T
ADVANCES IN
HEAT TRANSFER
Volume 10
Contributors to Volume 10 SESIM ABUAF RICHARD C. BIRKEBAK ROBERT COLE CLIFFO...
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T
ADVANCES IN
HEAT TRANSFER
Volume 10
Contributors to Volume 10 SESIM ABUAF RICHARD C. BIRKEBAK ROBERT COLE CLIFFORD J. CREMERS CHAIN GUTFINGER
J. 11. HELLMAN S. L. LEE
Advances in
HEAT TRANSFER Edited by
James P. Hartnett
Thomas F. Irvine, Jr.
Department of Energy Engineering University o j Illinois at Chicago Circle Chicago, Illinois
State University of New Y m k at Stony Brook Stony Brook, Long Island New York
Volume 10
@ ACADEMIC PRESS
1974 0
New York
A Subsidiary of Harcourt Brace Jovanovicb, Publiehers
London
COPYRIGHT C 1974, BY ACADEMICPRESS, INC. ALL RIGHTS RESERVED. NO PART OF THIS PUBLICATION MAY BE REPRODUCED OR TRANSMITTED IN % N Y FORM OR BY ANY MEANS. ELECTRONIC OR MECHANICAL. INCLL'DING PHOTOCOPY, RECORDING. OR ANY INFORMATION STORAGE AND RETRIEVAL SYSTEM, WIlXOUT PERMISSION IN WRITING FROM THE PUBLISHER.
ACADEMIC PRESS, INC.
111 Fifth Avenue, New York, New York 10003
United Kirigdom Editiori published b y ACADEMIC PRESS, INC. (LONDON) LTD. 24/28 Oval Road, London NWI
LIBRARY OF CONGRESS CATALOG CARD NUMBER: 63-22329
PRINTED IN THE UNITED STATES OF AMERICA
CONTENTS List of Contributors . Preface .
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Contents of Previous Volumes .
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Thermophysical Properties of Lunar Materials : Part I
Thermal Radiation Properties of Lunar Materials from the Apollo Missions RICHARD C. BIRKEBAK I . Introduction . . . . . . . . I1. Apollo Samples: Location and Description 111. Remote Sensing Results . . . . . IV. Thermal Radiation Measurements . . V. Summary . . . . . . . . . Nomenclature . . . . . . . . References . . . . . . . . .
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1 4 7 12 34 35 35
Thermophysical Properties of Lunar Media :Part I1
Heat Transfer within the Lunar Surface Layer CLIFFORD J . CREMERS
I . Introduction . . . . . . . . . I1. Thermal Conductivity . . . . . . . I11. Specific Heat . . . . . . . . . IV. Thermal Diffusivity . . . . . . . V . Thermal Parameter . . . . . . . VI . Heat Transfer in the Lunar Surface Layer . VII . Reference Values of Thermophysical Properties Nomenclature . . . . . . . . . References . . . . . . . . . . V
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39 42 59 64 70 72 79 80 80
CONTENTS
vi
Boiling Nucleation ROBERTCOLE I . Introduction
86 87 92 111. Honiogcncous Sucleation . . . . . . . . . . . IV . Superheat Limits . . . . . . . . . . . . . 95 i'. Heterogeneous Sucleation . . . . . . . . . . 111 VI . Suclratinn from a Preexisting Gas or Vapor Phase . . . 117 V11. Size Ilangt of Active Cavities . . . . . . . . . 127 VIII . Stability of Sucleation Cavities . . . . . . . . . 134 IX . 3Iinirnum Boiling Superheat. . . . . . . . . . . 148 Somenclature . . . . . . . . . . . . . . 162 References . . . . . . . . . . . . . . . 163 .
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I 1 . lundanicntal Equations of Surface Science .
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Heat Transfer in Fluidized Beds
CHAIM GUTFINGER A N D KESIMABUAF 1. I1. 111. IV .
Introduction . . . . . . . . . . . . General Description of Fluidized Bed Behavior . . . Hrat Transfer betwxm Solid Particles and a Fluid . . Heat Transfer between a Fluidized Bed and a Surface Somenclat ure . . . . . . . . . . . . Kefcrenccs . . . . . . . . . . . . .
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167 169 171 180 213 214
Heat and Mass Transfer in Fire Research
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S. L . LEE A N D J. JI . HELLMAN I. I1. 111. IV. V. VI . VTI . VIII .
Introduction . . . . . . Pyrolysis . . . . . . . Ignition . . . . . . . . The Pliinict . . . . . . . Fire Spread . . . . . . . Instrunwntation in Fire Rrsearch Fire Research and the Fire Fighter Concluding Remarks . . . . References . . . . . . .
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. 230 226 . 23.5 . 245 . 260 . 272 . 275 . 280 . 281 .
Author Tndes
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Subject Indes
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LIST OF CONTRIBUTORS NESIM ABUAF, Laboratory for Coating Technology, Department of Mechanical Engineering, Technion-Israel Institute of Technology, Haifa, Israel RICHARD C. BIRKEBAK, Department of MechanicaE Engineering, University of Kentucky, Lexington, Kentucky ROBERT COLE, Department of Chemical Engineering and Institute of Colloid and Surfuce Science, Clarkson College of Technology, Potsdam, New York CLIFFORD J. CRERIERS, Department of Mechanical Engineering, University of Kentucky, Lexington, Kentucky CHAIM GUTFINGER, Laboratory for Coating Technology, Department of Mechanical Engineering, Technion-Israel Institute of Technology, Haifa, Israel J. M. HELLMAN, Power Systems, Westinghouse Electric Corporation, Pittsburgh, Pennsylvania
S . L. LEE, Department of Mechanics, State University of New York at Stony Brook, Stony Brook, New York
Vii
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PREFACE The serial publication Advances in Heat Transfer is designed to fill the information gap between the regularly scheduled journals and university level textbooks. The general purpose of this series is to present review articles or monographs on special topics of current interest. Each article starts from widely understood principles and in a logical fashion brings the reader up to the forefront of the topic. The favorable response to the volumes published to date by the international scientific and engineering community is an indication of how successful our authors have been in fulfilling this purpose. The Editors are pleased to announce the publication of Volume 10 and wish to express their appreciation to the current authors who have so effectively maintained the spirit of the series.
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CONTENTS OF PREVIOUS VOLUMES Volume 1
The Interaction of Thermal Radiation with Conduction and Convection Heat Transfer R. D. CESS Application of Integral Methods to Transient Nonlinear Heat Transfer THEODORE R. GOODMAN Heat and Mass Transfer in Capillary-Porous Bodies A. V. LUIKOV Boiling G. LEPPERTand C. C. PITTS The Influence of Electric and Magnetic Fields on Heat Transfer to Electrically Conducting Fluids MARYF. ROMIG Fluid Mechanics and Heat Transfer of Two-Phase Annular-Dispersed Flow MARIOSILVESTRI AUTHOR INDEX-SUBJECT
INDEX
Volume 2
Turbulent Boundary-Layer Heat Transfer from Rapidly Accelerating Flow of Rocket Combustion Gases and of Heated Air D. R. BARTZ Chemically Reacting Nonequilibrium Boundary Layers PAUL M. CHUNG Lorn Density Heat Transfer F. M. DEVIENNE Heat Transfer in Non-Newtonian Fluids A. B. METZNER Radiation Heat Transfer between Surfaces E. M. SPARROW AUTHOR INDEX-SUBJECT
INDEX
xi
CONTENTS OF PREVIOUS VOLUMES
xii
Volume 3
The Effect of Frcc-Stream Turbulence on Heat Transfer Rates ,J, KESTIS Heat and Mass Transfer in Turbulent Boundary Layers A. I. LEONT'EV Liquid Metal Heat Transfer RALPHP. STEIN Radiation Transfer and Interaction of Convection with Radiation Heat Trarisfcr K. VISKASTA -4Critical Survey of the Major Methods for Measuring and Calculating Dilute Gas Transport Properties A. -4. WESTEXBERG AUTHOR ISDEX-SUBJECT
INDEX
Volume 4
Advances in Free Convection A. ,J. EDE Heat Transfer in Biotcch~iology ALICEIf. STOLL Effects of Reduced Gravity on Heat Transfer
ROBERTSIEGEL Advances in Plasma Heat Transfer E. R. G. ECKERTand E. PFENDER Exact Similar Solution of the Laminar Boundary-Lager Equations C. FORBES DEWEY, JR. and JOSEPH F. GROSS AUTHOR INDEX-SUBJECT
INDEX
Volume 5
Applic*ationof Monte Carlo t o Heat Transfer Problems JOHNR. HOWELL Film and Transition Boiling DKANE P. JORDAE; Convcct ion Heat Transfer in Rotating Systems F R . 4 N K ICREITH Thermal Radiation Properties of Gases
C. L. TIES Cryogenic Heat Transfer JOHX A. CLARK AUTHOR INDEX-SUBJECT
INDEX
CONTENTS OF PREVIOUS VOLUMES
xiii
Volume 6
Supersonic Flows with Imbedded Separated Regions A. F. CHARWAT Optical hlethods in Heat Transfer W. HAUFand U. GRIGULL Unsteady Convective Heat Transfer and Hydrodynamics in Channels E. K. KALININ and G. A. DREITSER Heat Transfer and Friction in Turbulent Pipe Flow with Variable Physical Properties B. S. PETUKHOV AUTHOR INDEX-SUBJECT
INDEX
Volume 7
Heat Transfer near the Critical Point W. B. HALL The Electrochemical Method in Transport Phenomena T. MIZUSHINA Heat Transfer in Rarefied Gases GEORGES. SPRINGER The Heat Pipe E. R. F. WINTERand W. 0. BARSCH Film Cooling RICHARD J. GOLDSTEIN AUTHOR INDEX-SUBJECT
INDEX
Volume 8
Recent Mathematical Methods in Heat Transfer I. J. KUMAR Heat Transfer from Tubes in Crossflow A. ~ K A U S K A S Natural Convection in Enclosures SIMONOSTRACH Infrared Radiative Energy Transfer in Gases R. D. CESSand S. N. TIWARI Wall TurbuIence Studies 2. ZARIE. AUTHOR INDEX-SUBJECT
INDEX
xiv
CONTENTS OF PREVIOUS VOLUMES Volume 9
Advaiiccs in Thcrmosyphon Technology 1).JAPIKYE Heat Transfer to Flowing Gas-Solid lfixtures CREICHTON A. DEPEW and TEDJ. KRAMER Condensation Heat Transfer HERMAN ~ I E R T EJR. , Xatural Convection Flows and Stability B. GEBHART Cryogenic Insulation Heat Transfer C. L. TIESand G. R. CUNNINGTON AUTHOR INDEX-SPBJECT
INDEX
ADVANCES IN HEAT TRANSFER
Volume 10
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Thermophysical Properties of Lunar Materials: Part I THERMAL RADIATION PROPERTIES OF LUNAR MATERIALS FROM T H E APOLLO MISSIONS
RICHARD C. BIRKEBAK Department of Mechanical Engineering, University of Kentucky, Lexingfon, Kentucky
I. Introduction . . . . . . . . . 11. Apollo Samples: Location and Description 111. Remotesensing Results . . . . . IV. Thermal Radiation Measurements . . A. Definitions . . . . . . . . B. Measurement Techniques . . . . C. Experimental Results . . . . . V. Summary. . . . . . . . . . Nomenclature . . . . . . . . References . . . . . . . . .
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I. Introduction
For eons men have looked upon the moon, speculated about its nature, and wondered about its origin. Men have dreamed of visiting the lunar surface and have written books on their speculations. The Apollo program has culminated these aspirations and made them a reality. The landing of men on the lunar surface and subsequent return of lunar samples has led and is leading to a better understanding of the origin of the solar system and moon-earth system. There have been a number of soft landings on the moon in the past several years including five unmanned Surveyor flights and five manned Apollo flights by the United States, and several unmanned Luna flights by 1
2
RICHARD C. BIRKEBAK
the Soviet Union.’ Several of these missions included provision for measurement of lunar surface temperatures and heat fluxes. Ironically, the first flight which included such experiments was the Apollo 13 flight which was aborted before a landing could take place. A successful heat flow experiment was installed by the Apollo 15 crew at Hadley Rille and it returned the first direct measurements of heat flux and temperature from the moon. An unfortunate accident by one of the Apollo 16 astronauts terminated the Apollo 16 heat flow experiment. The other actual measurements of lunar temperatures have been remote measurements from earth in which infrared or microxave radiation emitted by the dark moon, either at lunar nighttime or during an eclipse, was analyzed to j4eld an apparent radiation temperature. The successful landings on the moon of the Apollo flights and the return of samples of lunar surface material has permitted the measurement of the thermophysicai properties necessary for heat transfer calculations. These explorations have also proven what was previously hypothesized from remote thermal radiation measurements and laboratory studies [l], that the lunar surface is covered to a depth of several meters or more, a t least in the mare regions, with a layer of fine particulate soil. There is a hard substratum below these “fines” and there are many rocks and sometimes boulders scattered about as well. However, these occur randomly and may be considered perturbations in the porous, powdery surface layer [2, 31. Man has learned much about the moon’s optical properties, temperature, surface features, and thermophysical properties by using remote sensing techniques from astronomical, infrared, microwave, and radar measurements. The returned lunar samples are allowing scientists to compare physical properties obtained directly from these samples with those inferred from remote sensing results. Thc thermal radiation properties described herein have and are being used in heat transfer calculations [4-7) for the prediction of lunar surface temperatures, spacecraft temperatures, and temperature variation of scientific equipment placed on the lunar surface. The proper design and operation of such systems or structures which may be constructed for the lunar surface depend to a large degree on a complete knowledge of the thermal transport properties of the material in the lunar surface layer. Accurate data on the local thermal environment are also needed, particularly on the moon %-herethere are widc extremes of temperature. However, up to the Apollo 15 mission there has not been any direct measurements of 1 Subsequent to the writing of this paper the hpollo 17 mission was successfully completed. The returned lunar material is now being studied.
LUNARPROPERTIES I
3
the temperature field in the surface layer, nor had there been any reports until recently of the actual properties of the lunar material. We became involved in the Lunar Sample Analysis Program of the National Aeronautics and Space Administration in October 1966 when our group was selected as one of the initial 110 groups to study lunar material. Our group was selected to measure the thermophysical properties of lunar materials. This article reviews our results and those of other investigators on the thermal radiation properties of lunar material returned by the Apollo 11, 12, 14, and 15 missions and also, where possible, compares these results with remote sensing data.
FIG.1. Apollo mission landing sites (NASA).
4
RICHARD C. BIRKEBAK 11. Apollo Samples :Location and Description
On July 20, 1969, astronaut Armstrong stepped onto the lunar surface in the Sea of Tranquility a t the location 0.67'N and 23.49"E. This site is shown on the photograph of the lunar surface, Fig. 1. During the extravehicular activity (EVA) phase the astronauts collected about 21.5 kg of lunar material. About one-half of the returned lunar material was finegrained soil (called fines) and half was selected rock fragments. All of the samples were Collected near the lunar module in an area approximately 7 x 22 meters. A complete description of the Apollo 11 samples is found in the Proceeditrgs of the Apollo 11 Luuar Science Covference [Z]. Each lunar specimen as cataloged by SASA's Lunar Heceiving Laboratory is specified by a number which identifies the Apollo mission and sample. A five-digit number is used, succeeded by two or three more digits; this refers to a particular split of the main sample. Documented sample histories include in many cases the sample location and orientation on the surface of the moon. The saniple series begin with 10000, 12000, and 14000 referring to samples from the Apollo 11, 12, and 14 missions, respectively.
FIG.2. Apollo 11 rock chip 10047.
LUNAR PROPERTIES I
5
FIG.3. Apollo 11 rock chip 10048.
Photographs of three rock chips from the Apollo 11 mission are shown in Figs. 2 4 , and illustrate the variation in textural nature of the rocks. These chips are from larger parent rocks. Rock number 10047 is a coarsegrained, vuggy, ophitic cristobalite basalt [2], 10048 a breccia [2], and 10057 a fine-grained, vesicular to vuggy, granular basalt [2]. The Apollo 11 lunar fines consisted of a distribution of small crystalline fragments and glassy fragments with a variety of shapes. Particle sizing of the fines [S] showed a range from 200 pm down to less than 1 pm, with most of the particles being a t the small diameter end of the range. Much larger rock fragments were in the initial soil sample but were removed prior t o this study [S]. The other Apollo fines have similar distributions when compared to that of Apollo 11 fines. The second manned lunar landing mission, Apollo 12, landed on the Ocean of Storms with coordinates 3.0"s latitude and 23.4'W longitude on November 19, 1969 [a]. During this mission two EVA'S were carried out which explored the lunar surface. Approximately 34 kg of material was collected with 82% being rock samples and the remainder of fines. The third lunar landing was made a t Fra Mauro a t latitude 3.66'5,
6
RICHARD C. BIRKEBAK
FIG.4. Apollo 11 rock chip 10057.
longitude 17.48OW by the Apollo 14 lunar module on February 4, 1971. This niission provided an exceptionally rich harvest for lunar science. The Apollo 14 crew returned 43 kg of lunar material. The Apollo 14 samples may he contrasted with the samples returned from the Mare Tranquillitatis and the Oceanus Procellarum in that their chemical composition is quite different, and the Apollo 14 rocks exhibit characteristics that suggest they are ejects from the Imbrium Basin [9]. On July 30, 1971 the rip0110 1.5 mission, the fourth in the series, landed in the Hadlty-Apennine region of the moon at a latitude of 26.1°N and longitude of 3.65OE [lo]. Four EVA'S were performed on the lunar surface and for the first time a lunar Rover was used to transport the astronauts. Astronauts Scott and Irwin brought back 77 kg of samples from the Hadley region [lo]. To date, the oldest lunar material returned were the soils and breccias from Apollo 11 with ages of approximately 4.6 billion years [a]. The rocks
LUNARPROPERTIES I
7
from Apollo 11 were younger by one billion years. In the oldest Apollo 12 material, the soils are one billion years younger than the Apollo 11 samples. 111. Remote Sensing Results
Prior to the Apollo, Surveyor, and Luna missions the only way that the surface of the moon was studied was by remote means, i.e., by optical and radar astronomical measurements. From those remote sensing results it has been possible to deduce many of the thermophysical properties of the lunar surface [l]. Hapke [l] reviews the optical remote sensing results prior to 1970 that appear in the literature. The general conclusions that he makes, and that are well known to people working in this area, are the five following characteristics. (1) The moon has a low albedo with an average value of near 7%. (2) The spectral albedo increases monotonically from 0.3 to 2.5 pm but has small and sometimes distinct variations in the spectrum. (3) The lunar surface backscatters strongly, i.e., the moon’s brightness peaks strongly a t full moon when the sun is almost directly behind the observer. (4) The degree of polarization of the lunar surface changes with phase angle (the angle between the observer and moon and sun) in a distinct manner. (5) The previous four statements hold for every type of surface feature on the moon. The most significant remote sensing results that have been reported to date are by McCord and Johnson [ll, 121, McCord et al. [13], and Adams and McCord [141. These data are the results of very careful experimental work. The ubiquity of the results over the lunar surface as stated in conclusion (5) is probably due to the fact that almost the entire lunar surface is covered with fines, but this does not mean that signification differences do not occur. The remote sensing data for normalized spectral reflectance is shown in Fig. 5. The results were measured for regions on the moon of approximately 18 km in diameter. Starting from the top curve and proceeding downward the results are for (a) the upland or highlands region, (b)-(d) the mare regions, ( e ) the upland bright craters, and (f) and (g) bright mare craters on the lunar surface. The curves have the form or trend as described in conclusion ( 1 ) , however, there are significant differences. All curves indicate an absorption band near or a t 0.95 pm. This band is due to clinopyroxene in the lunar fines and exposed rocks, and the depth of
RICHARD c. BIRKEB.4K
8
a
"I
0.3
I
I
I
0.5
I
I
1
I
I
I
I
I
0.9 WRVELENGTH ( p m ) 0.7
1
I
I
I
1.1
FIG.5. Normalized bidirectional spectral reflectance (taken from McCord et al. [13]): (a) Sea of Moisture; (b) Sea of Tranquility; (c) Sea of Serenity; (d) Sea of Cold; (e) Tycho; (f) Sea of Moisture; (g) Aristarchus.
these bands is an indication of the amount of this mineral [14]. The slope of the curves is a function of the chemical composition of the lunar material and the amount of breccia and glass fragments in the fines [14]. McCord et al. El31 have normalized these results to a selected area in the Sea of Serenity. By doing this they have been able to emphasize spectral differences. The data in Fig. 5 have been normalized in this matter and the results are shown in Fig. 6. Clearly evident are different spectral types. From this type of procedure the composition and age of a given area on the moon can be inferred.
