the cross-section of the tube remains unchanged. The integral in Eq. (8.22) should be replaced by an integral along the path of a highly convoluted tube-like pore. In this case, the concept of the fractal dimension should be introduced because the length of a highly convoluted tube is no longer proportional to the linear length scale of the tube in the z-direction (e.g. h pore ) (Mandelbrot 1982). According to the lengthd

/2

fr area relation for a fractal path, the integral along the path is proportional to A pore

fr or h pore , where d fr ( 1 ≤ d fr < 2 ) is the fractal dimension of the path of a pore

d

2 and A pore ∝ h pore is the characteristic area covering over the path. speaking, the fractal dimension represents the degree of complexity of pathway. In order to take the fractal nature of pores into account, Eq. generalized using a Riemann-Liouville fractional integral of the order (Nishimoto 1991)

Loosely the pore (8.22) is d fr , i.e.,

2 Dmeff / Dm = 1 + [ v n ( h pore ) / v n ( 0 ) − 1 ] N pore π rpore l −2

+ N pore 2π rpore l −2 v n−1 ( 0 )

³

h pore 0

v n ( z )( dz )

d fr

.

(8.24)

1− d

Note that a unitary constant with the dimension [ m fr ] is implicitly embedded in the third term in the right-hand side of Eq. (8.24) to make Eq. (8.24) dimensionally consistent. This dimensional constant is implicitly contained in all the results derived from Eq. (8.24). In a simplified case where v n (z) = const . across a thin layer, a generalized expression for Dmeff is

D meff Dm

= 1+

−1 2 aV r pore § h pore ¨ Γ ( 1 + d fr ) ¨© h

· ¸ ¸ ¹

d fr − 1

h

d fr

,

(8.25)

where Γ ( 1 + d fr ) is the gamma function. Here, h pore is interpreted as a linear length scale of a convoluted tube in the z-direction and aV is the volume fraction

186

8. Time Response

of the apparent cylindrical pores. Eq. (8.25) clearly shows that the effective d diffusivity Dmeff is not only proportional to h fr , but also related to the porosity −1 parameters aV r pore and h pore / h . For d fr = 1 , Eq. (8.25) is simply reduced to Eq. (8.23) for the straight cylindrical pores.

8.2.3. Diffusion Timescale

For a porous polymer layer where diffusion is Fickian under some microscopic assumptions (Cunningham and Williams 1980; Neogi 1996), the diffusion equation Eq. (8.1) is still a valid phenomenological model as long as the diffusivity Dm is replaced by the effective diffusivity Dmeff . Hence, an estimate for the diffusion timescale of a porous PSP layer is h 2 / Dm τ diff ∝ . (8.26) d fr −1 −1 2 aV rpore § h pore · d fr ¨ ¸ 1+ h Γ ( 1 + d fr ) ¨© h ¸¹ Eq. (8.26) as a generalized form of Eq. (8.13) clearly illustrates how the fractal −1 dimension d fr and the porosity parameters aV r pore and h pore / h affect the −1 response time of a porous PSP. For aV rpore << 1 or h pore / h << 1 , Eq. (8.26) naturally approaches to the classical square-law estimate Eq. (8.13) for a homogenous polymer layer. −1 >> 1 and h pore / h ≈ 1 , another asymptotic On the other hand, for aV rpore

estimate for τ diff is a simple power-law as well

τ diff ∝ h 2 −d fr / Dm .

(8.27)

The estimate Eq. (8.27) is asymptotically valid for a very porous polymer layer. The exponent in the power-law relation between the response time τ diff and thickness h deviates from 2 by the fractal dimension d fr due to the presence of the fractal pores in the polymer layer. The relation Eq. (8.27) provides an explanation for the experimental finding that the exponent q in the power-law relation τ diff ∝ h q is less than 2 for a porous PSP. In addition, this relation can serve as a useful tool to extract the fractal dimension of the tube-like pores in a very porous polymer layer from measurements of the diffusion response time. For example, the fractal dimension d fr of a pore in the polymer Poly(TMSP) is

d fr = 1.71 , while for GP197/BaSO4 mixture the fractal dimension d fr is close to one. In addition, based on the experimental results shown in Fig. 8.5, we know that the fractal dimension d fr for Poly(TMSP) linearly decreases with temperature in a temperature range of 293.1-323.1 K. This implies that the geometric structure of a pore in Poly(TMSP) may be altered by a temperature

8.3. Measurements of Pressure Time Response

187

change. Note that the diffusivity Dm of oxygen mass transfer is also temperaturedependent, but it is independent of the coating thickness h. Therefore, the experimental results in Fig. 8.5 mainly reflect the temperature effect on the geometric structure of pores in the polymer rather than the diffusivity. Table 8.1. Response times and luminescent lifetimes of PSPs Paint

Thickness (µm)

Lifetime (µs)

Response time

Comments

References

LPSF1 (pyrene) PSPL2 (pyrene) PSPL4 (pyrene) PSPF2 (pyrene) PF2B (Ru(dpp))

2 20 5

5 ms 0.2 s 0.172 s 0.1-2.6 ms 0.48 s

Borovoy et al. (1995) Fonov et al. (1998) Fonov et al. (1998) Fonov et al. (1998) Carroll et al. (1996b)

5 5 5 50

0.88 s 1.2 s 2.4 s 0.82 s

OPTROD formulation OPTROD formulation OPTROD formultation OPTROD formulation McDonnell Douglas (MD) formulation MD formulation MD formulation MD formulation concentrated luminophore near outer surface of the binder

13

PF2B (Ru(dpp)) PF2B (Ru(dpp)) PF2B (Ru(dpp)) PtOEP/polymer

15 25 35 19

PtOEP/GP197 PtOEP/GP197 PtOEP/GP197 Ru(dpp)/RTV Ru(dpp)/RTV Ru(dpp)/RTV Ru(dpp)/RTV Ru(dpp)/PDMS PtOEP/GP197 PtOEP/copolymer H2TFPP/silica H2TFPP/TLC luminophore/AA

22 26 32 6 11 16 20 4-5 -

50 50 50 5 5 5 5 5 50 50

1.4 s 1.6 s 2.4 s 22.4 ms 58.6 ms 148 ms 384 ms 3-6 ms 2.5 s 0.4 s 1.5-10 ms 25 µs 18-90 µs

Ru(dpp)/FIB and alumina PtTFPP/FIB and alumina PtTFPP/porous ceramic Ru(dpp)/AA Ru(dpp)/TLC

-

5

<500 µs

-

50

<500 µs

-

50

60 µs

Ponomarev & Gouterman (1998) Ponomarev & Gouterman (1998) Scroggin (1999)

-

5 5

80 µs 70 µs

Sakaue et al. (2001) Sakaue et al. (2001)

silica with a binder depended on the luminophore and anodization processes approached the apparatus response time approached the apparatus response time

Carroll et al. (1996b) Carroll et al. (1996b) Carroll et al. (1996b) Carroll et al. (1996b) Carroll et al. (1996b) Carroll et al. (1996b) Carroll et al. (1996b) Winslow et al. (1996) Winslow et al. (1996) Winslow et al. (1996) Winslow et al. (1996) Hubner et al. (1997) Baron et al. (1993) Baron et al. (1993) Baron et al. (1993) Baron et al. (1993) Mosharov et al. (1997)

8.3. Measurements of Pressure Time Response The fast time response of PSP was achieved by Baron et al. (1993) using a commercial porous silica thin-layer chromatography (TLC) plate as a binder; the observed response time of this PSP was less than 25 µs. Although this fragile PSP cannot be practically used for wind tunnel testing, Baron’s work suggest that a short response time of PSP can be obtained using a porous material as a binder. Mosharov et al. (1997) reported that the response time of anodized aluminum

188

8. Time Response

(AA) PSP was in a range of 18-90 µs, depending on a luminophore and on some features of an anodization process. Asai et al. (2001, 2002) also measured the response time of an AA-PSP with Ru(dpp) as a luminophore using a pressure chamber with a solenoid type valve. According to Jordan et al. (1999b), a sol-gelbased PSP achieved the frequency response of as high as 6 kHz. Ponomarev and Gouterman (1998) and Scroggin et al. (1999) developed binders by mixing hard particles with polymers to increase the degree of porosity. Ponomarev and Gouterman found that increasing the number of hard particles above a critical pigment volume concentration drastically shortened the response time. Table 8.1 summarizes the response times of some PSP formulations along with their luminescent lifetimes. Solenoid valve type switching has been used to generate a step change in pressure for measurements of the response time of PSP by a number of researchers (Engler 1995; Carroll et al. 1995, 1996; Winslow et al. 1996; Mosharov et al. 1997; Fonov et al. 1998). Figure 8.8 shows a typical pressure jump apparatus used by Asai et al. (2002) for testing the time response of PSP. This apparatus had a small test chamber connected directly to a fast opening valve having a time constant of a few milliseconds. Sample plates used in this apparatus were typically aluminum coupons coated with PSP. Figure 8.9 shows the time response of the luminescent intensity for several PSP formulations using PtOEP as a probe molecule in binders GP197, AA, and Poly(TMSP) to a step change in pressure from vacuum to the atmospheric pressure. The pressure signal from a kulite® pressure transducer was also shown in Fig. 8.9 as a reference. The PSP based on GP197 was very slow and its time constant was in the order of seconds. Figure 8.10 shows the thickness effect on the time response of PtOEP in GP-197 to a step change of pressure (Carroll et al. 1996). In contrast, AA-PSP had the sub-millisecond time response, and Poly(TMSP)-PSP had a comparable response time to AA-PSP since Poly(TMSP) having a very large free volume is very porous. The time constant of Poly(TMSP)-PSP was about a few milliseconds. Jordan et al. (1999b) conducted frequency response experiments of sol-gel-based PSP using a speaker driver producing an oscillating pressure wave, and achieved the frequency response as high as 6 kHz. For a porphine-based PSP on a silica-gel TLC plate, Sakamura et al. (2002) utilized Cassegrain optics to detect a periodic pressure fluctuation of about 1 kHz in a chapped impinging air jet. The aforementioned measurements indicate that a high porosity is required to achieve the high time response of PSP. This viewpoint was examined by Asai et al. (2001) for a mixture of GP-197 with hard particles of BaSO4. Figure 8.11 shows the reduced response time to a step change of pressure with elevating the concentration of BaSO4 as a result of an increased porosity. Asai et al (2001) also noticed that a fast-responding porous PSP usually had lower temperature sensitivity.

8.3. Measurements of Pressure Time Response Light Guide from Xe Lamp

Pressure Transducer

Bandpass Filter for Excitation Light Photomultiplier Tube (PMT) Sharp Cut Filter

PSP Sample

Solenoid Valve

Dichroic Filter Vacuum or Atmosphere

Bandpass Filter for Luminescence Emission

Fig. 8.8. Schematic of a pressure jump apparatus. From Asai et al. (2002)

1.0 0.0 -1.0 -2.0 Kulite(ref)

-3.0 -4.0 0

50

100

150

200

250

300

350

400

time, msec

(a) 1.5 1.4

GP197

1.3 1.2 1.1 1.0 0

50

100

150

200

250

300

350

400

time, msec

(b) 1.0 0.8

Anodized

0.6 0.4 0.2 0.0 0

(c)

50

100

150

200

250

time, msec

Fig. 8.9. (cont.)

300

350

400

189

190

8. Time Response 1.0 0.9

poly(TMSP)

0.8 0.7 0.6 0.5 0.4 0

50

100

150

200

250

300

350

400

time, msec

(d)

Fig. 8.9. Time response of several PSPs to a step change in pressure, (a) kulite sensor (reference), (b) GP197-PSP, (c) AA-PSP, and (d) poly(TMSP)-PSP, where PtOEP is used a probe molecule. From Asai et al. (2002)

1.2

(P - Pmin)/(Pmax - Pmin)

1.0 0.8 0.6 Pressure transducer 22 µm paint 26 µm paint 32 µm paint

0.4 0.2 0.0 0

1

2

3

4

Time (second) Fig. 8.10. Time response of PtOEP in GP197 to a step change of pressure, depending on the paint thickness. From Carroll et al. (1996)

8.3. Measurements of Pressure Time Response

191

1.2 1.0 0.8 increasing particle numbers

0.6

BaSO4:GP197=0g:1g

0.4

BaSO4:GP197=0.5g:1g

0.2

BaSO4:GP197=2g:1g

0.0

transducer

-0.2 -1

0

1

2

3 4 time, sec

5

6

7

8

Fig. 8.11. Effect of the BaSO4 particle concentration in the polymer GP-197 on the time response of BaSO4/GP197 PSP at 313.1 K. From Asai et al (2001)

Another apparatus for creating a step pressure change is a shock tube (Sakaue et al. 2001; Teduka et al. 2000). A shock tube can generate a pressure rise in a few microseconds, and therefore it is a good device for testing a porous PSP having a response time less than a millisecond. Figure 8.12 shows a schematic of a simple shock tube for testing the time response of PSP (Sakaue et al. 2001). The shock tube had a 55×40 mm cross-section, a 428 mm long driver section, and a 485 mm long driven section. An aluminum foil diaphragm was burst by a pressure difference between the driver and driven sections, where the driver pressure was one atmospheric pressure. A pressure transducer (PCB Piezotronics model 103A11), which was connected to a 2 mm diameter pressure tap on the shock tube wall, was used to measure the unsteady reference pressure. Absolute pressures were measured using an Omega pressure transducer connected to the driven section. PSP was applied to a 25.4 mm square aluminum block flush mounted to the shock tube wall. The reference pressure transducer and PSP sample were mounted 300 mm from the diaphragm. A 532-nm laser was used as an illumination source for PSP and the laser spot size was about 2 mm on the sample surface. The luminescent emission from PSP was collected by a PMT through a long pass filter (> 570 nm) and the readout voltage from the PMT was acquired using a LeCroy oscilloscope. The response time of the PMT was about 2 µs. The time resolution of the apparatus was also limited by the laser spot size. The laser spot size d spot and the shock velocity u s gives the limiting detectable pressure rising time t lim it = d spot / u s (about 3-5 µs) for this setup.

192

8. Time Response

steady absolute pressure transducer driven section (low pressure, p1) driver section (atmosphere, p4) unsteady pressure transducer PSP flow directions

vacuum

diaphragm PMT green laser

oscilloscope

Fig. 8.12. Schematic of a simple shock tube setup for testing PSP time response. From Sakaue (1999)

AA-PSP pressure tap theoretical calculation

pressure (kPa)

100

80

incident normal shock

60

40

reflected normal shock

20 0.0

0.3

0.6

0.9

1.2

1.5

time (ms) Fig. 8.13. Pressure data obtained from AA-PSP with a thickness of 9 µm and pressure transducer compared with theoretical calculation. From Sakaue (1999)

Figure 8.13 shows typical pressure signals from a Ru(dpp) AA-PSP (9 µm thick) and the pressure transducer along with the theoretical pressure jumps associated with the incident and reflected normal shock waves. This AA-PSP was able to follow the sharp pressure rises after the incident and reflected shock waves passed through the laser-illuminated spot. Figure 8.14 shows the normalized pressure signals from the AA-PSP with different thickness values (4.3, 9.0, 13.2, and 27.2 µm). It was found that the diffusion response time of this AA-PSP

8.3. Measurements of Pressure Time Response

193

followed the power-law relation τ diff ∝ h 0.573 . Figure 8.15 shows a comparison of the time response of four PSP formulations to a step change of pressure. These formulations used the same probe molecule Ru(dpp) with four different binders: AA, TLC, polymer/ceramic (PC), and conventional polymer RTV. The response times of AA-PSP and TLC-PSP were in the order of ten microseconds, whereas the conventional RTV-PSP had a much longer response time (in the order of hundred milliseconds). In addition, it was found that PC-PSP had a longer response time (about 1 ms) than the thicker but more porous TLC-PSP. For a very porous PSP, the porosity of a binder had more pronounced influence on the time response of PSP than the binder thickness. This is consistent with the theoretical analysis presented in Section 8.2.

normalized pressure

1.2 1.0 0.8

l = 4.3 µm, τ = 34.8 µs l = 9.0 µm, τ = 70.9 µs l = 13.2 µm, τ = 80.0 µs l = 27.2 µm, τ = 102 µs

0.6 0.4 0.2 0.0 0.0

0.1

0.2

0.3

0.4

0.5

0.6

time (ms) Fig. 8.14. Normalized pressure response of AA-PSP with different values of the paint thickness l. From Sakaue (1999)

normalized pressure

1.2 1.0 0.8 0.6

AA-PSP4 TLC-PSP polymer/ceramic PSP

0.4 0.2 0.0 0.0

(a)

0.2

0.4

time (ms) Fig. 8.15. (cont.)

0.6

0.8

194

8. Time Response

normalized pressure

1.2 1.0 0.8 0.6 0.4

polymer PSP

0.2 0.0 0

(b)

50

100

150

200

250

300

350

400

time (ms)

Fig. 8.15. Comparison of the time response among (a) porous Ru(dpp)-based PSPs (AAPSP, TLC-PSP, and PC-PSP) and (b) conventional polymer PSP Ru(dpp) in RTV. From Sakaue (1999)

8.4. Time Response of Temperature Sensitive Paint Similar to PSP, TSP has two characteristic timescales: the luminescent lifetime and the thermal diffusion timescale. The luminescent lifetimes of EuTTA-dope and Ru(bpy)-Shellac TSPs at room temperature are about 0.5 ms and 5 µs, respectively. The time response of EuTTA-dope TSP is intrinsically limited by its long luminescent lifetime, while Ru(bpy)-Shellac TSP has a much shorter luminescent lifetime. Overall, the time response of TSP is strongly dependent upon the boundary conditions of heat transfer in a specific application. Based on the transient solution of the heat conduction equation, the thermal diffusion time for a thin TSP coating is in the order of h 2 / α T , where h is the coating thickness and α T is the thermal diffusivity of TSP. In a convection-dominated case, the thermal diffusion time can also be expressed as hk / α T hc , where k is the thermal conductivity and hc is the convective heat transfer coefficient. In general, the thermal diffusion time is much larger than the luminescent lifetime for many TSP formulations, and therefore thermal diffusion limits the time response of TSP. In contrast to PSP where oxygen diffusion always obeys the no-flux condition at a solid boundary, heat transfer to the substrate through a non-adiabatic wall inevitably affects the thermal time response of TSP in actual experiments. Hence, the timescale of TSP depends on not only the thermal conductivity of the paint itself, but also the boundary conditions in a specific heat transfer problem for TSP application. To measure the time response of TSP to a rapid change of temperature, Liu et al. (1995c) conducted experiments of pulse laser heating on a metal film and step-like jet impingement cooling.

8.4. Time Response of Temperature Sensitive Paint

195

8.4.1. Pulse Laser Heating on Thin Metal Film

We consider short-pulse laser heating on a thin metal film to determine the thermal diffusion timescale of TSP applied to the film. The heat conduction equation for this problem is

∂θ = αT ∇ 2θ , ∂t

(8.28)

where θ = T − Tin is a temperature change of the film from an initial temperature

Tin and α T is the thermal diffusivity of the metal film. The Lapalce operator in Eq. (8.28) is defined as ∇ 2 = ∂ 2 / ∂r 2 + r −1 ∂ / ∂r + ∂ 2 / ∂ z 2 , where r is the radial distance from the center of a hot spot heated by a laser and z is the coordinate normal to the metal film directing from the heated side to other side. The initial temperature Tin is assumed to be the ambient temperature. After heated by a laser pulse, the film is cooled down due to natural convection on both the sides of the metal film. When the surface temperature of the metal film decreases fast enough along the radial direction from the center of the hot spot (i.e., rθ → 0 as r → ∞ ), we introduce a spatially averaging operator

< θ >2 =

2π Aeff

³

∞

0

rθ dr

,

(8.29)

where Aeff is the effective area of the hot spot. Hence, applying the spatially averaging operator to Eq. (8.28), we have the unsteady 1D heat conduction equation ∂ < θ >2 ∂ 2 < θ >2 = αT . (8.30) ∂t ∂ z2 The initial and boundary conditions for Eq. (8.30) are < θ > 2 ( z , 0 )= 0,

∂ < θ > 2 ( 0, t ) = Plaser δ ( t ) − hc < θ > 2 ( 0 , t ) ∂z ∂ < θ > 2 (η m , t ) −k = hc < θ > 2 ( η m , t ) ∂z −k

(8.31)

where hc is the average heat transfer coefficient of natural convection, k is the thermal conductivity, δ(t) is the Dirac-delta function, η m is the metal film thickness, and Plaser represents the strength of the pulse-laser heat source. There are two physical processes involved: rapid heating of the film by the laser pulse and relatively slow cooling process due to natural convection. At the beginning, since the film is heated in a very short time interval, the natural convection terms in the boundary conditions can be neglected; thus, the problem is simplified for the rapid heating process. For a thin metal film ( η m << 1), application of the Laplace transform Θ ( z , s ) = La( < θ > 2 ) to Eqs. (8.30) and (8.31) yields

196

8. Time Response

Θ ( η m ,s ) =

2 Plaser α T

exp( − s / α T η m )

k s

1 − exp( −2 s / α T η m )

≈

Plaser α T exp( − η m s / α T ) , k ηm s (8.32)

where s is the complex variable in the Laplace transform. The inverse Laplace transform leads to an asymptotic expression for the laser heating when t is small

< θ >2 =

Plaser α T erfc( τ 1 / t ) . kη m

(8.33)

The characteristic timescale for the laser heating is τ 1 = η m2 /( 4α T ) . For the slow cooling process due to natural convection after the pulse-laser heat source ceases, we introduce an additional average operator across the metal film

< θ >3 =

1

ηm

³

ηm 0

< θ > 2 dz .