LUN.4R PROPERTIES
1
9
Adams and JIcCord [14] have shown that the spectral reflectance for the Sea of Tranquility obtained by remote sensing agrees well with that obtained in the laboratory. The laboratory data also enabled hlcCord et al. [131 to correct their remote sensing results for atmospheric absorption, etc. The comparison of these results is shown in Fig. 7. According to Hapke [l] the most accurate presently available integral phase function distribution of reflected light from the moon was measured by Rougier [15]. A plot of his results is shown in Fig. 8. The normalized photometric distribution is presented as a function of phase angle. ( I n
I0
L
-1
I-
-1
W J
LL W
I I :
0.3
0.5
0.7
0.9
1.1
HAVELENGTH ( p n )
FIG.6. Ratio of the reflectance of a lunar area to the Sea of Serenity (taken from MeCord et al. f13j): (a) Seaof Tranquility, (b) Sea of Moisture, (c) Luna 16 landing site, (d) Fra Mauro, (e) Le Monnier, (f) Sea of Moisture, (9) Plato, (h) Sea of Cold.
10
RICH.4RD
c. BIRKEBllK
APOLLO II SITE
n
-MOLL0
II SOIL S A M P L E
0
071-
TELESCOPE MEASUREMN
‘
061-
L
!
04 05
I
I
1
I
I
06 07 0 8 0 9 10 WAMLENGTH ( p m )
I
II
FIG. 7. Compnrison of telescopic and laboratory-obtained reflectances for the Sen of Tranquility.
engineering practice we would refer to these as normalized bidirectional reflpctances.) The lunar surface strongly backscatters the incident beam of sunlight. Hapke [lS] formulated a theory that predicted this effect. Later improvements were made by Alorozhenko and Yanovitsliii [l?]. In arriving a t his theory, Hapke assumed that the lunar material had a “fairycastle structure”; i.e., the grains of the soil stuck together in such a manner that the overall structure was very porous so that light could penetrate from any direction. From remote sensing results and laboratory studies on siniulated lunar material, Hapke as well as others came to the conclusion that thc surface of the moon was covered mainly ttith very small particles. This was evcntually borne out by the analyses of the returnad lunar samples and photographs returned of the lunar surface from the Apollo, Surveyor, arid Luna missions. As difficult as it is in the visible portion of the spectrum to obtain reliable remote sensing data, the problem in the infrared is even more so. The total
LUNARPROPERTIES I
11
al U
5
-
08-
[L
-
120
180
Z
60
0 Phase Angle
180
120
60
FIG.8. Normalized bidirectional reflectance function.
emittance of the lunar surface has been usually assumed to be unity, a blackbody. However, the remote sensing results of Murcray [lS] and Murcray et al. [19] made from a mountain top and from balloons gave data that showed that the moon was not a blackbody. A result of theirs is shown in Fig. 9 for a spectral range from 7.0 to 13.5 pm. These results will be discussed later. If it were possible to obtain reliable emittance data, especially where the maximum value occurs [ZO], then one could determine something about the mineralogy of the lunar surface. The maximum emittance location has been shown by Salisbury et al. [20] and Cone1 [21] to depend on the chemical composition of the substances that make up a powered material.
I .o,
J
I
u.I
I
I
I
1
Mare lmbrium
t
I
o 0.5 -6
I
7
I 8
1
9
I 1 I 10 I t 12 Wavelength ( p n )
I
12
14
FIG.9. Remotely obtained spectral emittance of Mare Imbrium.
RICHARD C. BIRKEBAK
12
IV. Thermal Radiation Measurements During the lunar day the dominating or controlling parameters that affect the temperature of the lunar surface or objects on the surface are the thermal radiation characteristics of the lunar material. These characteristics includc the bidirectional and directional reflectance and emittance of the lunar surface. It has been shown in Cremers et al. [S] that the directional solar albcdo has the greatest effect on lunar surface temperature than any other single thermophysical property. This variable reflectance effect is clearly showi in Fig. 10 where the temperatures differ substantially just after sunrise and before sunset. Table I compares the constant and variable property results for specific lunation times. The maximum differences occurs for a lunation fraction of 0.24 and 0.76 where the variable property calculated temperatures are 43.7"K and 64.1"K lower, respectively. In addition t o the necessity of knowing the thermal radiation characteristics for heat balance calculations, they also are useful in remote sensing work as shown in the previous section. The spectral signature of a substance can be used to identify, in part, its mineral constituents; that is, the location of absorption bands in reflectance curves can usually be associated with a given mineral. And the determination of the spectral
I 0 2
I
I 04
06
I
08
J
10
Fraction of Local Lunation
FIG.10. Lunar surface temperature variation. p
and
E.
~
Variable A@), t ( T ) ,- - - constant
LUNARPROPERTIES I
13
reflectance gives us both thermal data as well as some spectral signature data as to the mineralogy of the material.
A. DEFINITIONS I n the literature on the photometry measurements on the moon one finds at least four different kinds of reflectances (albedos) used. Because the moon is a spherical body, it is natural that there arise albedos that take this into account. These definitions are presented here for the convenience of the reader. 1. Bond Albedo
The ratio of the amount of light reflected by a spherical body in all directions to that incident on the body is defined as the Bond albedo, B. 2. Geometric Albedo
As is often the case in photometry, albedo is defined in terms of a Lambertian surface. The geometric albedo p is the ratio of the brightness [radiance] of a body at zero phase angle to the brightness (radiance) of a Lambertian disk of the same angular diameter as the body and perpendicular to the sun's rays. The phase angle V , is the included angle between the source, sample, and observer. These two albedos are related to each other by the following equations: B = q-p where
TABLE I COMPARISON OF TEMPERATURE FOR CASEOF VARIABLE SURFACE PROPERTIES WITH THATOF CONSTANT SURFACE PROPERTIES~ Fraction of lunation, 7 0 0.24 0.25 0.50 0.75 0.76 0
(OK)
variable 389.3 161.2 134.4 94.7 86.1 125.4
(Noon) (Sunset) (Midnight) (Sunrise)
Cremers et al. [6].
Temp.
6
Cremen et al. [5].
p ( ~ ) , e(T)
Constantbp, 389.4 204.9 147.5 96.8 87.8 189.5
RICHARD C. BIRKEBAK
14
and the quantity +( 1’) is called the integral phase function. It describes the manner in which the light from the lunar surface is distributed. The function Cp ( 1.) is taken to be 1 a t 1’ = 0.
3. A’omal Albedo ( A )
If the curvature effects are eliminated, that is, if we consider a flat surfwv, tht. analogy to the geometric albedo is the normal albedo ( A ) . It is thc brightness of an area a t an arbitrary angle of illumination, to the hrightncss of a Lambertiun disk under the same solid angle but at zero angle of illurnination. This albedo is the most frequent one reported because of the following reason. The photometric distribution function of the lunar surfacc behaves in such a manner that the normal albedo is independent of the direction of illumination and viewing. The fourth albedo found in the literature is the analogy to the spherical Bond albedo, it is th r hemispherical albedo. This albedo is the same as the dirrctional reflectance described next. 4. Directtom1 ReJlectance
Thc directional refiectance is used mainly in the calculation of the heat balance and temperatures of the lunar surface. It is defined in the following manncr: Let the incident radiation be contained in a solid angle An, oriented a t a specific anglc \k relative to the surface normal (Fig. l l a ) , and let reflected radiation be collected over the entire hemispherical space above the surface. We thcn define the directional hemispherical reflectance as ~ ( 9= )der,h/dei(Q)
(3)
nhcw de,,h is the reflected radiant energy that is collected over the entire hcmisphcrical spare and de, is the radiant energy contained in the incident h r w ~ In ~ . gcncral, the magnitude of de,,i, will depend upon the angle of illuniination of the incoming beam. Thc directional reflectance can also be understood to mean the following. Let t hr surface under study be illuminated hemispherically with diffuse radiation e , , h while the reflected radiance ir(0) is collected in a small solid anglc A9, (Fig. 1l b ). The hemispherical directional reflectance is defined as P(e> = ir(e)/ (ei,h/r) (4)
With the use of reciprocity, the reflectances in Eqs. (3) and (4) can be shown to bc. identical if tlie solid angles are the same, Anl = An,. p ( 9 ) = p(e)
for 6
= 9
(5)
LUNARPROPERTIES I
15
The measurement of p ( 0 ) with the integrating sphere is called the reciprocal mode.
5 . Bidirectional ReJtectance The angular distribution of reflected radiation from a surface can be described by the bidirectional rejectance. The bidirectional reflectance is defined as the ratio of the radiance of the reflected light in the direction of viewing e to the incident energy per unit time and surface area contained within a solid angle dQiin the direction Q, Pb(\k,
e)
=
?r
dirt*, 8)/dei(Q)
(6)
where dir is the reflected radiance and dei (9) is the incident flux of energy. 6. Directional Emittance
The directional spectral emittance of a sample is defined as the ratio of the radiance of radiation from the sample to radiance of radiation from a blackbody a t the same temperature, 4 0 , A,
T) = is(6, A, T)/iB(A,2')
(7)
Normal
Incident Radiation Reflected Radiation
Normal
T , [ $ z ; M Hemispherically Irradiated
(b)
FIG.11. Definition of coordinates: (a) directional hemispherical technique; (b) hemispherical directional technique.
16
RICHARD C. BIRKEBAK
where 9 is the angle of viewing, T the temperature of the sample, and is and iu are the radiance of the sample and blackbody, respectively. These thermal radiation property definitions are used in the following sections to describe the radiation characteristics of the lunar material. B. 3IEASUREMENT TECHHIQUES In this section we will briefly describe the experimental techniques used by us to determine the thermal radiation characteristics of lunar material. 1. Directional Reflectance Apparatus
The directional reflectance was obtained with a sample, center mounted in an integrating sphere reflectometer. The sphere coating was magnesium oxide. The sphere system was constructed with the sample held in a horizontal position, a necessity for powders, while by rotation of the sphere and external optics, angles of illumination or viewing up to approximately 75" are obtained. Since the theory of the integrating sphere is well known, it will be only briefly reviewd. Radiation directed on a test sample within the integrating spherc is reflected onto the sphere wall. If the wall is coated with a highly reflective and diffuse material, then any radiation hitting the wall is reflected diffusely throughout the sphere. The total radiation incident on a given area will be a summation of radiances from the multiple reflections. A detector mounted at the sphere wall measures radiance of the radiation striking a given area within the sphere. Our integrating sphere was operated in the reciprocal mode, that is, the samplc was illuminated by diffuse light from the sphere walls. The ratio of radiancr when the center-mounted sample was viewed to the radiance when the wall was viewed is the directional reflectance p ( 0 ) [Eq. (4)]. As represented in Eq. (5) this measurement is equivalent to illuminating the sample at an angle of incidence equal to the angle of viewing 0. A sketch of the apparatus used in this research is shown in Fig. 12. The integrating sphere was constructed of stainless steel hemispheres, 0.20 m in diameter, flanged and joined by a copper gasket seal. The interior of the sphere was smoked with NgO until a uniform coating of 2 mm thickness was obtained. Ports were provided on the sphere for the test sample, detector optics, light source, and vacuum pump. The actual sample transfer system [22] was Constructed so that the sample could be located along the diametral plane of the sphere and always held in a horizontal position under vacuum condition. The sample size was 25 mm in diameter by 6.0 mm in depth. The viewing optics were arranged so that the sample or sphere wall
LUNARPROPERTIES I
VIEWING PORT
17
* OPTICS AND SOURCE
AXIS OF ROTATION
' TO VACUUM MANIFOLD
FIG.12. Schematic of integrating sphere.
could be viewed by rotating the optical bench, Fig. 12. The spectral results were obtained with a Perkin-Elmer 112 U spectrometer having a tungsteniodine source and a lead-sulfide detector. The total or white light measurements were made with a 1000-W tungsten-iodine lamp (DXW) with a reflector and with a Kipp-Zonen CA-1 thermopile. Details of the design and construction are presented in a technical report, Birkebak and Cremers [23]. The measurements were obtained automatically by joining the spectrometer and its associated electronics to a minicomputer. 2. Bidirectional ReJEectance Apparatus The bidirectional reflectance measurements were made with a goniometric system designed so that the samples could be viewed and illuminated while under vacuum conditions. A schematic of the apparatus is shown in Fig. 13. The energy from the sample is reflected from three diagonal mirrors before it emerges from the system. It is then focused onto the entrance slit of the spectrometer or onto a detector. For this system the surface could be illuminated a t a fixed angle of illumination (\E) and the angle of viewing (0) varied or, by reversing the optical path, the angle of illumination was varied and the angle of viewing was held fixed.
RICHARD c. BIRKEBAK
18 Source ,OPtlCS
+;;r-, Fugn E
Rotating Arm
toble
I
To Vocuurn Moni f old
FIG. 13. Bidirectional reflectance system.
3. Spectral Emittance Apparatus
The nature of the sample dictated that we use a horizontal samplc in the measurements. The sample was mounted in a sample heating cup and positioned in a known radiation environment as shown in Fig. 14. Besides the sample holder a heated reference blackbody was placed in the environment chamber. Transfer optics were used to view either the sample or blackbody and to direct the encrgy into a Perkin-Elmer 112 U spectrometer.
Woler-Cooled Vacuum Chomber
Somple
8 Angle of Viewing
Holder or
Blackbody
FIG. 14. Schematic of emittance system.
LUNARPROPERTIES I
19
The spectrometer was interfaced with a Hewlett-Packard 2114B minicomputer. This syatem allowed us to automatically scan the wavelength range of interest and to perform the necessary operations required to obtain data. A complete discussion of the analysis of this technique is given elsewhere [24]. The working equation used by the system to obtain the spectral emittance is:
(8) where A(S), A(B), A(R) and Ts, TB, TR are the detector output and thermocouple readings for the sample, heated reference blackbody, and blackened surrounds, respectively.
C. EXPERIMENTAL RESULTS Before discussing the experimental results obtained on the returned lunar samples, the following facts should be kept in mind. A number of investigators have recognized that the density (packing, compactness) of the lunar fines will effect the measured properties [25-281. However, only Birkebak et al. [26] actually specify the bulk densities used in their experiments. Hapke et al. [25] discuss the change in albedo with packing and describe various ways to change the material density but do not give any quantitative results for the density. From the description given in the various papers reviewed it appears that many of the investigators sifted or gently poured the lunar fines into their sample holders. We have carried out several experiments using these methods and find that the bulk density can range from approximately 900 to 1100 kg/m3. However, these surfaces are very susceptible to vibrations and settle slowly. 1. Bidirectional ReJlectance Results
As important as the knowledge of the bidirectional reflectance distribution is to the heat balance calculations on structures on the lunar surface, only a limited amount of data is available: In their original papers, Birkebak et al. [29a, b] and Gold et aE. [8] and later, Gold et al. [27] and O’Leary and Briggs [30], present bidirectional reflectance results. As discussed in Section 111 on remote sensing, the geophysicists p r e sented their results for a fixed angle of observation and variable angle of illumination; whereas, in thermal property measurements we usually
20
RICHARD C. BIRKEBAK
FIG. 15. Normalized bidirectional reflectance-Apollo 11 sample No. 10084.68.
present the bidirectional reflectances for a fixed angle of illumination and variable angle of viewing. Therefore, direct comparison is not possible of the two results obtained in the laboratory on lunar fines. The results of Hirkebak et al. [29a, b] are shown in Fig. 15. The sample was illumination with white light (1000-W tungsten-iodine lamp) at angles of lo", 30", and 60". We have normalized the results with respect to the specular ray direction, = +O. A perfectly diffuse surface would give a horizont.al line. It is quite apparent that the lunar material backscatters very strongly in the direction of illumination.
FIG.16. Bidirectional reflectance as a function of phase angle V. Symbols: 0, Apollo 12 soil; 0, Apollo 11 soil; -, moon (normalized to Apollo 11); e, angle of viewing; A, 0.56 fim.
LUNARPROPERTIES I
21
The backscatter peak could not be measured with our present equipment. However, the peak is estimated to have a value as high as 2-3. This explains why the moon appears so bright during opposition (zero phase angle). In the laboratory if one illuminates the lunar fines at an angle of 30" and then moves one's head aver the hemispherical space above the surface, one can physically see this distribution of reflected light; a very interesting and rewarding experience. There is a slight wavelength effect that we have found and which has also been determined by O'Leary and Briggs [30]. As one approaches zero phase angle, and also for large phase angles, the color of the fines changes from a grayish-blue to a reddish hue. The results of O'Leary and Briggs [30] and Gold et al. [27] are shown in Fig. 16. Their results of reflectance are plotted against phase angle. The solid curve is the moon remote sensing data [31] normalized with respect to the normal albedo of Apollo 11. 2. Directional ReJectance Results We will first discuss directional reflectance made on lunar rock chips. Although these results are not useful in heat transfer calculations, they are useful in obtaining spectral signatures of the various minerals. Second, we will discuss the results obtained on the lunar fines, which, as we have stated previously, covers almost the entire moon to several meters or more in depth.
a. Lunar Rock Chips. The ApoIIo astronauts have brought back many rocks that weighed more than several kilograms. However, most investigators received only a small rock chip or thin section that weighed around 3.0 g. Because these chips were so small in size it was difficult to obtain representative reflectance results. Many of the returned rock had surfaces which could be identified from photographs as having been exposed to the lunar environment, and as a result one could sometimes readily see differences in surface properties. Adams and McCord [14], Birkebak et al. [29a, b], Adams and McCord [32], Conel and Nash [33], Gold et al. [S], Nash and Conel [34], and Perry et al. [35,36] have all presented reflectance spectra for various lunar rocks. The reflectance results for the three rock chips shown in Figs. 2, 3, and 4 are given in Fig. 17. Clearly evident are a number of distinct absorption bands. Adams and McCord [32] have presented diffuse reflectance for mineral separates for Apollo 12 basalt. They have demonstrated that the major absorption bands can be attributed to Fez+ in pyroxene. All observed bands are attributed to electronic transitions in iron and titanium. Adams and McCord [37] have determined the relationship between the wavelength of the two major bands and the pyroxene composition. One band occurs
22
RICHARD
-
c. BIRKEBAK
-1
9p 6
5'
06
I
08
I
10
I
12
1
14
I
16
I
20
18
Wavelength ( prn)
Fro. 17. Typical directional spectral reflectance of lunar rock chips-Apollo
11 mission.
between 0.9 and 1.0pm and the second near 2.0pm. The depth of the absorption bands is also a function of the average pyroxene composition and in the breccias, also of the glass content. The bands degrade from rocks to breccias to the fines material, and their depth or strength correlates with the percent increase of dark glass [14], a conclusion also reached by Cone1
0.5
I.o 1.5 2.0 WAVELENGTH ( p n )
2.5
FIG.18. Directional reflectance as a function of glass content-Apollo 12 mission. Symbols: a, 12063, 79 whole-rock powder; b, +20% glass; c, +55% glass; d, 12070, I l l surface fines; e, 1'2063, 79 whole-rock glass. (Reproduced from Adams and McCord I321.)
LUNARPROPERTIES I
23
and Nash [33]. The effects of the addition of artificially made glass from the crystalline lunar rock is shown in Fig. 18. Perry et al. [35,36] have made reflectance measurements on lunar samples from Apollo 11, 12, 14, and 15. The spectra were obtained from polished specimens and over a wavelength range of 5-500 pm. The resulting spectra are very complex and are of more interest to the geophysicists than to the thermal engineer. No meaningful thermal property data can be obtained from these results. b. Lunar Fines. Before we begin to discuss the directional reflectance properties of lunar fines it is desirable to reiterate the various parameters that affect the reflectance. It seems reasonable to assume that the bulk density or compaction of the material will affect the reflectance. The surface may become more compacted around equipment on the moon due to intentional packing or because of astronaut activities. Another reason for looking at the effect of density is that we still do not know what the exact density of the lunar surface is or how it varies over the lunar surface. Estimates [lo J of the soil density from in-place measurements range from 800 to 2150 kg/m3. However, it should be kept in mind that only the upper 10 mm or so actually affect the thermal radiation characteristics and the lower densities, therefore, could be reasonable estimates. When a fines sample is prepared by simply pouring it into a container and carefully leveling the surface, the bulk density achieved depends on the distribution of particle size in the fines. With this procedure followed for the Apollo 14 and 15 fines, bulk densities of nearly 1000 kg/m3 were obtained. Slightly higher values were obtained for the Apollo 11 and 12 samples. To achieve higher bulk densities [26] the fines were packed by use of a vibrating tool held on the sample holder edge. Initial smoothing and packing of the surface was achieved with a stainless steel spatula. Whether this procedure gives a surface texture close to that of the fines on the moon is open to question at this time. A second parameter that affects the directional reflectance is the angle of illumination. The studies of our group [26, 29b, 38-40] are the only ones, to our knowledge, that have been made on lunar fines. As we discussed earlier, the heat flux to or from the lunar surface is greatly influenced by the angle of illumination that the solar energy makes with the lunar surface [6].
(i) Spectral directional reflectance for fines. The smooth curves for our data which are shown in the figures in this section are fit through data points taken at 0.02 pm intervals to 1.0 pm and 0.05 pm interval to 2.2 pm. The spectral directional reflectance curves for fines from Apollo Missions 11, 12, 14, 15, and 16 are shown in Fig. 19. The results are for a bulk density of approximately 1600 kg/m3 for each sample and for an angle of illumina-
24
RICHARD
42rI
I
I
I
c. BIRKEBAK I
I
I
I
I
1
A
3 6 L-
-s -
-
34
-
32
-
30-
4
/ /
2826-
p -
24-
n"
22-
r
0 20-
-" 9
18-
160
I4
-
12I0
--
61 0 2
I 0 4
I 06
I 08
I 10
I 12
I
I
I
14
16
10
I 2 0
1I 2 2
Wavelength ( p m )
FIG.19. Spectral directional reflectance of lunar fines from Apollo 11, 12, 14, 15, and 16 missions. Angle of illumination S lo", bulk density Z 1600 kg/m3.
tion of approximately 10". It is readily apparent by comparing Figs. 17 and 19 that the spectral results for fines are very different than for rocks. It is difficult sometimes to identify absorption bands in the fines data. The pyroxene band near 1.0 pm is apparent in the Apollo 12, 14, and 15 samples but undetectable by us in the Apollo 11 and 16 samples. The results of Adams and Jones [41] and Conel and Kash [33] show a single, very shallow absorption band centered at 0.95pm for the Apollo 11 sample. Other investigators [27, 301, however, did not find any band features in this region of the spectrum. Both the results of Birkebak and Damon [40] and Adams and McCord [37] show an absorption band for the Apollo 14 sample centered at 0.93 pm and this band is due to pyroxene [37]. Also, a band is clearly evident at 1.8 pm. The variation in reflectance from one Apollo sample to another is associated with its chemical composition and glass content [25, 32-34, 37, 411. As the lunar fines become "lighter in color," an increase in reflectance, we find fewer opaque materials in the fines. Adams and McCord [37] have discussed the lighter appearances of Apollo 14 fines and have related it to the fines having lower overall iron and titanium content. The presence or
LUNARPROPERTIES I
25
absence of the absorption bands are a function of the dark glass content and the crystal/glass ratio. The disappearance of the pyroxene band near 1 pm may be caused instead by extensive impact melting and shock alteration of the soil [32]. Material taken from the core tube samples or trench below 70 mm or so from the surface has a higher reflectance than the surface fines. The darkening of the surface material takes place due to meteorite impactinduced vitrification and by regional contamination by iron- and titaniumrich mare material. The average composition of the Apollo 11, 12, 14, 15, and 16 fines are given in Table I1 [lo, 431. B. Glass [42] has reported that glass particles in the fines with low TiOzand FeO content ( <1%) and high A1203 ( ~ 3 3 % ) are colorless: as the Ti02 and FeO content increases approximately 3 and 20%, respect,ively,and with a decrease in A1202 from 33 to lo%, the color of the glass changes from transparent pale green to yellow-green to yellowbrown to red and dark opaque red-brown. The crystal-to-glass ratio is also an indication of the maturity [37] of the material: Apollo 11 fines were approximately 50% glass, Apollo 12,20% glass, and Apollo 14, 40-75% glass [37]. Our Apollo 11, 12, and 15 samples can be classified as mare material, and Apollo 14 and 16 as lunar highlands material. TABLE I1 AVERAGE COMPOSITION OF LUNARFINES Lunar fines sample no. (% abundance) Compound
10084a
12070“
14163”
15021“
68841b
SiOz TiOz AlzOa FeO MnO MgO CaO Mg?O K20
41.86 7.56 13.55 15.94 0.21 7.82 12.08 0.40 0.13 0.11 0.15 0.32
45.91 2.81 12.50 16.40 0.22 10.00 10.43 0.41 0.25 0.27 0.08 0.43
47.17 1.79 17.22 10.35 0.14 9.37 10.95 0.66 0.58 0.46 0.08 0.22
46.56 1.75 13.73 15.21 0.20 10.37 10.54 0.41 0.20 0.18 0.06
-
45.08 0.59 26.49 5.65 0.07 6.27 15.30 0.41 0.11 0.12 0.08 -
100.13
99.71
98.99
99.21
100.16
PZOS S CrzOa
b
“Apollo 15 Preliminary Science Report” [lo]. “Apollo 16 Lunar Sample Information Catalog” [43].
RICHARD c. BIRKEB.4K
26 20
19I 8-
Apollo 10084,68 Angle of Illumination lo0
-5 17- 1615+
X -
14-
L
$ 13-
-0"
12-
c
g
0
Il-
109-
-
8-
-
7-
-
6I
I
I
I
I
I
1
I
FIG.20.
11. I
24 -
23 -
Apollo 12070,125 Angle of Illumination = 1 5 O
22 -
21 -
-2 20-
g 19-
2
-x +
18-
-
17-
L
$
16-
15-
;" 14-
-
13-
-
E
0
-
I2-
-
III 0-
981 0 4
1
06
I
08
1
I
1
I
10 12 14 16 Wavelength ( p m )
I 18
1
2 0
22
FIG.21. Spectral directional reflectance BS a function of bulk density-Apollo 12.
LUNARPROPERTIES I 35
I
I
I
I
I
I
I
27 I
I
I
30 -
-8 0
Density ( k q / m 3 )
25-
0 C
+.
0
se
-
20-
0
0 ._ Z 15-
Angle O f illumination =15O
!2
-
0
-
10 -
5 51
02
04
0.6 06
0.8 0 8
10 1.2 12 1.4 Wavelength ( p m )
1.6 16
1. 1 88
2.0 2 0
2.2 2 2
FIG.22. Spectral directional reflectance &s a function of bulk density-Apollo
14.
The spectral reflectances reported by other investigators show similar trends as ours. It is difficult to compare the results since they refer their reflectances to MgO samples and do not give the bulk density of their material. The spectral directional reflectance of Apollo 11, 12, and 14 samples as a function of bulk density are presented in Figs. 20-22. In general, the reflectance increases with density for all wavelengths in the W, visible, and near-IR regions. The Apollo 11 and 12 samples had very similar particle distributions for the smaller-size particles ( < 10 pm) for a given size of particle. The Apollo 11 and 12 fines had essentially the same number of particles. This being the case, it is not surprising that their reflectances reach maximum values for the same density. The Apollo 14 fines have more particles [45] in this smaller particle range and their effect is seen in the results. Figure 22 shows that the Apollo 14 fines spectral reflectance reaches a maximum value for smaller bulk densities than the Apollo 11 and 12 samples, and this we attribute to the increased amount of small particles. As the surface becomes more compacted, that is, a greater number of particles per unit volume, the porosity decreases and hence fewer number of cavities to trap and absorb radiation are present, and as a result the reflectance increases. Further increase in density has no effect.
RICHARD C.BIRKEBAK
28
Angle O f illurnmotion
a, V
6
c
..Y
25-
W u
0
/ 20-
Apollo 14163 Density = 1 0 9 5 k g / m 3
C
0
c
V
15-
10
-
51
I
I
I
I
I
I
1
1
1
Wavelength ( p m )
FIG.23. Spectral directional reflectance as a function of angle of illumination-Apollo 14. TABLE I11
SOLAR ALBEDOFOR LUNAR FINESO Angle of illumination (degrees) Sample density (kg/m3)
10
15
20
30
45
60
Apollo 11, 10084 1300 1400 1600 1800
0,076 0.087 0.099 0.101
-
0.082 0.095
0.095 0.113 0.113 0.116
0.108 0.132 0.133 0.132
Apollo 12, 12070 1300 1600 1800
0.101 0.119 0.120
Apollo 146, 14163 1095 1300 1590 Apollo 15, 15041 1615 Birkebak [48].
b
-
0.102
0.084 0.102 0.107 0.108
-
0.106 0.114 0.126
0.109 0.115 0.131
0.122 0.136 0.138
-
0.216 0.241 0.262
0.250 0.281 0.297
0.162
0.193
-
-
-
-
-
0.18 0.212 0.213
-
-
0,194 0.222 0.221
-
0.137
-
0.146
Birkebak and Dawson [40].
LUNARPROPERTIES I 50 -
45
-
I
I
I
1.2 1.4 1.6 Wavelength ( p m )
1.8
I
I
I
0.6
0.8
1.0
I
I
29
-
40 -
$
v
2 c
35
-
0 +
0 W
5! 30-
0 C
0 .z 250 5 ! .-
n
20 -
I5
-
0.2
0.4
2.0
2.2
FIG.24. Spectral directional reflectance as a.function of angle of illumination-Apollo 14.
The effect of the angle of illumination is presented in Figs. 23-25 for the Apollo 14 fines [40]. The results for the other Apollo samples show the same features and trends. The reflectance increased with angle of illumination and this is what one would generally expect. (ii) Solar reJEectance. The solar reflectances were calculated from the spectral directional reflectance (Sect. C,2,i), spectral emittance results are to be discussed in the next section, and the spectral solar distribution of Johnson [44]. The solar reflectance (albedo) is defined as
pm=
1
X4.0
h0.3
P ( ~ , ~ ) S A ~ X / ~ ~ ~ S (9) I ~ ~
where p ( X, 0) is the spectral directional reflectance, e is the angle of illumination, X is the wavelength, and S h is the spectral value of the incident solar energy. The solar reflectance for the Apollo 11, 12, 14, and 15 samples are pre-
RICHARD C. BIRKEBAK
30
40 -
35 1
30Angle O f Illumination
20
i L
-
Apollo 14163 Oensrfy = 1 5 9 0 k g / m 3
Y -
02 02
0 4I 04
I 06 06
0 8I 08
1I0 10
1 I I2 14 1I6 I2 14 16 Wavelength ( p m )
1 18 18
2I0 20
22 22
FIG.%.Spec ral directional reflectance as a function of angle of illumination-Apollo
4.
sented in Table 111. Clearly evident is both a bulk density and angle of illumination effect. The change in solar reflectance with angle of illumination is characteristic of dielectric materials. The results for the Apollo 11, 12, and 14 samples were fitted to Eq. (10) and when B = go', the solar reflectance is 1 : p,(B) = A BB CBz DOs E84 FB5 (10)
+ +
+
+
+
where the coefficients are given in Tables IV and V. 3. Spectral Emittance
The spectral emittance [24, 381 of sample 12070 as a function of bulk density for an angle of viewing of 15' is shown in Fig. 26. Each curve represents an average of 3 or more runs and were drawn through data points taken every 0.25 pm. The bandwidth for these measurements varied from 0.5 pm a t 2.5 pm to 0.36 pm at 14.75 pm. The estimated error in these measurements is flojo. The sample surface temperature used in Eq. (8) was calculated from the measured sample temperature gradient, the temperature measured near the surface and from the known sample thickness and thermocouple locations. The temperature gradient in the test fines is similar to that during lunar
LUNAR PROPERTIES I
31
TABLE I V COEFFICIENTS FOR DIRECTIONAL REFLECTANCE E~WATION~ p.(O) = A + B f I + C B Z + D b + E B L Density (kg/ma) Apollo 11, 10084 Coefficient
AX BX CX DX EX 0
1300
1400
1600
Apollo 12, 12070 1800
1300
1600
1800
10 0.7835 0.8896 1.005 1.0349 1.0098 1.192 1.20 102 -0.3452 -0.3304 -0.2674 -0.3472 -0.06783 -0.002479 -0.1041 1W 0.3444 0.3405 0.2895 0.3316 0.09985 -0.002695 0.1411 105 -0.9604 -0.9379 -0.8452 -0.9191 -0.3515 -0.07244 -0.4614 10' 0.8298 0.8059 0.7554 0.7960 0.4136 0.2184 0.4869
Birkebak [48].
night. The surface temperature for all measurements was approximately 380"K, a temperature very near the maximum temperature experienced by the sample on the lunar surface [4-61. The spectral emittance has a maximum of 0.995 at approximately 8.5 pm and a minimum of 0.71 at approximately 3.75pm for a density of 1910 kg/m3. An absorption band is apparent and appears centered at 5.5 pm. The maximum emittance occurs at the so-called Christiansen frequency where the index of refraction of the surrounding medium and fines are equal and where internal scattering is a minimum. The effects of density on emittance are very evident in Fig. 26. As the wavelength increases from 2.5 to 14 pm, the wavelength-to-particle-size TABLE V DIRECTIONAL REFLECTANCE COEFFICIENTS-APOLM 14 p.(B) = A
Density (kg/ma) 1095 1300 1590 0
A
B
x 10%
+ BB + CfIa + Db + EP + C
X 108
0.18 0.052501 -0.11451 0.212 0.045952 -0.092297 -0.51630 0.213 0.3863
Birkebak and Dawson [40].
D X 1W
FB6
E X 106
F X 108
0.073283 -0.151057 0.056681 -0.11649 0.22219 -0.36203
0.106163 0.084766 0.20621
RICHARD C. BIRKEBAK
32 I
I
I
-
10-
-. .-
09-
8
1
O$b
e
[
Reflectance 261
"0
c
'207-
0
W
1350kg/m' 1800kg/ma
06-
ratio is such that beyond approximately 8 pm the density of the material is unimportant in the radiative transport process. Comparison of 1 minus the reflectance results near 2 p m for various densities with the emittance data are good for the highest density but poor in agreement for the lowest density. This is not an unexpected result for the lowcr densities, since the fines have a tendency to settle duc to vibration if kept for a period of time greater than several hours in the test apparatus. The emittance results from Apollo 12, 14 [40], and 15 arc compared in Fig. 27 for a density of 1600 kg/m3. All results have maximum emittance between 8 and 9 pm. The Apollo 14 maximum is at approximately 8.25 pm and Apollo 15 at approximately 8.4 pm. Logan et al. [46] have also measured the emittance for Apollo 14 sample 14259 over a smaller wavelength
I600 kq/rn3 Angle O f Viewing =15"
Density
o Reflectance Measurement 0
05?
A : ; : ; ; ;
Ernittance M e a s u r e m e n t s Logan eta1.(1972)
Ib
Ill
:I
I;
Wavelength ( p r n )
FIG.27. Spectral emittance of ApoUo 12, 14, and 15 lunar fines.
1:
LUNARPROPERTIES I
33
range than ours. They do not specify a bulk density for their measurement. They report a maximum emittance at 8.24 pm. Agreement of their results with ours is excellent. All samples have minimums at approximately 3.53.6 pm. Minimum value for Apollo 14, the lowest for all samples tested, is 0.60, for Apollo 12 the minimum is 0.73.
a. Total Emittance. The total normal emittance as a function of surface temperature was calculated using
where €(A, 8, T) is the directional spectral emittance, 0 is the angle of viewing, T is the temperature of the sample, and &(A, T ) is the Planckian radiance distribution. The total emittance for Apollo 12 sample 12070 as a function of density and temperature is represented in Fig. 28. Also shown are total emittance data obtained directly from Apollo 11 sample 10084. Over the expected temperature range on the moon, 90-400°K, the total emittance varies from approximately 0.972 t o 0.927. The equation representing the emittance as a function of temperature for a bulk density of 1910 kg/m3 [38] is:
a(T) = 0.9843 - 0.2037 X lo3 T
- 0.6765 X 10+ T3
+ 0.1863 X
T2
+ 0.6436 X lo-" T4
(12)
where T is the absolute temperature in degrees Kelvin. The Apollo 11 measurements are for a bulk density of 1600 kg/m3. Over the limited temperature range of these results the total emittance varied between 0.89 and 0.98 f 0.01. Many investigators who have studied the
092-
80
Apollo Sample 12070
120
160
200
-
240
Temperature
200 O
320
360
400
K
FIG.28. Total emittance of Apollo 11 and 12 lunar fines.
440
RICHARD c. BIRKEBAK
34
Apol lo 14163 0.94 Apollo 10084 0.92 0
0.90 80
I 120
1 160
I 1 200 240 280 Temperature OK
I
1
90
I
320 360 400 4 4 0
FIG.39. Total emittance of Apollo 11, 12, and 14 lunar fines for a bulk density of 1600 kg/ms.
lunar surface temperature variation have assumed an emittance of unity, but from our results they can be as much as 9% high. In Fig. 29 the total emittance of Apollo 11, 12, and 14 samples are compared for a bulk density of 1600 kg/m3. The Apollo 14 sample [47] shows the same general trend as the Apollo 12 results. At the lower temperature the results are identical but the total emittances are different for the higher temperatures. The spectral characteristics for the shorter wavelengths account for the difference in the total emittance of the two Apollo samples. Birkebak and hbdulkadir [47] have fitted a third-order polynomial to the Apollo 14 results and obtained
c(T)
= 0.9696
+ 0.9664 X
- 0.31674 X
T
T2 - 0.50691 X
T3
(13)
where T is in degrees Kelvin. At 90°K the total emittance is 0.976 and decreases to 0.925 at 400°K.
V. Summary The thermal radiation properties of lunar fines and rocks have been reviewed. Only those papers which present results that have a direct bearing on heat transfer calculations have been considered. Two papers which were not reviewed but which deal with infrared measurements are by Bastin et al. [49] and Ade et al. [50]. Their results for the most part are for the far infrared region. The reviewed properties have been used by Cremers et al. [4-6] to calculate the temperature variations and heat flow on the lunar surf ace.
LUNARPROPERTIES I
35
ACKNOWLEDGMENTS I thank Ariono Abdulkadir, Mark and Todd Birkebak, and Charles Neville for their assistance in data reduction and equipment design. I also want to acknowledgemy coinvestigators Jim Dawson and Cliff Cremers for their support on our project. Our research was supported by the National Aeronautics and Space Administration under Contract NAS9-8098 and grants NGR 1&001-060 and 18-001-026.