(8.34)

Applying the operator Eq. (8.34) to Eq. (8.30) leads to a simple lumped model for the cooling process

d < ș >3 2α h α P į(t) = − T c < ș > 3 + T laser . Șm k k Șm dt

(8.35)

The solution to Eq. (8.35) is

< θ >3 =

Plaser α T exp( − 2t / τ 2 ) . kη m

(8.36)

Eq. (8.36) describes an exponential decay of the averaged temperature, which gives the characteristic timescale τ 2 = kη m /( 2α T hc ) for the cooling process due to natural convection. Obviously, for the problem of pulse laser heating on a thin film, there are the fast timescale τ 1 = η m2 /( 4α T ) and slow timescale τ 2 = kη m /( 2α T hc ) . The time response of Ru(bpy)-Shellac TSP to a rapid temperature rise was tested by utilizing short pulse laser heating on a 25-µm thick steel film. Figure 8.16 is a schematic of the experimental set-up. One side of the steel film was heated by a pulse laser beam with a 8-ns duration from a Nd:YAG laser (532 nm at an 800-mJ maximum output) through a focusing lens. The opposite side of the steel film was coated with a 10-µm thick Ru(bpy)-Shellac TSP illuminated by a 457-nm blue beam from a 1-mW Argon laser at the hot spot. The response of the luminescent emission from TSP to pulse laser heating was detected using a PMT, and the signal was acquired using an oscilloscope (Tektronix TDS 420). The surface temperature was calculated from the luminescent intensity using a priori calibration relation for TSP. Figure 8.17 shows a typical transient response of the surface temperature to pulse laser heating on the steel film. The surface

8.4. Time Response of Temperature Sensitive Paint

197

temperature increases rapidly after heating at the film and then decays due to natural convection. To estimate the response times, the asymptotic solutions Eq. (8.33) and Eq. (8.36) were used to fit the experimental data. The response time of TSP for the laser heating process was τ 1 = 0.25 ms, while the time constant for the cooling process by natural convection was τ 2 = 12.5 ms. 532 nm pulse green beam YAG Laser lens 25 microns thick steel foil painted side

550 nm LP filter

457 nm blue beam PMT Argon laser for illumination

Fig. 8.16. Schematic of a pulse laser heating setup for testing TSP time response. From Liu et al. (1997b)

(deg. C)

25 paint measurement 16erfc[(τ1/t)0.5], τ1 = 0.25 ms 16exp(-2t/τ2), τ2 = 25 ms

20 15 10 5 0 -5

0

5

10

15

20

25

time (ms) Fig. 8.17. Temperature response of Ru(bpy)-Shellac TSP to pulse laser heating on a steel foil. From Liu et al. (1997b)

198

8. Time Response

8.4.2. Step-Like Jet Impingement Cooling

Sudden fluid jet impingement to TSP coated on a hot body, which produces a rapid decrease of the surface temperature, can be used for testing the time response of TSP. A lumped heat transfer model gives an approximate solution for a temporal evolution of the temperature on a paint layer during step jet impingement cooling T − Tmin = exp( − t / τ 3 ) , (8.37) Tin − Tmin where Tin is the initial temperature of the paint and Tmin is the minimum temperature of the paint that is asymptotically reached as t → ∞. The timescale for this cooling process is τ 3 = kh /( α T hc ) , where hc is the average heat transfer coefficient of the impinging jet and h is the paint thickness. Figure 8.18 shows an experimental setup for step jet impingement cooling. A 475-nm blue laser beam was used for illumination at the impingement point. The luminescent intensity was measured using a PMT and then was converted into temperature using a priori calibration relation. To achieve a small response time, a sub-zero temperature impinging Freon jet generated by a Freeze-it£ sprayer was utilized, where a mechanical camera shutter was used as a valve to control issuing of the jet. After the shutter opened within 1 ms, the Freon jet impinged on the o surface of a hot soldering iron (about 100 C) which was coated with a 19-µm thick Ru(bpy)-Shellac TSP. Figure 8.19 shows a rapid decrease of the surface o temperature on the thin paint coating to the minimum temperature of about 44 C. The measured timescale τ 3 of TSP for this cooling process was 1.4 ms. Cool air impingement jet was also tested; the measured timescales were 16 ms and 25 ms for 19 µm and 38 µm thick Ru(bpy)-Shellac TSP coatings, respectively.

Hot body

550 nm LP filter

paint

457 nm blue beam PMT jet

Argon laser for illumination

Fig. 8.18. Schematic of a step-like jet impingement cooling setup for testing TSP time response

8.4. Time Response of Temperature Sensitive Paint

199

1.5

(T - Tmin)/(Tmax - Tmin)

exp(- t/τ), τ = 1.4 ms Ru(bpy)-Shellac paint

1.0

0.5

0.0 0

5

10

Time (ms)

Fig. 8.19. Temperature response of Ru(bpy)-Shellac TSP to step-like Freon jet impingement cooling

9. Applications of Pressure Sensitive Paint

9.1. Low-Speed Flows

9.1.1. Airfoil Flows PSP measurements are challenging in low-speed flows where a change in air pressure is very small. The major error sources, notably the temperature effect, image misalignment and CCD camera noise, must be minimized to obtain acceptable quantitative pressure results at low speeds. Brown et al. (1997, 2000) made baseline PSP measurements on a NACA 0012 airfoil at low speeds (less than 50 m/s). The experiments systematically identified the major error sources affecting PSP measurements at low speeds and developed the practical procedures for minimizing these errors. After all efforts were made to reduce the errors, reasonably good pressure results were obtained at speeds as low as 10 m/s. Brown (2000) conducted three sets of tests (Cases I, II and III) with increasingly improved instrumentation arrangement and data processing. All the tests were made in The NASA Ames Research Test Facility Wind Tunnel having a 12-in high, 12-in wide and 24-in long test section. The Mach number ranged from 0.02 to 0.4. PSP measurements were conducted on an unswept stainless steel NACA 0012 airfoil with a 3-in chord and 9-in span. The airfoil was mounted vertically, and there is a 1.5-in gap between the airfoil’s edges and the top/bottom of the test section. Sixteen mid-span pressure taps (0.048-in diameter) were machined into the upper surface of the airfoil. Each test case was conducted consistently using the same test equipment. Images were obtained using a 14-bit Photometrics CH250 CCD camera with a Melles Griot filter (650±20 nm) attached to a 50-mm Nikor lens. Data were collected on a PC using associated Photometrics imaging software. Two Electrolite UV lamps provided illumination for PSP. Pressure tap measurements were performed with differential pressure meters connected to the airfoil via Tygon tubing. The airfoil was coated with FIB-7 basecoat and PtTFPP/FIB-7 PSP developed by the University of Washington. The white basecoat provided surface scattering to enhance the luminescent emission received by the camera. Application of the basecoat and PSP was performed using a commercial spray air gun. The

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basecoat was lightly buffed to reduce surface roughness. The sufficiently thick PSP topcoat applied to the basecoat was insured to be as uniform as possible. After completing the PSP application, a hot-air gun was used to raise PSP above o its glass transition temperature of about 70 C. This annealing process reduced the temperature sensitivity of PSP. The first set of tests (Case I) provided useful PSP testing experience to identify the potential problems. The airfoil was secured onto the tunnel test section with o the angle of attack of 5 . The camera and two UV lamps were secured onto a rigid double U-frame surrounding the test section mounted on the ground floor by bolts, which were approximately 18 inches away from the test section. The camera viewed perpendicularly the airfoil on which ten registration marks were placed for image registration. The total thickness of the basecoat and PSP was about 34 µm and the roughness of PSP was about 2.6 µm. The tests were run at 10, 20, 30, 40 and 50 m/s. For each tunnel run period, the tunnel settling temperature was recorded just priori to and just after image acquisition. The temperature change o was within 0.17 C during a single period of image acquisition, depending on the flow velocity. The typical results for a speed of 30 m/s and the angle of attack of o 5 are shown in Figs. 9.1-9.3. Figure 9.1 is the in-situ Stern-Volmer plot for PSP obtained using pressure tap data, indicating a large variation and a poor correlation between the luminescent intensity and pressure. The corresponding PSP image is shown in Fig. 9.2, where flow is from left to right. Although the low-pressure region near the leading edge is visible in the PSP image, apparent striation patterns and granular features corrupt the quality of the PSP data. This random spatial noise can be clearly seen in the chordwise pressure distribution at the mid-span, as shown in Fig. 9.3. The PSP data at speeds of 10, 20, 40 and 50 m/s had similar noise patterns. Several problems were identified that might contribute to the large spatial noise. First, scratches on the tunnel plexiglass wall caused the streaky patterns. Secondly, PSP suffered from a considerable thickness variation due to poor application of the paint. The effect of the surface roughness could not be completely corrected using the image registration technique for the non-aligned wind-off and wind-on images. The third problem was related to model motion with respect to the lamps. Since the lamps were fixed on the ground floor, the test section underwent a lateral oscillation estimated to be on the order of 10 Hz relative to the lamps. If the model moved in a non-homogenous illumination field, the effect of the motion could not be corrected using the image registration technique. Also, this problem exaggerated the second problem associated with the surface roughness. Note that these problems might not be serious for PSP measurements in high subsonic, transonic and supersonic flows. In Case II tests, a new test section plexiglass wall was installed to replace the scratched one. The model was cleaned and repainted carefully; thus, the roughness of the PSP layer was reduced to 0.89 µm from 2.6 µm in Case I. In order to reduce the relative motion between the model and lamps, a new mounting structure for the camera and lamps was designed and constructed, which was secured to the test section rather than the ground floor. Therefore, the lateral and vertical shifts in the image plane due to the motion were reduced to 0.43 and 0 pixels from 2.41 and 1.9 pixels in Case I, respectively. In addition, to reduce the

9.1. Low-Speed Flows

203

temperature change between the wind-off and wind-on images, the experimental procedure was revised such that the tunnel was run for one hour and the wind-off image was taken immediately after the wind-on image. In this way, the temperature distribution on the model in the wind-off case was close to that in the wind-on case. Figures 9.4-9.6 show results obtained in Case II tests for a speed of o 30 m/s and the angle of attack of 5 . The in-situ Stern-Volmer plot in Fig. 9.4 has a better linearity and an improved correlation with the pressure tap data. The PSP image in Fig. 9.5 is also considerably improved, clearly showing not only a correct chordwise pressure profile, but also the 3D effect near the airfoil edges. The pressure tap gutter lines are also visible in the image since the gutter line epoxy has a different thermal conductivity from the stainless steel such that a small temperature difference exists. As shown in Fig. 9.6, the chordwise pressure distribution at the mid-span clearly shows a reduced noise level compared to the corresponding result in Case I. In Case III tests, careful application of PSP led to a further reduction of the paint roughness to 0.46 µm. To increase the statistical redundancy in image registration, all 16 pressure taps were used in images as registration marks, in addition to the original eight registration marks applied to the paint surface. For better in-situ calibration of PSP, 32 ‘virtual pressure taps’ located at 10 pixels above and below the spanwise location of the actual taps were created and used in images under the assumption of two-dimensionality of flows near the mid-span. As shown in Fig. 9.7, it was found that the use of the additional virtual taps provided an accuracy of 10% better than that achieved by using the actual taps only in least-squares estimation for in-situ calibration. The results of Case III tests are shown in Figs. 9.7-9.9 for a speed of 30 m/s and the angle of attack of 5o. Overall, the results indicate the improved quality of the PSP data and a reduced noise level compared to Case II. The valuable lessons learned from this study of low-speed PSP measurements are summarized as follows. (1) Vibration and model movement with respect to cameras and lamps must be minimized to reduce the image registration error. (2) The temperature-induced errors must be minimized. Not only the tunnel test section, but also the model surface should reach a stable equilibrium state of temperature priori to acquisition of the wind-on images. It is highly suggested that the wind-off image should be acquired immediately after the corresponding windon image as soon as the tunnel is shut down. (3) The quality of application of both the basecoat and PSP topcoat to a surface is critical and the paint roughness must be minimized to obtain good results at low speeds. (4) In-situ PSP calibration utilizing a sufficient number of pressure taps is required to eliminate the systematic errors and obtain quantitative results. (5) Image registration is critical to reduce the spatial noise. (6) Scientific-grade CCD cameras (14 and 16 bits) should be used, and averaging a large number of images should be performed to reduce the photon shot noise and other random noises. Note that some of the above procedures for controlling the error sources are not generally applicable to large production wind tunnels.

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Fig. 9.1. In-situ calibrated Stern-Volmer plot in Case I for 30 m/s and α = 5

o

Fig. 9.2. Calibrated PSP image in Case I for 30 m/s and α = 5 . From Brown (2000) o

Fig. 9.3. Chordwise pressure profile at mid-span in Case I for 30 m/s and α = 5

o

9.1. Low-Speed Flows

Fig. 9.4. In-situ calibrated Stern-Volmer plot in Case II for 30 m/s and α = 5

205

o

Fig. 9.5. Calibrated PSP image in Case II for 30 m/s and α = 5 . From Brown (2000) o

Fig. 9.6. Chordwise pressure profile at the mid-span in Case II for 30 m/s and α = 5

o

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9. Applications of Pressure Sensitive Paint

Fig. 9.7. In-situ calibrated Stern-Volmer plot in Case III for 30 m/s and α = 5

o

Fig. 9.8. Calibrated PSP image in Case III for 30 m/s and α = 5 . From Brown (2000) o

Fig. 9.9. Chordwise pressure profile at the mid-span in Case III for 30 m/s and α = 5

o

9.1. Low-Speed Flows

207

9.1.2. Delta Wings, Swept Wings, and Car Models PSP measurements on delta wings, swept wings and car models at low speeds were performed at ONERA in France and DLR in Germany to optimize their paint formulations, hardware and software for low-speed measurements (Engler et al. 2001a). It is realized that PSP measurements at low speeds require the accuracy of 0.1% over a pressure range of 800-1000 mb. This accuracy is difficult to achieve using a typical PSP with a temperature sensitivity of 1%/K because a temperature change of 0.1 K could produce an error as large as a required pressure resolution. Furthermore, the accuracy of PSP is further reduced due to the camera noise and variation of the excitation intensity during a test run. The most common procedure to deal with the temperature effect is application of in-situ calibration to correlate the local luminescent intensity to the corresponding pressure tap data under an assumption that the temperature distribution on a model is uniform. In this case, the temperature-induced error is absorbed into an overall fitting error in in-situ calibration. Even though some systematic errors are removed, it is impossible for this procedure alone to reduce the error to a level equivalent to that caused by a temperature change of 0.1 K on a non-uniform thermal surface in wind tunnel tests. After investigating lowspeed PSP measurements in large production wind tunnels at NASA Ames, Bell et al. (1998) pointed out that the most significant errors were due to the temperature effect of PSP and model motion. Therefore, a better solution is the combined use of in-situ calibration with a temperature-insensitive PSP. An illumination field should be measured in order to correct both the spatial and temporal excitation variations on a surface. Furthermore, a large number of images (up to 64) should be averaged to reduce the camera noise. Engler et al. (2001a) tested three Pyrene-based PSP formulations for lowspeed measurements. One was the B1 PSP developed by OPTROD in Russia, in which a pressure-insensitive reference dye was added to correct the excitation variation when performing a ratio between the pressure and reference emissions. The temperature sensitivity of the B1 PSP was 0.5%/K which could not be neglected when a high accuracy for pressure measurements was required. Another was the PyGd PSP developed at ONERA, containing Pyrene as a pressure-sensitive dye and a gadolinium oxysulfide as a reference component. The two components absorbed the ultraviolet excitation light and emitted the luminescence at different wavelengths. Besides its high sensitivity to pressure, the PyGd PSP displayed a very low temperature sensitivity of 0.05%/K because the temperature sensitivity of the reference component was almost the same as Pyrene and thus an intensity ratio between the two components compensated the temperature effect of Pyrene. Therefore, this paint was suitable to low-speed PSP measurements. The PdGd PSP, developed at ONERA mainly for transonic flows, was also tested to evaluate its feasibility and accuracy of measurements at low speeds. This paint was a mixture of PSP and TSP, containing a pressuresensitive component Palladium octaethylporphine (PdOEP) and a temperaturesensitive component Gadolinium oxysulfide having a temperature sensitivity of 1.5%/K.

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Illumination system used was a Mercury light filtered in a UV range (325±15nm or 340±35nm) and a xenon-flash lamp equipped with four optical outputs with 25-Hz repetition rate (308 nm); the lights were connected to liquid light guides to illuminate models. Cooled CCD cameras (512×512, 1024×1024 or 1340×1300 pixels) with back illuminated detectors were used. A filter holder was placed in the front of the lens or the CCD chip. The filters separated the emitted lights from the pressure component (430-510 nm) and from the reference component (615-625 nm). For the PdGd paint, the third filter was required for the temperature-sensitive component at 480-520 nm. The exposure time was typically 1-30 seconds, depending on the illumination source, camera, and size of a test section. Filter-shifting device and two-camera system were developed to acquire the pressure and reference images. Preliminary measurements at low speeds were made on a delta wing to identify the major error sources and evaluate the performance of different paints (B1, PyGd and PdGd) under the same flow conditions. The delta wing with a 500-mm chord and a swept angle of 75° was successively painted with the three PSPs. The model was mounted in the ONERA low-speed research wind tunnel having a test section of 1-m diameter and the maximum speed of 50 m/s. The model was equipped with 47 pressure taps used to assess the accuracy of PSP. Ten images for each filter setting (blue or red filter) were taken using the CCD cameras (512×512 and 1340×1300 pixels) for frame averaging.

0

pressure taps

-4

Fig. 9.10. The pressure coefficient Cp map obtained using the PyGd PSP on a delta wing at 25 m/s. From Engler et al. (2001a)

Figure 9.10 shows a typical image of the pressure coefficient C p on the 75°o delta-wing obtained using the PyGd PSP at 25 m/s and the angle of attack of 32 . The leading-edge vortex signature was clearly visualized on the model and the secondary vortices were distinguished from the primary vortices. Figure 9.11 shows the distributions of C p obtained using the B1, PyGd and PdGd PSPs at the chordwise station equipped with pressure taps, where the error bars of 1 mb (0.0145 psi) indicate the accuracy of PSP measurements. The results obtained

9.1. Low-Speed Flows

209

using the PyGd PSP are in good agreement with the pressure tap data and less noisy compared to those given by the B1 and PdGd PSPs. This is due to not only much higher luminescent emission from the PyGd PSP, but also very low temperature sensitivity of the PyGd PSP. Spatial averaging was applied to the PSP data over a 3-pixel-radius circle around each pixel. Since a 3-pixel radius in a 512×512-pixel camera corresponded to a larger area on the surface, spatial averaging on the image plane was more effective for the 512×512-pixel camera, which was evidenced by a reduced noise level of the results. Since the PdGd PSP was a mixture of PSP and TSP, the temperature fields were also obtained, indicating a temperature increase of 0.2 K on the wing surface from the left to right. Moreover, by comparing the TSP images taken before and after the test, a temperature increase of 1.6 K was observed in a test run of 30 minutes due to the heat dissipated by the motor of the wind tunnel. Other researchers also measured the pressure distributions on delta wings using PSP at low speeds (Morris 1995; Shimbo et al. 1997; Le Sant et al. 2001a; Verhaagen et al. 1995). The flow over a delta wing is particularly suitable to testing the capability of PSP at low speeds since there is a relatively large pressure change induced by the leading edge vortices on the upper surface. 0.5 0 -0.5 -1 Cp -1.5 -2 Kp 400 512x512, radius=3 1340x1300, radius=3

-2.5 -3 -150

-100

-50

0

50

100

150

100

150

y (mm)

(a) 1 0.5 0 -0.5 cp

-1 -1.5 -2 Kp 400 512x512, radius=3

-2.5

1340x1300, radius=3

-3 -150

(b)

-100

-50

0 y (mm)

Fig. 9.11. (cont.)

50

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9. Applications of Pressure Sensitive Paint

2 1.5 1 0.5 0 Cp

-0.5 -1 -1.5 -2

Kp 400 512x512, radius=3 1340x1300, radius=3

-2.5 -3 -150

(c)

-100

-50

0

50

100

150

y (mm)

Fig. 9.11. Comparison of PSP measurements with pressure tap data on a delta wing at the chordwise location x = 400 mm at 25 m/s, (a) PyGd PSP, (b) B1 PSP, (c) PdGd PSP. From Engler et al. (2001a)

Measurements on swept wings were performed in the Low-Speed-Wind-Tunnel (LSWT) of Daimler-Chrysler Aerospace at Bremen in German. This Eiffel-type wind tunnel with a 2.1×2.1 m test section was operated in a range of velocities from 30 to 75 m/s. Images were acquired at 10 minutes after the tunnel was turned on to stabilize flow temperature and minimize the temperature effect on PSP. During the tests, all ambient light sources were covered and the test section was painted black to minimize reflection of the luminescent light on the walls. After preliminary tests on a swept constant-chord half-wing model to examine the performance of the PSP system, PSP measurements were made on an Airbus A340 half-model. Figure 9.12 shows the wing of the Airbus model coated with different paints including ‘Göttingen Dyes’ (GD) PSPs and B1 PSP of OPTROD. A large number of pressure taps on the wing were available for comparison. Figure 9.13 shows a raw blue image of the wing of the Airbus model illuminated with a 308nm diffuse lamp when the integration time of the CCD cameras was 32 s for 16 images acquired. The GD146 PSP gave the most sensitive signal. Figure 9.14 shows a comparison of PSP measurements with pressure tap data along a chord at the spanwise location AB indicated in Fig. 9.13 on the Airbus model at 60 m/s and the angle of attack of 16o. Figure 9.15 shows a similar comparison between PSP and pressure taps for the wing/slat configuration of a swept constant-chord halfwing model at 60 m/s and the angle-of-attack of 16°. The resolution of ∆C p = 0.02 was achieved on the swept wings at 60 m/s.

9.1. Low-Speed Flows

211

Fig. 9.12. Airbus A340 half model tested with different PSPs. From Engler et al. (2001a)

Fig. 9.13. Raw blue image obtained using two separate CCD cameras and a 308-nm lamp for excitation, where the integration time for 16 images was 32 seconds. From Engler et al. (2001a)

Fig. 9.14. Comparison of PSP and pressure tap data at 60 m/s and the angle of attack of 16 along the line A-B on the Airbus A340 half model. From Engler et al. (2001a)

o

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9. Applications of Pressure Sensitive Paint

Fig. 9.15. Comparison of PSP and pressure tap data for the wing/slat configuration of a o swept constant-chord half-wing model at 60 m/s and the angle of attack of 16 . From Engler et al. (2001a)

Engler et al. (2001a) and Aider et al. (2001) measured the pressure distributions on car models at low speeds. The models were a Daimler Benz and a PSA Peugeot Citroen (900 mm long, 400 mm wide and 350 mm high). The tests were conducted in the ENSMA’s T4P low-speed wind tunnel at Poitiers in France and in the Daimler Benz wind tunnel at Sindelfingen in Germany. The maximum velocity of these tunnels was 65 m/s and the free-stream turbulence intensity was less than 1%. Figure 9.16 shows typical PSP data mapped onto a CFD grid of the Daimler Benz model, where 64 raw images were averaged to reduce the camera noise. The total time to acquire all the wind-on and wind-off images was longer than one hour since the powerful 308-nm light sources were not available for these tests and a long integration time for the camera was required. Fortunately, the static temperature of flows in the wind tunnels was stable enough such that an error produced by a long-time temperature shift in the tunnels was small. Figure 9.17 shows a comparison between PSP and pressure tap data along the centerline of the Daimler Benz model. The absolute pressure accuracy of about 1 mb (0.0145 psi) was achieved after a large number of images were averaged. Figure 9.18 presents a comparison between PSP and pressure taps on the rear window of the PSA Peugeot Citroen model at 40 m/s along the left-hand sideline A and the centerline C equipped with pressure taps. In this case, the absolute pressure accuracy was better than 1 mb. There was an interesting difference between the pressure distributions along the sideline A and centerline C. There was only one pressure minimum point along the centerline C through the roof/window junction. In contrast, two pressure minimum points existed along the sideline A, which corresponded to the roof/window junction and a vortex system around the car, respectively. PSP was able to visualize the pressure signatures associated with complex flow patterns that were completely missed in pressure tap data such as a pressure peak between the two pressure minimum points along the sideline A.