NOMENCLATURE A, B B B
C C2 D E F e i P ! I
R S Sx
T V
Coefficients in Eq. (10) Blackbody Bond albedo Coefficient in Eq. (10) Second radiation constant Coefficient in Eq. (10) Coefficient in Eq. (10) Coefficient in Eq. (10) Radiant energy per unit area and time Radiance (energy per unit time, projected area, and sterradian) geometric albedo Phase integral Reference Sample Spectral solar distribution Temperature ( O K ) Phase angle-angle between the sun, moon, and earth (degr-1
A( )
Detector output
c
x
e P
a(V)
AQ
Emittance Wavelength (micrometers) Angle of viewing (degrees) Angle of illumination (degrees) Directional reflectance Phase integral function (the amount of light reflected into unit solid angle around the direction toward the observer a t phase angle V) Solid angle-sterradian
SUBSCRIPTS b Bidirectional reflectance B Blackbody h Hemispherical reflectance 1 Incident r Reflected R Reference S Sample S Solar x Wavelength
REFERENCES (Z.Kopal, ed.), 2nd Ed., Ch. 5. Academic Press, New York, 1971. 2. PTOC.Apollo 11 LUWT Sci. Conf., Science 167 (1970). 3. “Apollo 12 Preliminary Science Report,’’ NASA Spec. Publ. NASA SP-235 (1970). 4. C. J. Cremers, R. C. Birkebak, and J. E. White, A I A A J . 9, 1899 (1971). 5. C. J. Cremers, R. C. Birkebak, and J. E. White, The Moon 3, 246 (1971). 6. C. J. Cremers, R. C. Birkebak, and J. E. White, Int. J . Heat Mass Transfer 15,1045 (1972). 7. J. A. Bastin and E. L. C. Bowell, in “Geology and Physics of the Moon” (G. Fielder, ed.), Ch. 11. Elsevier, Amsterdam, 1971. 8. T. Gold, M. J. Campbell, and B. T. O’Leary, PTOC.Apollo 11 Lunar Sci. Conf.; Geochim. Cosmochim. Actu, Suppl. 1,3, 2149 (1970). 9. “Apollo 14 Preliminary Science Report,’’ NASA Spec. Publ. NASA SP-272 (1971). 10. “Apollo 15 Preliminary Science Report,” NASA Spec. Publ. NASA SP-289 (1972). 11. T. B. McCord and T. V. Johnson, J . Geophys. Res. 74, 4395 (1969). 12. T. B. McCord and T. V. Johnson, Science 169,855 (1969). 1. B. Hapke, i n “Physics and Astronomy of the Moon”
36
RICHARD C. BIRKEBAK
13. T. B. McCord, M. P. Charette, T. V. Johnson, L. A. Lebofsky, and C. Pieters, J. Geophys. Res. 77, 1349 (1972). 14. J. B. Adams and T. B. McCord, Proc.Apollo 1I Lunar Sci.Conj.; Geochim.Cosmochim. Acta Suppl. 1, 3, 1934 (1970). 15. BI. Rougier, Ann. Observ. Strasbourg 2, 203 (1933). 16. B. W. Hapke, J. Geophys. Res. 68,4571 (1963). 17. A. V. Morozhenko and E. G. Yanovitskii, Sou. Astron.-AJ 15, 134 (1971). 18. F H. Murcray, J . Geophys. Res. 70,4959 (1965). 19. F. €I. Murcray, D. G. Murcray, and W. J. Williams, J. Geophys. Res. 75,2662 (1970). 20. J. W. Salisbury, R. K. Vincent, L. M. Logan, and G. R. Hunt, J. Geophys. Res. 75, 2671 (1970). 21. J. E. Conel, cited in Salisbury et al. [20], p. 2676. 22. R. C. Birkebak, C. J. Cremers, and W. E. Lyons, Rev. Sci. Instrum. 42,1715 (1971). 23. R. C. Birkebak and C. J. Cremers, “Thermophysical Properties of Lunar Material.’’ TR2, High Temp. and Therm. Radiat. Lab., Univ. of Kentucky, Lexington, 1971. 24. R. C. Birkebak, J . Heat Transfer Sa, 323 (1972) 25. B. W. Hapke, A. J. Cohen, W. A. Cassidy, and E. N. Wells, Proc. Apollo 11 Lunar ~Sci.Conf.;Geochim. Cosmochim. Acta Suppl. 1, 3, 2199 (1970), 26. R. C. Birkebak, C. J. Cremers, and J. R. Dawson, Proc. Lunar Sci Conj., 2nd; Geochim. Cosmochim. Actu Supp1. 2, 3, 2197 (1971). 27. T. Gold, B. T. O’Leary, and M. Campbell, Proc. Lunar Sci. Conj., 2nd; Geochim. Cosmochim. Acla Suppl. 2,3,2173 (1971). 28. J. E. Geake, A. Dollfus, G. F. J. Garlick, W. Lamb, G. Walker, G. A. Steigmann, and C. Titulaer, Proc. Apolh 11 Lunar Sci. Conj.; Geochim. Cosmochim. Acta Suppl. 1, 3, 2127 (1970). 29a. R. C. Birkebak, C. J. Cremers, and J. P. Dawson, Science 167, 724 (1970). 29b. R. C. Birkebak, C. J. Cremers, and J. P. Dawson, Proc. Apollo 11 L U ~Sci. T Conj.; Geochim. Cosmochim. Actu Suppl. 1, 3, 1933 (1970). 30. B. T. O’Leary and F. Briggs, J . Geophys. Res. 75,6532 (1970). 31. B. Hapke, Science 159, 77 (1968). 32. J. B. Adams and T. B. McCord, Proc. Lunar Sci. Conj., 2nd; Geochim. Cosmochim. Acla Suppl. 2, 3, 2183 (€971). 33. J. E. Conel and D. B. Nash, Proc. Apollo 11 L u m r Sci. Conj.; Geochim. Cosmochim. Actct Suppl. 4, 3, 2013 (1970). 34. D. B. Nash and J. E. Conel, Proc. Lunar Sci. Conj., 2nd; Geochim. Cosmochim. Acta S u p p l . 2, 3, 2235 (1971). 33. C. H. Perry, D. K. Agrawal, E. Anastassakis, R. P. Lowndes and N. E. Tornberg, Proc. Lunar Sci. Conj., 3rd; Geochim. Cosmochim. Acta, Suppl. 3, 3, 3077 (1972). 36. C. H. Perry, D. K. hgrawal, E. Anastassakis, R. P. Lowndes, A. Rastogi, and N. E. Tornberg, The Moon 4, 58 (1972). 37. J. B. Adams and T. B. McCord, Rev. Abstr., Lunar Sci. Conf., 3rd Lunar Sci. Inst., Houston, Contrib. No. 88 (1972). 38. R. C. Birkebak, The Moon 4, 128 (1972). 39. R. C. Birkebak and J. P. Dawson, Rev. Abstr., Lunar Sn’. Conf., 3rd Lunar Sci. Inst., Houston, Contrib. No. 88 (1972). 40. It. C. Birkebak and J. P. Dawson, The Moon 5, 157 (1972). 41. J. B. Adams and R. L. Jones, Science 167, 737 (1970). 42. B. Glass, Rev. Abstr., Lunar Sci. Conj., 3rd Lunar Sci. Inst., Houston, Contrib. No. 88 ( 1972).
LUNARPROPERTIES I
37
43. “Apollo 16, Lunar Sample Information Catalog,” Lunar Receiving Lab., NASA, MSC 03210 (1972). 44. F. S. Johnson, J. Meteorol. 11,431 (1954). 45. T. Gold, E. Bilson, and M. Yerbury, Rev. Abstr., Lunar Sei. Conf., 3rd Lunar Sci. Inst., Houston, Contrib. No. 88 (1972). 46. L. M. Logan, G. R. Hunt, S. R. Bolsamo, and J. W. Salisbury, Rev. Abslr., Lunar Sci. Conf., 3rd Lunar Sci. Inst., Houston, Contrib. No. 88 (1972). 47. R. C. Birkebak and A. Abdulkadir, J. Geophys. Res. 77, 1340 (1972). 48. R. C. Birkebak, AZAA J. 10, 1064 (1972). 49. J. A. Bastin, P. E. Clegg, and G. Fielder, Proc. Apollo 11 Lunar Sci. Conf.;Geochim. Cosmochim. A c h Suppl. 1, 3, 1987 (1970). 50. P. A. Ade, J. A. Bastin, A. C. Marston, S. J. Pandya, and E. Puplett, Proc. Lunar Sci. Conf., $4; Geochim. Cosmochim. Acta Suppl. 2,3, 22 (1971).
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Thermophysical Properties of Lunar Media: Part I1 HEAT TRANSFER WITHIN THE LUNAR SURFACE LAYER
CLIFFORD J. CREMERS DepaTtment of Mechanical Engineering, University of Kentucky, Lezington, Kentucky I. Introduction . . . . . . . . . . . 11. Thermal Conductivity . . . . . . . . A. Lunar Rocks . . . . . . . . . B. LunarFines . . . . . . . . . . 111. Specific Heat . . . . . . . . . . A. Lunar Rocks . . . . . . . . . B. LunarFines . . . . . . . . . . IV. Thermal Diffusivity . . . . . . . . A. Lunar Rocks . . . . . . . . . B. Lunar Fines . . . . . . . . . . V. Thermal Parameter . . . . . . . . VI. Heat Transfer in the Lunar Surface Layer . . VII. Reference Values of Thermophysical Properties Nomenclature . . . . . . . . . . References . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . , . . . . . . . . . . . , . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
39 42 42 45
59 59 63 64 64
68 70 72
79 80 80
I. Introduction Heat transfer within the lunar surface layer depends on several thermophysical properties of the lunar regolith, that is, the material making up the surface layer. These include the thermal conductivity, specific heat, thermal diffusivity, and thermal parameter. The thermal conductivity is a transport property defined by the Fourier law of heat conduction. It relates the flow of heat in an opaque quiescent medium to the temperature gradients therein. The specific heat relates 39
40
CLIFFORD J. CREMERS
internal energy change to temperature change of a medium. Together, the thermal conductivity and specific heat are key transport properties for encrgy transfer calculations in solid media. Once they are known, the energy equation, xhich is just a statement of the first law of thermodynamics, can bc solved for the temperature field in a medium with known boundary conditions. This along with Fourier’s law permits calculation of local heat AUXPS. The other two properties mentioned in the first paragraph of this section arc ddined in terms of the thermal conductivity, specific heat, and density. The thermal diffusivity is given by a = k / p c and the thermal parameter is given by y = ( k p ~ ) - ~ Both / ~ . of these derived properties are useful in the solution of t h r transient energy equation, and their magnitudes give insight to thc thermophysicai nature of the medium in question. This has been particularly true in the study of energy transfer on the moon. Thv thermal parameter is of particular historical interest in lunar research a5 it appears as a parameter in constant property solutions of thc transient cnergy equation describing heat transfer on the moon. Such solutions formerly werc compared with remote earth-based measurements of lunar tempt>raturcs inferred from infrared and microwave radiation measurements. The value of the thermal parameter which gave best agreement with measurement was then used as a clue as to the constitution of the lunar surface layer. Tht. nature of the moon’s surface had been open t o question until fairly recently. Certainly, telescopic observations had shown that the surface was composed of dielectric material, probably similar to terrestrial rocks of one sort or another. However, the first breakthrough did not come until 1929 when Epstein [l] analyzed the infrared eclipse data of Pettit and Nicholson [ 2 ] , Thr conclusion drawn from the low inferred value of y was that the moon’s surface \\-as similar in character to pumice stone. Pcttit [3], using an improved technique, again measured the infrared radiation from thc moon during an eclipse. Wesstdink [4] analyzed this later data and obtained about the same value for y as Epstein had. However, he showed that the resultant inferred thermal conductivity was about 12 times less than that measured for pumice stone. He compared his results with those obtained from vacuum samples of finely divided pon-dcrs and concluded that the moon must be covered with a layer, probably thin, of powdered rock. Subsequent refinements on Wesselink’s model (e.g., Jaeger [ 5 ] ) showed that the measured radiation could be best explained by a model which has a thin (several millimeters) layer of dust over a solid rock substrate. This idea has been popular until fairly recently. Beginning in the early 1960’s significant observations were made a t
LUNARPROPERTIES I1
41
millimeter and centimeter wavelengths. Much of this work is summarized by Krotikov and Troitsky [ 6 ] . Assuming constant properties, these measurements indicated a homogeneous, highly insulating surface for a depth of several meters with a thermal parameter on the order of one-third that indicated by infrared measurements. These apparent contradictions in the properties of the lunar surface layer led to contradictory and disturbing conclusions when interpreted in the light of constant properties. Linsky [7], in a review of possible models of the lunar surface, interprets the problem in the following way. The apparent contradiction can be explained if one or both sets of observations has been interpreted incorrectly. Alternatively, there must be a mechanism whereby the lunar material can exhibit insulating properties (large thermal parameter) at the surface during lunar nighttime for the infrared measurements. At the same time it must exhibit a significantly smaller thermal parameter at depths on the order of a meter where the observed long-wave radiation originates. At nighttime, then, near the surface the product (kpc) must be considerably smaller than it is farther below the surface. At the same time, however, the long-wave data apparently do not allow the surface material to exhibit different thermal properties on the average during a lunar day than the material below it. The conclusion is that the thermal conductivity and specific heat both increase with temperature. The reasoning that led to these conclusions, based on data acquired at a distance of almost 4 X lo5km, is ingenious, and the later landings on the moon with the subsequent return and analysis of the samples showed how correct the conclusions were. There have been a number of soft landings on the moon in the past several years including five unmanned Surveyor flights and five manned Apollo flights by the United States, and several unmanned Luna flights by the Soviet Union. Only two of these missions, Apollo 15 and Apollo 16, included provision for on-site measurement of surface layer thermophysical properties and then only the thermal conductivity. Unfortunately, a mishap caused the destruction of the Apollo 16 experiment. The only other flight which included such experiments was Apollo 13 which was aborted before a landing could take place. Consequently, there is only one set of on-site data available at this time.' The successfullandings on the moon of the Apollo flights, along with the return of samples of the surface material, have permitted the measurement of the thermophysical properties necessary for heat transfer calculations. These explorations have also proved what was previously hypothesized1 Subsequent to the preparation of this manuscript, the Apollo 17 mission was successfully carried out. Thermal conductivity and heat flow data were telemetered to earth and are now being analyzed.
42
CLIFFORD J. CREMERS
that the lunar surface is covered to a depth of several meters or more, at least in thc mare regions, with a layer of fine particulate soil (or fines as it has been called). There is a hard substratum below these fines and there are many rocks and sometimes boulders scattered about as well. However, these occur randomly and may be considered perturbations in the porous powdery surface layer. Heat transfer within the surface layer will depend primarily on the properties of the fines. Consequently, a great deal of effort has gone into the measurement of the properties of this material from returned samples, with somewhat less effort being expended on the rocks and rock chips. In what follows, reference will be made to these samples by sample number as cataloged by the Manned Spacecraft Center, NASA, Houston, Texas. For further information on the location of the samples on the moon, their collection and handling, the interested reader is referred to references [S-10) as v-ell as to the Office of the Curator, NASA, Houston. As only a minute portion of the moon’s surface has been visited so far, there is little justification for rejecting all of the previous models of lunar simulation. Some of these may well apply in areas not yet sampled. For that, reason results of property measurements on simulated lunar materials will be presented where appropriate as well as measurements made on the actual samples themselves. 11. Thermal Conductivity
A. LUNARROCKS There had not been much work of note regarding the thermal conductivity of lunar rocks prior to the return of the Apollo samples. By the time scientists became concerned with lunar heat transfer, it had already been established that the moon was apparently covered with a layer of dust or fines. Wechsler and Glaser [11] reviewed conductivity measurements of a number of candidate materials, including rocks. They also made measurements of both conductivity and specific heat on some of the more promising materials. Some of their results are shown in Table I. Note that in all cases the thermal conductivity increases with temperature. The conductivities reported by \.7.’echsler and Glaser were obtained using the line heat-probe technique which is a variation of the line heat-source technique to be described later in the discussion concerning the lunar fines. For this method, a hole slightly larger than the probe is drilled in the rock to be tested and the probe is then inserted. Good thermal contact is insured by using mercury and Wood’s metal as contact agents. The thermal conductivity of a synthetic lunar rock and a number of
LUNAR PROPERTIES I1
43
TABLE I THERMAL PROPERTIES OF SELECTED ROCKS~ ~~~~
~
~
~~
Specific heatb (J/kg-"K) Material Semiwelded tuff6 Obsidian Basalt" Altered rhyolite Serpentine Granodioritec
~
Thermal conductivity (W/m-"K)
293498°K
293-823 OK
293°K
493°K
693°K
837 879 879 879 1088 879
1005 1005 963 963 1256 1005
0.54 0.96 1.25 0.71 3.00 1.72
0.54 1.05 1.47 0.80
0.63 1.13 1.68 0.88
1.76
1.77
-
-
From Wechsler and Glaser 1111. Average values within given temperature range. c Thermal conductivity, Univ. of Calif. data, Stephens [12].
0
b
terrestrial igneous rocks at temperatures near melting is given by Murase and McBirney [13]. Their results all fall between 4.2 and 42 W/m-OK. This is on the order of a factor of ten or more larger than the conductivities of the solid materials. There have been only a few studies of the thermal conductivity of the returned lunar rocks themselves. These have all been from the Apollo 11 mission and only one study involved a direct measurement, an indifferent one at that, which serves to indicate the difficulty in this kind of experiment. Warren et al. [14] made a rough determination of the thermal conductivity of lunar rock 10046. This measurement was really a by-product of their specific heat measurement (discussed on p. 62). At about 4°K) they measured the temperature differenceacross the rock, assumed a linear temperature gradient, and calculated a thermal conductivity of 1.05 X W/m-"K which is extremely low for rock of any type. However, it is well known that phonon conduction decreases significantly with temperature for rocks at temperatures below 100-200"K1and so these results must stand, at least until more detailed measurements are made at such low temperatures. There are three other sets of rock thermal conductivities and these are derived from measured thermal diffusivities and specific heats using the relation k = apc. Horai et al. [15) measured the thermal diffusivity of four different rocks of two different types (these measurements are discussed in detail in Sect. IV, A). The samples analyzed were 10020 and 10057 (finegrained vesicular crystalline igneous rocks-type A), along with 10046 and 10065 (breccias-type C) . The specific heat was calculated as a function of temperature from the known mineral composition for these two classes of rocks. The results are shown in Fig. 1.
CLIFFORD J. CREMERS
44 3
I
i
I
0 Y
E
3-
1
0
2-
-
c
0
>
0
"
r
-\ U
-
- - - - _----_
/-
I0 0 I7,64 ( Bas tin
eta/.[ 181)
1
0
FIG.1. Thermal conductivity of lunar and terrestrial rocks: -, terrestrial basalt [12]; - -, samples 10020, 10057 [15]; - -, samples 10046, 10065 [15]; 0, sample 10057 [16].
-
-4second set of conductivities was derived by Robie and Hemingway [lS] from the diffusivity data of Horai et al. [15] for rock 10057, only using their own measured specific hcats for the same rock. These results are given in Table I1 and they are also displayed in Fig. 1. It is significant to note the diffcrences between the results of Horai et al. [15] and Robie and HemingTABLE I1 CALCULATED THERMAL CONDUCTIVITY
Temp. (OK) 149 166 208 304 313 344 345 435 436
OF
LUNARBASALT(10057p Calculated thermal conductivity (W/m-"K)
Measured diffusivityb Measured specific heatc (m8/sec) (J/kg-"W 4.148 X lo2 4.680 5.802 7.531 7.660 8.079 8.096 9.335 9.347
11.94 X lo-? 11.03 9.06 6.44 6.86 6.06 5.91 5.37 6.55
From Robie and Hemingway [16].
b
Horai et al. [15].
1.683 1.753 1.787 1.649 1.787 1.666 1.628 1.704 2.080 c
Robie et al. [17].
LUNARPROPERTIES I1
45
way [16]. Whereas the former show that the conductivity of this particular basaltic rock has a significant dependence on temperature, the latter show that it has very little dependence on temperature. Also shown for comparison is a conductivity curve obtained for terrestrial basalt by Stephens [12]. The fairly good agreement between the latter two sets of data indicates that perhaps the specific heat assumption of Horai el al. [15] leaves something to be desired. Bastin et al. [lS] used a method of measurement whereby a thermal step function was applied to the sample by a straight electrically heated wire. Then from an independent measurement of the specific heat the conductivity was again derived as above. No details were given as to the sample temperature and so presumably it was at room temperature conditions. They obtained a range of conductivities of 0.209-0.837 W/m-OK for the type A rock (no identification given) and breccia (10065). This result is also shown in Fig. 1. In summary there is not much that can be said concerning the thermal conductivity of lunar rock. Perhaps the best values one can use for heat transfer calculations involving this material are those for corresponding terrestrial types of rocks. An excellent summary of the available data for these is given in Wechsler and Glaser [ll]. B. LUNARFINES
It was mentioned previously that there has long been a suspicion that the lunar surface layer was composed primarily of powdered rock, soil or fines as it has lately been called. This has been found to indeed be the case a t all the manned and unmanned mission sites visited to date. In fact, orbital photography gives the indication that this particulate layer exists almost universally on the moon. Consequently, considerably more effort has been expended on determining the thermophysical properties of this material than has been expended on the rocks. This is true for both simulated and actual lunar fines. In what follows, then, it will be frequently possible to make direct comparisons between the simulated lunar specimens and the actual samples. The measurement of the thermal conductivity of a particulate medium such as the lunar fines is not straightforward. Any porous material with an internal temperature gradient will transfer heat through a complicated interaction between phonon conduction through the particles and their contact surfaces plus radiation which can be scattered in the voids and transmitted or absorbed and reemitted by the solid material. Under lunar conditions, of course, there is no problem caused by gaseous conduction or convection because of the extremely low pressures (on the order of Torr) .
CLIFFORD J. CREMERS
46
One has, then, a heat transfer problem involving both conduction and radiation. If the heat flux is to be considered as an entity rather than as a two-component flux, thcn Fourier's law may be used, provided that it is recognized that the thermal conductivity so defined is only an "effective" one rather than a basic property of the material. A number of authors, beginning with Wesselink [4] and including Watson [19], Clegg et al. [20], and Wildey [21], have shown that consideration of a radiative component of the heat flux leads to a cubic temperature dependence of thc thermal conductivity. The derivation due to Clegg et aZ. [20] is conceptually the most satisfying and its essential arguments follow. The net heat flux is assumed to be the sum of phonon conduction plus radiative transport, or Q = Qc Qr. The following assumptions are then made :
+
(1) the surface layer is flat, homogeneous, deep, and in local thermodynamic equilibrium; (2) scattering of thermal radiation within the surface layer is negligible; (3) the medium is optically thick so that the Rosseland mean absorption coefficient may be used; and (4) the optical depth (inverse absorption coefficient) is small compared with T(dT/ax)-' where T is the temperature at a depthx below the surface.
The radiative transfer equation for the net flux change in the direction s is dI,/ds
=
~ y l ( B. J,)
(1)
where J , is the intensity of radiation of frequency P and B, is the Planck blackbody function. ~ y is l the given from the optical absorption coefficient by ~ y = l ~ , [ l- exp (- h v / k T ) ] . s is the position coordinate in the direction of net flux. If Eq. (1) is solved for J , by the variable coefficient method, there results for the intensity of flux at any point 0 m
J,(O)
B,(-r,) exp(-rv) drv
= 0
where the point in question is taken as the origin of coordinates and where dry = K,' ds. Xow B,( - T") can be expanded in a Taylor series about the origin under the condition that the point is much farther from the surface than 1/~yl.Then if a Cartesian coordinate system is introduced so that the direction 5 is directed vertically down from the surface, the substitution dry = K: dxlcos e may be made. Here 0 is the angle between the direction of the radiation and the x axis. One then finds that the total downward
LUNAR PROPERTIES I1
47
radiant energy flux is 2~[J.cosBsinBdB
=
47r aB, - -K y l ax
(3)
at least to a second order approximation. The total downward radiant flux taken over all frequencies is then given by Qr= =
1 aB, -$/,- -ax dv K;
---
dv
(4)
and if the Rosseland mean absorption coefficient is introduced so that
and if
then there results
The total heat flux, then, due to both conduction and radiation may be written Q =
- k c -aT - - - - -16 uT3 aT az 3 z’(T) ax
- - [ k c + k r ] aT
(8)
where
k r = - 16 - UP (9) 3 i?(T) is the radiative component of the effective thermal conductivity and k, is the solid or phonon conductivity. In practice, z‘(T) does not vary significantly with temperature, nor does k,, at least when compared with kr. Consequently, this elementary theory predicts an effective conductivity of the form
k=A+BTa
(10)
As will be seen in the following, this expression fits the thermal conductivity data fairly well. In addition, Linsky [7] and Winter and Saari [48] in their
48
CLIFFORD J. CREMERS
developmerits of lunar surface models showed that the assumption of thermal behavior implied by Eq. (10) led to good agreement between temperatures predicted by the models and those obtained from remote microwave or infrared radiation measurements. It is obvious from Eq. (10) and the prim discussion that ambient pressure, temperature, and saniplc porosity are important parameters affecting the thermal conductivity of porous materials. As the porosity of a particulate medium is a function of the density of the material, given that the particle sizes and shapes are fixed by other considerations, the final constraints on thc nwasurcment of this property of the lunar fines are straightforward. An experiment to measure the thermal conductivity of the lunar fines or any powdered material in vacuum must provide a low pressure to suppress gaseous effects, and provision must also be made for control of sample density and ambient temperature for proper determination of the thernial conductivity over the range of lunar temperatures and surface layer densities. Tiicre are many methods that have been developed to measure the thcrmal conductivity of a solid substance. Only a limited number of these are applicable t o powdered low-conductivity materials. Watson [19] and Bastin et al. [lS] used radiation techniques whereby the specimen sits on a heated surface for which the temperature can be measured as a function of time. A radiation detector monitors the flux from the free surface of the sample as a function of time after a step in the heating is applied. The response is a function of the heat capacity as well as the thermal conductivity and so the method is really a variation of a common method of thermal diffusivity measurement. Excellent reviews of early efforts for measuring conductivities of evacuated powder samples are given by Wechsler and Glaser [ll], Wechsler and Glaser [22 3, Weehsler and Kritz [23], and Xechsler and Simon [24]. Most of the methods used required fairly large amounts of material to be tested. Sample size was an important consideration in planning the experiment for the lunar samples themselves because only a few grams of lunar fines time to be made available. Using expected densities, this meant only about 2 cms of material. After a great deal of experimenting, it was decided that thc line heat-source technique was the best available method. The theoretical treatment of this approach is given by Carslaw and Jaeger [25] and the errors involved in its application are given by Blackwell [26]. Variations of the method have been used previously to determine the thermal conductivities of simulated lunar samples under vacuum, e.g., Wechsler and Glaser Ell, 221 and Fountain and West [27], and also of other poor conductors, e.g., Mulligan [28]. The test cell and method used arc, described in detail by Cremers [29].
LUNARPROPERTIES I1
49
Briefly, the application of this method as used for the lunar sample analysis requires that a long (length-to-diameter ratio greater than 30) line heat-source be embedded in the material to be tested. For such a source in an infinite medium, it can be shown that after an initial period during which the probe heat capacity is dominant, the temperature change at any point in the medium over a time period from tl to tz is given by
T2 - TI = q/(47rk) ln(tz/tl)
(11)
Here q is the heat-source strength and k is the thermal conductivity of the medium. Note that k must be considered constant over the temperature range Tz- TIunder consideration. Equation (11) is the usual working equation for the line heat-source method. It is apparent that if the conditions for the model are met in the experiment, a plot of temperature versus the logarithm of time will result in a straight line, the slope of which is q/47rk. The measurement of q and the slope of the curve then yields the thermal conductivity k. The lunar samples which were made available for analysis were limited in volume so that it became imperative to measure the temperature as close to the source as possible to minimize deviations from the infinite medium assumption. For this reason the line source itself, a 36 AWG (0.127-mm diam. ) Chromel-A wire, was calibrated as a resistance thermometer. Then with the wire in place in the sample the voltage change over about 22 mm of the wire was monitored during heating along with the voltage itself and the current flow. The current through the wire was controlled by a constantcurrent power supply which supplied a current constant to within four significant figures. The voltage change during a run was 0.25% at the maximum, and so the heat generation was constant to within this value as well. Axial heat conduction loss was minimized by providing an extra 20 mm of heating wire beyond the voltage taps and outside of the sample. The test cell was constructed of Teflon and held about 5 g of the lunar fines a t a density of 1100 kg/m3. The size of the sample when in the cell was about 25 x 13 x 13 mm. The lowest density of the fines, that achieved by light pouring, was about 1100 kg/m3 for the Apollo 14 fines and about 1300 kg/m3 for the Apollo 11 and Apollo 12 fines. To obtain greater densities the cell was vibrated with a Vibrotool etching tool to cause uniform settling and packing. The vacuum chamber was of stainless steel and was approximately 0.3 m high. The chamber was pumped with a Welsh Turbomolecular pump to provide a pressure on the order of 10-6 Torr. It will be seen later that this is well below the pressure at which gaseous effects are apparent. Electrical feedthroughs were provided for power and for temperature control and sensing.
CLIFFORD J. CREMERS
50
TABLE I11 VACUUM THERMAL CONDUCTIVITY OF TERRESTRIAL TO LUNARFINEB MATERIALS SIMILAR
Material Olivine Olivineb Basalto Basalt" Chondrite Tektite Glass beadsb G l m beads= Pumice Granite Hornblendeb a
Density (kg/ma)
Temp. (OK)
Thermal conductivity (W/m-"K)
n,a.d 1070 1270 1490 n.a. n.a. 1380-1680 1460 802 1130 1100-1500
295 298 283 283 295 28 1 298 298 296 297 298
6 . 0 x 10-a 4.56 2.0 2.6 4.1 2.3 1.65 2.5 1.4 2.1 3.45
Wechster and Glaser (111. b Watson 1191. Data not available. nett el al. [so].
~Ber-
An inner stainless-steel chamber of double-walled construction WBS used for ambient temperature control. A heating tape wrapped about the outer wall provided higher than room temperatures, and liquid nitrogen or expanding freon passed through the jacket provided low temperatures. A thermistor attached to the chamber actuated the heater for temperature control, and a thermocouple immersed in the sample indicated the sample temperature. Data were taken and processed by a small laboratory computer. 3Ieasurements of the thermal conductivity of simulated lunar fines are summarized in Table 111. In many cases the numbers given represent averages of a number of published data values for roughly similar conditions. Details as to particle-size range, method of packing, and method of measurement, as well as further data may be obtained from the references cited in Table 111. Wechsler and Glaser [ll] in their study of postulated lunar materials reported measurements of the thermal conductivity of glass beads and powdered rocks. The latter consisted of basalt, chondrite, tektite, olivine, pumice, and granite. The densities are not all the same and presumably they represent values for the material as settled after a slight disturbance. Watson [19] did a study of heat transfer on the moon and as part of this he measured the thermal conductivity of glass microbeads, both crushed and
LUNARPROPERTIES I1
51
uncrushed, crushed quartz, olivine, and hornblende. Bernett et al. [30] reported measurements on basalt a t several densities. Note that the thermal conductivity values in Table 111are all given for temperatures just below 300°K. As the temperatures at the lunar equator vary from about 100°K to 400"K, the values given in Table I11 are of only limited use in making calculations involving simulated lunar models. The temperature dependencies of the thermal conductivity of glass beads, olivine, and basalt have been established by several authors. These terrestrial materials were suspected to be close in nature to the lunar fines. The Apollo samples have all had significant amounts of glass in them (up to about 50% for the Apollo 11 fines), and the lunar rock, which in powdered form makes up a great deal of the remainder of the fines, is similar to terrestrial basalt. Data of Watson [19] and Wechsler and Simon [24] for glass microbeads are shown as least-squares curves in Fig. 2. In both cases, the plots represent least-squares curves of the form of Eq. (10) fitted to the experimental data. Curves for crushed quartz are also shown for comparison. Similar data on olivine from Watson [19] and basalt from Wechsler and Simon [24] and Fountain and West [27] are shown in Fig. 3. The coefficients of Eq. (10) used in presenting the above data are given in Table IV. Bernett et al. [30] also measured the conductivity of olivine basalt as a function of temperature over the approximate range 200450°K.
I00
I 200
I
I
300
400
Tempe ro t ure
500
(OK
FIG.2. Thermal conductivity of glass beads and crushed quartz. -Wechsler and Simon [24], - - Watson [19].
-
CLIFFORD J. CREMERS
0 100
300
200
400
Ternperoture
500
(OK)
FIG.3. Thermal conductivity of some evacuated terrestrial rock powders. TABLE IV
THERMAL CONDUCTIVITY COEFFICIENTS A AND B Material
Glass beads Crushed quartz Olivine Basalt
Apollo 11 10084,68 Apollo 12, 12001,19
Apollo 14, 14163,133
Density (kg/ms)
A (W/m-"K)
4.66 x lo-' 1420 1380-1680 7 . 0 25.2 1000 1220-1460 33.5 1370 10.9 1430 6.14 700 5.09 1130 8.87 1300 12.37 1500 16.42 14.25 1300 18.68 1640 17.93 1950 1300 9.22 1640 1970 1100 1300
9.85 11.5 8.36 6.19
FOR
Ea. (10)
B (W/ni-'K4) 2.99 X lo-" 3.4 3.03 4.2 12.6 2.14 1.64 1.90 2.43 3.43 1.72 2.29 1.47 3.19 2.06 1.59 2.09 2.49
Ref. Wechsler and Simon [24] Watson [191 Werhsler and Simon 1241 Watson 1191 Watson 1191 Werhsler and Simon [24] Fountain and West [27] Fountain and West [27] Fountain and West [27] Fountain and West [27] Cremers I381 Cremers 1381 Cremers (381 Cremers and Birkebak 1371 Cremers 1401 Cremers 1411 Crerners (421 Cremers 1421
LUNARPROPERTIES I1
53
TABLE V OF LUNARFINES THERMAL CONDUCTIVITY
Sample
Density (kg/m)
Apollo 15, on site" Apollo 11, 10084,68 Apollo 12, 12001,lQ
n.a.b 1300 2300 2250 Variable 1300 1300
Apollo 14, 14163,133
1300
Apollo 11, 10084,111 Luna 16
Q
b
Temp. (OK)
Thermal conductivity (W/m-"K)
i .05 x 10-3 n.a. n.a. 0.08 n.a. 0.63 293-313 2.01 250 14-25 1.88 298 1.77 298
298
1.28
Ref. Bastin et al. [18] Ade et al. [31] Vinogradov [33] Avduevskii ct al. [34] Langseth et al. [35] Cremers et al. [32] Cremers and Birkebak [371 Cremers [42]
Three determinations made, each at a different depth from the surface. Data not available.
However, the data given are too few and the scatter is too great to permit seeking a model such as Eq. (10) which will approximate the data. The thermal conductivity of the lunar fines themselves have recently been determined by several investigators. The results are summarized in Table V. Bastin et al. [lS] deduced the thermal conductivity of an "average" sample of Apollo 11 fines from the measured specific heat and previous remote measurements of microwave radiation absorption. Later, Ade et al. [31] from the same laboratory measured a much lower conductivity, perhaps using the same sample. They did not compare their second result with the first; however, they noted that their value was considerably less than that published by Cremers et al. [32]. They explain this by saying that the two determinations refer essentially to different situations. In one case the fines are put in a container, while in the other the mean conductivity of the top few centimeters of the surface of the moon is, in effect, determined in situ. A lower degree of compaction of the fines on the lunar surface and also the possibility of adsorbed gases at interparticle contacts in the laboratory determinations are both factors which could account for a discrepancy in the observed direction. Vinogradov [33] and Avduevskii et al. [34] report thermal conductivity measurements on the same sample of material from the Luna 16 mission Their results differ by about a factor of three. No information is given as to methods of measurement. Langseth et al. [35] made in situ measurements with the implanted heat
CLIFFORD J. CREMERS
54 4
7
1
I
Somple 10084.68
I
I
1640kq/m3
1
,
1950 k g / m 3
3 c
I
I 100
I
I
I
200
300
400
Temperature
500
(OK)
FIG.4. Thermal conductivity of Apollo 11 fines.
flow probes at the Apollo 15 site. They report conductivities which are about a factor of ten greater than any others previously reported. The probe is described by Langseth et al. [SS] and is essentially a ring heat source which is implanted in the surface laycr by a driving mechanism. The timetemperature responsc of a sensitive resistance thermometer network in the probe is used to deduce the conductivity through solution of the governing temperature equation for the ring source. Several individual points for the returned Apollo 11, 12, and 14 samples arc given in Table V for purposes of comparison xvith the above data. These are part of a larger collection of data reported by Cremers and co-workers [32, 3742). The measurements reported in these papers were all made using the line heat-source technique described previously. In all cases Eq. (10) was found to represent the data adequately and the coefficients A and B are given in Table IV. The data as correlated by this expression are plotted in Figs. 4-6. Curves for several densities are presented for each sample because, as explained prcviously, the effective thermal conductivity of a particulate medium is expected to be a function of density as well as temperature. Thc lonest dcnsity given in each case is that obtained with the lightest packing of the conductivity cell. This should represent the density of the uppcr centimeter or so of the lunar surface layer or in general the surface layer as ejected or moved and resettled without packing. Note that this density is 1300 kg/m3 for the Apollo 11 and 12 samples, but only 1100
LUNARPROPERTIES I1 I
I
55 I
Sample 12001.19
Temperature
(OK)
FIQ.5. Thermal conductivity of Apollo 12 fines.
kg/m3 for the Apollo 14 samples. Measurements on the Apollo 14 sample at densities greater than 1300 kg/m3 are in progress at present. The intermediate density shown for the Apollo 11 and 12 samples, 1640 kg/m3, is the same as the average core-tube density for the Apollo 11 site as reported by Fryxell et al. [43], and so it should be close to the true surface
-
3
Y
I
I
I
Sample 14163,133
0,
I00
200
300 Temperoture
400 (OK)
FIG.6. Thermal conductivity of Apollo 14 fines.
500
56
CLIFFORD J. CREMERS
_ _ __ ___ _ _
S o m p i e 12001. I 9 Basatt[271
I
1
I 10
FIG. 7. Thermal conductivities of several lunar samples and terrestrial basalt at a density of 1300 kg/ms.
layer density a t that location. The densities of 1950 and 1970 kg/m3 which are reported for the Apollo 11 and 12 samples respectively were the highest that could be obtained in the laboratory with these samples without resorting to extreme measures for packing. In the case of the latter sample, this was also ttpproxiniately the average density of the tore-tube sample as reported by Carrier et al. [44], and so it should be close to the true surface layer density at that location. The densities higher than the minimum in each case were arrived at by vibrating the test eel1 with a Vibrotool etching tool. The lunar conductivity data are compared with one another and with the terrestrial basalt data of Fountain and West [27] in Fig. 7. The highest density given for the basalt was 1500 kg/ni3 and so comparisons with this material at the higher densities used for the fines are precluded. The differences from one curve to another are not too great when the data scatter is taken into account. As a measure of the scatter, a n estimate of the error incurred in using Eq. (10) is given by the standard error of the estimate which is defined as
In Eq. (12), k represents the measured value at a given temperature and
k’ represents the value calculated at that temperature using Eq. (10). N is
LUNARPROPERTIES I1
57
the number of data points. In all cases reported by the author, S has been below 2 x W/m-OK. Differences in slope between the basalt data and those of the lunar fines probably represent the effects of different particle sizes and shapes rather than compositional differences. The basalt was sieved to a rather narrow size range of 37-62 pm, while the Apollo lunar fines varied in size from about 500 pm down to less than 1 pm with most of the particles at the low end of the range as reported by Gold et aZ. [45], King et al. [46], and Gold et al. [47]. The Apollo 12 fines appeared to be somewhat coarser and this observation was borne out in the size distribution measurements. This would tend to reduce the solid conduction component. A number of previous studies, including those mentioned above, have also shown that the fraction of glassy particles varies significantly from one site to anot,her. The different internal structure and surface character of the glassy particles would affect both the conductive and radiative components of the effective conductivity. Assessments of the thermal character of the lunar regolith frequently mention the ratio of radiative to conductive components of the effective thermal conductivity [e.g., 7, 20, 481. This ratio has been predicted by a number of previous investigators for simulated lunar soil, and it is easily TABLE VI TO CONDUCTIVE COMPONENTS OF EFFECTIVE THERMAL RATIOOF RADIATIVE CONDUCTIVITY
Medium Simulated lunar Simulated lunar Simulated lunar Simulated lunar Basalt Basalt Basalt Basalt Apollo 10084,68 Apollo 10084,68 Apollo 12001,19 Apollo 12001,19 Apollo 14163,133 Apollo 14163,133
Density (kg/m8)
Temp.
-
350 300 300 350 350 100 350 100 350 100 350 100 350 100
-
1500 1500 1130 1130 1950 1950 1970 1970 1100 1100
(OK)
krlkc 1, 0.50 1.08 0.734 1.17 0.895 0.021 0.918 0.021 0.352
0.008 0.593 0.014 1.072 0.025
Values for dielectric constants of 2.5 and 1.5,respectively.
Ref. Linsky [7] Clegg et al. [20] Winter and Saari [48] Winter and Saari [48] Fountain and West [27] Fountain and West [27] Fountain and West [27] Fountain and West I271 Cremers [38] Cremers [38] Cremers [41] Cremers [41] Cremers [42] Cremers [42]
CLIFFORD J. CREMERS
58 I0 O
f
1
I
10'
lo2
I"
10-2
100
10'
Ambient Air Pressure ( T o r r )
FIG.8. Pressure effects on thermal conductivity. 0Sample 12001,19 [41], 0 sample 10084,138 1381, V Luna-16 fines [34], A terrestrial basalt [22].
calculated for actual samples once the coefficients of Eq. (10) are known. Some results for this ratio are given in Table VI. It is apparent that there is somenhat lower fraction of energy transmitted by radiation than by phonon conduction in the Apollo fines as compared with the basalt or soil models. As mentioned in the last paragraph, these differences are connected with variations in particle structure, size, and shape between the various samples or models. The thermal conductivity of the lunar fines as a function of ambient prtsure is shown in Fig. 8. The hpollo 11 data are for a density of 1640 kg/m3, the Apollo 12 data are for a density of 1970 kg/m3, the basalt data of Wechsler and Glaser [ 2 2 ] are for a density of 1270 kg/m3, and the Luna-16 data of Avduevskii et al. [34] are for a density of 2250 kg/m3. The agreement here is good. However, this is somewhat deceptive after considering the prcvious figures because this is a log-log plot. The increase in conductivity is almost a factor of I00 over the range of pressures given. It appears from this data and the data for other simulated lunar soils presented by Wechsler and Clascr [22] that the pressure effect is concentrated in the range above Torr The conductivity has a constant value with respect to pressure below this level. This is evidenced by comparing the results at lo-* Torr in Fig. 8 with those of Figs. 4-6 The latter data were obtained at pressures on the order of Torr, and they are not substantially different from the lo-* Torr data. The radiative transfer and
LUNAR PROPERTIES I1
59
solid conduction apparently dominate the energy transfer at these low energy levels.