9.1. Low-Speed Flows

213

0.4

Cp

0.2 0.0 -0.2 -0.4 -0.6 -0.8 -1.0

Fig. 9.16. Pressure image mapped onto a surface grid of the Daimler Benz model with arrangement of pressure taps at 60 m/s. From Engler et al. (2001a) Cp

0.4 0.2 0.0

-0.2

10 mb

-0.4 -0.6

PSP PSI

-0.8 -1.0 0.0

0.5

x/l

1.0

Fig. 9.17. The pressure coefficient distribution obtained from PSP compared with pressure tap data at the centerline on the Daimler Benz model at 60 m/s. From Engler et al. (2001a) 1.006 1.004 1.002

C

P (bar)

1.000 0.998 0.996

C

0.994

A

0.992

A

0.990 0.988 0.986 200

250

300

350

400

450

500

X (mm)

Fig. 9.18. Comparison of PSP with pressure tap data along the sideline A and centerline C on the rear window of the PSA Peugeot Citroen model at 40 m/s. From Engler et al. (2001a)

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9.1.3. Impingement Jet Torgerson et al. (1996) conducted PSP experiments in a low-speed impinging jet to determine the limiting pressure difference that can be resolved using a laser scanning system combining an optical chopper or acoustic-optic modulator with a lock-in amplifier. They tested three PSP formulations, Ru(dpp) in GE RTV 118, PtTFPP in model airplane dope and PtTFPP/Green-Gold in dope. Ru(dpp) in GE RTV 118 had a relatively low temperature sensitivity of 0.78%/°C compared to 1.8%/°C for PtTFPP-dope PSP. PtTFPP/Green Gold in dope was a twoluminophore PSP where Green Gold served as a pressure-insensitive reference dye. They compared the intensity ratio method, phase method and two-color ratio method to evaluate their feasibility for low-speed PSP measurements. The paint was coated on a white Mylar film attached on an aluminum impingement surface that was located at 10 mm away from a 5-mm diameter nozzle. A laser beam modulated by an optical chopper provided illumination for PSP at 457 nm. A 0.2mm laser spot was scanned across the impingement plate. The luminescent emission was detected using a PMT through a long-pass filter (>600 nm). The PMT signal was input into a lock-in amplifier connected with a PC either to reduce the noise for intensity-based measurements or to extract the phase angle for phase-based measurements. For Ru(dpp) in GE RTV 118, a typical chopping frequency was 500 Hz with a lock-in time constant set to 200 ms. Pressure was calculated from the intensity ratio and the phase angle after five scan ensembles were averaged. Figure 9.19 shows the pressure distributions on the impingement plate converted from the intensity ratio of Ru(dpp) in GE RTV 118, where the lateral coordinate is normalized by the nozzle diameter. These results indicated that the laser scanning system, working with Ru(dpp) in GE RTV 118, was able to measure an absolute pressure difference as low as 0.05 psi with a reasonable accuracy. However, it was found that the PtTFPP-dope PSP exhibited a stronger temperature effect distorting significantly the pressure distribution near the shear layer region of the impinging jet. Phase measurements in the wind-off case for Ru(dpp) in GE RTV 118 and PtTFPP in dope led to a somewhat surprising finding that the phase angle showed a repeated variation or pattern over a scanning range even when pressure and temperature were uniformly constant. The phase variation introduced a considerable error in low-speed PSP measurements although it might not be significant for PSP application to high-speed flows. The phase variation was attributed to microheterogeneity of a polymer environment around a probe molecule that locally altered the luminescence and quenching behavior. To correct this intrinsic pattern of the phase angle (or lifetime), a ratioing process is still needed. Similarly, for the two-luminophore paint PtTFPP/Green-Gold in dope, a two-color intensity ratio was not constant over a scanning range because the two dyes were not homogeneously mixed into the binder. In this case, a ratioof-ratios of the signals was used to remove this effect.

9.2. Subsonic, Transonic, and Supersonic Wind Tunnels

215

0.5

y/d = 2

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0

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Fig. 9.19. Pressure distributions in a low-speed impinging jet obtained using a laser scanning system. From Torgerson et al. (1996)

9.2. Subsonic, Transonic, and Supersonic Wind Tunnels Most PSP measurements were conducted in high subsonic, transonic and supersonic flows since PSP is most effective in a range of the Mach numbers from 0.3 to 3.0. Experiments on various aerodynamic models with PSP in large production wind tunnels have been made at three NASA Research Centers (Langley, Ames and Glenn), the Boeing Company at Seattle and St. Louis, AEDC, and Wright-Patterson in the United States. Also, PSP has been widely used in wind tunnels at TsAGI in Russia (Bukov et al. 1993, 1997; Troyanovsky et al. 1993; Mosharov et al. 1997), British Aerospace and DERA in Britain (Davies et al. 1995; Holmes 1998), DLR in Germany (Engler et al. 1995, 1997a, 2001b), ONERA in France (Lyonnet et al. 1997), and NAL in Japan (Asai 1999). Besides predominant applications of PSP in external aerodynamic flows, PSP has been used to study supersonic internal flows with complex shock wave structures in turbomachinery (Cler et al. 1996; Lepicovsky 1998; Lepicovsky et al. 1997; Taghavi et al. 1999; Lepicovsky and Bencic 2002). This section describes typical PSP measurements in subsonic, transonic and supersonic flows. 9.2.1. Aircraft Model in Transonic Flow Engler et al. (2001b) measured the pressure distributions and aerodynamic loads on an AerMacchi M-346 Advanced Trainer Aircraft model at the angles of attack from -4° to 36° and the angles of sideslip from -13° to 13° over a Mach number range of 0.6-0.95. Their experiments represented a good example of PSP

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9. Applications of Pressure Sensitive Paint

application to a complex model with flaps, air brakes, rudders and ailerons in a production wind tunnel, which utilized a two-luminophore PSP, eight CCD cameras and 16 fiber optics illumination heads. In addition, control of PSP hardware and interface with a standard wind tunnel data acquisition/processing system became an operational issue in a production wind tunnel. Experiments were conducted in the industrial wind tunnel with a 1.8×1.8 m test-section at DNW-HST in Amsterdam, The Netherlands. The AerMacchi M346 advanced trainer aircraft model had a 1.2-m length and a 1.0-m span. Figure 9.20 shows a surface grid and a painted model with exchangeable flaps, air brakes, rudders and ailerons. Since a total of 19 configurations were tested, 20 additional model parts were painted besides the basic model. All the parts of the complex model were illuminated and captured by CCD cameras placed around it in order to measure the aerodynamic effects at high angles-of-attack and angles of sideslip for maneuvers influenced by flaps, air brakes, rudders and ailerons. To overcome the problems of shadows and inhomogeneous illumination for excitation, the Pyrenebased two-luminophore B1 PSP from OPTROD was employed. In addition, since this PSP had weak temperature dependency, the error due to the temperature effect could be reduced.

rudder horizontal

aileron

tails

ou tboard droop

inboard dr oop variable flaps

(a)

(b)

Fig. 9.20. The AerMacchi M-346 advanced trainer aircraft model, (a) surface grid, (b) PSP coated model. From Engler et al. (2001b)

As shown in Fig. 9.21, at each of four observation directions, an UV light source connected to four 20-m long optic fibers; thus, a total of 16 fiber optics heads connected with four UV light sources illuminated the whole model from all the four directions. Eight cooled 12-bit CCD cameras were used for image acquisition. At each observation direction, a twin-CCD-camera unit with different filters was used to acquire in parallel the pressure signal at 450-550 nm (blue) and reference signal at 600-650 nm (red). Figure 9.21 shows a twin-CCD-camera unit and illuminator heads installed on the wall of the test-section. The use of the twinCCD-camera unit eliminated a filter-shifting device that could not be immune

9.2. Subsonic, Transonic, and Supersonic Wind Tunnels

217

from unsteadiness of the light sources. In this arrangement of cameras and lights, the exposure time was typically 15 seconds for a camera placed at 1 m away from the model. As PSP was integrated into a standard wind tunnel measurement system, accurate and rapid acquisition and transmission of data became an important issue to decrease the wind tunnel run time. An automatic trigger and data exchange system was used. After acquisition of a set of ‘blue’ and ‘red’ images by the four twin-CCD-camera units (eight CCD cameras), a TTL ready signal from the PSP system was sent to the wind tunnel control/data system, and the flow parameters and model attitudes were adjusted and recorded for next run. After the above process was completed, a TTL trigger signal from the tunnel control/data system activated all the cameras and lights for new PSP measurements. Given limited illumination sources (16 illuminator heads) for the complex model, shadows were inevitably generated mainly by vertical rudders on the fuselage and horizontal tails. The effect of shadows was largely eliminated using the ratio-of-ratios approach for the pressure (blue) and reference (red) images in the wind-on and wind-off cases (four images in total). In some areas without PSP like registration markers, screws and damaged spots, pressure was given by a proper interpolation scheme from PSP data around these areas.

Fig. 9.21. PSP system including twin-CCD-camera units, fiber optics illuminators, computers for data/image acquisition. From Engler et al. (2001b)

Figures 9.22 and 9.23 show the distributions of the pressure coefficient Cp on the upper surface of the model for the clean configuration and the configuration o with positive and negative ailerons at Mach 0.6 and the angle-of-attack of 14 . It

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9. Applications of Pressure Sensitive Paint

can be seen that the pressure distribution is significantly altered from one configuration to another. The pressure distributions along the lines on the wings indicate a symmetric pressure field with respect to the model centerline for the clean wing configuration, in contrast to the asymmetric one for the configuration with the positive and negative ailerons. Figure 9.24 shows a typical pressure field mapped onto a 3D grid of the model. PSP data were first mapped onto the upper, lower, left and right parts of the model grid, and then these parts were merged into a complete 3D surface of the model. From the 3D PSP data on the model surface, Engler et al. (2001b) calculated the coefficients of the normal force (CN), pitching moment (CPM), rolling moment (CRM), wing root torsion moment (CTM), outboard droop hinge moment (ODHM), and horizontal tail normal force (CNHT). Figure 9.25 shows the aerodynamic force and moment coefficients obtained from PSP along with data given by a balance at Mach 0.95 on the configuration with the leading edge droop set to zero. In Fig. 9.25, D1 denotes the data obtained by a six-component balance during PSP tests and D2 denotes balance measurements on the same model without PSP in previous wind tunnel tests. The PSP-derived aerodynamic loads were in reasonable agreement with the balance data except for the horizontal tail normal force. Previous balance data indicated the existence of the forebody side force at high angles-of-attack, which was caused by the asymmetric boundary layer separation and vortex system. In these cases, PSP indeed showed the asymmetric pressure fields on the wings.

0

Cp

0.

1 -1.5 -2

Cp

600

700

800

700

800 x 900

x 900

0 0.

-1 1.5

-2

600

Fig. 9.22. The pressure coefficient (Cp) distributions along the lines on the upper surface on the model for the clean configuration at Mach 0.6 and the angle of attack of 14°. From Engler et al. (2001b)

9.2. Subsonic, Transonic, and Supersonic Wind Tunnels

219

0

Cp

0.5

-1 -1.5 -2

600

700

800 x 900

0 Cp -0.5 -1 -1.5 -2

600

700

800

x

900

Fig. 9.23. The pressure coefficient (Cp) distributions along the lines on the upper surface on the model for the configuration with the positive and negative ailerons at Mach 0.6 and the angle of attack of 14°. From Engler et al. (2001b)

Fig. 9.24. Typical pressure distribution mapped onto a surface grid of the model. From Engler et al. (2001b)

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9. Applications of Pressure Sensitive Paint

M= 0.95

M=0.95

(a) Aircraft normal force coefficient

M= 0.95

(b) Aircraft pitching moment coefficient.

M= 0.95

(c) Aircraft rolling moment coefficient

(d) Wing root torsi on moment coefficient

M= 0.95

(e) Outboard droop hinge moment coefficient

M= 0.95

(f) Horizontal tail normal force coefficient

Fig. 9.25. The coefficients of aerodynamic loads obtained from PSP compared with the force balance data. From Engler et al. (2001b)

9.2. Subsonic, Transonic, and Supersonic Wind Tunnels

221

9.2.2. Supercritical Wing at Cruising Speed Using porphyrin-based PSPs (FIB, Uni-Coat, Sol-gel, FEM, and PAR paints), Mebarki and Le Sant (2001) studied the pressure fields on the supercritical wing of a Dash 8-100 aircraft model at the cruising Mach number 0.74. Experiments were conducted in a blow-down pressurized tri-sonic wind tunnel at the Institute for Aerospace Research (IAR) of National Research Council (NRC) in Canada. At Mach 0.74, the total pressure of flow was changed from 1.4 bar to the maximum value of 3.1 bar, and accordingly the unit Reynolds number from 18.7 to 49 millions/m. The duration of a run depended on the Mach number and total pressure p0. At Mach 0.74, the run duration varied from 11 seconds at Rec = 6 6 8.51×10 and p0 = 3.14 bar to 37 seconds at Rec = 3.81×10 and p0 = 1.41 bar, where Rec is the Reynolds number based on the mean chord. The start-up time to establish stable flow was 2 seconds. The supercritical wing without a nacelle had a zero swept angle at the 60% chord line. The steel wing with an aluminum half fuselage was mounted on an external sidewall balance. The overall length, wingspan and mean chord of the model were 1.73, 1.1 and 0.203 m, respectively. The airfoil sections were designed to sustain extensive laminar flow on the surface. The wing was equipped with four rows of 32 pressure taps (stations A, B, C and D), which were located at 11%, 27%, 35% and 57% of the wingspan, respectively. The ceiling of the test section was equipped with 20 optical windows. To provide fairly uniform and stable illumination, 16 cooled green halogen lamps (Iwasaki JY 1562 GR/N/CG 50W) with filters (color filter KOPP 4-96) were used for all the PSP formulations since they used the same porphyrin molecule (PtTFPP) as a probe. A 12-bit CCD Photometrics camera (1024×1024 pixels) and an Infrared Agema 900 camera (136×272 pixels) were mounted in the plenum shell. The CCD camera, equipped with two interference filters (Andover 650FS40 and Melles Griot 03FIB014) in parallel, recorded the luminescent emission of PSP from the wing root (station A) to approximately 85% of the wingspan. The infrared camera focused on three rows of taps (from station B to D), thus covering 30% of the wingspan. Of the porphyrin-based (PtTFPP) PSP formulations used, the PAR PSP from IAR and FEM PSP from NASA Langley were not commercially available, and three other paints, the FIB PSP, Sol-gel PSP and UniCoat PSP, were commercially produced by Innovative Scientific Solutions Inc. (ISSI) in Dayton, Ohio. Figure 9.26 shows a comparison of pressure results obtained using the FIB PSP with the pressure tap data at the spanwise stations B (27% wingspan) and C (35% 6 wingspan) for four angles of attack at Mach 0.74 and Rec = 3.8×10 , where in-situ calibration was applied. An average error in Cp was about 0.02, corresponding to 1.4% of the full pressure range at those locations. Figure 9.27 shows the distributions of Cp along with the corresponding temperature distributions obtained using an infrared camera for the angles of attack of 0, 1, 3 and 5 degrees at Mach 6 0.74 and Rec = 3.8×10 . A shock across which a rapid change of pressure occurred o can be clearly identified in these PSP images. At the angle of attack of 5 , the wedge-like patterns at the spanwise stations C and D can be observed in the PSP images, which are associated with flow separation triggered by surface

222

9. Applications of Pressure Sensitive Paint

imperfections near the leading edge of the wing. Fluorescent oil flow visualization on the surface confirmed this observation. As shown in Fig. 9.27, infrared thermography visualizes a surface temperature change induced by the flow separation at these stations and indicates that small turbulent wedges are generated by surface imperfections at the angles of attack of 0, 1 and 3 degrees. However, these turbulent wedges did not significantly alter the pressure distributions. In addition, using the Uni-Coat PSP, they studied the Reynolds number effect on the pressure distribution on the wing. Mebarki and Le Sant (2001) evaluated the accuracy of PSP measurements at Mach 0.74 for all the PSP formulations through in-situ calibration. Table 9.1 summarizes the accuracy of the PSP results in terms of the absolute difference in Cp and the percentage error (%FS) over the full-scale range of Cp that is defined as the maximum range of Cp measured during a run on the wing upper surface by 39 pressure taps. The exposure times of the camera used for the PSP formulations are also listed in Table 9.1, depending on the luminescent intensity of a particular paint. Generally speaking, the accuracy was fairly good for all the PSPs at different Reynolds numbers despite their different temperature sensitivities, because a temperature variation over the wing chard during a run was relatively o small (less than 2 C). Table 9.1. Absolute and relative accuracy of PSP formulations in Cp PSP UniCoat Sol-gel FIB FEM PAR

M = 0.74, Rc = 3.8 mil t (ms) %FS ∆Cp 50 0.04 3.2

M = 0.74, Rc = 8.5 mil t (ms) %FS ∆Cp 75 0.10 8.4

125 500 500 250

250 1000 1000 500

0.04 0.02 0.02 0.03

2.8 1.4 1.7 2.2

0.04 0.03 0.04 0.03

Station C

Station B -1.6

-1.6

o

α=0 α=1o α=3o o α=5

-1.4 -1.2

α =0 o α =1 o o α =3 α =5 o

-1.4 -1.2

-1

CP

-1

CP

3.1 2.7 3.3 2.6

-0.8

-0.8

-0.6

-0.6

-0.4

-0.4

-0.2

-0.2 0.2

0.6

0.4

x/c

0.8

0.2

0.6

0.4

0.8

x/c

Fig. 9.26. Comparison of PSP results (lines) obtained using the FIB PSP with pressure tap 6 data (circles) at M = 0.74 and Rec = 3.8×10 . From Mebarki and Le Sant (2001)

9.2. Subsonic, Transonic, and Supersonic Wind Tunnels Cp ¯ FLOW

223

T (deg. C)

a =0o -0.2

-0.4

a =1o -0.6

-0.8

a =3

o

-1

-1.2

a =5o -1.4

B

C

D

-1.6

Fig. 9.27. The distributions of the pressure coefficient Cp on the wing upper surface obtained with the FIB PSP and the corresponding temperature distributions obtained using 6 an infrared camera at M = 0.74, Rec = 3.8×10 , and AoA = 0, 1, 3 and 5 degrees. From Mebarki and Le Sant (2001)

9.2.3. Transonic Wing-Body Model Shimbo et al. (2000) conducted PSP measurements on an 8%-scaled model of the Mitsubishi MU-300 business jet at the Mach numbers 0.6-0.8 and the angles-ofattack 0-4.6 degrees in the 2-m transonic wind tunnel at the National Aerospace Laboratory (NAL) in Japan. The main objective of their tests was to examine the feasibility of PSP combined with TSP for correcting the temperature effect of PSP. The model was equipped with 32 pressure taps in four rows on the upper surface of the starboard wing. A water-cooled 14-bit CCD camera (1008×1018 pixels) attached with optical filters was used. A xenon lamp was used as an excitation light source and the light was introduced through optic fibers to light reflectors. Each light reflector had an optical filter such that only the UV light went through for paint excitation. The classical PSP, PtOEP in GP-197, was applied on the upper surface of the starboard wing for pressure measurements, whereas a typical TSP, EuTTA in PMMA, was applied on another wing for temperature measurements. Since the emission peaks of both PSP and TSP were close in the emission spectra, the luminescent intensity from both PSP and TSP were acquired on the same image using the CCD camera mounted on the ceiling of the test section. Assuming the flow symmetry with respect to the model centerline, Shimbo et al. (2000) used the temperature distributions on one of the wings obtained by TSP to correct the temperature effect of PSP on another wing.

224

9. Applications of Pressure Sensitive Paint

Figure 9.28 shows typical pressure fields on the wing surface obtained using a combination of PSP and TSP at Mach 0.75 for the angles of attack of 2.3 and 4.7 degrees. A shock on the wing is clearly seen in the PSP images. For a quantitative comparison, the pressure distributions obtained using a combination of PSP and TSP and in-situ calibration at four spanwise locations are shown in Fig. 9.29 along with the corresponding pressure tap data for Mach 0.75 and the angle of attack of 2.3. In this example, a combination of PSP and TSP was able to give reasonable pressure results without utilization of any pressure tap data for correcting the temperature effect.

(a) M = 0.73, AoA = 2.3 deg.

(b) M = 0.75, AoA = 4.7 deg.

Fig. 9.28. Typical pressure fields on the Mitsubishi MU-300 business jet model obtained using a combination of PSP and TSP at Mach 0.73 and α = 2.3 and 4.7 degrees. From Shimbo et al. (2000)

9.2. Subsonic, Transonic, and Supersonic Wind Tunnels y/s=0.19

Cp

-1

-1.5 -1

-0.5

-0.5

0

0

0

20

40 60 x/c [%]

80

100

y/s=0.55

Cp

0

-1.5

-1

-1

-0.5

-0.5

0

0

20

40 60 x/c [%]

20

80

100

0

40 60 x/c [%]

80

100

80

100

y/s=0.85

Cp

-1.5

0

y/s=0.32

Cp

PSP/TSP in situ o tap

-1.5

225

20

40 60 x/c [%]

Fig. 9.29. Comparison between PSP (lines) and pressure tap data (circles) for the Mitsubishi MU-300 business jet model at Mach 0.73 and α = 2.3 deg. PSP data were obtained using a combination of PSP and TSP as well as in-situ calibration. From Shimbo et al. (2000)

9.2.4. Laser Scanning Pressure Measurement on Transonic Wing Torgerson (1997) demonstrated a phase-based laser scanning system for PSP measurements on a transonic airfoil in the Boeing Company model transonic wind tunnel. A 10% thick airfoil having a sharp leading edge and a small amount of camber was used, which was equipped with 19 pressure taps along the upper surface for a comparison with PSP data. The airfoil was coated with a Rutheniumbased PSP. The scanning system had a small air-cooled argon-ion laser for excitation and a PMT as a detector. The blue laser beam was modulated using an electro-optic modulator before scanning over the airfoil surface with a computercontrolled mirror, enabling the PMT signal to be processed using a two-phase lock-in amplifier. Both the phase and intensity signals were recorded during scanning over the airfoil such that a comparison between the intensity and phase methods could be made. Figure 9.30 shows a typical pressure distribution at Mach 0.8, indicating that both the phase and intensity methods compared favorably with the pressure tap data after in-situ calibration was applied. Nevertheless, phase-based measurements had the advantage that the wind-off data were not required.