111. Specific Heat A. LUNARROCKS The specific heat of dielectric materials is primarily a function of molecular structure. It is a mass-specific property and so does not depend on density per se. However, because its magnitude depends on the available atomic and molecular energy storage mechanisms, it is a strong function of temperature. The measured values of this property for rocks do not vary greatly from one specimen to another for two reasons: (a) the major chemical constituencies of most representative rock materials are essentially the same, and (b) the calorimetric measurement of specific heat is quite refined. Winter and Saari [48] plotted data for magnesium silicate, calcium feldspar, diabase, diorite, granite, basalt, silica glass, and quartz, and found that the data were adequately represented by the empirical equation c = -34 T'" 8 T - 0.2 T3" (13)
+
over the range of temperatures from a few degrees Kelvin to 400°K. The units of c in Eq. (13) are Joules per kilogram per degree Kelvin. Data presented by Bernett et al. [30] for silica sand and olivine are substantially in agreement with the representation given by Eq. (13). Robie et al. [17] suggest that this equation is useful (&lo%) for substances having a mean atomic weight on the order of 20-21, but is not generally applicable for materials of different mean atomic weight. Wechsler and Glaser [ll, 221 present specific heats of basalt, pumice, and a number of other candidate materials for lunar surface layer shnulation. Their results are average values over temperature ranges of several hundred degrees above room temperature. Data from Wechsler and Glaser [ll] are included in Table I. All their data are in substantial agreement with that represented by Eq. (13). The specific heats of a number of lunar rocks were measured by Robie and Hemingway [lS] and Robie et al. [17] using a low temperature adiabatic calorimeter. They made their measurements over the approximate range of lunar diurnal temperatures and so the data are particularly valuable. The technique and apparatus are described in Robie et al. [17]. Measurements are presented for two Apollo 11 samples (vesicular basalt10057 and breccia-10021) and one Apollo 12 sample (olivine dolerite12018, 84). Their results are presented in Tables VII-IX and the envelope of the data is shown in Fig. 9. The correlation arrived at by Winter and
CLIFFORD J. CREMERS
60
TABLE VII EXPERIMENT.4L SPECIFIC
0
HEATMEASUREMENTS FOR LUNARSAMPLE 10057 (VESICULAR B.+S.ALT)~
Temp. (OK)
Specific heat (J/k-"K)
96.43 103.54 111.50 120.38 129.30 137.57 14.5.76 154.71 163.10 171.35 179.25 186.82 199.29 201.87 209 .68 217.74 255.75
258.7 274.6 296.0 324.8 352.5 379.7 405.6 432.4 457.9 483.9 506.5 530.4 549.2 568.5 583.9 601.5 617.0
Temp.
(OK)
231.55 239.78 247.68 255.59 263.63 271.93 280.23 288.28 293.21 301.01 309.16 316.53 325.72 333.76 341.59 348.44
From Robie et al. [ 17).
Temperoture ( O K )
FIG.9. Specific heats of lunar rocks and fines.
Specific heat (J/kg-W 632.9 645.5 660.1 676.0 689.0 703.7 717.9 730.5 738.4 748.5 763.7 771.1 782.8 792.0 805 .O 814.2
LUNARPROPERTIES I1
61
TABLE VIII EXPERIWENTAL SPECIFIC HEATMEASUREMENTS FOR LUNAR SAMPLE 10021,41 (BRECCIA)~
0
Temp. (OK)
Specific heat (J/kg-"K)
Temp. (OK)
Specific heat (J/kg-"K)
98.52 106.64 115.66 124.71 134.06 144.6 149.77 155.34 161.04 166.52 170.23 180.38 190.50 200.17
258.7 287.2 318.6 349.1 378.4 411.5 423.6 439.9 462.6 473 .O 496.9 518.2 540.8 565.5
215.92 224.86 233.44 242.6 253.1 264.05 274.64 284.9 294.84 302.83 311.81 320.58 329.14 337.33
600.7 616.6 631.7 650.9 669.8 691.5 708.3 725.9 743.9 753.9 766.5 779.4 792.8 806.2
From Robie and Hemingway [16]. TABLE IX
EXPERIMENTAL SPECIFIC HE.4T MEASUREMENTS FOR LUNARSAMPLE12018,84 (OLIVINEDOLERITE)"
0
Temp. (OK)
Specific heat (J/kg-"K)
Temp. (OK)
Specific heat (J/kg-OK)
96.05 104.40 112.88 121.69 127.19 134.76 141.92 148.73 149.06 158.61 167.66 176.3 184.58 193.14 201 .98
233.2 252.9 293.4 323.6 345.8 369.2 392.2 413.2 419 .O 442.0 467.2 490.6 512.4 535 .o 556.3
210.5 218.75 222.65 231.20 240.23 249.38 258.64 267.60 276.6 285.6 293.03 301.98 310.7 319.59 328.64
578.1 598.2 608.2 627.5 648.8 666.8 686.5 704.5 720.4 739.7 746.8 766.0 782.4 797.0 809.2
From Robie and Hemingway [16].
CLIFFORD J. CREMERS
62
TABLE X EXPERIMEXT.AL SPECIFIC HEATMEASUREMENTS FOR LUNARSAMPLES 10017 (VESICULAR BASALT)A N D 10046 (MICROBRECCIA)'
Rock 10017
Rock 10046
Temp. (OK)
Specific heat (J/kg-"K)
2.344 2.393 2.472 2.713 2.876 3.028 3.399 3.483 3.819 4.036 4.27 4.43 4.52 4.53 4.54 4.70 4.97
1.934 1.950 1.921 2.022 2.034 2.085 2.214 2.223 2.340 2.394 2.545 2.553 2.679 2.721 2.637 2.470 2.805
Temp. (OK)
Specific heat (J/kg-"W
3.08 3.26 3.32 3.54 3.71 4.05
1.172 1.758 1.465 1.884 1.59 1.005
From Warren el al. (141.
Saari [48], Eq. (13), is also shown for comparison. Note that the agreement is extremely good. As was noted before, this is to be expected. Also shon-n on Fig. 9 are theoretical curves for the specific heats of a vesicular crystallinc igneous rock (10020) and another breccia sample (10046). Thcw curves are calculated from an expression derived by Horai et a / . [15] using the known mineral composition of the samples and the thrrniodynamic data for these minerals. Again the agreement is quite good. d single nieasurcment on a third breccia sample (10065) by Bastin et nl. [18] indicates a specific heat of 837 J/kg-OIi. S o information is given as to measurement method or sample temperature, and so presumably it is a rooni-tcmperaturc value. The specific heat of lunar rock at extremely Ion- temperatures was measured by Warren et al. [I41 in their broader study of elastic and thermal properties. The results for two rocks (10017 and 10046) are given in Table X. The authors found that the measured specific heats did not agree u-ith simple Debye theory which is valid for low temperatures. Using
LUNARPROPERTIES I1
63
this approach, the specific heat was calculated directly from the low temperature acoustic velocity, which was measured separately. However, the measured values were over 100 times larger than the predicted values. Hemingway and Robie [49] recently published some smoothed values of the specific heat of an Apollo 14 breccia (14163,186). These are also included in the data envelope in Fig. 9. It should be noted that the specific heats of samples from the Sea of Tranquility, the Ocean of Storms, and Fra Mauro are quite similar, being within 10% of one another a t all temperatures between 100" and 400'K.
B. LUNARFINES The available specific heat measurements on lunar fines are considerably fewer than are those for the rocks. This is particularly true of simulated lunar fines. The reason for this being, of course, that there is substantially no difference between the specific heat of a rock and its powder. As all reasonable simulations involved powdered rock of one sort or another, the specific heat measurements were simply made on the parent rock. TABLE XI EXPERIMENTAL SPECIFICHEATMEASUREMENTS FOR LUNAR SAMPLE10084 (FINES)" Specific heat Temp.
(OK)
95.17 99.56 105.16 112.25 119.98 127.19 134.50 142.83 152.61 162.69 167.02 176.27 185.10 193.60 202.94 213.07 222.84 224.85
From Robie et al. [17].
(JhOK) 268.7 278 .O 291.8 313.1 336.1 358.3 382.2 401.9 445.4 473.4 478.9 507.3 528.3 548.8 574.7 594.4 615.3 614.9
Temp. (OK)
Specific heat (J/kg-"K)
299.00 231.49 233.93 239.78 246.27 253.83 262.18 270.31 278.22 285.93 293.46 300.84 308.07 327.71 332.70 337.93 343.43
619.5 627.5 627.9 642.1 651.3 664.7 681.1 695.7 710.8 721.7 727.1 740.1 750.1 784.0 794.9 798.3 802.9
64
CLIFFORD
J. CREMERS
Thcre are t\\ o sets of specific heat measurements available on the Apollo lunar fines. Kobie el al. [17] mcasurcd the specific heat of Apollo 11 fines sanipl(x 10084. Their results are tabulated in Table X I. The data also fall into the envelope shown on Fig. 9. Hemings-ay and Hobir [49] also presented some preliminary results on the Apollo 14 fines (14321, 153). These data also fall into the envelope. S o t e that there is very little difference between the specific heats of the fines and rocks. 3Ieasurenients 011 the Soviet Luna-16 f i r m reported by Vinogradov [33] show a specific heat of 712 J/kg-"I<. Yo mention is made of the temperature for I\ hich this riumbclr is valid. Other measurements on the Luna-16 sample by Xvducdtii el al. [34] show a specific heat of 741 J/kg-OK. The latter value is reportrd for the temperature range 273"-373"1<. Both the Luna-16 values arc in close agreement with the data of Robie et al. [17] and Hemingway and Robie [49].
IV. Thermal Diffusivity
LVXARROCK:, The thermal di ffusivity is a transport property usually associated with transient heat transfer by conduction. It is defined as the thermal conductivity divided by the product of density times specific heat, or a = k / p c . It usually appears explicitly in constant property analyses of transient heat conduction problems \\hen the thermal conductivity can be factored from the heat Conduction derivatives and is then divided by the pc product from the encrgy storage term. As the thermal conductivity and specific heat of lunar media are both highly temperature dependent, the thermal diff usivity is uf liniited usefulness in analyses of lunar heat transfer. 1)irtict nieasurrments of the thermal diffusivity of trrrcstrial gcologiral materials abound in the literature. Hou ever, efforts to determine this property for candidate rocks for lunar simulation have been fen-. Usually thr specific heat and thermal conductivity are measured along with the density of the material. Then the diffusivity is calculated from data such a? those presented by Wechsler and Glaser [22]. Thc. most extensive data available on the measured diff usivity of lunar rocks are presented by Horai et al. [lj]. One set of these has alrcady h c n prest1ntt.d in Table I f ; that for Apollo 11 rock 10057, a basalt. The other saniplcs on rt hich measurements are reported are 10020, a fine-grained vesicular crystalline igneous basalt like 10057, as well as 10046 and 10065, which are breccias. The Angstrom method described by Iianamori et al. [50, 51) was used in the above measurements which covered a temperature range of 143"-
LUNAR PROPERTIES I1
I00
I
1
1
200
300
400
Temperature
65
500
(OK)
FIG.10. Thermal diffusivity of lunar rocks from Apollo 11. Samples: A 10020, 10046, V 10065.
0 10057, 0
423"K, approximately the range of lunar diurnal temperatures. All samples were rectangular prisms 1 X 1 x 2 cm in size. The thermal diffusivity was determined from the phase lag and the amplitude decay with distance of a periodic temperature wave. The geometry used was one in which the temperature wave propagates through the specimen in the direction perpendicular to the long axis of the prism. Dow Corning-4 heat sink compound was used to obtain good thermal contact between the sample and heater and between the sample and the thermocouple. A temperature wave of 5"-15"K in amplitude and 0.008-0.02Hz in frequency was found to be adequate for the above measurements. A dc component of the temperature wave heated the samples about 100°K above the ambient temperature which was controlled by either liquid nitrogen or solid carbon dioxide in order to obtain the desired sample temperature. The results of the measurements are given in Table XI1 in addition to those already given in Table 11. The data are plotted against temperature in Fig. 10. Also shown are least-squares curves giving the diffusivity as an inverse function of temperature, a relationship which is
CLIFFORD J. CREMERS
66
TABLE XI1
THERMAL DIFFUSIVITY OF APOLLO11 LUNAR~ ~ A T E R I I L Frequency of temp. wave Sample
Temp. (OK)
10020
171 173 222 315 315 414 415 149 166 208 304 313 344 345 435 436 162 176 181 205 313 330 371 430 433 178 190 191 295 404 414
10057
I0046
10065
(Hz) 2.0 x lo-' 1.5 1.2 1 .o 1.5 2.0 1 .o 2.0 10-2 1.5 1.5 1.5 1.o 1.5 2.0 1.2 0.8 0.8 x lo-* 0.8 1 .o 0.8 0.9 0.7 0.8 0.9 0.8 0.8 x
x
1.o
1.2 0.8 0.8 0.9
Thermal diffusivit,y (m4/sec) 9.48 x 10.75 8.99 8.29 6.21 4.26 4.91 11.94 11.03 9.06 6.44 6.86 6.06 5.91 5.37 6 ..55 7.47 6.59 5.37 5.85 3.75 3.60 3.28 3.26 3.25 6.83 x 4.72 4.65 4.63 3.15 2.69
10-7
x 10-7
x 10-7
10-7
appropriate for many solids. These are = 0.378 X lo4 T
(Y-'
+ 0.314 X lo6
(14)
for the fine-grained vesicular crystalline igneous rocks, 10020 and 10057, and 01-l = 0.648 X lo4 T 0.595 X lo6 (15)
+
for the breccias, 10046 and 10065.
LUNARPROPERTIES I1
67
Horai et al. [52 J measured the thermal diffusivity of two Apollo 12 rocks, samples 12002 and 12022, both of which are crystalline igneous rocks (olivine dolerite). They found an almost identical variation of thermal diffusivity with temperature for the two rocks which is given by the empirical relation = 0.58 x 104 T - 9.0 x 10' (16) The data show that the diffusivity of the Apollo 12 rocks is more temperature dependent than that of the Apollo 11 crystalline rocks. The authors relate this to the higher olivine and pyroxene contents of the former. Equation (16) is also shown on Fig. 10 for comparison. Mizutani et a2 [53] measured the thermal diffusivity of Apollo 14 sample 14311,50 which is identified as a polymict fragmental rock. The measurements were made in air a t atmospheric pressure and at lo-' Torr using the modified Angstrom method of Kanamori et al. [51] again. The results and best-fit curves are shown in Fig. 11. The thermal diffusivity was found to be substantially lower under vacuum than in atmospheric air. The possible reason is suggested wherein gas in microcracks and pores contributes significantly to the heat transfer a t higher pressures. The authors suggest that the low values of vacuum thermal conductivity due to microcracks and pores may be significant in the
I
I
I
S a m p l e 14311.50 0 I otm o Vacuum
I00
I
1
200
300
I 400
I
500
Temperature ("K)
FIG.11. Thermal diffusivity of lunar rock from Apollo 14.
10
CLIFFORD J. CREMERS
68
thernial evolution of the moon because these discontinuities may persist to a fairly deep level owing to the low pressure in the moon. B. Lvzv.4~FINES There are, to the author's knowledge, no direct measurements of the thermal diffusivity of either simulated or actual lunar fines. However, there have been several calculated values for both classes of samde. Wechsler and Glaser [22] calculated the thermal diffusivity of glass microbeads, expanded perlite, pumice powder, basalt powder, and granite powder from separate measurements of thermal conductivity and specific heat. Their results for vacuum conditions on the order of 10-l Torr and below are summarized in Table XIII. Here, in many cases, average values for several runs are recorded. Also shown are some data presented by Bernett et al. [30] for powdered basalt. It is not possible to calculate the thermal diffusivity for the Apollo 11 conductivity data of Bastin et al. [l8] and Ade et al. [31] as these are not accompanied by corresponding density values that would permit such a TABLE XI11 THERMAL DIFFUSIVITY AND THERMAL PARAMETER OF SIMULATED LUNARFINE M AT E RI AL S~
Material Glass beads 1150 /r] Glass beads [SO p ] Glass beads 129 4 Expanded perlite Pumice Pumice Pumice Granite Granite Basalt Basalt Basalt Basalt Basalt Basalt
Density (kg/m3) Temp. 1460 1460 1460 137 877 877 877 1130 1130 1270 1270 1270 1570 1570 1570
(OK)
298 298 298 298 277 328 296 297 353 283 33 1 221 213 273 363
Thermal diffusivity Thermal parameter (mz/sec) (mz-"K-secl/e/J) 3 . 9 x 10-9 2.3 2.0 12.7 2.80 3.22 2.05 2.22 2.65 1.9 2.34 2.04 1.1 1 .o 1.05
1.25 x 10-2 1.63 1.76 8.18 2.73 2.21 3.27 2.24 2.08 2.16 1.83 2.32 1.28 1.63 1.43
First twelve entries in table are from Wechsler and Glaser [22];last three entries are from Bernett et al. [do]. 0
LUNARPROPERTIES I1
69
TABLE XIV
THERMAL DIFFUSIVITY OF LUNARFINESFROM: blT bzTa b3Ta b4T4(m2/sec)
COEFFICIENTS FOR CALCUL.4TING SMOOTHED VALUES OF
a =
+ +
+
Density (kg/ms) bo X 109
Sample Apollo lla Apollo 11s Apollo 11Apollo 12b Apollo 12b Apollo 12b a
bo
1300 1640 1950 1300 1640 1970
+
bl X 10"
bz X 10"
bs X 10"
b4 X 101a
-1.145 -1.190 -0.945 -0.731 -0.624 -0.610
5.501 5.714 4.478 3.52 3.00 2.93
-1.195 -1.241 -0.960 -0.742 -0.645 -0.635
0.999 1.037 0.783 0.622 0.540 0.531
1.099 1.142 0.915 0.707 0.601 0.586
Sample 10034,68 from Cremers [38].
Sample 12001,19 from Cremen [41].
calculation. However, the specific heat data of Robie et al. [17] can be used with the conductivity data of Cremers et al. C32, 37-41] to calculate the thermal diffusivity over the approximate range of lunar temperatures. It should be noted that the specific heat data are valid only for the Apollo 11 fines. However, evidence previously cited indicates that all the lunar fines shouId have substantially the same specific heats. The thermal diff usivities for the ApolIo 11 (10084, 68) and Apollo 12 (12001, 19) are plotted in Figs. 12 and 13, respectively. 3I
0
u , v)
N
E m-
0
2 ...
I
X
=3
Sample 10084,68
c 0I
0
100
200 Temperoture
300 (OK)
FIG.12. Thermal diffusivity of fines from Apollo 11.
400
70
CLIFFORD J. CREMERS I
I
I
1 Sample 12001.19
Ixx) kg/m3
1640 kg/rn3
I970 g / m 3
I00
200 Temperalure
xx) (OK)
FIG.13. Thermal diffusivity of fines from Apollo 12.
The curves shown in Figs. 12 and 13 are fourth-order polynomials fitted to the diffusivity data calculated from the smoothed thermal conductivity values of Crrmcrs el al. C37-411 and the smoothed specific heat data of Robie et al. [17]. The resultant coefficients of curves which are displayed are given in Table XIV for the Apollo 11 and Apollo 12 samples. The thermal diffusivity of the Luna-16 sample can be calculated from the two sets of specific heat and conductivity data previously mentioned. mz/scc, The data of Vinogradov [33] indicate a diffusivity of 1.34 X which is presumably valid for room-temperature conditions (297"K), while the data of Avduevskii et al. [34] indicate a diffusivity of 1.2 X m?/scc for thc temperature range 293O-313OIi. These values are close to those for the Apollo 12 fines presented in Fig. 13.
V. Thermal Parameter Constant property analyses of heat conduction problems in which the boundary conditions are periodic with time are often cast in terms of the thermal parameter [54]. This property is defined as y = (kpc)-"2
(17)
It can be shown that for many problenis the amplitude of the heat flux variation a t any position is proportional to y-'. One such problem is that of a semiinfinite solid such as the lunar surface under periodic solar heating. Consequently, it can be expected that the amplitude of the temperature
LUNAR PROPERTIES I1
71
TABLE XV
PARAMETER OF LUNAR SURFACE LAYER THERMAL
Reference
Thermal parameter X lop (mL"K-secl'*/J)
Wesselink [4]
2.39
Jaeger [51
1.20
Krotikov and Troitsky [6]
0.84
Linsky 171"
1.60-2.12
Linsky 171"
2.33-2.46
Linsky (7jo
0.60-2.57
Linsky (71"
1.10-2.57
Linsky [7]"
1.60-2.12
Lucas el al. [63J
0.60-3.11
Muncey [56]*
0.48-0.72
Murray and Wildey 1611.
1.91,0.72
Low [62]
2.39
Avdeuvskii et al. [34]
1.73
Cremers [41]d
3.95, 1.84
Source Compared with I R eclipse data of Pettit [3] Compared with I R eclipse data of Pettit and Nicholson [2] Compared with own radio measurements Compared with radio measurements of Krotikov and Troitsky [6]. Variable property model with dielectric constant of 2.5 Compared with radio measurements of Krotikov and "Yoitsky [6]. Variable property model with dielectric constant of 1.5 Compared with radio measurementsof Krotikov and Troitsky [6]. Twolayer model of constant properties Compared with radio measurementsof Krotikov and Troitsky [6]. Twolayer model of constant properties Compared with I R eclipse data of Pettit (31 Compared with temperature data from Surveyor spacecraft Compared with IR eclipse data of Pettit and Nicholson [2]. Variable property model Compared own I R data with prediction of Jaeger [51 Compared own I R data with prediction of Weselink [4] Calculated from properties of Luna-16 sample, p = 22.50 kg/m* Calculated from properties of Apollo 12 sample, p = 1970 kg/m*
c Nighttime and sunset values, 5 Evaluated a t 300°K. Evaluated a t 350°K. d Evaluated at 100"and 350°K' respectively. respectively.
72
CLIFFORD
J.
CREhtERS
variation on the moon will be a strong function of the thermal parameter. Sufficient data have been presented in the preceding sections to permit thr c,alculation of the thermal parameter for any temperature, and so the rrsults of such calculations nil1 not be repeated here. In Section VII, suggested rcfercncc valucs of this property \\ill be prcscrited for use in constant property analysrs. There is reason, however, for discussing this property furthw from a historical viewpoint. Until the moon landings, all thermal analyses of the lunar surface layer had to proceed with the use of physical properties of an assumed medium. Thc results of thcse analyses were then compared with remote infrared or micron ilvc radiation measurements made from earth. The values of the thermal parameter which gavr the best agrecment between prediction and rcmote ni~~asureni(~nt \\ere then used to infer the character of thc lunar surface layer. It ivas known, for instance, as early as 1948 [4] that thr lunar surface was covered nith a layer of porous material. However, whether it hvas a solid matrix or powdery one was not knonn for certain until the Survryw sorirs of flights. It has already hern noted that the therniophysical properties of the moon arc highly tcnipcraturc> drpendent. Consequently, the thermal parameter 11 ill also he a function of temperature and a nonlinear one a t that. This explains why it was difficult for past invrstigators to grt complete agrcemcnt between thi. constant property predictions and the rcmote nicasurement~.For instance, it is pointed out in the recent work by Winter atid Saari [48] that for constant property models a thcrmal parameter of 0.0311 n~2-oIi-sec1’2/.Jis achieved by matching theory with experimental data during the umbra1 phase of an eclipsc. However, this leads t o unacceptably low calculated values of lunar nighttime temperatures. When y is set equal to 0.0191 to reproduce measured nighttime temperatures, there is substantial disagrerment with eclipse measurements. Somr estimated values of the thermal parameter from the literature are givrn in l’ahk XV. Thew were obtained by comparing lunar temperatures dt-duccd from radiation measurements with those predicted by constant propcrty thvory. Also included arc values calculated from the measured propcrties of the Apollo 12 fines at a density of 1970 k g / d for a typical daytime temperature of 350°K and also for a typical nighttimcl temperature of 100°K. The thermal conductivity and specific heat for these calculations arc’ taken from Figs. 5 and 9 respectively.
VI. Heat Transfer in the Lunar Surface Layer A numtwr of investigators [4, 5, 54-36] have Calculated surface temperatures a t the lunar equator using constant thermophysical propertics
LUNARPROPERTIES I1
73
obtained for an assumed medium. Others have suggested certain models for the temperature variation of the thermal conductivity and specific heat without making calculations of the actual temperature distribution. The most advanced work previous to the Apollo program has been done using measured values of the thermophysical properties of an assumed medium [7, 19,48,57-591. The merit of this work lies more in what the investigators inferred about the moon than in the temperatures which were calculated. The temperature distributions were compared with those obtained from earth-based microwave and infrared measurements. Excellent working models for the lunar surface layer were constructed from which thermal and mechanical calculations could be carried out. Many previous papers [2, 60-621 have reported direct, although remote, measurements from which the lunar surface temperature was calculated. Photometric scans of the lunar disk during eclipses or lunar nighttimes were made through several infrared and microwave windows in the atmospheric absorption spectrum. All lunar radiation in the absence of sunlight is emitted radiation, and so the temperature can be evaluated using the Planck distribution law. These measurements yield spatially integrated values of the lunar emission over areas on the order of 20-50 km in diameter. This can cause some difficulty in interpretation because of the known existence of thermal anomalies on the moon caused either by density variations in the surface layer or by significant local heat flow from the lunar interior. The only localized experimental determinations of the temperature of the lunar surface before Apollo have been obtained through an ingenious application of the heat balance to spacecraft components. These experiments are summarized in Lucas et al. [63], Vitkus et al. [64-66], and Stimpson and Lucas [67]. The temperatures of two component-panels of the Surveyor I, 111, V, VI, and VII landing vehicles were obtained by analyzing data telemetered from the vehicles. These temperatures were then used in a heat balance involving conduction through components and radiation exchange between the panels and the lunar surface as well as with other components of the spacecraft. An error analysis on the calculations showed that the nighttime temperatures were accurate to within 8"K, while the daytime temperatures were good to within 12"40"K, depending on sun angle. The longest time period covered was about twothirds of a lunar day. This was done on the Surveyor V mission. The Apollo 13 flight was the first lunar mission which carried a probe for direct measurement of the temperature in the lunar surface layer. The flight was aborted on the way to the moon because of a system malfunction and consequent failure. Two probes were later included on the Apollo 15 flight and were success-
74
CLIFFORD J. CREMERS
fully implanted on the moon. The probe design is described by Langseth et al. [36], and the Apollo 15 results are described by Langseth et al. [35] The temperature measured 1 m below the surface was 250.7OK at one probe and 252.3°K at the other probe. Both values are at least 25°K higher than mean temperatures calculated for constant density models. The steady temperature gradient at depths where the temperature variations caused by lunation and damped out was measured to be 1.75"I
In Eq. (18) it is assumed that the specific heat and thermal conductivity are explicit functions of temperature and that the density is constant with depth. The latter msumption is borne out by observations made by the Apollo 12 astronauts and reported in reference [8]. However, this is at variance with the arguments of Langseth et al. [35] which explain the anomalously high heat flus measured by probe at the Apollo 15 site. It is convenient to express Eq. (18) in terms of dimensionless variables. Because the problem is periodic, it is convenient to make the time dimensionless with the period of lunation P which is 2.55143 x lo6see so that T = t/P. The length variable x is made dimensionless with the wavelength of the first fundamental wave of the constant property solution of Eq. (18). That is, [ = s/(4~a*P)"'.Here a* is the thermal diffusivity evaluated at the average lunar temperature, that is, the temperature far below the moon's surface. The dimensionless equation can then be expanded and
LUNARPROPERTIES I1 written as
aT -=-
ar
[1dk (aTat >"+$I
a -4na* k d T
-
75
(19)
where k and a are both functions of temperature. Consideration must now be given to the boundary conditions on Eq. (19). The condition at large depth to be imposed on Eq. (19) is that the heat flux goes to zero. The Apollo 15 heat-flux probe has shown that the average lunar heat flux is much less than that caused by insolation and cooling near the surface. In addition it is required that the problem be periodic with a period already mentioned. The condition at the surface is expressed by a heat balance between the incoming solar radiation and the energy which is emitted to space, plus that which is conducted into the surface layer. As the sun's angle with respect to the normal varies during the day, the fraction of incoming radiation which is absorbed also changes. These conditions are written as
The insolation term is z(7)
= s[1
- r ( T ) ] COS A COS@ + 2AT]
(21)
during the half-period of daytime, and I ( T ) = 0 during the half-period of nighttime. In Eq. (20), e is the total hemispherical emittance which is a function of temperature, and in Eq. (21)) T ( T ) is the directional reflectance which will vary with the sun's angle of incidence, and so it can be expressed as a function of the time variable r. A is the latitude and @ is longitude of the lunar site in question. S is the solar constant which was taken as 1395 W/m2 [68]. Recent measurements indicate that 1353 W/mz is perhaps a better value to use [69]. Equation (19) was solved on the IBM 360-65 digital computer using a modified Runge-Kutta scheme. Initially, the directional reflectance and temperature dependent emittance were not available for use in Eqs. (20) and (21). Results for the Apollo 11 and 12 sites for constant values of these properties are given by Cremers et al. [70] and Cremers et al. [71]. The noon, sunset, midnight, and sunrise temperatures are given in Table XVI. Later, when the directional reflectance and temperature dependent emittance became available, Cremers et al. [39] recalculated the Apollo 12 temperatures. The effect of a directionally dependent reflectance should be significant because if a constant reflectance is assumed, the surface immediately begins absorbing a given fraction of radiation a t sunrise and
CLIFFORD J. CREMERS
76
TABLE XVI CONPARISON OF bZE 9SURED AND CALCULATED LUNAR SURFACE
Source Apollo 11 Cremers [38] Apollo 1 1 Cremers [all Wesselink [4] Jaeger 151 Linsky 171 Pettit and Nicholson [2] Sinton [%I Saari 1721 Low 1621 Ingrao et a!. [73] Stimpson and Lucas 1671
Noon
Sunset
TEMPERATURES ("K)4
Midnight
395 389 370 368
152 134 144 178
101 95 98 97
374 389
181
120 122 104
Sunrise 92.9 86.1 90 89 89 109 90
393 386-390
14G200
100-112
From Cremers el a l . [70].
continues absorbing this fraction until sunset. In the real case, however, a t grazing angles the reflectance is near unity and so there is little absorption. Inclusion of the directional dependence of the reflectance has the important cffcct of moderating changes between night and day temperatures in periods near sunset and sunria.. Thv rrsults 0htainc.d for the complete variable property case for the Apollo 12 sitr are given in Fig. 14. A comparison between temperatures from the prescnt study and the results of the above analysis in which the reflrrtance and cmittance were held constant at mpan values is given in T a b h XVII and by the dashed line in Fig. 14. Notr that at noon there is practically no difference because the sun is directly overhead and the normal reflectance was that used in the constant surface property analysis. The only difference between the two calculations is in the emittance. The really significant differences in the two models are just before sunset and just after sunrise. The maximum differences occur a t 7 = 0.24 where the tenipcraturr is loner by 43.7"K in the variable property case and a t T = 0.76 when the temperature is lower by 64.1°1iin the variable property case. The temperatures at the Apollo 12 site were compared in Table XVI with thosc calculated for the ApolIo 11 site. It should be reemphasized that there were no total directional reflectances or temperature dependent emittances available when the latter calculations were made, and so constant radiative properties were assumed. The generally loit er temperatures in the Apollo 12 case are due primarily to the lesser amount of energy
LUNARPROPERTIES I1
77
400
300
5 200 W
a E al
+ I00
I
I
I
0.2
0
I
06 0.0 Fraction O f L o c a l L u n a t i o n
0.4
10
FIG.14. Temperature variation on the moon during a lunation.
calculated to be absorbed during the day. This difference is caused by taking the directional dependence of reflectance into account. The most significant differences occur again just before sunset and just after sunrise when the constant surface property model deviates the most from the actual situation. The differences in conductivity and diffusivity become TABLE XVII COMPARISON OF TEMPERATURES FOR THE CASEOF VARIABLE SURFACE PROPERTIES WITH THAT OF CONSTANT SURFACEPROPERTIESO Temperature (OK) .
Time 0 (Noon) 0.24 0.25 (Sunset) 0.50 (Midnight) 0.75 (Sunrise) 0.76 a
~
~~
Variable T , 389.3 161.2 134.4 94.7 86.1 125.4
From Cremers et al. [39].
~~
E
Constant T, 389.4 204.9 147.5 96.8 87.8 189.5
E
CLIFFORD J. CREMERS
78
most apparent beneath the surface. The amplitude of the diurnal variation at depths of 20 and 50 mm is on the order of 20°K greater in the Apollo 1I case. It is of historical interest to compare the present results with some prior calculations of lunar temperatures which were based on assumed properties. Thwv calculations wcre usually made in terms of the thermal parameter. For thc studirbs of Cremers et ul. [39, 70, 711, the value of the thermal parameter based on reference properties (discussed in Sect. VII) is about 2.4 X in SI units. For comparison, temperatures were calculated by Wessrlinli [4] ( y = 0.28 x 10-7, Jaeger [S] (y = 2.39 X and Linsky [7] ( y = 2.39 X 10-9, among others. Wesselink and Jaeger assumed constant properties throughout, and the numbers takcn from Linsky xwre calculated for an assumed medium with temperature depcndcnt specific heat and thermal conductivity. The results of these calculations are given in Table XVI along with those from calculations based on the Surveyor studies. Also shotvn in Table XVI are the results of remote measurements of lunar surfarc trmpcratures. These include temperatures inferred from mcasuremeiits of infrared or microwave radiation during lunar nighttimes or during eclipses by Pcttit and Sicholson [2], Sinton [ 5 5 ] , Saari [72], Low [62], Ingrao et al. [73], and Stimpson and Lucas [67]. In the latter paper several
0
0
I
I
0.2
04
Dimensionless D e o t h
I
I
08
06 X/(4
T Qf
PI”*
FIG.15. Temperature variation on the moon as a function of depth.
1
10
LUNARPROPERTIES I1
79
separate determinations are made of each temperature and the results are presented here as a range. Considering the assumptions required to deduce temperatures from the data and the wide area from which the measured radiation originates, the agreement is quite good. Figure 15 shows the variation of temperature with depth for several times during the lunar day as calculated from Eq. (19). It is seen that the temperature wave damps out rapidly with distance because of the excellent insulating characteristics of the lunar surface material. In both the Apollo 11 and 12 cases, the daily variation in temperature drops to about 1' at about E = 0.85 which corresponds to a depth of only 0.172 meters. The steady temperature on the moon below this depth is 225'K, considerably below that measured for the Apollo 15 site.
VII. Reference Values of Thermophysical Properties
It is frequently of interest to have relevant reference values of the thennophysical properties available for computational convenience because in many analyses the constant property assumption will suffice. There are two ways of calculating meaningful reference properties for the typical lunar problems. One way is to calculate the integrated average of the property in question over the temperature range of interest. That is, for a TABLE XVIII CONDUCTIVITY, THERMAL DIFFUSIVXTY, AND THERMAL AVERAGE VALUESOF THERMAL P ~ R A M E T E RFOR THE APOLLO FINES SAMPLES' Thermal conductivity (W/meters-"K) Density (kg/mJ)
I x lo"
k*
x lo"
Thermal diffusivity (m'/sec) ti X 109
(I* x 109
7 x 10'
2.04 2.11 1.64
2.73 2.12 2.06
2.81 2.17 2.08
1.58 1.21 1.08
2.91 2.77 2.48
3.11 2.87 2.47
Apollo 11 1300 1640 1950
1.77 2.32 2.09
1.61 2.12 1.95
2.34 2.42 1.85
Apollo 12 1300 1640 1970
1.52 1.37 1.45
1.28 1.21 1.33
1.95 1.44 1.29
4
From Cremers el al. [38,411.
Thermal parameter (m" "K-sec1n/J)
*
y*
x 10'
CLIFFORD J. CREMERS
80
propwty p ( 2') the integrated average jj is given by fj
=
(Tmax
- Tinin)-'/
Tmax
p(T) dT
(22)
Tm*o
In Eq. (22) T,,,,, and T,,, are the extreme temperatures of the problem. A second way is to simply evaluate the property at a mean value of temperature. That is, p* = p("). The obvious temperature to use here is the average temperature of the lunar surface layer. As the properties k, a, and c of the lunar fines are nonlinearly dependent on temperature, there will be a difference in the two sets of calculations Cremcra C38, 41) carried out the reference property calculation for the Apollo 11 and 12 fines samples. The rcsults are given in Table XVIII. The tempPraturrs used are taken from Cremers ef al. [39, 701, respectively.
ACKSOWLEDGMESTS The aiithur wishes to express his gratitude to the National Aeronautics and Space Administration for financial support for the investigations of lunar thermophysical properties. Many thanks are also due to Beverly Martin and Lynda Young who typed the manuscript and to Carla Cremers who helped organize much of the author's own data as well as those of others. xOXENCL.4TURE
A
B C
I J k P P
Q T
S
s t
T X
Coefficient of Eq. (10) Planck blackbody function; coefficient of Eq. (10) Specific heat Insolat ion Radiative intensity Thermal conductivity Period of cyclic heat flux Heat flux per unit length Heat flux per unit area Surface reflectance General direction Solar constant Time Temperature Distance from surface
GREEKSYMBOLS Thermal diffusivity Thermal diffusivity a t average lunar temperature p Longitude y Thermal parameter (lipc)-l/* c Surface emittance e Angle from surface normal K Absorption coefficient h Latitude Dimensionless distance z/(47ra*P)"* p Density T Dimensionless time t / P a a*
So DSCRIPTS
c r Y
0
Conduction Radiation Frequency Surface
1. P. Epstein, Phys. Rev. 33, 269 (1929). 2. E. Petitt and S. B. Nicholson, Astrophys. J . 71, 102 (1930). 3. E. Pettit, Asfrophys. J . 91, 408 (1940).
LUNARPROPERTIES I1
81
A. J. Wesselink, Bull. Aslron. Znst. Neth. 10, 351 (1948). J. C. Jaeger, Aust. J. Phys. 6, 10 (1953). V. D. Krotikov and V. S. Troitaky, Sou. Astron.-AJ. 6, 841 (1963). J. L. Linsky, Icurw 5,606 (1966). “Apollo 11 Preliminary Science Report” NASA Spec. Pdl. NASA SP-214 (1969). “Apollo 12 Preliminary Science Report’lNASA Spec. Publ. NASASP-235 (1970). “Apollo 14 Preliminary Science Report” NASA Spec. Publ. NASA SP-272 (1971). A. E. Wechsler and P. E. Glaser, Zcarus 4,335 (1965). D. R. Stephens, High Temperature Thermal Conductivity of Six Rocks. Univ. of California, Lawrence Radiat. Lab., Rep. UCRL 7605 (1963). 13. T. Murase and A. R. McBirey, Science 170, 165 (1970). 14. N. Warren, E. Schreiber, and C. Scholz, Proc. Lunar Sci. Conf., M ,Geochim. Cosmochim. Acta Suppl.. 2, 3, 2345 (1971).* 15. K. Horai, G. Simmons, H. Kanomori, and D. Wones, Proc. Apolb 11 Lunar Sci. Conf.; Geochim. Cosmochim. Actct Suppl. 1,3, 2243 (1970).f Geodrim. Cosmochim. 16. R. A. Robie and B. S. Hemingway, Proc. Lunar Sci. Conf., M , Acta Suppl. 2, 3, 2361 (1971). 17. R. A. Robie, B. 5.Hemingway, and W. H. Wilson, Proc. Apollo 11 Lunar Sci. Conf., Geochim. Cosmochim. Acta Suppl. 1, 3, 2361 (1970). 18. J. A. Bastin, P. E. Clegg, and G. Fielder, Proe. Apollo 11 Lunar Sci. Conf., Geochim. Cosmochim. Acta Suppl. 1, 3, 1987 (1970). 19. K. Watson, I. The Thermal Conductivity Measurements of Selected Silicate Powders in Vacuum from 150”-350”K;11. An interpretation of the Moon’s Eclipse and Lunation Cooling as Observed through the Earth’s Atmosphere from 8-14 Microns. Ph.D. Thesis, California Inst. of Technol., Pasadena, 1964. 20. P. E. Clegg, J. A. Bastin, and A. E. Gear, Men. Not. Roy. Astron. Soc. 133,66 (1966). 21. R. L. Wildey, J . Geophys. Res. 72,4765 (1967). 22. A. E. Wechsler and P. E. Glaser, Thermal Conductivity of Non-Metallic Materials. A. D. Little, Inc., Cambridge, Massacuhsetts, Rep. NASA Contract NAS8-1567 (1964). 23. A. E. Wechsler and M. A. Kritz, Proc. Themz. Conductivity Conf., 6th, Univ. Denver p. 11-D-1 (1965). 24. A. E. Wechsler and I. Simon, Thermal Conductivity and Dielectric Constant of Silicate Materials. A. D. Little, Inc., Cambridge, Massachusetts, Rep. NASA Contract No. NAS8-20076 (1966). 25. H. S. Canlaw and J. S. Jaeger, “Conduction of Heat in Solids,” p. 334. Oxford Univ. Press, London and New York, 1959. 26. J. H. Blackwell, Can. J. Phys. 34,412 (1956). 27. J. A. Fountain and E. A. West, J. Geophys. Res. 75, 4063 (1970). 28. J. C. Mulligan, J. Geophys. Res. 75, 4180 (1970). 29. C. J. Cremen, Rev. Sci. Instrum. 42, 1694 (1971). 30. E. C. Bernett, H. L. Wood, L. D. Jaffee, and H. E. Martens, AZAA J. 1,1402 (1963). 31. P. A. Ade, J. A. Bastin, A. C. Marston, S. J. Pandya, and E. Puplett, Proc. Lunar Sci. Conf., 2nd, Geochim. Cosmchim. Acta Suppl. 2,3,2203 (1971). 32. C. J. Cremers, R. C. Birkebak, and J. P. Dawson, Proc. Apollo 11 Lunar Sci. Conf., Gwchim. Cosmochim. Acta Suppl. 1, 3, (1970). 33. A. P. Vinogradov, Proc. Lunar Sci. Conf., grid, Geochim. Cosmochim. Acta Suppl. 2, 1, 10 (1971); also in J. Brit. Interplanet. Soc. 24,475-495 (1971). 4. 5. 6. 7. 8. 9. 10. 11. 12.