226

9. Applications of Pressure Sensitive Paint 12

Intensity Phase Pressure taps

Pressure, psia

10

M=0.80

8

6

4

0.0

0.2

0.4

0.6

0.8

1.0

x/c

Fig. 9.30. Pressure distribution on a transonic airfoil obtained using a laser scanning system based on the phase and intensity methods. From Torgerson (1997)

9.2.5. Boundary Layer Control in Supersonic Inlets Bencic (2002) applied PSP to boundary layer control experiments in supersonic inlets through mass removal in the 1×1 foot Supersonic Wind Tunnel at NASA Glenn. The tests investigated shock/boundary-layer interactions that caused a reduction in the inlet performance due to boundary layer separation. As shown in Fig. 9.31, the test setup consisted of a porous boundary layer control device replacing a wind tunnel sidewall panel. The boundary layer bleed used a pressure difference generated by a suction plenum mounted to the backside of the porous surface to remove the low momentum fluid in the boundary layer. The bleed control panels were painted with a silicone-based Ruthenium PSP (Boeing PF2B). Reference images were taken at reduced pressure of approximately 12 kPa since this facility had the capability to be brought to near vacuum conditions quickly. The reduced reference pressure was used because it was in the range of pressures measured on the porous plates during wind tunnel operation. A constant exposure time was used for both the wind-off and wind-on images, producing images that filled about 80% of the full-well capacity of the CCD camera. Each image was ensemble average of eight frames to further reduce the photon shot noise. Reduction of the acquired data was performed using the intensity-based method plus in-situ calibration based on data from 16 pressure taps located in the painted sections. Typical PSP images are shown in Figs. 9.32, 9.33 and 9.34 for three surface bleed configurations C1, C6 and C3 that denote the standard 90° bleed hole configuration, the pre-conditioned 90° bleed hole configuration and the 20° inclined bleed hole configuration, respectively (Willis et

9.2. Subsonic, Transonic, and Supersonic Wind Tunnels

227

al. 1995). Each image was acquired at a nominal tunnel speed of Mach 2.0 under the similar conditions of the total mass flow through the bleed hole regions. The PSP images show the surface pressure normalized by the wall static pressure measured upstream of the fenced porous plate insert. The orifice and row interactions, which were clearly evident in these figures, were undetectable with conventional pressure tap instrumentation. The significant result from this test was the performance increase of 50% in removing mass by the pre-conditioned 90° configuration compared to the standard 90° orifice as reported by Willis et al. (1995). This increase was due to a combination of flow turning and the pressure gradient acting across the flush inlet. The performance differences between these configurations can be seen as larger pressure excursions as noted by the change in lower scale in Figs. 9.32, 9.33 and 9.34. The more efficient configurations in Figs. 9.33 and 9.34 generally showed a higher level of interaction between adjacent rows compared to the standard 90° configuration in Fig. 9.32. The PSP measurements had an error of 0.3 kPa or less in these examples. A systematic shift was found between PSP and pressure tap data in the bleed hole region compared to the solid region upstream and downstream of the porous region. This shift was due to a temperature difference in the aluminum insert plate caused by the airflow through the orifice holes. Clearly, simultaneous full-field temperature measurements (TSP or infrared thermography) are needed to compensate for the temperature sensitivity of PSP to minimize the errors associated with the effect. The experiments of Bencic (2002) represent a typical PSP application to complicated geometric configurations in turbomachinery flows. PSP provides a powerful diagnostic tool for turbomachinery flows with complex shock wave structures where a pressure field cannot be mapped with conventional techniques in a high spatial resolution. PSP has been used for pressure measurements in narrow supersonic channel, shock/wall interaction, stator vanes, transonic fan cascade, mixer-ejector nozzles, and jet/flow interaction (Lepicovsky and Bencic 2002; Taghavi et al. 1999; Lepicovsky 1998; Lepicovsky et al. 1997; Cler et al. 1996; Everett et al. 1995). However, confined spaces by multiple surfaces in turbomachinery cause significant inter-reflection of the luminescent light between neighboring surfaces and this self-illumination complicates the data processing to extract correct values of pressure on these surfaces. So far, a correction scheme for the self-illumination was made only for simple geometric configurations such as a corner between two planes. For complex geometry in turbomachinery, an efficient numerical scheme for correcting the self-illumination effect have to be developed based on an accurate model for the bi-directional reflectance distribution function of PSP (see Section 5.3).

228

9. Applications of Pressure Sensitive Paint

Fig. 9.31. Test setup of a bleed control panel as a boundary layer control device. From Bencic (2002)

Fig. 9.32. Normalized surface pressure map P/Ps on the control panel with a standard multiple 90° bleed hole configuration, where Ps is the wall static pressure measured upstream of the fenced porous plate insert. Tunnel flow is from left to right. From Bencic (2002)

9.2. Subsonic, Transonic, and Supersonic Wind Tunnels

229

Fig. 9.33. Normalized surface pressure map P/Ps on the control panel with a multiple preconditioned 90° bleed hole configuration, where Ps is the wall static pressure measured upstream of the fenced porous plate insert. Tunnel flow is from left to right. From Bencic (2002)

Fig. 9.34. Normalized surface pressure map P/Ps on the control panel with a multiple 20° inclined bleed hole configuration, where Ps is the wall static pressure measured upstream of the fenced porous plate insert. Tunnel flow is from left to right. From Bencic (2002)

230

9. Applications of Pressure Sensitive Paint

9.3. Hypersonic and Shock Wind Tunnels PSP application in hypersonic flows is more difficult because high enthalpy of flows may produce such a large temperature increase on a model that the temperature effect of PSP is overwhelming. Since hypersonic wind tunnels are usually short-duration tunnels, a very thin PSP coating is required not only to sustain high skin friction, but also to achieve a short response time. However, the luminescent emission from a very thin PSP layer is weak and thus a low SNR becomes a problem. The short run-time limits the exposure time of a CCD camera to collect photons and further reduces the possibility of improving the SNR. Kegelman et al. (1993) conducted PSP measurements on a 1/6-scale Pegasus launch vehicle model and a shock/boundary-layer interaction model in the NASA Langley Mach 6 High Reynolds Number Tunnel. The McDonnell Douglas PSP and TSP were used in their tests. The pressure distributions obtained using PSP on the Pegasus model were in qualitative agreement with the Navier-Stokes code results over most of the wing. However, considerable discrepancies between the PSP data and CFD results were observed near the leading edge and wing tip where high temperature generated by aerodynamic heating exceeded the workable temperature range of the paint. Quantitative PSP results, which were compared favorably with the pressure tap data, were obtained on the surface of a flat-plate model on which an oblique shock impinged; the accuracy of about 0.1 psia was reported. Using fast-responding PSP formulations, Troyanovsky et al. (1993) carried out semi-quantitative PSP visualization in shock/body interaction in a Mach 8 shock tube with a duration of 0.1 s. Borovoy et al. (1995) measured the pressure distribution on a cylinder at Mach 6 in a shock wind tunnel with a duration of 40 ms, and achieved reasonable agreement with the theoretical solution and pressure transducer measurements. Jules et al. (1995) used a McDonnell Douglas PSP to study shock/boundary-layer interaction over a flat-plate/conical-fin configuration at Mach 6, showing a systematic shift compared to pressure tap measurements. Hubner et al. (1997, 1999, 2000, 2001) measured the pressure distributions on a wedge and an elliptic cone at Mach 7.5 in the Calspan hypersonic shock tunnel with a run-time of 7-8 ms. To reduce the temperature effect of PSP, they applied PSP directly on the metal model surface rather than a white basecoat. However, for a very thin layer of PSP without a white basecoat, the luminescent intensity of PSP was so low that only 5-12% of the CCD full-well capacity was utilized. Buck (1994) discussed simultaneous temperature and pressure measurements on dyed ceramic models using luminescent materials in hypersonic wind tunnels. 9.3.1. Expansion and Compression Corners Nakakita et al. (2000) used anodized aluminum (AA) PSP to measure the pressure fields on the expansion corner and compression corner models at Mach 10 in the NAL Middle Scale Shock Tunnel with a duration of 30 ms. More recent measurements in shock tunnels were made using AA-PSP on a wing-body model, a hemisphere and scramjet inlet models (Nakakita and Asai 2002;

9.3. Hypersonic and Shock Wind Tunnels

231

Sakaue et al. 2002b). AA-PSP with a probe molecule Ru(dpp) was used since it had a very short response time of about 30–100 µs. Furthermore, because AAPSP on aluminum models was binder-free and pure aluminum models had high thermal conductivity, an increase of the surface temperature was relatively small o (less than 2 C) in most parts of the model during a run in the shock tunnel. The NAL Middle Scale Shock Tunnel had the total temperature of 1180 K, total pressure of 3.4 MPa, Pitot pressure of 7800 Pa, Mach number of 10.4, and 5 Reynolds number 1.6×10 based on the 0.1-m model span. Figure 9.35 shows an optical system for illumination and measurements, which was set at the front of an optical window of a vacuum tank and 1.3 m away from the model. A highly stable continuous xenon lamp (fluctuation of the light intensity was much smaller than 1%) was used as an illumination light source and the illumination light was transmitted through a light guide and projected onto the model by a lens at the exit of the light guide. A cooled 14-bit CCD camera (Hamamatsu C4880-07) attached with an image intensifier (Hamamatsu C6245MOD) was used to detect the luminescent emission from PSP. The intensifier enhanced the capability of the camera to measure weak luminescence in a short exposure time at the cost of introducing additional noise. The spatial resolution of the CCD camera was originally 1008×1018 pixels. However, after 2×2 binning was applied to reduce the shot noise and readout noise, the spatial resolution was reduced to 504×509 pixels. To separate the illumination light from the luminescent emission, a band-pass filter (460±50nm) was placed between the exit of the light guide and the condenser lens transmits; another band-pass filter (600-800nm) was mounted in the front of the intensifier to eliminate the illumination light projected to the CCD camera. The exposure time for the camera was 20 ms. Figure 9.36 shows the expansion corner and compression corner models made of pure aluminum. Both models had an upstream plane connected to a downstream plane. The expansion corner model had the downstream plane deflecting outward 15o relative to the upstream one, whereas the compression o corner model had the downstream plane having a 30 ramp against the upstream one. There were six pressure taps connected Kulite (XCS-093-5A) pressure transducers on each model to provide reference pressure data for comparison. The expansion corner model was tested at the angles of attack of 10, 20, 30 and 40 degrees. Figure 9.37 shows a typical PSP image and a Schlieren image along with a comparison plot of PSP data with pressure tap data at the angle of attack o of 40 . In Fig. 9.37, the horizontal axis is the coordinate along the model surface normalized by the length of upstream plane Lp and the vertical axis is the local pressure normalized by the Pitot pressure P02. PSP data were in good agreement with the pressure tap data. On the expansion corner model, the flow field on each plane can be considered as a 2D wedge-flow where pressure on the surface is constant. As shown in Fig. 9.37, the pressure distributions are nearly uniform on the upstream and downstream planes. The Schlieren images indicate a shock wave at the leading edge and an expansion fan at the corner of the model. The compression corner model was also tested at the angles of attack of 0, 10, 20, and 30 degrees. Figure 9.38 shows a typical PSP image, a Schlieren image, and a pressure distribution plot for the compression corner at the angle of attack of

232

9. Applications of Pressure Sensitive Paint

o

30 . The Schlieren image indicates a much more complicated flow field including shock/boundary-layer interaction and shock/shock interaction on the compression corner model. The high-pressure region was associated with shock/shock interaction near the corner. Again, PSP data were in good agreement with the pressure tap data.

Fig. 9.35. Optical system for PSP measurements and calibration in the NAL Middle Scale Shock Tunnel (viewing from the ceiling). From Nakakita et al. (2000)

9.3. Hypersonic and Shock Wind Tunnels

233

=

>

Fig. 9.36. Experimental models: (a) Expansion corner model and (b) Compression corner model. From Nakakita et al. (2000)

234

9. Applications of Pressure Sensitive Paint

PSP (3runs) Pressure Transducer (3runs)

P/P02 (P02=8,000Pa)

0.8 0.6 0.4 0.2 0.0 -0.5

0.0

0.5

1.0 X/Lp

1.5

2.0

2.5

Fig. 9.37. PSP image, Schlieren photograph, and pressure distribution on the expansion o corner model at Mach 10 and the angle of attack of 40 . From Nakakita et al. (2000)

9.3. Hypersonic and Shock Wind Tunnels

P/P02 (P 02=8,000Pa)

1.4

235

PSP (3runs) Pressure Transducer (3runs)

1.2 1.0 0.8 0.6 0.4 0.2 0.0 -0.5

0.0

0.5

1.0 X/Lp

1.5

2.0

2.5

Fig. 9.38. PSP image, Schlieren image, and pressure distribution on the compression corner o model at Mach 10 and the angle of attack of 30 . From Nakakita et al. (2000)

236

9. Applications of Pressure Sensitive Paint

9.3.2. Moving Shock Impinging to Cylinder Normal to Wall Asai et al. (2001) demonstrated the feasibility of Ru(dpp) AA-PSP for timeresolved unsteady pressure measurements in the NAL 0.44 m Hypersonic Shock Tunnel. Figure 9.39 is a schematic of the experimental setup for the shock tube tests. A circular block of a 12 mm diameter was installed vertically in the center of a PSP-coated part flush mounted on the shock tube wall. Calibration of PSP was made by adjusting the test section pressure prior to running the shock tube. Full-field measurements were acquired using a CCD camera with an intensifier that can be gated at successive instants after incidence of a moving shock wave. Illumination for PSP was provided by a flash lamp. Sequential images were obtained from 475 to 530 µs in an interval of 5 µs. The camera gating time was set at 10 µs. Figure 9.40 shows a time sequence of images of an unsteady pressure field induced by a moving shock wave interacting with the stationary circular block, where the shock speed was 610 m/s. Because the observation window flush mounted on the surface of the tube acted like a 2D concave lens, the images were compressed vertically so that a circular section of the cylinder looked like an ellipse. As shown in Fig. 9.40, a curved high-pressure region induced by the reflected shock was formed in the front of the block after the incident plane shock impinged to the block. At the same time, a part of the incident shock continued traveling downstream after it was deflected, and the expansion waves were generated. A pair of symmetric vortices, which are visualized as the low-pressure regions in Fig. 9.40, formed and grew behind the circular block.

PSP coating model with BAR Shock tube

36.95mm 73.9mm

Xenon flash lamp

Optical window Dichroic Beam Splitter

Optical fiber Image Intensifier Flash lamp driver Cooled CCD camera

Fig. 9.39. Schematic of an experimental setup for time-resolved PSP measurements in a shock tube. From Asai et al (2001)

9.4. Cryogenic Wind Tunnels

237

Fig. 9.40. Sequential images of unsteady pressure field induced by interaction between a moving shock wave and a circular cylinder block, where the speed of the shock is 610 m/s and the interval between two images is 5 µs. From Asai et al (2001)

9.4. Cryogenic Wind Tunnels PSP measurements were made in cryogenic wind tunnels where the oxygen concentration in the working nitrogen gas is extremely low and temperature is as low as 90 K (Asai et al. 1997a; Upchurch et al. 1998). The development of cryogenic PSP formulations was motivated by the needs of global pressure measurement techniques in large-scale pressurized cryogenic wind tunnels such as the National Transonic Facility (NTF) at NASA Langley and the European Transonic Wind Tunnel (ETW). Asai et al (1997a) developed a binder-free PSP coating on an anodized aluminum surface and measured the surface pressure distributions on a 14% thick circular-arc bump model in a small cryogenic wind tunnel in the National Aerospace Laboratory (NAL) in Japan. PSP data were in good agreement with pressure tap data at 100 K over a range of the Mach numbers of 0.75-0.84. However, the methodology of coating on an anodized surface cannot be applied to stainless steel models typically used in cryogenic wind tunnels. Upchurch et al. (1998) developed a polymer-based cryogenic PSP that could be universally applicable to all types of surfaces including stainless steel and this paint was successfully demonstrated in pressure measurements on an airfoil in the 0.3-m cryogenic tunnel at NASA Langley. Asai et al. (2000, 2002) also presented a polymer-based cryogenic PSP formulation applied to cryogenic wind tunnels and short-duration shock tunnels, which was based on a polymer named Poly(TMSP) having extremely high gas permeability. This PSP can be dissolved

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9. Applications of Pressure Sensitive Paint

into a solvent and applied using an airbrush to any model surface including stainless steel in contrast to AA-PSP only applicable to aluminum or aluminum alloy. Hitherto, cryogenic PSP measurements have not been conducted in NTF and ETW due to safety concerns on injection of a small amount of air (oxygen) into the tunnels. Therefore, small cryogenic tunnels are more suitable to preliminary pioneering experiments since they are more adaptable and relatively inexpensive to run. Asai et al. (2000, 2002) described application of Poly(TMSP)-based PSP and AAPSP data to a circular-arc bump model and a delta wing model in the 0.1-m Transonic Cryogenic Wind Tunnel at NAL. Figure 9.41 is a schematic of the tunnel operated by controlling both liquid nitrogen injection and gaseous nitrogen exhaust. A small amount of air was injected just downstream of the test section, and the oxygen concentration in flow was measured from sampled exhaust gas using a Zirconia (ZrO2) sensor. The oxygen concentration was varied from near zero to 2000 ppm by adjusting the flow rate of the injected air. Figure 9.42 is a schematic of the optical setup for experiments. The model mounted on the sidewall was viewed through a 70mm diameter window on the opposite sidewall. A 300-watt xenon lamp with a band-pass filter (400±50nm) was used for illumination. A dichroic mirror (550 nm) was used to separate the luminescent emission of PSP from the excitation light. A 14-bit cooled CCD digital camera with a band-pass filter (650±20 nm) placed before the lens was used for luminescence measurements. As shown in Fig. 9.43, a 2D bump model and a clipped delta wing were used for experiments. The cross-section of the aluminum bump model was a 14% circular arc having the chord length of 50 mm. The bump model was equipped with 16 pressure taps at the mid-span. The Poly(TMSP)-PSP were coated in two 8mm wide strips on the surface using an airbrush, while other two strips were anodized to make AA-PSP using a method developed by Sakaue et al. (1999). The stainless steel delta wing model had a 65o-sweep angle and a sharp leading edge, on which an array of eight taps was installed at 80% of the 60-mm model chord. The model was o strut-mounted on the sidewall at the angle of attack of 20 . The Poly(TMSP)-PSP was applied to the whole upper surface of the delta wing using an airbrush.

Fig. 9.41. Schematic of the NAL 0.1 m Transonic Cryogenic Wind Tunnel. From Asai et al. (2002)

9.4. Cryogenic Wind Tunnels

239

Fig. 9.42. Schematic of an optical setup for PSP measurements in the NAL 0.1 m Transonic Cryogenic Wind Tunnel. From Asai et al. (2002)

50mm

Pressure Taps (0.3mm x 16)

(47.563)

65deg

Removable Strip

48 60

5

8 static pressure taps at x/c=80%

(a)

(b)

Fig. 9.43. (a) Circular-arc bump model, and (b) 65-degree sweep delta wing model for cryogenic PSP measurements. From Asai et al. (2002)

In experiments, the Mach number was set at either 0.4 or 0.82, and the total temperature and pressure in the tunnel were maintained at 100 K and 190 kPa, respectively. The oxygen concentration was varied up to 1000 ppm. Figure 9.44 shows in-situ calibration results for Poly(TMSP)-PSP at the total temperature Tt = 100 K and [O2] = 1000 ppm, indicating the linear Stern-Volmer relation between the luminescent intensity ratio Iref/I and the relative pressure p/pref. Since the model surface was fairly isothermal in cryogenic flows, a single calibration curve was used for data reduction on the entire surface of the model. Figure 9.45 shows the

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9. Applications of Pressure Sensitive Paint

pressure distribution obtained using in-situ calibration on the bump model at Mach 0.82 and Tt = 100 K, where the image at Mach 0.4 was used as a reference image since the tunnel could not run below that speed. The PSP-derived pressure data were in good agreement with the pressure tap data after in-situ calibration is applied. It was found that the use of a priori calibration did not produce results consistent with the pressure tap data because the slope of a priori calibration curve was twice as large as that of the in-situ calibration curve. For the delta wing model, the raw images were taken at Mach 0.4 and 0.75, the total temperature Tt = 100 K, and the oxygen mole fraction [O2] = 997 ppm. Figure 9.46 presents a ratio of the wind-on image at Mach 0.75 to the reference image at Mach 0.4, visualizing the leading edge vortices. The primary and secondary separations were clearly observed. Figure 9.46 also shows the spanwise distributions of the intensity ratio I/Iref on the wing at four chordwise locations. The intensity ratio profiles were noisy because the intensity difference between the images at Mach 0.4 and 0.75 was relatively small. The PSP measurements on the delta wing were basically qualitative.

1.0 y=0.3557x + 0.6408 0.9

0.8

J JJ JJ J

J J J J J J J J J

M=0.82 Mach = 0.82 PtPt=190kPa = 190 kPa TtTt=100K = 100 K [O2]=1000ppm [O2] = 1000 ppm

0.7

0.6

0.4

J

0.5

0.6

0.7

0.8

0.9

1.0

P/Pref Fig. 9.44. In-situ calibration for Poly(TMSP) PSP at the total temperature Tt = 100 K and [O2] = 1000 ppm. From Asai et al. (2002)

9.4. Cryogenic Wind Tunnels

241

-1.0

-0.5

J

J

J

JJ J

J

J

J

0.0 J

J

J

JJ

J

J

J

0.5

TAPS

CRYO-PSP 1.0 0.0

0.2

0.4

x/c

0.6

0.8

1.0

Fig. 9.45. The pressure coefficient distribution on the bump model obtained using cryogenic PSP compared with pressure tap data at Mach 0.82. From Asai et al. (2002)

Fig. 9.46. Intensity ratio image of a delta wing and spanwise intensity distributions at 20, 40, 60, and 80% chords for M = 0.75, Tt = 100 K, Pt = 190 kPa and [O2] = 997 ppm. From Asai et al. (2002)

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9. Applications of Pressure Sensitive Paint

9.5. Rotating Machinery PSP is a promising technique for measuring the surface pressure distributions on high-speed rotating blades in turbomachinery where conventional techniques are particularly difficult to use. Using a laser scanning system, Burns and Sullivan (1995) measured the pressure distributions on a small wooden propeller at a rotational speed of 3120 rpm and a TRW Hartzell propeller at a rotational speed of 2360 rpm. Mosharov et al. (1997) obtained the pressure distributions on propellers using a CCD camera system with a pulse light source. PSP measurements on helicopter rotor blades were carried out at TsAGI (Bukov et al. 1997; Mosharov et al. 1997) and NASA Ames (Schairer et al. 1998b). Navarra et al. (1998) obtained pressure images on a rotor blade using an ICCD camera system. Hubner et al. (1996) suggested a lifetime imaging method for PSP measurements on a rotating object based on detecting the luminescent decay traces of a rotating painted surface on a CCD camera. Here, we describe two typical PSP measurements on rotating blades where a laser scanning system and a CCD camera system were used respectively. 9.5.1. Laser Scanning Measurements Using a laser scanning system, Liu et al. (1997a) and Torgerson et al. (1997, 1998) performed PSP measurements on rotor blades in a high-speed axial flow compressor (the Purdue Research Axial Fan Facility) and an Allied Signal F109 turbofan engine. They used Ru(dpp) in GE RTV 118 mixed with silica gel particles as PSP and Ru(bpy) in Shellac as TSP. PSP and TSP were coated on blades by dipping them into the paints, resulting in about 20-µm thick coatings. Figure 9.47 is a schematic of a laser scanning system used for PSP and TSP measurements in the compressor facility where optical access is very limited. An air-cooled Argon laser with the filtered output at 488 nm was used as an illumination source; the laser was mounted upstream of the inlet contraction. The laser beam focused by a lens passed between upstream inlet guide vanes and illuminated rotor blades in a 1-mm diameter spot. Using a computer-controlled scanning mirror, a laser spot scanned across 21 spanwise (radial) locations along each blade. As a blade rotated and cut the laser beam, the beam illuminated the painted blade across its chord, and at least 100 data points were obtained across the chord, depending on the rotational speed of the blade. The luminescent emission from the paints was detected using a PMT attached with a long-pass filter for eliminating the excitation light. Data were acquired using a PC with a 12-bit A/D converter operating at the maximum rate of 500,000 samples/s. The pressure and temperature distributions were calculated using a priori calibration relations for both PSP and TSP.

9.5. Rotating Machinery

Computer Controlled Scanning Mirror

243

Variable inlet Guide Vanes Compressor Rotor

Long Pass Filter Photomultiplier Tube Argon-ion Laser (488 nm) Inlet Contraction

Fig. 9.47. Laser scanning system for PSP and TSP measurements in a high-speed axial flow compressor with very limited optical access. From Liu et al. (1997a)

Figure 9.48 shows typical raw intensity signals from PSP and TSP on the suction surface of the painted blades at the rotational speeds of 1000, 13500 and 17000 rpm. As the rotational speed increased, the luminescent intensity of TSP decreased due to the increased surface temperature. A change in the luminescent intensity distribution of PSP was mainly caused by a pressure variation on the surface. In particular, a rapid decrease in the luminescent intensity, which occurred in a region from the 90th to 100th data point (0.6 to 0.67 chord) at 17,000 rpm, corresponded to a large pressure jump generated by a shock. The luminescent signal at the lowest speed of 1000 rpm was used as the reference intensity (nearly wind-off). Figure 9.49 shows the temperature distributions on the suction surface at 50% span at different rotational speeds. The temperature distributions appeared to be flat over a large portion of the chord, and the mean temperature increased with the rotational speed due to friction heating. The highest temperature on the blade surface was about 43oC at the speed of 17800 rpm. The pressure distributions on the surface were obtained using a priori calibration relation of PSP where the temperature effect of PSP was corrected based on the TSP data. Figures 9.50, 9.51 and 9.52 show the chordwise distributions of the relative pressure p/p0 at 25%, 50%, and 75% spans for different rotational speeds, where p0 is the upstream stagnation pressure (one atmosphere pressure in this case). The formation of a shock was evidenced by an abrupt increase in the pressure distributions at the speeds of 17000 and 17800 rpm. As the rotational speed increased, the shock became stronger and its location moved downstream. Figure 9.53 shows a composite representation of the pressure and temperature distributions mapped onto a surface grid of blade at the speed of 17800 rpm.

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9. Applications of Pressure Sensitive Paint

3000 Luminescent intensity (counts)

PSP

TSP

2500 2000 1000 rpm 1500 1000 500

17000 rpm

13500 rpm

0 0

50

100

150

200

250

300

data point

Fig. 9.48. Raw PMT signals from PSP and TSP at three rotational speeds of 1000, 13500, and 17000 rpm. From Liu et al. (1997a)

60 R = 5 in (midspan)

temperature (deg. C)

55 50

increase of rotational speed

45 40 35 30 25 20 15 0.0

0.2

0.4

0.6

0.8

1.0

x/c

Fig. 9.49. Chordwise surface temperature distributions at 50% span at different rotational speeds of 10000, 13500, 14750, 16000, 17000, and 17800 rpm. From Liu et al. (1997a)

9.5. Rotating Machinery

1.3

1.1 1.0 p/p0

25% span

10,000 rpm 14,500 rpm 16,000 rpm 17,000 rpm 17,800 rpm

1.2

0.9 0.8 0.7 0.6

increasing rpm

0.5 0.0

0.2

0.4

0.6

0.8

1.0

x/c Fig. 9.50. PSP-derived pressure distributions at 25% span. From Liu et al. (1997a)

1.3

1.1 1.0 p/p0

50% span

10,000 rpm 14,500 rpm 16,000 rpm 17,000 rpm 17,800 rpm

1.2

0.9 0.8 0.7 0.6 increasing rpm

0.5 0.0

0.2

0.4

0.6

0.8

1.0

x/c Fig. 9.51. PSP-derived pressure distributions at 50% span. From Liu et al. (1997a)

245

246

9. Applications of Pressure Sensitive Paint

1.3 14,500 rpm 16,000 rpm 17,000 rpm 17,800 rpm

1.1 1.0 p/p0

75% span

10,000 rpm

1.2

0.9 0.8 0.7 0.6 increasing rpm

0.5 0.0

0.2

0.4

0.6

0.8

1.0

x/c Fig. 9.52. PSP-derived pressure distributions at 75% span. From Liu et al. (1997a)

Fig. 9.53. Pressure and temperature distributions on compressor blades at the speed of 17800 rpm. From Torgerson et al. (1998)

9.5. Rotating Machinery

247

9.5.2. CCD Camera Measurements Using a CCD camera system, Bencic (1997, 1998) conducted full-field PSP and TSP measurements on rotating blades of a 24-inch diameter scale-model fan in the NASA Glenn 9×15 ft low speed wind tunnel at rotational speeds as high as 9500 rpm. PSP measurements with a CCD camera on high-speed rotating blades presented challenging problems, such as limited optical access to the entire surface of blades, very short light duration for sufficient illumination, detection of weak luminescence from high-speed rotating blades, and quantitative measurements without standard instrumentation for in-situ calibration of PSP. A 25%-scale model fan used for experiments was a single rotation, ultra high bypass fan. Two blades were painted, one with a proprietary Boeing TSP and other with a Boeing PSP (PF2B) on a white primer basecoat. Figure 9.54 shows o the painted fan blades installed 180 apart in the fan test rig. The traditional intensity-based method was used for both PSP and TSP, requiring two images for each of the paints to determine the pressure and temperature fields. Nine black targets were applied to both PSP and TSP painted blades for image registration. Both PSP and TSP were illuminated at wavelengths centered at 450 nm with multiple filtered and focused xenon flash quartz lamps with a 2-3 µs flash duration. The flash duration was short enough to freeze the motion of the blades with minimal blurring. Note that a 2-µs flash duration roughly corresponded to 0.5-mm blurring on blades at the highest speed.

Fig. 9.54. PSP and TSP painted blades mounted in an ultra-high bypass ratio fan rig. From Bencic (1997)

Bencic (1997, 1998) used a 14-bit cooled scientific CCD camera (512×512 pixels) that was fitted with a 200-mm lens attached with a band-pass filter around 600 nm for both PSP and TSP. Image acquisition and pulsed excitation were synchronized with the position of the rig using a trigger signal from a magnetic speed sensor. Using a delayed trigger signal, blade motion could be stopped o anywhere in a full rotation of 360 . Therefore, a PSP blade image was acquired

248

9. Applications of Pressure Sensitive Paint o

and then, by delaying the trigger signal in a 180 phase angle, a TSP image was o taken since the PSP and TSP coated blades were installed 180 apart, as shown in Fig 9.54. Images were acquired and integrated over two hundred revolutions under excitation of multiple flashes while the camera shutter was kept open until achieving an acceptable CCD well capacity. Two wind-off reference images and two data images of TSP and PSP were taken at each fan operating condition of interest. TSP images were used to correct the temperature effect of PSP. Figures 9.55 and 9.56 show, respectively, the temperature images and pressure images at the test points 4950B, 5800B, 7450B and 7875B that correspond to the speeds of 4950, 5800, 7450 and 7875 rpm, o respectively. The surface temperature change on the blade was as large as 20 C under the operating conditions. TSP visualized flow separation occurred approximately at 75% span and 60% chord at the test points 7450B and 7875B.

Fig. 9.55. Temperature fields on the TSP-coated blade at four rig speeds of 4950, 5800, 7450 and 7875 rpm. From Bencic (1997)

9.6. Impinging Jets

249

Fig. 9.56. Normalized pressure fields on the PSP-ccoated blade at four rig speeds of 4950, 5800, 7450 and 7875 rpm. From Bencic (1997)

9.6. Impinging Jets Using PSP and TSP complemented with Schlieren flow visualization, Crafton et al. (1999) studied subsonic jets and sonic under-expanded jets impinging on a flat plate at an oblique incidence angle from a converging nozzle. Results were o obtained on two geometric configurations at the impingement angles of 10 and o 20 and the impingement distances of 3.8 and 4.5 diameters of the jet, respectively. The jet velocity was varied from Mach 0.3 to Mach 1.0. PSP was used to measure the pressure distributions, and TSP to measure the distributions of temperature and the heat transfer coefficient on the impingement surface. Figure 9.57 shows the jet and impingement plate configuration. The jet facility consisted of a 5-in diameter by 12-in long settling chamber with a 1.5-in radial inlet and a 5-mm diameter o nozzle with a 15 convergence angle. The settling chamber was instrumented with a J-type thermocouple to monitor the total temperature of the jet; the total pressure was set using a regulator and monitored using a 0.2 psi resolution Heise pressure gauge. Compressed air was supplied to the nozzle from an air compressor system. The impingement plate was an 8-in high, 12-in long and 1.5-in thick aluminum plate. The normalized geometric impingement distance (H/D) and the impingement angle (θ) were varied independently to produce multiple o o impingement configurations. The impingement angles of 20 and 10 were tested, o where 90 corresponded to normal impingement. The geometric impingement distance (H) was four jet diameters. The coordinate system (S,Y) on the impingement plate was defined in such a way that the origin coincided with the

250

9. Applications of Pressure Sensitive Paint

geometric impingement point, the S-coordinate was along the surface of the impingement plate in the mainstream direction, and the Y-coordinate was along the surface of the impingement plate in the cross-mainstream direction. Air inlet 0.5 cm nozzle

Impingement distance

Impingement plate

H θ

Plenum

Internal diffuser

Geometric impingement point

Impingement angle

Fig. 9.57. Schematic of an obliquely impinging jet test facility. From Crafton et al. (1999)

In experiments, Ru(dpp) in RTV was used as PSP and Ru(bpy) in model airplane dope was used as TSP. PSP and TSP, coated on the surface of the impingement plate, were excited to luminesce by a blue LED array at 460 nm. The luminescent emission, filtered using a long-pass optical filter (>570 nm) to eliminate the excitation light, was detected using a 16-bit Photometrics CCD camera. A ratio between the flow-on and flow-off reference images was converted to pressure or temperature using a priori calibration relations. The temperature distribution on the impingement surface in a sonic jet is shown in Fig. o 9.58 for H/D = 3.8, θ = 10 and p0/pa = 2.7, where pa is the atmospheric pressure. o The surface temperature varied by less than 0.5 C from the region outside of the influence of the jet to any location inside the region of jet impingement. This temperature difference would result in an error of about 0.1 psi in PSP measurements if the temperature effect of PSP was not corrected. Figure 9.59 o shows the pressure distribution obtained using PSP at H/D = 3.8, θ = 10 and p0/pa = 2.7. The pressure pattern associated with shock cells in the sonic jet was clearly visualized. The pressure on the impingement plate varied by more than 8 psi, suggesting that the temperature-induced PSP measurement error was less than 3% of the full range of pressure. Figure 9.60 shows the streamwise pressure distributions for different total pressures (p0/pa) of the jet at the impingement o o angles of 10 and 20 . The subsonic pressure distributions showed a single pressure peak at the stagnation point. This peak pressure location changed with the impingement angle. The first pressure peak in the multi-peak pressure distributions of the sonic impinging jet coincided with the single peak in the subsonic pressure distributions. The first pressure peak corresponded to the stagnation point. In these cases, the first pressure peak location (the stagnation point) was always found somewhere upstream (toward the nozzle) of the geometric impingement point. In fact, the deviation of the stagnation point from the geometric impingement point is an intrinsic property of the non-orthogonal viscous stagnation flow (Dorrepaal 1986; Liu 1992). Theoretically, this deviation o decreases to zero as the impingement angle approaches to 90 . Crafton et al.

9.6. Impinging Jets

251

(1999) discussed a correlation of the peak pressure location with the geometric impingement point, which was related to the impingement distance H and the impingement angle θ. An insight into the multi-peak pressure distribution was gained by Schlieren flow visualization. Figure 9.61 shows a composite representation of the streamwise pressure distribution and Schlieren image for the o sonic jet impinging at 10 . The locations of the shock waves corresponded to the pressure peaks on the impingement surface. 301

po/pa 2.71 H/D 3.8 12 θ 10o

300.8

10

300.4

8

300.2

6

300

S/D

14

300.6

4

299.8

2

299.6

0

299.4

-2

299.2 299 -5

0

5

Y/D

Temperature [K]

Fig. 9.58. Temperature distibution on the impingement surface of a sonic jet. From Crafton et al. (1999)

19

po/pa 2.71 H/D 3.8 12 θ 10o

14

18 17

S/D

10

8

16

6

15

4

14

2

13 0

12

-2

11 -5

0

Y/D

5

Pressure [psia]

Fig. 9.59. Pressure distribution on the impingement surface of a sonic jet. From Crafton et al. (1999)

252

9. Applications of Pressure Sensitive Paint

19

θ = 10, H/D = 3.8

Pressure [psia]

18

po/pa 1.07 po/pa 1.14 po/pa 1.27

17

po/pa 1.55 16

po/pa 2.10 po/pa 2.71

15 14 13 12 -4

0

4

8

12

16

S/D 19

θ = 20, H/D = 4.5

Pressure [psia]

18

po/pa 1.07 po/pa 1.14 po/pa 1.27

17

po/pa 1.55 16

po/pa 2.10 po/pa 2.71

15 14 13 12 -4

0

4

8

12

16

S/D

Fig. 9.60. Streamwise pressure distributions along the axis of symmetry. From Crafton et al. (1999)

po/pa 2.71 H/D 3.8 θ 10o

Fig. 9.61. Composite representation of the streamwise surface pressure distribution with the corresponding Schlieren image for a sonic jet. From Crafton et al. (1999)

9.6. Impinging Jets

253

Using the same impinging jet facility running under different geometry and flow conditions, Guille (2000) conducted PSP and TSP measurements for a direct comparison of an intensity-based CCD camera system with a fluorescent lifetime imaging (FLIM) system developed by the Defense Evaluation and Research Agency (DERA) in Britain (Holmes 1998). The FLIM system consisted of an array of modulated LEDs, a phase-sensitive CCD camera, a modulation control box with an analog-to-digital converter, and a PC for image acquisition and processing. The CCD full-well capacity was limited to 80,000 electrons. The camera can be modulated up to 300 kHz with a 95% modulation depth. The control box contained a computer-controlled frequency source, 12-bit A/D converter, computer interface, and modulation electronics. The image readout rate was limited by the data rate of the link between the control box and computer. The LED array, which was used as a modulated light source, was composed of 100 blue LEDs. The illumination output was 7 W/m2 at a distance of 50 cm. The fluctuation of the lamp was 0.1% per hour under laboratory conditions after a warm-up period of 5 minutes. The modulation frequency for the FLIM system was set to 150 kHz in their experiments. Figures 9.62 and 9.63 show the temperature distributions and pressure coefficient distributions obtained by the intensity-based CCD camera system and FLIM system, respectively, where the coordinates were normalized by the nozzle diameter (D). The pressure coefficient Cp was defined as C p = ( p − p atm ) / q exit , where q exit is the dynamical pressure of the jet at the exit. The intensity-based CCD camera system and FLIM system gave at least qualitatively consistent results. The results from the FLIM system were much noisier perhaps due to relatively high photon shot noise although it had an advantage of requiring no reference image.

300

300

299 298

298

0

296 295

5

297

0 s /D

s /D

297

296 295

5

294

294 293

10 0 b/D

293

10

292

292 -5

(a)

299

-5

-5

-5

5

T(K)

0 b/D

5

T(K)

(b)

Fig. 9.62. Temperature distributions obtained using (a) the intensity-based CCD camera system and (b) the FLIM system. From Guille (2000)

254

9. Applications of Pressure Sensitive Paint

0.12

0.12

-5

0.1

-5

0.1

0.06

0

0.04

0.08

0 0.06

s /D

s /D

0.08

0.04

5

0.02

5

0

0.02 0

10

-0.02

10 -5

0 b/D

-0.02

5

-5

Cp

(a)

0 b/D

5

Cp

(b)

Fig. 9.63. The distribution of Cp obtained using (a) the intensity-based CCD camera system and (b) the FLIM system. From Guille (2000)

Sakaue et al. (2001) utilized an oscillating nitrogen impinging jet generated by a miniature fluidic oscillator to test the time response of several porous PSP formulations: anodized aluminum (AA) PSP, thin-layer chromatography (TLC) PSP and polymer/ceramic (PC) PSP. The frequency response of AA-PSP, TLCPSP and PC-PSP measured previously in a shock tube was 12.2 kHz, 11.4 kHz and 3.95 kHz, respectively. Figure 9.64 shows Schlieren images visualizing the flow structures of an unsteady nitrogen jet from a fluidic oscillator.

0° phase

180° phase

fluidic oscillator hot wire

Fig. 9.64. Schlieren images of jet oscillation from a fluidic oscillator. From Sakaue et al. (2001)

Figure 9.65 is a schematic of the experimental setup for oscillating jet experiments. A porous PSP sample was placed under a fluidic oscillator in parallel to the nozzle centerline. A blue LED array was used as an excitation light source and a Photometrics 12-bit CCD camera (512×752 pixels) was used to capture PSP images through a long-pass filter (>580 nm). The excitation light source was pulsed and synchronized with flow oscillation through a pulse generator based on the flow structure signature sensed by a miniature microphone. A light pulse width was 12 µs, corresponding to 6% of a flow oscillation period

9.6. Impinging Jets

255

when the fluidic oscillator was operated at 5 kHz. By controlling a trigger delay in the pulse generator, flow images at different phases were obtained. Figure 9.66 shows the luminescent intensity ratio images visualizing the flow structures of the impinging nitrogen jet at different phases obtained using AA-PSP, TLC-PSP and PC-PSP. The flow structures visualized by all three PSPs were similar to those observed in the Schlieren images. TLC-PSP images and AA-PSP images were captured in the total exposure times of 10 s and 11 s (50,000 and 55,000 light pulses), respectively. AA-PSP provided the sharpest images of the flow structures, indicating a high frequency response. N2 gas supply pulse generator fluidic oscillator

microphone signal

triggered pulse (triggering LED)

microphone blue LED pulsed illumination

porous PSP PSP long pass filter

oscillating jet CCD

Fig. 9.65. Schematic of an oscillating jet impingement setup. From Sakaue et al. (2001) 1.0 0.8 0.6 0.4 0.2 0.0

(a) TLC-PSP 1.0 0.8 0.6 0.4 0.2 0.0

(b) AA-PSP 1.0 0.8 0.6 0.4 0.2 0.0

(c) PC-PSP Fig. 9.66. Intensity ratio images of jet oscillation from a fluidic oscillator. From Sakaue et al. (2001)

256

9. Applications of Pressure Sensitive Paint

9.7. Flight Tests Using PtOEP in silicone resin, McLachlan et al. (1992) measured the surface pressure distributions on a fin attached to the underside of an F-104 fighter jet in flight. A self-contained data acquisition system was installed inside the fin, which consisted of an 8-bit digital video camera and an UV lamp triggered remotely to excite PSP. PSP was applied to a Plexiglas panel mounted flush with the fin. The luminescent emission from PSP was transmitted through the Plexiglas into the fin where it was subsequently recorded by the video camera. Two tests were flown at night at the Mach numbers 1.0-1.6 at altitudes between 30,000 and 33,000 ft. Pressure taps mounted on the fin were used to calibrate PSP in-situ. Results showed a favorable comparison to the pressure tap data at the Mach numbers greater than 1.3, and the accuracy of about ±0.24 psi was reported. Houck et al (1996) performed flight tests using PSP on a Navy A-6 Intruder where PSP was painted on an Mk76 practice bomb. The data acquisition system consisted of a battery-operated strobe light for excitation that was synchronized with a Nikon 50mm film camera used to measure the luminescent emission. This system was selfcontained and mounted onto a bomb rack adjacent to the practice bomb. Three night flights were flown at altitudes between 5,000 and 10,000 ft at the Mach numbers 0.4-0.82. After flight, the negative films were developed and digitized by projecting them onto a 14-bit CCD camera. No in-situ calibration was done such that only qualitative results were presented and the temperature effect was unable to be accounted for. Using a similar film camera system, Fuentes and Abitt (1996) measured the pressure distributions on a Clark-Y airfoil mounted underneath the wing of a Cessna 152 aircraft. In general, issues associated with film developing and processing make film-based systems more difficult for quantitative measurements. Using a portable 2D phase-based laser-scanning lifetime system, Lachendro et al. (1998, 2000) conducted in-flight PSP measurements on a wing of a Raytheon Beechjet 400A aircraft. Flight conditions were chosen to produce such a wing pressure distribution that could be easily detected by the laser scanning system. Thus, two flight conditions were considered: (1) 31,000 ft and Mach 0.75, and (2) 21,000 ft and Mach 0.69. These Mach numbers represented the maximum cruise Mach number obtainable at the respective altitudes. Also, pressure data in the above flight conditions were available from a flight test previously conducted by Mitsubishi Heavy Industries (MHI). Since this aircraft was a derivative of the Mitsubishi-designed Diamond II, it had been extensively studied in flight and wind tunnel testing (Shimbo et al. 1999). The previous data were used to validate the feasibility and accuracy of in-flight PSP measurements. The minimum and maximum pressures and temperatures from both numerical calculations and MHI flight tests were used as the design boundaries for selecting proper PSP and TSP formulations for in-flight tests. A total of six in-flight tests were made. Three tests were conducted at Purdue University on a university-owned and -operated Beechjet 400A aircraft; three other tests were performed at Raytheon Aircraft Company in Wichita, Kansas on a Beechjet 400A aircraft designated solely for inflight testing. In order to make in-flight PSP measurements, a lifetime-based or phase-based technique is more suitable because this technique does not require

9.7. Flight Tests

257

reference signal (or image) used in conventional intensity-based systems and therefore it is not affected by wing and fuselage deformation. The lifetime-based technique is also insensitive to the ambient light from the Moon and stars. Additionally, the system must be able to collect data over a large distance. In the tests conducted by Lachendro et al. (1998, 2000), PSP and TSP measurements were made at distances greater than 16 feet away from the photodetector. To improve the SNR, a coherent light source such as a laser should be used. A compact laser scanning system was specially designed for phase-based PSP and TSP measurements at large distances. The laser scanning system was designed to be as small as possible so as to easily fit inside the aircraft. In addition, it was built to be robust and allow easy modification to optical arrangement. The laser scanning system consisted of scanning/positioning and data acquisition parts. Two 5-in diameter Velmex programmable rotary tables were mounted orthogonally to each other via an aluminum angle bracket. Mounted onto the vertical stage was an 8×5 in aluminum backing plate that served as the mounting surface for the laser scanning system plate. This allowed the scanner to position the laser spot on a wing. The rotary stages were controlled through the serial port of a PC using a Velmex’s NFS-90 stepper motor controller. A LabVIEW interface program allowed for generation of a series of points distributed across a wing surface, and then a surface grid formed by these points could be scanned repeatedly by the system with a minimal deviation of the points from one scan to another. The angular positioning resolution was ±0.0125° and the corresponding position resolution was ±1 mm at a distance of 16 feet. Figure 9.67 shows the laser scanning system plate mainly comprised of a UniPhase solid-state Nd:YAG laser (532 nm and 50 mW), a PMT, and an electrooptic (E-O) modulator with a driver. Data acquisition hardware is shown in Fig. 9.68. For phase-based measurements, a laser beam was passed through the E-O modulator (Lasermetrics model 3079FW) for modulation. The input beam to the E-O modulator was polarized using two Glan-Thompson polarizers. The first polarizer was placed at the output of the laser to control the intensity, whereas the second polarizer mounted at the end of the E-O modulator controlled the depth of modulation. The beam was then passed through a Melles Griot 6X beam expander/focuser, allowing for tightly focusing the scanning spot at a distance greater than 1 m. The luminescent emission from PSP was collected through a 3in convex lens (f-number 1.86) and then was focused through a spatial aperture located in the front of a long-pass filter (> 570 nm). The filtered emission was passed into a PMT (Hamamatsu Model HC-120), and the PMT output was sampled by a 16-bit A/D converter in a lock-in amplifier (EG&G model 5302). The two-channel lock-in amplifier was capable of simultaneously measuring the magnitude and phase of the luminescent signal. Data from the lock-in amplifier was acquired through the GPIB interface into a PC using a LabVIEW program that coordinated positioning of the scanning system with data acquisition. The luminescent intensity and phase were recorded at each specified location of the laser spot on the wing surface and saved for subsequent data analysis.

258

9. Applications of Pressure Sensitive Paint

E-O Modulator

Polarizing Optic

Linear Traverse

6X Beam Expander/ Focuser

Laser Path

Gimballed Mirrors

Focusing Lens P.M.T . Polarizing Optic

1/4 20 Optical Breadboard Longpass Filter

Spatial Aperture

532nm, 50mW, Nd: YAG Laser

Fig. 9.67. Laser scanning system plate for flight test. From Lachendro (2000)

Scanning Head D.C./A.C. Inverters

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G.P.I.B

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Serial

Laptop

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P.M.T. & Laser Power Supplies

Fig. 9.68. Data acquisition hardware of a laser scanning system for flight tests. From Lachendro (2000)

Four PSP formulations, Ru(dpp) PSP and three PtTFPP PSPs in different binders, were developed for in-flight tests. These paints were chosen based on their overall performance in a pressure range of 1-7 psi and a temperature range of –50 to 0°C. PtTFPP in the FEM co-polymer binder was much less temperaturesensitive than other paints. Due to photosensitivity of the paints, they were applied to the wing only just before a flight after the wing was cleaned with an ethanol-based solvent. For the first flight test, two PSPs and one TSP were used and sprayed separately onto 75-in long and 3-in wide strips on an adhesive-backed monocoat film. As illustrated in Fig. 9.69, the strips wrapped around the leading edge and positioned streamwise to the trailing edge. For the other three flight tests, as shown in Fig. 9.69, the painted strips were placed at 31%, 55% and 85% spans that corresponded to the locations in the MHI flight test. At each location, PSP and TSP strips were placed side by side.

9.7. Flight Tests

259

532nm Nd: Yag laser scanning from cabin window

Mylar strips coated with PSP and TSP

η=0.

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Fig. 9.69. PSP and TSP installation for flight tests. From Lachendro (2000)

Somewhat unexpectedly, Lachendro et al. (1998, 2000) found a considerable temperature variation across the wing chord that was caused by wing fuel tanks warmed by moving fuel and relatively cooled stringers. Due to poor temperature sensitivity of TSP over the testing temperature range, the temperature effect of PSP could not be corrected based on TSP data. Instead, they had to use a simple heat transfer model to estimate the mean temperature on the wing in the flight conditions. The chordwise pressure distributions were obtained at 31%, 55% and 85% span. Figure 9.70 shows the pressure coefficient Cp given by PSP at 21,000 ft and Mach 0.69 compared to the existing MHI fight test data. The distribution of Cp was calculated from a priori calibration relation of PSP using the mean wing temperature of –5°C estimated based on a heat transfer model. It was noted that the first data point near the leading edge in the MHI flight test data was likely erroneous and it could be disregarded. Near the trailing edge after x/c = 0.75, the PSP data were significantly lower than the MHI flight test data. This was because the mean temperature of –5°C used for PSP data reduction over the whole wing section led to an underestimated value of Cp at the thin trailing edge that was actually colder than the middle portion of the wing. Since the temperature variation caused by moving fuel was not large at 21,000 ft, the PSP data in this case did not exhibit a significant pattern produced by the temperature variation across the wing section.

260

9. Applications of Pressure Sensitive Paint

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Fig. 9.70. The distribution of Cp obtained by Ru(dpp)-based PSP at 21000 ft and Mach 0.69 compared with the MHI flight test data. From Lachendro (2000)

9.8. Micronozzle PSP is a molecular sensor that can be used for global pressure measurements in MEMS devices. Huang et al. (2002) used PSP to measure the pressure distribution in a Mach 3 micronozzle fabricated with a high-accuracy CNC machine. Generally, an imaging system for PSP (or TSP) applied to MEMS devices must use an optical microscope and a close-up lens with a CCD camera to achieve a sufficiently high spatial resolution. In experiments, Ru(dpp) was used as a probe luminphore mixed with RTV as the binder dissolved in dichloromethane. Using a CCD camera with a close-up lens, a spatial resolution of 12 µm was achieved. Figure 9.71 is a schematic of the experimental setup for PSP measurements in a micronozzle. The micronozzle was connected to a vacuum pump, and one valve was used to control pressure at the micronozzle exit and another valve to change the inlet pressure from the atmosphere. Two pressure transducers were used to monitor the pressure signals at the micronozzle inlet and exit. Figure 9.72 shows a schematic of the micronozzle and a typical pressure image in the supersonic regime in the micronozzle where the total pressures at the nozzle inlet was 11.45 psi and the estimated Reynolds number based on the nozzle diameter was about 8000. Figure 9.73 shows a comparison of the PSP data with an inviscid flow solution for local pressure and Mach number. The PSP data are in agreement with the inviscid flow solution in the convergent and throat regions of the nozzle. However, the Mach number obtained by PSP in the downstream region after the nozzle was significantly lower than that predicted by the inviscid flow solution after the Mach number reached 2.5. This discrepancy may be due to the significant boundary-layer growth that was not taken into account in the inviscid flow solution.

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10. Applications of Temperature Sensitive Paint

10.1. Hypersonic Flows The global surface heat transfer distributions on a waverider model at Mach 10 were measured by Liu et al. (1994b, 1995b) using EuTTA-dope TSP. The experiments were conducted in the Hypervelocity Wind Tunnel No. 9 at the Naval Surface Warfare Center (NSWC), a blow-down facility operating at the Mach Numbers of 8, 10, 14 and 16.5 with the corresponding maximum Reynolds numbers per foot of approximately 50 ×10 6 , 20×10 6 , 3.8×10 6 and 3.2×10 6 , respectively. The test cell diameter was 5 feet and the length was over 12 feet, which allowed for testing of large model configurations. Tunnel 9 used nitrogen as the working gas. The waverider model had an overall length of 39 inches, a span of 16.2 inches and a base height of 6.8 inches. The model was fabricated in eight parts. The body consisted of four sections manufactured from 6061-T6 aluminum. The nose, both leading edges, and the main cavity cover plate were manufactured from 17-4 PH stainless steel. Surface static pressures were measured at 32 locations on the model with Kulite pressure transducers (Model XCW-062-5A). Measurements of surface temperature rise were made using Medtherm model TCS-E-10370 coaxial thermocouples. A 0.1-mm-thick white Mylar layer covered the lower half of the windward side of the model from the centerline to the outboard edge. EuTTA-dope TSP (about 10 µm thick) was brushed on the Mylar layer. Ultraviolet illumination to excite the paint was provided by four 40-watt fluorescent black lights. Two CCD video cameras, viewing the front and back of the model separately, were used to image the TSPcoated surface. The analytical and numerical analyses of heat transfer on a thin insulating layer on a semi-infinite metallic body gave an estimate of required thickness of the insulating layer (about 0.1 mm). It was also proven that the discrete Fourier law was reasonably accurate as a simple heat transfer model for calculating heat flux from time-dependent TSP measurements in this case. The experiment was run at the freestream Mach number of 10, average total o pressure of 1300 psia and average total temperature of 1840 R. The wind tunnel run time was 2.3 seconds. The angle of attack was set at 10 degrees. Figure 10.1 shows windward side heat transfer maps of the lower half of the waverider (58% of the total length is shown in the images) at 0.37, 0.57, 0.77, 1.04 and 1.24 seconds after the wind tunnel started to run. The gray intensity bar in Fig. 10.1 2 denotes heat flux in kW/m . The bright regions represent high heat transfer and

264

10. Applications of Temperature Sensitive Paint

dark regions low heat transfer. In these maps, the low heat transfer region (dark region) downstream of the leading edge corresponds to laminar flow. Transition from laminar to turbulent flow can be easily identified as an abrupt change from low to high heat transfer. Also observed was a movement of the transition line toward the leading edge as the laminar region diminished when the surface temperature increased with time. Figure 10.2 shows typical temporal evolutions of heat transfer obtained by TSP at the locations near the thermocouples. The heat transfer history obtained by TSP was in agreement with that given by the thermocouples at these locations.

Fig. 10.1. Sequential heat transfer maps of the windward side of the waverider model at Mach 10. From Liu et al. (1995b)

10.1. Hypersonic Flows

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Hubner et al. (2002) applied TSP with a high-speed imaging system to measure full-field surface heat transfer rates on a 25°/55° indented cone model in shortduration hypersonic flows. Tests were performed in the 48-inch hypersonic shock tunnel (HST) and the LENS I tunnel facilities at the Calspan-University of Buffalo Research Center (CUBRC). Nominal test conditions ranged between the Mach numbers 9.5 and 11.1 and the Reynolds numbers 140,000 and 300,000 per meter with run times less than 10 ms. The indented cone model had the back diameter of 0.262 m. The model was fitted with a sharp-nose cap (0.194 m long) or a blunt-nose cap (6.4 mm radius). Over sixty platinum thin-film heat transfer gauges were aligned along a ray on the model. Additional gauges were installed azimuthally along the flare (aft) cone near the region of shock/boundary-layer interaction. TSP and an insulating layer were applied to 50% of the model for the HST tests and 25% of the model for the LENS I tests. TSP used Ru-phen as an active sensing molecule. While Ru-phen itself exhibited oxygen quenching and hence pressure sensitivity, the luminophor was dissolved into an oxygen-impermeable polyurethane binder. TSP was applied over a white polyurethane insulating layer, and both were sprayed using conventional aerosol/airbrush equipment. The nominal TSP thickness and insulator thickness were 5-10 µm and 100-150 µm, respectively (+/-5 µm). Both

266

10. Applications of Temperature Sensitive Paint

TSP and the insulating binders were polyurethane, thus exhibiting similar thermal characteristics. The average thermal conductivity and diffusivity of the insulator -7 2 were 0.48 W/(K-m) and 2.7×10 m /s, respectively, in a temperature range of 293323 K. The required insulating layer thickness was estimated to be the order of 100 microns for a run time of 10 ms based on a 1D transient heat transfer analysis assuming a step change in the heat transfer rate on a semi-infinite body. By minimizing the TSP thickness relative to the insulator thickness (while still achieving viable intensity measurements), the shortest time constant of TSP was achieved. TSP was excited using a photographic xenon flash unit. Ultraviolet to blue excitation filters and orange-red emission filters were required to separate the luminescent emission from the excitation light. A combination of two Schott glass filters was utilized to filter the xenon flash excitation. For emission filtering, a 650 nm interference filter (80 nm bandpass) was used in conjunction with a high-pass Schott glass filter. A fast-framing CCD camera system was used, allowing on-chip framing rates from 15 to 1,000,000 frames per second (fps) with a frame capacity of 17 frames. The practical framing rates for the measurement system used at the CUBRC facilities were 100 to 5000 fps, depending on the duration of a test run, the desired sampling rate, and the ability to effectively detect the emission from TSP in short exposures. The advantage of the flexible framing rate was the ability to choose from a single long-exposure image or several short-exposure images during a single tunnel test. The frames were stored on the chip until all 17 frames were acquired, then data were transferred to a PCinstalled frame grabber card. The CCD camera had a full-well capacity of 220,000 electrons and a readout noise of 70 electrons. The effective spatial resolution per frame was 248 by 248 pixels. Figure 10.3 shows a typical Schlieren image of the flow field around the indented cone model. Visible was the intersection of the forebody shock and the aftbody (flare) shock. There was a separation region induced by the shock/boundary-layer and shock/shock interactions. The flow separation existed over the leading cone, and the flow reattached over the flare cone. Figure 10.4 is an in-situ calibrated heat transfer image for the model with the sharp-nose cap at Mach 9.6 and Re = 270,000 per meter in the LENS I tsets. The image shows a stabilized axisymmetric pattern although the asymmetric flow appeared in the transient stage of the onset of flow. Clearly present were the separated (violet) and shock/boundary layer interaction (yellow-red) regions. Where flow separation was present, the corresponding surface heat transfer rate was low (violet). Figure 10.5 shows the centerline heat transfer distributions obtained from TSP and gauge measurements. The relative rms calibration error of TSP measurements with the gauge measurements was 15%, which was mainly due to the high-frequency unsteadiness in the flow.

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10. Applications of Temperature Sensitive Paint

surface heating. The first image taken just prior to the onset of flow indicates uniform temperature. The following two images, acquired while the tunnel conditions rose to the desired freestream conditions, show the flare shock impingement just aft of the intersection of the leading and flare cones. Afterwards, the separation region grew upstream and the shock impingement moved downstream. As time increased, the separated region and shock impingement boundary appeared to become stable and axisymmetric. Figure 10.7 shows the corresponding heat transfer results calculated from the time-dependent intensity ratio data along the centerline of the model. First, the intensity-ratio data was converted to temperature using a priori TSP calibration, and the heat transfer rate was calculated using a transient heat transfer model when the thermal properties of the coating were given. The heat transfer model was based on a solution of the 1D heat conduction equation for a semi-infinite layer. Note that some useful solutions of the heat conduction equation were given by Schultz and Jones (1973) for the determination of the heat transfer rate in short-duration tunnel testing. As shown by the thin line in Fig. 10.7, although the trend matched that of the gauge measurements, the values of the heat transfer rate obtained by this approach were over-predicted by 20 to 50%. This bias error might be due to the differences between a priori TSP calibration experiments and actual experiments (such as test set-up differences that led to spectral leakage, background illumination, etc.), and uncertainties associated with the thermal properties of the TSP and insulator. In-situ calibration with gauge measurements can account for this bias error. When the intensity ratio data was calibrated with the gauge data (thick line), excellent agreement was achieved. Besides the indented cone model, Hubner et al. (2001) also measured the temperature distributions on an elliptic cone lifting body in short-duration hypersonic flows. Recently, Matsumura et al. (2002) and Schneider et al. (2002) used TSP to detect heat transfer signatures induced by streamwise vortices shed from roughness elements on hypersonic models in the Ludwieg tubes.

Fig. 10.6. Time-dependent intensity-ratio measurements on the sharp-nose indented cone in the 48-in HST at Mach 11.0 and Re = 140,000 per meter. Images are shown at successive 1 ms intervals (actual acquisition rate was 2000 fps). From Hubner et al. (2002)

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270

10. Applications of Temperature Sensitive Paint

relative-intensity ratio could be used to determine temperature based on a priori calibration relation without using a wind-off reference image. In fact, this kind of thermographic phosphor was a two-color TSP. A three-color CCD camera was used to acquire red, green and blue images even though only red and green images were used for phosphor thermography. An estimated error in phosphor o o thermography was about 3 C over a temperature range of 22-170 C, and the total uncertainty in heat transfer measurements in typical hypersonic tunnels was less than 10%. Liquid crystal (LC) thermography has been applied to heat transfer measurements in hypersonic flows (Jones and Hippensteele 1988; Babinsky and Edwards 1996). Compared to polymer-based TSPs and thermographic phosphors, thermochromic liquid crystals have a relatively narrow bandwidth o of temperature sensitivity (typically 32-42 C). Currently, there are two implementation methods of LC for extracting quantitative heat transfer information. The first approach is to use LC with a very narrow bandwidth of about half a degree C. When a transient change in temperature occurs on a model surface during a run in a short-duration tunnel, temperature at which a single color of LC appears (usually yellow) is visualized most likely in a narrow strip or contour moving on the surface. The temporal evolution of the strip or contour with the specific temperature on the surface is recorded in a series of images, and then the heat transfer rate on the surface can be estimated based on certain transient heat transfer model. The instrumentation for the narrow-band approach is simple with a CCD video camera attached with a band-pass filter. The spatial resolution of measurement is limited by the frame rate of the camera. An alternative is the wide-band approach that utilizes the full range of colors (or hue) displayed by LC over a wider range of temperature, which allows global heat transfer mapping using a single image frame if the temperature-sensitive range of LC covers a temperature change experienced on the whole surface. Using this approach, Babinsky and Edwards (1996) obtained reasonable results of the heat transfer flux with the o total uncertainty of 7% on a cylinder/15 -flare model in hypersonic flows. o Note that the wide-band of LC (about 10 C) is, in fact, not wide compared to the usable temperature ranges of polymer-based TSPs and thermographic phosphors.

10.2. Boundary-Layer Transition Detection TSP was utilized as a technique for visualizing flow transition (Campbell et al. 1992; Campbell 1993; McLachlan et al. 1993b; Cattafesta et al. 1995; Asai et al. 1997b, 1997c). Since convection heat transfer is much higher in turbulent flow than in laminar flow, TSP can visualize a surface temperature difference between the laminar and turbulent flow regions. Typically, at low speeds, model (or flow) needs to be heated or cooled to generate a temperature change across the transition line. However, at higher Mach numbers, artificial heating is not necessary because friction heating is able to produce a significant temperature difference between the laminar and turbulent flow regions. Using EuTTA-dope TSP,

10.2. Boundary-Layer Transition Detection

271

Campbell et al. (1992, 1993) visualized transition patterns on a Boeing symmetric airfoil and a symmetric NACA 654-021 airfoil in a low-speed wind tunnel and determined the dependency of the transition location on the angle of attack. In o their experiments, the airfoil models were pre-heated to about 50 C with a spot lamp prior to a run to produce a sufficient temperature difference between the turbulent and laminar flow regions by subsequent convection cooling. McLachlan et al. (1993b) reported a similar transition detection experiment for a NACA64A010 airfoil using a proprietary TSP. Asai et al. (1997b) used a EuTTA-based TSP to visualize transition on a 10-degree cone model at the Mach numbers 1.62.5 in a quiet supersonic wind tunnel. Transition detection was made using EuTTA-dope TSP for a trapezoidal wing (Trap Wing) semispan model at the Mach numbers 0.15-0.25 and Reynolds 6 6 numbers 3.5×10 -15×10 over a range of the angles of attack from -4° to 36° in the NASA Ames 12-Ft Pressure Wind Tunnel (Burner et al. 1999). The transition detection system consisted of three scientific-grade cooled CCD cameras, several flash UV lights for illumination, and a computer for data processing. EuTTAdope TSP was coated on white paint stripes along the main wing, slat, and trailing edge flap of the upper wing surface. The white basecoat was used to enhance surface scattering and increase the luminescence emission from TSP. TSP was applied only on the slat and the first 20% of chord on the main wing and flap since previous testing of this model in the Langley 14×22 Ft tunnel had shown that transition would always occur upstream of these locations. TSP data were obtained with the three cameras viewing the slat, flap, and wingtip of the model. The following data acquisition procedure was used. The tunnel was first run for an extended period, without cooling, to raise the temperatures of the flow and the model. Reference images of the ‘hot’ model were taken at several different angles of attack (AoA). The cooling system was then activated, and ‘run’ images were taken over the same AoA sequence while the flow cooled. The cooling sequence generally required 2-3 minutes during which the flow temperature dropped at about 5 °R/minute. Internal model temperatures, measured with thermocouples, lagged the flow by from 2°R (slat) to 10°R in the main wing. Figure 10.8 shows a typical transition image of the slat and main wing of the Trap Wing in the landing configuration at the angle of attack of 24°, Mach 0.15, and the total pressure of 1 atm. Bright regions in the image were hot relative to dark regions. The slat was dark relative to the main wing because its smaller mass allowed it to follow more rapidly the drop in the flow temperature. Since the flow cooled the model, boundary layer transition was indicated by a sharp decrease in brightness in the image. This effect was seen clearly on the main wing where transition occurred at 10-15% chord except in the turbulent wakes behind the slat brackets. Using a Ruthenium-based TSP, Cattafesta et al. (1995b, 1996) conducted transition detection on several 3D models over a wide speed range in the NASA Langley Supersonic Low-Disturbance Tunnel. Figure 10.9 shows a heat transfer image mapped onto the half of the CFD model surface grid of a swept-wing model, visualizing transition on the model at Mach 3.5. The bright region corresponded to the turbulent boundary layer where the heat transfer rate was higher than that in the laminar boundary layer. The onset of transition was demarcated in the image as a bright parabolic band on the wing where the cross-

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10. Applications of Temperature Sensitive Paint

flow instability mechanism dominated the transition process. No transition was observed near the centerline of the model because near the symmetric plane of the model the stability was mainly controlled by the Tollmien-Schlichting instability mechanism that was weaker than the cross-flow instability mechanism.

Fig. 10.8. Transition image of the upper surface of the Trap Wing model at the angle of attack of 24° and Mach 0.15. From Burner et al. (1999)

10.2. Boundary-Layer Transition Detection

273

Y

Z

X

0

50

250

80 60 40 20

350

0

300

X (mm)

Y (mm)

-50 200

100

150

50

0

Z (mm)

Fig. 10.9. Heat transfer image of transition on a half of a CFD grid of a swept-wing model at Mach 3.5. From Cattafesta et al. (1996)

Cryogenic TSP formulations, originally developed at Purdue University, were used to detect transition on airfoils in the 0.1-m transonic cryogenic wind tunnel at the National Aerospace Laboratory (NAL) in Japan and the 0.3-m cryogenic wind tunnel at NASA Langley. In the NAL tests, two TSP formulations, Ru(trpy)GP197 and Ru(VH127)-GP197, were used by Asai et al. (1996, 1997c) in a temperature range of 90-150 K for two NACA 64A012 airfoil models made of white glass ceramic (MACOR®) and stainless steel. The stainless steel model was covered with a thin white Mylar insulating layer to achieve a larger surface temperature variation. In these tests, the total temperature varied from 90 to 150 K, the Mach number from 0.4 to 0.7, and the Reynolds number based on the chord from 2.2 to 8.5 millions. In order to enhance a temperature difference across the transition line, Asai et al. (1996, 1997c) employed both a transient method of rapidly changing the freestream temperature and a steady internal heating method. A rapid change of the freestream temperature was achieved by injecting liquid nitrogen into the tunnel; the maximum temperature drop was about 7.5 K in 10 seconds. The CCD camera system used for cryogenic TSP transition detection was the same as that for cryogenic PSP measurements at NAL described in Chapter 9. Figure 10.10 shows a typical luminescent intensity ratio image of Ru(VH127)-GP197 TSP on the stainless steel NACA 64A012 airfoil model covered with a Mylar film at Mach 0.4 and the total temperature of 150 K, where flow was from left to right. Bright and dark regions represented high and low heat transfer, respectively. A turbulent wedge generated by a small roughness element placed near the leading edge was clearly visible as well as the natural transition line near 70% chord. Quantitatively, the surface temperature was calculated from the luminescent intensity using a priori calibration relation. Figure 10.11 shows the normalized chordwise surface temperature distributions at the natural and forced transition locations on the stainless steel model, where the total temperature was rapidly changed from 150 to 142.5 K by injecting liquid nitrogen to the tunnel. Natural transition was shown as a sudden decrease in the chordwise

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10. Applications of Temperature Sensitive Paint

temperature distribution. Figure 10.12 shows transition images on the stainless steel airfoil model for different Reynolds numbers based on the chord at Mach 0.4. Using several cryogenic TSPs, Popernack et al. (1997) also detected boundarylayer transition on a laminar-flow airfoil model in the NASA Langley 0.3-m cryogenic wind tunnel. A typical transition image on this airfoil is shown in Fig. 10.13, clearly visualizing a number of turbulent wedges tripped by surface roughness and the natural transition location. Transition detection on a swept wing was recently made using cryogenic TSP in the European Transonic Wind Tunnel (ETW) (Fey et al. 2003).

Fig. 10.10. Relative luminescent intensity image indicating transition on a NACA 64A012 airfoil at Mach 0.4 in the NAL 0.1 m transonic cryogenic wind tunnel, responding to a decrease in the total temperature from T01 = 150 K to T02 = 142.5 K. From Asai et al. (1996)

1.2 natural transition

(Ts - T02)/(T01 - T02)

1.0

0.8

0.6

forced transition

0.4

0.2 0.0

0.2

0.4

0.6

0.8

1.0

x/c

Fig. 10.11. Normalized chordwise surface temperature distributions in natural and forced transition regions on a NACA 64A012 airfoil at Mach 0.4 obtained from Figure 10.10. From Asai et al. (1996)

10.3. Impinging Jet Heat Transfer

275

Fig. 10.12. Transition images of a NACA 64A012 airfoil in the NAL 0.1 m transonic cryogenic wind tunnel for different Reynolds numbers at Mach 0.4. From Asai et al. (1996)

Fig. 10.13. Transition image on a laminar-flow airfoil model in the NASA Langley 0.3 m cryogenic wind tunnel (flow from right to left). From Popernack et al. (1997)

10.3. Impinging Jet Heat Transfer Using TSP complemented with hot-wire sensors and smoke visualization technique, Liu and Sullivan (1996) studied the relationship between heat transfer and flow structures in an acoustically excited impinging jet. Figure 10.14 is a schematic of a variable-speed air jet facility and the coordinate system. The facility consisted of two settling chambers. Air from a motor-driven centrifugal blower entered the first rectangular settling chamber (254×533×483 mm) and then passed through the second chamber that actually was a 178-mm long cylinder tube of a 48 mm diameter. A 25-mm long contoured nozzle was mounted at the end of the tube. The nozzle exit diameter D was 12.7 mm and the contraction ratio was 5.2. A loudspeaker attached to the opposite side of the first chamber to the nozzle induced organ-pipe resonance in the chamber, producing axisymmetric and planewave excitation at the jet exit. To measure the local convection heat transfer coefficient, air jet impinged on a 0.0254-mm thick, 115-mm wide and 130-mm long stainless steel sheet that was heated by passing an electric current of 25

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10. Applications of Temperature Sensitive Paint

Amperes. The sheet was stretched tautly by springs over two 12.5-mm diameter aluminum rods that also served as electrodes, and deformation of the sheet due to jet impingement was negligibly small. Given the uniform heat flux Qs from the heated sheet surface and the measured surface temperature Ts of the heated sheet, the convection heat transfer coefficient h = Qs /( Ts − T∞ ) and the Nusselt number

Nu = h D / k were calculated, where T∞ was the ambient temperature and k was the thermal conductivity of air. To measure the surface temperature Ts, EuTTA-dope TSP (about 10 µm thick) was coated on a 0.05-mm thick white Mylar film attached on the backside (relative to the jet impingement side) of the stainless steel sheet. A UV lamp was used to illuminate TSP. The luminescent intensity images were taken by a CCD viedo camera and digitized using a frame grabber with a spatial resolution of 512×512 pixels. The monochromatic excitation affected flow structures and therefore changed the heat transfer rate on the impingement surface. Figure 10.15 shows the 2D Nusselt number (Nu) distributions of the impinging jet at the excitation frequencies 950 Hz and 1750 Hz and without excitation for H/D = 1.125 and ReD = 12300. The natural frequency of the jet was 1750 Hz and the subharmonic frequency was 950 Hz. Clearly, the 2D heat transfer distribution was sensitive to the excitation frequency particularly in the wall-jet region. The transverse heat transfer distributions in the excited impinging jet for H/D = 1.125 are shown in Fig. 10.16, compared to the unexcited impinging jet. At the natural frequency of 1750 Hz, the local heat transfer coefficient in the wall-jet region (1< r/D <2) was considerably enhanced by excitation compared to the unexcited impinging jet. In contrast, at the subharmonic frequency of 950 Hz, the local heat transfer coefficient was reduced in the wall-jet region. Near the stagnation-point flow region (-1< r/D <1), the monochromatic excitation did not significantly affect the time-averaged heat transfer coefficient. In the wall-jet region, the heat transfer enhancement or reduction by excitation was related to the development of the large-scale vortical structures that were studied using smoke flow visualization coupled with hot-wire and hot-film measurements. When the excitation frequency was close to the natural frequency of the impinging jet, intermittent vortex pairing occurred, producing chaotic ‘lump eddies’ that contained a great deal of smallscale random turbulence. The random vortical structures enhanced the local heat transfer. When the forcing was near the subharmonic of the natural frequency, stable vortex pairing was promoted; resulting strong large-scale well-organized vortices induced unsteady separation of the boundary layer in the wall-jet region and caused a reduction in the local heat transfer coefficient. This experimental study demonstrated that TSP, complemented with other experimental techniques, provided an effective tool for study of basic fluid mechanics and heat transfer problems.

10.3. Impinging Jet Heat Transfer

heated steel sheet

277

air flow

painted side nozzle

loudspeaker

CCD Camera

electrode

UV lamp

spring VCR

PC

rectangular chamber

(a) H D y

O r

(b) Fig. 10.14. Experimental set-up: (a) Jet facility and TSP system, (b) Coordinate system. From Liu and Sullivan (1996)

(a) Fig. 10.15. (cont.)

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10. Applications of Temperature Sensitive Paint

(b)

(c) Fig. 10.15. Nusselt number distributions of the excited impinging jet for H/D = 1.125 and ReD = 12300 at different excitation frequencies: (a) 950 Hz, (b) 1750 Hz and (c) unexcited. From Liu and Sullivan (1996)

70 60 50 Nu 40 Unexcited fe = 950 Hz

30

fe = 1750 Hz

20 -3

-2

-1

0

1

2

3

r/D

Fig. 10.16. Transverse Nusselt number distributions of the excited impinging jet for H/D = 1.125 and ReD = 12300 at different excitation frequencies. From Liu and Sullivan (1996)

10.3. Impinging Jet Heat Transfer

279

Using EuTTA-dope TSP, through an optical microscope and a close-up lens attached with a CCD camera, Huang et al. (2002) measured the surface temperature distributions in impinging micro-jets. The tested micro-jets were a single jet of a 200-µm diameter, a multi-jet with 19 holes of a 200-µm diameter, and a multi-jet with 19 tubes of a 100-µm inner diameter. The experimental setup arrangement of micro-jet impingement was similar to that used by Liu and Sullivan (1996). Figure 10.17 shows a typical temperature map in the impinging multi-jet with 19 holes of a 200-µm diameter for H/D = 19.05, where the Reynolds number based on the diameter was about 300. Figure 10.18 shows the temperature distributions along the centerline of the multi-jet for three impingement distances from the surface.

Fig. 10.17. Surface temperature distribution of the impinging multiple-micro-jet at H/D = 19.05. From Huang et al. (2002)

Fig. 10.18. Surface temperature distributions along the centerline of the multiple-micro-jet at three impingement distances. From Huang et al. (2002)

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10. Applications of Temperature Sensitive Paint

10.4. Shock/Boundary-Layer Interaction Liu et al. (1995a) used EuTTA-dope TSP to measure the heat transfer rate in several typical shock/turbulent-boundary-layer interacting flows: sweptshock/boundary-layer interaction, flows over rearward- and forward-facing steps, and incident shock/boundary-layer interaction. TSP allowed quantitative measurements of heat transfer in complex 3D separated flows induced by shock/boundary-layer interaction. The experiments were carried out in a blowdown supersonic wind tunnel with a test cross-section of 44×56 mm at Purdue University. The test models were mounted on the floor of the test section that was about 33 cm downstream of the nozzle throat. The tests were performed at Mach 2.5, the total pressure of 2.9 atm. and the total temperature of 295 K. The incoming boundary layer on the floor of the test section was fully turbulent. The incoming turbulent boundary-layer thickness (δ ) in the test section was about 4.6 mm and the 5 Reynolds number Reδ based on it was 1.3×10 . A thin insulating layer covered the aluminum test section floor and surface of aluminum models that were thermally attached to the floor using high thermal conductivity grease. The insulating layer was composed of a 0.07-mm thick Scotch brand packing tape and 0.05-mm thick white Mylar film. TSP was applied on the surface of the white insulating layer. The purpose of using the insulating layer was two-fold. First, light scattering from the white layer significantly enhanced the luminescent intensity viewed by a camera. Secondly, the thin insulating layer produced a sufficient temperature difference across it such that a simple data reduction model could be used to calculate the heat transfer rate. Two UV lamps were used to excite the paint. A steady-state heat transfer model was used to calculate the heat flux q s from the measure surface temperature, and then the Stanton number St = q s / ρ ∞ u ∞ c p ( Taw − Ts ) was evaluated, where ρ∞ and u∞ are the freestream density and velocity of air flow, respectively, cp is the specific heat of air at a constant pressure, and Taw is the adiabatic wall temperature. An example was swept-shock/turbulent-boundary-layer interaction. As shown in Fig. 10.19, an attached planar shock generated by a sharp fin interacted with the incoming turbulent boundary layer on the floor, which produced complicated 3D flow separation. Previously, Settles and Lu (1985) suggested that except in the inception region near the leading edge of the fin, local physical quantities such as pressure and heat transfer rate on the floor approached a quasi-conical symmetrical state in which these quantities remained invariant along a ray from a virtual conical origin. Several heat transfer measurements were made in the quasiconical symmetry region using conventional heat transfer sensors distributed discretely along a fixed arc (Lee and Settles 1992; Rodi and Dolling 1992). Here, TSP was used to obtain a global heat transfer map in the inception region where the flow lacked the presumed quasi-conical symmetry and the heat transfer rate significantly changed along the radial direction. Figure 10.20 shows a typical heat o 5 transfer image in the inception region of the 10 fin at M∞ = 2.5 and Reδ = 1.3×10 . In the image, bright and dark regions correspond to high and low heat transfer, 2 respectively, and the intensity scale bar represents the heat transfer flux in kW/m . o The viewing polar angle of the camera was about 60 . The arrow indicates the

10.4. Shock/Boundary-Layer Interaction

281

incoming flow direction and the length of the arrow in the image corresponds to 10 mm in the actual length scale in the streamwise direction. The primary separation line was identified, and the highest heat transfer region was located in the neighborhood of the fin. Figure 10.21 presents the distributions of the relative Stanton number St/Str along four circular arcs with different radial distance R from the leading edge of the fin, where Str is the reference Stanton number in the undisturbed boundary layer upstream of the leading edge. As R increased, the distributions of the heat transfer rate tended to approach an asymptotic profile near the fin while the asymptotic tendency was not quite evident near the inviscid shock location. When the maximum relative Stanton number Stmax/Str was taken as a characteristic quantity, as shown in Fig. 10.22, it was found that Stmax/Str increased with the non-dimensional radial distance R/δ and approached the value measured previously using thin-film sensors by Lee and Settles (1992) in the quasi-conical symmetry region. Therefore, the asymptotic behavior of the heat transfer rate measured by TSP in the inception region supported the concept of the quasi-conical symmetry. Heat transfer measurements were also made using TSP for other shock/boundary-layer interactions such as rearward and forward facing steps and incident shock/boundary-layer interaction; comparisons of TSP measurements with previous results obtained by conventional techniques for these flows were discussed by Liu et al. (1995a). y

Sharp fin

U

α x O

β

R

z

Floor

Fig. 10.19. Fin geometry and coordinate system in swept shock/boundary-layer interaction. From Liu et al. (1995a)

Fig. 10.20. Heat transfer image in swept shock/boundary-layer interaction at Mach 2.5. 2 The intensity scale bar represents heat flux in kW/m . From Liu et al. (1995a)

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10.5. Laser Spot Heating and Heat Transfer Measurements

283

convection heat transfer was determined from the surface temperature response measured using TSP. Figure 10.23 is a general layout of the laser spot heating heat transfer system with TSP (LSH-TSP) that consisted of three sub-systems, one for temperature measurement and two for surface heating. The temperature measurement system was composed of an excitation laser, TSP, a band-pass filter and a photo-detector (PMT). The role of the temperature measurement subsystem was to measure the luminescent intensity and thus the surface temperature at a target point. The heating system was composed of a heating laser, an insulating layer and an absorbing layer, which created a local heat flux to the surface that was necessary to make heat transfer measurements. Note that Mayer et al. (1997) proposed a similar technique that used laser heating and an IR camera (rather than TSP) for wall-shear stress measurements based on the relationship between local heat transfer and shear stress. The temperature measurement sub-system was very similar to the laser scanning TSP system. A solid-state, diode pumped Nd:YLF laser with a frequency doubling crystal produced a 50-mW beam at 532 nm, which served as an excitation source for TSP. This beam was reflected off of a glass slide to reduce the power to approximately 2 mW. Excitation of TSP at this power level resulted in a significant luminescent signal while preventing excessive photodegradation of TSP by the excitation laser. The excitation beam was focused at a point of interest on the model surface. The luminescent emission from TSP was gathered by a collection lens and focused through a band-pass filter to a PMT. The PMT detected the luminescent intensity of TSP that was then converted to temperature using a priori TSP calibration relation. The heating subsystem was composed of a solid-state, diode pumped Nd:YLF laser which produced a 200-mW beam at 1064 nm (infrared) and optics to direct the beam at the surface. This wavelength was much longer than both the absorption and emission bands of a Ru(bpy)-based TSP used in their research, and any reflected IR radiation was effectively filtered by a band-pass filter. This beam was focused onto the absorbing layer on the surface that absorbed the radiation and heated up. The absorbing layer was another important element of this system. Figure 10.24 shows an idealized model surface that was first coated with an insulator and then a thin absorbing layer. The material of the absorbing layer absorbed radiation from the heating laser, causing the temperature of the absorbing layer to rise. The temperature gradient between the absorber and the TSP layer on the top resulted in heat conduction from the absorber to TSP. The heat generated in the absorbing layer and conducted through TSP was released through convection heat transfer at the TSP surface. Two absorbing layers were investigated. The first was a dark surface that absorbed IR radiation simply due to its color. Several dark surfaces such as fine-grit polishing paper and magnetic tape proved to work well as an absorber. The second option was an IR dye (IR26 from Lambdachrome Laser Dyes) that absorbed strongly at 1 µm. A small portion of the absorbed energy was re-emitted at a longer wavelength, but the majority of the energy went into heating up the absorbing layer. The laser dye can be mixed with a polymer applied as a separate layer, or mixed directly with TSP. Since adding the IR dye to TSP did not change the temperature sensitivity of TSP and it also simplified coating process, this option was chosen in their experiments.

284

10. Applications of Temperature Sensitive Paint

As shown in Fig. 10.23, the excitation and heating lasers were combined into a single, co-linear beam using a glass slide. The combined beam was focused at a target location on the model surface using a single lens. Since the optical path length between the focusing lens and the model surface varied during experiments, the optical system was designed with a large depth of field. In practice, alignment of the two spots over the whole surface of interest was ensured through visual inspection of a scan grid. Figure 10.25 shows the spectral arrangement of the components of the LSH-TSP system. The emission spectra of the lasers and IR dye did not overlap with the emission spectrum of the Ru(bpy)based TSP.

Excitation Laser (532 nm) Glass

Scanning Mirror

PMT

Heating Laser (1064 nm) Band-Pass Filter V∞

Absorbing Layer Painted Model

Fig. 10.23. Schematic of laser-spot-heating-TSP (LSH-TSP) system. From Campbell et al. (1998)

Heating Laser Heat conduction from absorbing layer to TSP Convection to Flow TSP Layer

TS

Absorbing Layer

TAB

Insulating Layer Model Surface

Fig. 10.24. Idealized surface model for the LSH-TSP system. From Campbell et al. (1998)

Normalized Spectral Characteristics

10.5. Laser Spot Heating and Heat Transfer Measurements

1

Ru(bpy) Abs. Heating Laser

0.8

285

IR 26 Ems.

BP Filter 0.6 Green Laser 0.4

IR 26 Abs.

Ru(bpy) Ems.

0.2 0 400

600

800 1000 Wavelength (nm)

1200

1400

Fig. 10.25. Spectral arrangement for the LSH-TSP system. From Campbell et al. (1998)

Campbell et al. (1998) calculated the convection heat transfer coefficient hc from a transient temperature history of the heated surface. Initially, temperature on the whole surface was equal to the ambient temperature. Activating the heating laser caused local temperature to rise and the luminescent intensity of TSP to decrease. The luminescent intensity of TSP continued to decrease until it reached a steady state when the input heat flux by the heating laser was balanced by the heat loss due to convection in flow and conduction into the model. A similar cycle was associated with the surface temperature response upon deactivation of the heating laser. In this case, the surface temperature decreased and the luminescent intensity increased until the surface temperature was equal to the ambient temperature. A simple lumped capacitance model of the surface indicated that the time constant of the cooling cycle was a function of the heat transfer coefficient. Since the heating laser was turned off, the solution was independent of the input heat flux, eliminating one unknown in data reduction. Figure 10.26 is a schematic of the surface used for a transient analysis of the cooling surface. The lumped capacitance analysis gives a solution for a temporal evolution of the surface temperature Ts at a heated spot

§ t · § t θ Ts − T∞ = = exp¨¨ − (1 + τ C )¸¸ = exp¨¨ − θ i Ti − T∞ © τh ¹ © τh

§ 1 ·· ¨¨ 1 + ¸¸ ¸¸ , Bi ¹ ¹ ©

(10.1)

where the time constant is defined as τ h = ρ c L / hc , the constant C = k / ρ c L2 is a correction term for heat conduction to the insulating layer, Bi = hc L / k is the Biot number, Ti is the initial surface temperature (the ambient temperature), and T∞ is the freestream temperature. In Eq. (10.1), ρ, c, and L are the density, specific heat, and thickness of the insulating layer, respectively.

286

10. Applications of Temperature Sensitive Paint

Heated Spot

V∞, T∞

Heat Loss (Convection) − h (TS − T∞ )

Measurement Location

L

Heat Loss (Conduction) −k

∂T ∂n

Substrate

TSP and Absorber Insulating Layer

Fig. 10.26. Schematic of transient heat transfer analysis. From Campbell et al. (1998)

In order to determine the convection heat transfer coefficient hc , the surface was first heated to a steady state and then the surface temperature response was recorded after the heating laser was turned off. The natural log of the nondimensional temperature was plotted versus time and the slope of the resulting curve was evaluated using the following relation

§ T − T∞ · § 1 · ¸ = −t¨ ln ¨¨ s + C ¸¸ . ¸ ¨ © Ti − T∞ ¹ ©τ h ¹

(10.2)

The slope was a sum of two terms: the time constant τ h that was a function of the heat transfer coefficient hc and the heat conduction term C. The conduction term C was experimentally determined for a given test configuration by making flowoff measurements. In such a case, the convection heat transfer due to natural convection was several orders of magnitude lower than the heat conduction into the model surface. Hence, the surface temperature response gave the conduction term at a location, and the heat conduction term was equal to the log-slope of the non-dimensional temperature response for a flow-off scan. This value was used to adjust the log-slope of flow-on scan data to account for the heat conduction effect. According to the transient model, higher heat transfer would be expected to produce a small time constant τ h . Figure 10.27 shows typical responses of the surface temperature to a pulsed laser heating at two different Reynolds numbers in an impinging jet. The steady-state temperature was higher at lower Reynolds numbers due to lower convection heat transfer. At higher Reynolds numbers, the steady state was reached much sooner and the time constant was smaller due to higher convention heat transfer. Figure 10.28 shows the natural log of the nondimensional temperature response θ / θ i for the first 0.5 seconds of the cooling cycle. The log-plots exhibited a linear behavior and the increased slope (the absolute value) with the Reynolds number, and demonstrated the sensitivity of the slope to the heat transfer rate. In preliminary tests, using the LSH-TSP system, Campbell et al. (1998) measured the Nusselt number distributions in an impinging jet at different Reynolds numbers and gave reasonable results.

10.5. Laser Spot Heating and Heat Transfer Measurements

287

Surface Temperature Change (°C)

50 ReD =5,700

40

30 ReD =23,000 ReD =5,700

20

ReD =23,000

10

0 0

1

2

3

4

5 6 Time (s)

7

8

9

10

Fig. 10.27. Surface temperature response to pulsed laser heating in an impinging jet. From Campbell et al. (1998)

0

Ln(θ/θi)

-0.1 -0.2 ReD 5,700 15,000 23,300

-0.3 -0.4 0

0.1

0.2

0.3 Time (s)

0.4

0.5

Fig. 10.28. Natural log-plot of the non-dimensional surface temperature response at three Reynolds numbers in an impinging jet. From Campbell et al. (1998)

Campbell et al. (1998) presented application of the LSH-TSP system to more o complex flows. Quantitative measurements were made on a 75 swept delta wing model using the LSH-TSP system in a region that was also visualized by TSP with a CCD camera at the same conditions, as shown in Fig. 10.29a. Figure 10.29b shows a map of the heat transfer coefficient hc in this region at the angle of attack o of 25 . Another experiment was performed for quantitative heat transfer measurements in an intersection of a strut and a wall that often occurred in air vehicles (e.g. the wing/body and stator/wall junction). Figure 10.30 shows schematically the primary horseshoe vortex developed around the base of a strut that influences the heat transfer distribution on the wall. A strut with a NACA 0015 airfoil cross-section and a 48-in chord was positioned vertically in the Boeing subsonic wind tunnel at Purdue University and it spanned the 48-in height of the test section. The flow velocity was about 90 ft/s and the Reynolds number

288

10. Applications of Temperature Sensitive Paint

was about 2.5 millions based on the chord. Another relevant length scale for this flow was the strut thickness of 7.2 in, and the Reynolds number based on it was about 350,000. The LSH-TSP system was used to measure the heat transfer rate on the large model in a large wind tunnel since heating the entire wall would be impractical. Figure 10.31 shows a map of the Stanton number on the surface around the strut. The heat transfer results were computed using the transient heat transfer model with heat conduction correction. The location on the surface was normalized by the approaching boundary layer displacement thickness δ * = 0.5 in. The largest variation in heat transfer appeared near the leading edge of the strut. There was a region of decreased heat transfer due to decelerating flow and local flow separation caused by the presence of the strut. Near the strut, heat transfer was enhanced by the primary horseshoe vortex that transported fluid outside the boundary layer to the wall.

(a) h (W/m2-°C) 0

120 110

-0.1

100

% Span

-0.2

90 80

-0.3

70 -0.4

60 50

-0.5

40 -0.6

30 20

-0.7 0.6

(b)

0.7

0.8

0.9

% Chord

Fig. 10.29. (a) TSP visualization with a CCD camera, and (b) quantitative heat transfer measurements using the LSH-TSP system on a 75-degree swept delta wing at the angle of o attack of 25 in low-speed flow. From Campbell et al. (1998)

10.6. Hot-Film Surface Temperature in Shear Flow

289

y

Incident Boundary Layer

u(y) Horseshoe Vortex Strut

Endwall

z Line of Separation

x

Fig. 10.30. Schematic of strut/endwall junction flow. From Campbell et al. (1998)

St 0

5 x 10-3 4.5 x 10-3

Z / δ*approach

5

4 x 10-3 10 3.5 x 10-3 15

3 x 10-3 2.5 x 10-3

20

2 x 10-3 -15

-10

-5 0 X / δ*approach

5

10

Fig. 10.31. Stanton number distribution around the strut obtained using the LSH-TSP system at 90 ft/s and the Reynolds number of about 2.5 millions based on the chord of the strut. From Campbell et al. (1998)

10.6. Hot-Film Surface Temperature in Shear Flow Through an optical magnification system, a very high spatial resolution can be achieved in TSP measurements on a small object. Liu et al. (1994a) used EuTTAdope TSP to measure a surface temperature field on a commercial flush-mounted hot-film sensor (TSI 1237) in a flat-plate turbulent boundary layer. As shown in Fig. 10.32, the sensor had a 0.127-mm streamwise length and a 1-mm spanwise length. TSP was applied to the hot-film sensor by dipping. Figure 10.33 shows the experimental set-up used for this study. The sensor was mounted flush with the surface of a flat plate with a 1:6 elliptical nose (the leading edge) that was installed in a low-speed blow-down wind tunnel at Purdue University. The sensor was located

290

10. Applications of Temperature Sensitive Paint

0.37 m downstream from the leading edge of the plate. The freestream velocity was 26 m/s in the experiments. A roughness band near the plate leading edge was used to produce artificial flow transition such that the boundary layer was fully turbulent downstream. The sensor was operated at a low overheat ratio of 1.07, where the cold resistance of the sensor was 5.14 Ω. The luminescent intensity images were obtained using a CCD video camera through an optical magnification system. The streamwise and spanwise surface temperature distributions were computed from the luminescent intensity images using a priori calibration relation. Figure 10.34 shows the non-dimensional streamwise surface temperature distributions at three spanwise locations, where Z is the spanwise coordinate, L is the streamwise length, w is the half-span width, and Tm is the maximum surface temperature. Liu et al (1994a) also derived the analytical solutions for a uniformtemperature (UT) film and uniform heat source (UHS) film on an adiabatic wall in shear flow for a comparison with TSP measurements. These solutions are also plotted in Fig. 10.34 as references. The temperature distributions on the TSI hotfilm sensor appeared to be nearly symmetric and largely deviated from the theoretical distributions of the UT and UHS films on an adiabatic wall. This deviation was mainly due to the dominant effect of heat conduction to the glass substrate and the streamwise diffusion effect (the finite Peclet number effect) that were neglected in the analytical solutions. This result indicated that the TSI hotfilm sensor had a large heat loss to the substrate that might limit the frequency response of the sensor. The measured spanwise temperature distribution on the TSI hot film is shown in Fig. 10.35 along with a theoretical temperature distribution given by a simple lumped model for comparison. As shown in Fig. 10.35, the theoretical distribution was in good agreement with the experimental data for the sensor in a region of ⏐Z⏐/w < 1.2. Outside of this region, the theoretical distribution underestimated the surface temperature since the lumped model neglected heat conduction into the substrate along the spanwise direction at the tips of the sensor.

Stainless steel tube Epoxy Glass base Platinum film Gold lead

3.2 mm 2.5 mm

1.5 mm

Fig. 10.32. Configuration of the TSI 1237 hot-film sensor

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Appendix A. Calibration Apparatus

For PSP, the relationship between the luminescent intensity (or lifetime) and air pressure is determined by calibration. Figure A1 shows a simple apparatus for calibration of PSP (Burns 1995). A PSP coating is applied to an aluminum block (1.5×1.5×0.625 cm) that is thermally anchored using high thermal conductivity grease to a Peltier heater/cooler controlling the surface temperature of the block. A thermometer inserted in the aluminum block near the painted surface is used to measure the temperature of the paint sample. The PSP sample on the block is placed inside a pressure chamber with an optical access window. Pressure inside the chamber is controlled and measured using a pressure transducer. An illumination light, typically from a UV lamp, LED array or laser, passes into the chamber through the window and excites the paint sample. The luminescent emission from the paint sample is collected with a lens, filtered by a long-pass or band-pass optical filter, and projected onto a photodetector like a photodiode, photomultiplier tube (PMT) or CCD camera. The photodetector output over a range of pressures and temperatures is acquired with a PC, where the dark current is subtracted from the intensity output. Therefore, a relation between the luminescent intensity and pressure is determined over a range of temperatures; the calibration data are typically fit using the Stern-Volmer equation for different temperatures. For lifetime or phase calibrations, a pulsed or modulated excitation light should be used. The set-up in Fig. A1 can be used for TSP calibration when the surface temperature of a TSP coating on the aluminum block is varied over a range of –15 to 150 oC by controlling the Peltier heater/cooler while the chamber pressure is kept constant. Thus, a calibrated relation between the luminescence intensity and temperature is obtained, which is typically represented by the Arrhenius plot over a certain temperature range. Note that an oven for calibrating fluorescent temperature sensors was described by Crovini and Fernicola (1992). This simple apparatus can be adapted for TSP calibration down to cryogenic temperatures (Campbell et al. 1994). In this o case, a TSP sample is thermally anchored to a copper bar cut at an angle of 45 at its top that rests in a container filled with liquid nitrogen. The sample temperature near the temperature of liquid nitrogen can be achieved due to heat conduction from liquid nitrogen to the sample through the copper bar. To prevent condensation of moisture from forming on the paint sample, the sample is purged with dry nitrogen gas. Using this apparatus, Campbell et al. (1994) examined the temperature dependencies of the luminescent intensity for many TSP formulations.

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Appendix A. Calibration Apparatus

Fig. A2. Calibration chamber for cryogenic PSP and TSP. From Erausquin (1998)

315

Appendix B. Recipes of Typical Pressure and Temperature Sensitive Paints

Recipes of Three PSP Formulations

(1) Ru(ph2-phen) or Ru(dpp) in RTV Ingredients: 4 mg of Bathophen Ruthenium Chloride [Ru(ph2-phen) or Ru(dpp)], 25 ml of dichloromethane, 7.5 ml of GE RTV 118, 2 g silica gel particles. Directions: Dissolve Ru(ph2-phen) in the solvent dichloromethane, add silica gel particles and then GE RTV 118, and stir until fully dissolved. (2) PtTFPP in RTV Ingredients: 6 mg of platinum meso-tetra(pentafluorophenyl)porphyrin (PtTFPP), 25 ml of dichloromethane, 7.5 ml of GE RTV 118, 2 g silica gel particles. Directions: Dissolve PtTFPP in the solvent dichloromethane, add silica gel particles and then GE RTV 118, and stir until fully dissolved. (3) PtTFPP in FEM (NASA Langley) Ingredients: 5.3 mg platinum meso-tetra(pentafluorophenyl)porphyrin (PtTFPP) (120 ppm), 12 g Polytrifluorethyl-co-isobutyl methacrylate (TFEM/IBM), 37.5 g Solvent DuPont 3602S, 3.6 g Solvent DuPont 3979S or 3696S. Directions: Dissolve the TFEM/IBM in the DuPont solvents, add PtTFPP, and stir until dissolved, and adjust the viscosity of the solution to 10.5 cp with the 3602S solvent. Allow the paint to cure at the room temperature for about 20 minutes before heating to 65°C for one hour.

318

Appendix B. Recipes of Typical Pressure and Temperature Sensitive Paints

Recipes of Two TSP Formulations

(1) Ru(bpy) in Clear Coat Ingredients: 6 mg of tris(2,2’-bipyridyl) ruthenium [Ru(bpy)], 20 ml of automobile Urethane Clear Coat (DuPont ChromaClear), 5 ml of activator, 10 ml dichloromethane. Directions: Dissolve Ru(bpy) in the solvent dichloromethane, sonicate for 5 minutes, add urethane clear, shake and sonicate. Just before painting (within 5 minuets) add the activator, shake and sonicate for 1 minute. Acetone is used as a solvent to clean up the paint. (2) EuTTA in Dope Ingredients: 12 mg Europium (III) Thenoyltrifluoroacetonate (EuTTA), 20 ml model airplane dope, 20 ml dope thinner. Directions: Mix EuTTA with the dope thinner, shake and then sonicate for a few minutes. Add the dope, shake and sonicate. Acetone is used as a solvent to clean up the paint.

Appendix C. Vendors

Chemicals (1) Frontier Scientific, Inc. (former Porphyrins Products) P.O. Box 31, Logan, Utah 84323-0031, USA Tel: (435) 753-6731, E-mail: [email protected], Web: www.frontiersci.com Products: Pt(III) meso-tetra(Pentafluorophenyl)porphine (PtTFPP) (PSP probe), Pt(II) Octaethylporphine (PtOEP) (PSP probe) (2) Sigma-Aldrich 3050 Spruce St., St. Louis, MO 63103, USA Tel: 800-325-3010, Web: www.sigmaaldrich.com Products: Tris(2,2’-bipyridyl)ruthenium(II) chloride hexahydrate [Ru(bpy)] (TSP probe), Dichlorotris(1,10-phenanthroline)ruthenium(II) [Re(ddp)] (PSP probe), Pyrene (PSP probe) (3) Gelest, Inc. 11 East Steel Road, Morrisville, PA 19067, USA Tel: (215)-547-1015, E-mail: [email protected], Web: www.gelest.com Products: Europium III Thenoyltrifluoroacetonate (EuTTA) (TSP probe) (4) GFS Chemicals, Inc. P.O. Box 245, Powell, OH 43065, USA Tel: (877)-534-0795, E-mail: [email protected], Web: www.gfschemicals.com Products: Terpyridine ruthenous dichloride [Ru(trpy)] (TSP probe), Ruthenium bis(4,4’,5,5’-tetramethyl-2,2-bipyridine)(2,2’:6’,2”-terpyridine) [Ru(tmb)2(trpy)] (TSP probe), Ruthenium bis(2,2’-bipyridine)(2,2’:6,2”terpyridine) [Ru(bypy)2(trpy)] (TSP probe), 1,10-phenanthroline ruthenous chloride [Ru(phen)3Cl2] (TSP probe), Tris(2,2’-bipyridine) ruthenous dichloride, hydrate [Ru(bypy)] (TSP probe), Tris(bathophenanthroline) ruthenium dichloride [Ru(bath)] (PSP probe)

320

Appendix C. Vendors

(5) Innovative Scientific Solutions, Inc. 2766 Indian Ripple Road, Dayton, OH 45440-3638, USA Tel: (937)-429-4980, E-mail: [email protected], Web: www.innssi.com Products: Unicoat PSP, FIB-based PSP top coat and base coat, PtTFPP sol-gel PSP, and Ru sol-gel PSP

Cameras (1) Roper Scientific, Inc. 3660 Quakerbridge Road, Trenton, NJ 08619, USA Tel: (609)-587-9797, E-mail: [email protected], Web: www.roperscientific.com Products: high-performance CCD cameras for scientific and technical applications (2) PixelVision 10500 SW Nimbus Avenue, Tigard, OR 97223-4310, USA Tel: (503)-431-3210, E-mail: [email protected], Web: www.pvinc.com Products: high-performance CCD cameras for scientific and technical applications (3) Hamamatsu Corporation (USA) 360 Foothill Road, Bridgewater, NJ 08807-0910, USA Tel: (908)-231-0960, E-mail: [email protected], Web: www.hamamatsu.com Products: digital CCD cameras and other photonics equipment

Color Plates

The following pages contain color plates of figures that are shown in black and white in the text to reduce the cost of reproduction. Fig. 1.6. PSP image for the F-16C model at Mach 0.9 and the angle-of-attack of 4 degrees. From Sellers (2000). Fig. 7.11. Typical pressure distribution obtained from PSP on a Cessna Citation model. From Kammeyer et al. (2002a). Fig. 9.8. Calibrated PSP image in Case III for 30 m/s and α = 5 . From Brown (2000). o

Fig. 9.13. Raw blue image obtained using two separate CCD cameras and a 308-nm lamp for excitation, where the integration time for 16 images was 32 seconds. From Engler et al. (2001a). Fig. 9.16. Pressure image mapped onto a surface grid of the Daimler Benz model with arrangement of pressure taps at 60 m/s. From Engler et al. (2001a). Fig. 9.24. Typical pressure distribution mapped onto a surface grid of the AerMacchi M346 advanced trainer model. From Engler et al. (2001b). Fig. 9.27. The distributions of the pressure coefficient Cp on the wing upper surface obtained with the FIB PSP and the corresponding temperature distributions obtained using 6 an infrared camera at M = 0.74, Rec = 3.8×10 , and AoA = 0, 1, 3 and 5 degrees. From Mebarki and Le Sant (2001). Fig. 9.28. Typical pressure fields on the Mitsubishi MU-300 business jet model obtained using a combination of PSP and TSP at Mach 0.73 and α = 2.3 and 4.7 degrees. From Shimbo et al. (2000). Fig. 9.32. Normalized surface pressure map P/Ps on the control panel with a standard multiple 90° bleed hole configuration, where Ps is the wall static pressure measured upstream of the fenced porous plate insert. Tunnel flow is from left to right. From Bencic (2002). Fig. 9.33. Normalized surface pressure map P/Ps on the control panel with a multiple preconditioned 90° bleed hole configuration, where Ps is the wall static pressure measured upstream of the fenced porous plate insert. Tunnel flow is from left to right. From Bencic (2002).

322

Color Plates

Fig. 9.34. Normalized surface pressure map P/Ps on the control panel with a multiple 20° inclined bleed hole configuration, where Ps is the wall static pressure measured upstream of the fenced porous plate insert. Tunnel flow is from left to right. From Bencic (2002). Fig.9.37. PSP image on the expansion corner model at Mach 10 and the angle of attack of o 40 . From Nakakita et al. (2000). Fig.9.38. PSP image on the compression corner model at Mach 10 and the angle of attack o of 30 . From Nakakita et al. (2000). Fig. 9.53. Pressure and temperature distributions on compressor blades at the speed of 17800 rpm. From Torgerson et al. (1998). Fig. 9.55. Temperature fields on the TSP-coated blade at four rig speeds of 4950, 5800, 7450 and 7875 rpm. From Bencic (1997). Fig. 9.56. Normalized pressure fields on the PSP-ccoated blade at four rig speeds of 4950, 5800, 7450 and 7875 rpm. From Bencic (1997). Fig. 9.63. The distribution of Cp obtained using (a) the intensity-based CCD camera system and (b) the FLIM system. From Guille (2000). Fig. 9.72. Pressure distribution in a micronozzle at the total pressure of 11.45 psi. From Huang et al. (2002). Fig. 10.4. Heat transfer rate results for the sharp-nose indented cone model in LENS I with an 8 ms delay from flow onset at Mach 9.6 and Re = 270,000 per meter. Color scale ranges 2 2 from violet = 0 W/cm to red = 100 W/cm . From Hubner et al. (2002). Fig. 10.17. Surface temperature distribution of the impinging multiple-micro-jet at H/D = 19.05. From Huang et al. (2002).

Color Plates

323

Fig. 9.8.

Fig. 1.6.

Fig. 9.13. Cp

0.4 0.2 0.0 -0.2 -0.4 -0.6 -0.8

Fig. 7.11.

-1.0

Fig. 9.16.

324

Color Plates

(a) M = 0.73, AoA = 2.3 deg.

Fig. 9.24.

Fig. 9.28.

+F ¯ FLOW

a =0o -0

-0

a =1o -0

-0

a =3

o

-1

-1

a =5

o

-1

Fig. 9.32. -1

Fig. 9.27.

Color Plates

Fig.9.38. Fig. 9.33.

Fig. 9.53.

Fig. 9.34.

Fig.9.37

Fig. 9.55.

325

326

Color Plates

Fig. 9.72.

Fig. 9.56. 0.12 0.1

-5

s/D

0.08 0.06

0

0.04 5

0.02

10

-0.02

0

-5

0 b/D

Fig. 10.4.

5

Cp

(a) 0.12 -5

0.1 0.08

0

s /D

0.06 0.04

5

0.02 0

10

-0.02 -5

(b) Fig. 9.63.

0 b/D

5

Cp

Fig. 10.17.

Index

absorption and emission spectra, 36, 40, 42, 43, 47 aerodynamic forces and moments, 150, 218 airfoil flows, 151, 159, 201, 273 amplitude demodulation method, 121, 164 amplitude modulation index, 116, 121 anodized aluminum (AA), 50, 182, 184, 188, 192, 230, 236, 238 Arrhenius relation, 8, 20, 31 bidirectional reflectance distribution function (BRDF), 98, 100 Biot number, 285 boundary-layer control, 226 calibration, 33, 131, 313 camera calibration, 82, 92 car models, 212 CCD camera, 3, 67, 70, 217 centroid, 103 collinearty equations, 83 compressibility effect, 107 cryogenic paints, 50, 237, 273 cryogenic wind tunnels, 237, 273 deformation surface grid, 112 delta-wing, 207, 239, 288 diffusion equation, 175, 195 diffusion timescale, 177, 182, 186, 187 direct linear transformation (DLT), 85 directional dependence, 69 effective diffusivity, 183 elemental error sources, 139, 170 error propagation, 138, 163, 164, 166, 167, 169 Euler orientation angles, 83

EuTTA, 48, 318 excitation, 15, 18, 62 excited states, 15 exterior orientation parameters, 84 filter leakage, 146 fixed pattern noise, 71 flight tests, 256 fluorescence, 15 fluorescence lifetime imaging (FLIM), 128 fractal dimension, 185 gated intensity ratio method, 123, 130, 134, 166 hot-film, 289 hypersonic flows, 230, 263 ideal pressure sensitive paint, 56, 106 image registration, 76, 102 inlets, 226 in-situ calibration, 5, 156 intensified CCD camera (ICCD), 128, 236 intensity ratio method, 69, 75, 137 interior orientation parameters, 84 internally gated CCD camera, 130 Laplace transform, 176, 195 laser heating, 195, 282 laser scanning system, 6, 74, 225, 242, 282 lens distortion, 84 lifetime, 17, 19, 26, 35, 45, 115, 163, 256 lifetime method, 115 limiting pressure resolution, 142, 153 limiting temperature resolution, 170 low-speed airfoil flow, 201 luminescence, 15

328

Index

luminescent intensity (radiance), 61, 65 impinging jet, 198, 214, 249 impinging jet heat transfer, 275 Jablonsky energy-level diagram, 16 Joukowsky airfoil, 151, 159 jet impingement cooling, 198 Karman-Tsien rule, 108 micronozzle, 260 model deformation, 76, 112, 137, 158, 160 multiple-luminophore paint, 54 noise floor, 71 non-Gaussian distribution, 158, 160 Nusselt number, 276 optimization method, 87 oxygen diffusion, 24, 175, 182 oxygen quenching, 17, 18, 19, 24 paint intrusiveness, 147 perspective center, 82 phase angle, 116, 131 phase method, 119, 163 Phong model, 99 phosphorescence, 15 photodetector response, 68 photon shot noise, 71, 142 platinum porphyrins, 35 porous pressure sensitive paint, 24, 50, 182, 230, 236 Prandtl-Glauert rule, 108 PtOEP, 12 PtTFPP, 36, 317 pressure-correction method, 107 pressure sensitive paint (PSP), 2, 11, 18, 24, 34, 137, 175, 201 pressure mapping error, 146 principal distance, 83 principal point, 83 pyrene, 42 Riemann-Liouville fractional integral, 185 radiance, 61, 62, 65, 92, 95 radiative energy transport, 62, 65 radiometric response function, 92 rotating machinery, 242, 247

Ru(bpy), 47, 318 Ru(dpp), 40, 317 Ru-pyrene, 57 Ru(trpy), 52 schlieren, 234, 235, 252, 267 self-illumination, 95, 148 shock, 191, 221, 223, 226, 230, 236, 243, 250, 266 shock/boundary-layer interaction, 230, 280 shock tube, 192, 230, 236, 263 solenoid valve, 188 spectral variability, 146 square law, 177, 182 Stanton number, 280 Stern-Volmer relation, 3, 21, 23, 26, 28, 30, 138 Stern-Volmer coefficients, 3, 21, 23, 26, 28, 30, 138 subsonic flows, 107, 151, 215 supercritical wing, 221 supersonic flows, 226, 271, 280 swept-wing, 210, 223, 271 temperature effect, 145, 149 temperature hysteresis, 171 temperature sensitive paint (TSP), 8, 31, 45, 169, 263 thermal diffusion, 194 thermal quenching, 31 thermochromic liquid crystal, 49, 270 thermographic phosphor, 49, 269 time response, 175, 182, 187, 194 transition, 263, 270 transonic flow, 215, 221, 223, 237, 256, turbomachinery, 227, 242 uncertainty, 137 upper bounds of elemental errors, 149 videogrammetric model deformation technique (VMD), 112 view factor, 95 volume fraction, 185 waverider, 263