* Publiihed by MIT Press, Cambridge, Massachusetts. t Published by Pergamon, New York.
82
CLIFFORD J. CREMERS
34. V. S. Avduevskii, N. A. Anfimov, M. Y. Marov, S. P. Shalaev, and S. P. Ekonomov, SOU.Phys.-Dokl., 16, 55 (1971). 35. bf. G . Langseth, Jr., S. P. Clark, Jr., J. Chute, Jr., and S. Kerhm, Rev. Abstr. Lunar Sci. Conj., 3rd Lunar Sci. Inst., Houston, Contrib. No. 88, p. 475 (1972). 36. M. G. Langseth, Jr., A. E. Wechsler, E. M. Drake, G. Simmons, S. P. Clark, Jr., and J. Chute, Jr., Science 168, 211 (1970). 37. C. J. Cremers and R. C. Birkebak, Proc. Lunar Sci. Conj., 8nd, Geochim. Cosmochim. Acla Suppl. 2, 3, 2311 (1971). 38. C. J. Cremers, AZAA J. 9, 2180 (1971). 39. C. J. Cremers, R. C. Birkebak, and J. E. White, Znt. J. Heat Mass Transjer 15, 1045 (1972). 40. C. J. Cremen, Moon 4, 88 (1972). 41. C. J. Cremen, Zcurus 18, 294 (1973). 42. C. J. Cremers, Proc. Lunar Sci. Conf., Srd, Geochim. Cosmochim. Acla Suppl. 3, 3,3611 (1973).* 43. R. Fryxell, D. Anderson, D. Carrier, W. Greenwood, and G. Heiken, Proc. Apollo 1 1 Lunar Sci. Conf., Geochim. Cosmochim. Acta Suppl. 1,3,2121 (1970). 44. W. D. Carrier, 111, S. W. Johnson, R. A. Werner, and R. Schmidt, Proc. Lunar Sci. Conf.. 2nd, Geochim. Cosmochim. Acla Suppl. 2, 3, 1959 (1971). 45. T. Gold, &I. J. Campbell, and B. T. O’Leary, Proc. Apdlo If Lunar Sci. Conf., Geochim. Cosmochim. Acla Suppl. 1, 3, 2149 (1970). 46. E. A. King, Jr., J. C. Butler, and M. F. Carman, Proc. Lunar Sci. Conf., 2nd, Geochim. Cosmochim. A& Suppl. 2, 1, (1971). 737 47. T. Gold, E. Bilson, and M. Yerbury, Rev. Abstr. Lunar Sci. Conf., Srd, Lunar Sci. Inst., Houston, Contrib. No. 88, p. 318 (1972). 48. I). F. Winter and J. M. Sasri, Astrophys. J . 156, 1135 (1969). 49. €3. S. Hemingway and R. A. Robie, Rev. Abstr. Lunar Sci. Conj., Srd, Lunar Sci. Inst., Houston, Contrib. No. 88, p. 369.(1972). 50. H. Kanamori, N. Fugii, and H. Mizutani, J. Geophys. R e . 73, 595 (1968). 51. H. Kananiori, H. Mizutani, and N. Fujii, J. Phys. Earth 17,43 (1969). 52. K. Horai, S. Baldridge, and G. Simmons, Proc. Lunar Sci. Conf., Houston, 1971. 53. H. Mizutani, N. Fujii, Y. Hamano, and M. Osako, Rev. Abstr. Lunar Sci. Conj., Srd, Lunar Sci. Inst., Houston, Contrib. NO. 88, p. 549 (1972). 54. J. C. Jaeger, Proc. Cambridge Phil. SOC.49, 355 (1953). 55. W. M, Sinton, in “Physics and Astronomy of the Moon” (Z.Kopal, ed.), p. 407. Academic Press, New York, 1962. 56. R. W, Muncey, Nature (London) 181, 1458 (1958). 57. J. Reichman, A I A A T h p h y s . Conj., Srd, Los Angeles AIAA Paper 68-746 (1968). 58. J. I).Halajian and J. Iteichman, Zcazus 10, 179 (1969). 59. J. Ulrichs and M. J. Campbell, Zcurus 11, 180 (1969). 60. Earl of Rose, PTOC.Roy. Soc., London 17, 436 (1869). 61. B. C. Murray and R. L. Wddey, Astrophys. J. 139, 734 (1964). 62. F. J. Low, Astrophys. J . 192, 806 (1965). 63. J. W. Lucas, J. E. Conel, and W. A. Hagemeyer, J. Geophys. Res. 72, 779 (1967). 64. G. Vitkus, J. W. L u w , and J. M. Saari, A I A A Thermophys. Conf.,Srd, Los Angeles, AIAA Paper 68-747 (1968). 65. G. Vitkus, R. R. Garipay, W. A. Hagemeyer, J. W. Lucas, and J. M. Saari, Lunar Surface Temperatures and Thermal Characteristics, Surveyor VI A Preliminary Report. N A S A Spec Publ. NASA SP-l66,97 (1968).
a,
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66. G.Vitkus, R. R. Garipay, W. A. Hagemeyer, J. W. Lucas, B. P. Jones, and J. M. Saari, Surveyor VII A Preliminary Report. NASA Spec. Publ. NASA SP-113,163 (1968). 67. L. D.Stimpson and J. W. Lucas, AIAA Themwphye. Conf., hth, San Francisco AIAA Paper 69-594 (1969). 68. F. S. Johnson, J. MetmoZ. 11, 431 (1959). 69. M.Baker, Opt. Spectra 6,32 (1972). 70. C. J. Cremers, R. C. Birkebak, and J. E. White, AIAA J. 9, 1899 (1971). 71. C. J. Cremers, R. C. Birkebak, and J. E. White, Moon 3,346 (1971). 72. J. M.Saari, Zmrua 3, 161 (1964). 73. H.C. Ingrao, A. T. Young, and J. L. Linsky, in “The Nature of the Lunar Surface” (W. N. Hess, D. H. Menzel, and J. A. O’Keefe, ed.), p. 185. John Hopkins hess, Baltimore, Maryland, 1966.
This Page Intentionally Left Blank
Boiling Nucleationt
ROBERT COLE Department of Chemical Engineering and Institute of Colloid and Surface Science Clarkson College of Technology. Potsdum. New York
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I. Introduction I1. Fundamental Equations of Surface Science A. The Laplace Equation B . The Kelvin Equation 111. Homogeneous Nucleation A. Stabilityof an Activated Cluster B . Rate of Appearance of Nuclei IV. Superheat Limits A . Simplified Classical Treatment B . Recent ExperimentalObservations C . Engineering Significance V. Heterogeneous Nucleation A. Nucleation from Plane Surfaces B . Nucleation from Spherical Projections and Cavities C. Vapor Trapping VI . Nucleation from a Preexisting Gas or Vapor Phase A. Experimental Evidence B . Behavior of Gas-Filled Cavities C . Behavior of Vapor-Filled Cavities VII . Size Range of Active Cavities A. Effect of Nonuniform Superheat B . Nucleation Criteria C . Analysis and Experiment D. Characterization of the Boiling Surface VIII . Stability of Nucleation Cavities A. Theoretical Treatment for Cylindrical Geometry . B . Experimental Findings
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86 87 88 89 92 93 94 95 95 99 107 111 111 113 116 117 118 120 122 127 127 128 129 133 134 134 146
t The basis of this work was completed while the author was on sabbatical leave with the Heat Transfer Group of the Eindhoven University of Technology. The Netherlands. 85
86
ROBERTCOLE
. . . . . . . . . . . . . . . .
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I S . Minimum Boiling Superheat A. Low Thermal Conductivity Liquids B. Liquid Metals Nomenclature References
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148 148 157 162 163
I. Introduction
One of the problems which has stimulated active engineering interest in the theory of riucleation from liquids is the prediction of the minimum boiling superheat. Consider the subcooled forced low boiling data of Fig. 1. The lines having a slope of unity are in the nonboiling region. When the wall temperature is increased sufficiently to cause boiling to begin, the curve turns sharply upwards. It is clear that the forced flow convective heat transfer equations grossly underestimate the heat flow density in the boiling region. In certain instances nucleation or boiling may be undesirable. The formation of vapor bubbles as a result of pressure reduction, is in fact identical to boiling. Damage resulting from cavitation can produce serious and sometimes even catastrophic results. Hydraulic machinery, valves, fittings, spillway crests, and conduit entrances and bends are all subject
BOILING NUCLEATION
87
to cavitation damage. Knapp et al. [2] present an outstanding discussion of the occurrence of cavitation and its effects upon flow properties and equipment performance. Under some conditions, explosive vapor formation can occur when molten metals are quenched. In the paper industry, sounds have been reported far below the surface of quench tank liquors which become deep, powerful rumbles or earthquake-like detonations. Such explosions have occasionally caused the unit or entire building to tremble. In rare instances tank tops have been blown off, welded side seams have split, and tanks have been displaced from foundations [3]. This review is concerned primarily with nucleation as applied to engineering heat transfer systems. Accordingly, in Section 11,the Laplace equation is developed using as a model, a wavy surface such as might exist in film flow. The Kelvin equation is derived from thermodynamic principles and from it the Laplace Kelvin equation is obtained; the latter equation being more often found in the engineering literature. A brief presentation of homogeneous nucleation appears in Section I11using the older but conceptually simpler kinetic theory approach. In Section IV, superheat limits as predicted by the homogeneous theory are developed and compared with experimental observations. Reference is made to recent evidence that homogeneous nucleation may be of great importance in some engineering situations. Heterogeneous nucleation is treated in Section V. The geometric conditions for vapor trapping, also presented in Section V lead to the conclusion in Section VI that nucleation in most boiling systems occurs from a preexisting gas or vapor phase. Sections VII-IX are concerned with the determination of nucleation criteria, the stability of nucleation cavities, and the prediction of minimum boiling superheat. 11. Fundamental Equations of Surface Science
Certain equations are fundamental to the science of surfaces and hence to a study of liquid-vapor interfaces. Two of these, the Laplace equation and the Kelvin equation will be developed here. The Laplace equation relates the pressures on opposing sides of a curved interface to its radii of curvature, and will be derived using a model surface typical of that found in wavy film-flow. The Kelvin equation relates the equilibrium vapor pressure of a liquid drop or vapor bubble to the external pressure and to the sphere radius. The equation will be derived under the condition that the “availability” of the system is stationary with respect to small variations of sphere radius; this approach being very similar to the kinetic method employed in nucleation theory.
ROBERTCOLE
88
A. THELAPLACEEQUATION The model consists of a wavy surface, one of whose radii of curvature is infinite. Thus the surface might be thought of as a wavy plane as shown in Fig. 2 ( a ) . An increment of the curve which results from a normal intersection of the x-y plane and the wavy film is illustrated in Fig. 2(b), together with the external forces acting on the surface. Under steady-state conditions, the equation of motion yields
C F = F,
18
+ F,
/,+A#
+ FpV+ F p L
=
0
(1)
where F, is the surface tension force, FpVis the force exerted by the vapor, and FpLis the force exerted by the liquid. Further,
F, =
ut(2)
Fp = P Asn(I)
and
(2)
Here t and n arc the unit tangent vector and the unit normal vector to the curve, respectively, and 1 represents a unit length along the surface, normal to the x-y plane. Substituting into Eq. ( 1 ) and forming the scalar product with i, the unit vector along the x axis i . CF = u cos y
I,+A~
- u cos y
la
+ (PL- Pv)As(sin y ) = 0
(3)
Dividing by As, taking the limit as As + 0, and using the definition of the derivative,
For constant
u,ignoring the trivial solution,
But dsldr
FIG. 2. Wavy gas-liquid interface (symbols with overhead arrows correspond to boldface symbols in the text).
BOILINGNUCLEATION
89
Fro. 3. Assumed equilibrium configuration for liquid-vapor single component system.
where R is the radius of curvature. Therefore, p L
-pv
=
g/R (7) For the more general surface where the second radius of curvature is not necessarily infinite, the equivalent expression is pL - p v =
+ R1’)
~(R1-l
(8)
Eq. (8) is known as the Laplace equation, When the surface is concave toward the vapor phase, the left side becomes Pv - PL.
B. THE KELVINEQUATION The system is illustrated in Fig. 3 and consists of a vapor phase (assumed spherical) at uniform temperature To and pressure Pv, immersed in a liquid phase at uniform temperature Toand pressure Po. The surroundings are also at uniform temperature Toand pressure PO. The equilibrium condition shall be considered to be that for which the “availability” remains stationary with respect to small variations of the bubble radius T . (aA/ar) =0 (9)
IT~.P~
The availability A is a measure of the maximum amount of useful work which can be extracted from a system during a given change in given surroundings, A U - ToS PoV (10)
+
Note that it is defined in terms of the constant temperature and pressure of the surroundings, whereas the Gibbs function G is defined in terms of the temperature and pressure of the system,
G
U - T S + PV
(11)
It is convenient to express the availability of the system as the sum of the contributions due to the liquid phase, the vapor phase, and the interface. Since the availability is defined in terms of the pressure of the surroundings, these terms are additive even though the pressure of the vapor differs from that of the liquid (by 2a/r according to the Laplace equation).
ROBERT COLE
90
Thc availabilky of the liquid is A L = moL(uL- TosL
+ Pov") = moLgL(To,Po)
(12) where u , s, L', and g are the intensive analogs of U , S, V , and G, and subscript zero means that the quantity is constant and evaluated at To and Po. As indicated in Eq. (12),the avaiIability and the Gibbs function are equivalent for the liquid phase because the temperature and pressure of t.he liquid are maintained the same as those of the surroundings. The availability of the interface is
The availability of the vapor may be expressed in terms of the availability at Toand Poby a Taylor series expansion about TO,PO,
+
A'(To, P') = A"(To, Po) ( a A v / a P ) I ~ o , ~ o ( p '- PO) 4(d2Av/aP2) I T ~ . P ~-( Pol2 P~
+
+ -..
(14) Using standard thermodynamic equaIities and assuming the vapor phase to behave ideally, A'(T0, Pv)= Av(To, Po)
For the condition
mv + 2Pov -
(PV -
Eq. (15) becomes
Av(To, Pv) = Av(To, Po)
m' (P' + 2PO'
- Po)2
Po and substihting from the Laplace equation for Pv - Po, m v 2a2 Av(To, P ' ) = A'(T0, Po) -POV Po+
+
Thus upon addition of Eqs. (12) , (13), and (18), the total availability is A = ( m - %')goL
= mgoL
+
20 + 4rr20 + moVgOV+ m-v -
$dpoV(goV
POV POT2
- SOL)
+ 4w*a
(19)
BOILING NUCLEATION
91
Note that the enclosed expression in the third term of Eq. (19) must be taken as unity as a result of the approximation expressed by Eq. (16), i.e,
I Hence,
+ Q(u/rPo)= 1 + + [ ( P v - Po)/Po] = 1 A = mgoL + -$K@piJv(gov - goL) f 4R?%
(20) (21)
From the equilibrium condition
(aA/ar) I T ~ , P ~
=
and therefore,
+
4 ~ r ~ p o ~-( goL) g 0 ~ 8wu = 0
(22)
goL - gov = 2u/poVr
At a flat interface ( r = 03 ) , the pressure in both phases is identical and equal to the equilibrium vapor pressure. Thus,
V
dgv = (R,To/M)
/
PO
dP/P
(26)
Pm
Therefore, gov =
gm
- (tl,To/M) In(Pm/Po)
(27)
goL =
gm
-
(28)
In like fashion, [(pm
- P0)/pL]
Substituting Eqs. (27) and (28) into Eq. (23) yields R~ToPo' P m lnM Po
poV
2u
PL
r
- - ( P m- Po) = -
or since
(R,T~pov)/M= Po = PL Eq. (29) may be expressed as
Equation (31) relates the equilibrium vapor pressure of a bubble to its radius. When the second term on the left is neglected, it is known as the Kelvin equation. In the boiling literature, Eq. (31) is generally found in somewhat differ-
ROBERT COLE
92
ent form. Expanding the logarithmic term,
(
, p-LP L ){1 pl. P____
-i(1 P, pL- P L
)+;(p-p~~~j...I
-PV ( P , - P L )
= 2a -;
r
PL
I “LPLI
5
1
(32)
In analogy to Eq. (16), for the condition (P, - PL)/PL
<< 1
(33)
Eq. (32) becomes [(PL
- PV)/PLl(Poa
- PL) = 2a/r
(34)
We shall call Eq. ( 3 4 ) the Laplace-Kelvin equation. Equation (34)also is obtainrd directly from this analysis by assuming the vapor phase to be incompressible; it is also obtained directly from a simple force balance on the height of liquid in a capillary tube immersed in a pool of liquid in equilibrium with its vapor (assuming the vapor phase to be incompressible). 111. Homogeneous Nucleation
The theory of homogeneous nucleation has developed from the early ideas of Becker and Doring [4], Volmer [5], and Frenkel [6], emphasizing the kinetic approach, to the more recent statistical mechanical concepts put forth by Reiss [7], Lothe and Pound [S], and Reiss, Katz, and Cohen [9]. I n addition to the books by Volmer [ 5 ] and Frenkel [S], nucleation symposia sponsored by thc American Chcmical Society in 1952 [lo] and in 1965 [ l l ] have contributed greatly to the state of the art. A thorough review of theory and experiment to 1963 is provided by Kirth and Pound [12]. Included is a section on ebullition and cavitation in liquids, i.e., boiling nucleation. A volume edited by Zettlemoycr [13] serves a need as an excellent source and reference treatise. The conceptuaIly simpIer kinetic approach will be employed for the discussion to follow. The niolecules of which the liquid is composed are considered to have a distribution of energies such that only a very small fraction have energies considrrably greater than the average. Such “activated” molecules, their excms energy being called the “energy of activation” are presumed to initiate the process by means of which a vapor bubble is brought into existence. Since the probability of a sufficient number of such highly activated niolccules being in the same region of space at about the same time is negligibly small, thc nucleation process is considered to occur by the step-
BOILINGNUCLEATION wise collision process
A,*
+ A1
~
93
A:+,
(35)
where A+* represents an activated cluster of z single molecules, A1 is a single unactivated molecule, and &+I is the activated cluster of z 1 single moIecuies resulting from the colhion of A,* and Ax. Processes other than the one indicated here, such as the collision of two activated clusters are considered improbable. As indicated, the process is assumed reversible so that it is never certain that a particular cluster will become sufficiently large (and hence contain sufficient energy) for it to spontaneously explode into a vapor bubble.
+
A. STABILITY OF AN ACTIVATED CLUSTER The thermodynamic procedure for determining the stability condition of a cluster of activated molecules is similar to that employed in developing the Kelvin equation in Section I1,B. The system is again that of Fig. 3 except that the vapor bubble of radius r is now a spherical cluster of activated molecules with radii of molecular dimensions. It is of course rather presumptuous to assume that fragments of this size have the thermodynamic features of macroscopic bubbles. At equilibrium, the availability of the system is to remain stationary with respect to small variations of the molecular cluster radius r. The total availability of the system is approximated by
+
A = nLgL n*g*
+ uiu
(36)
Expressing the number of activated molecules in the cluster as n* = +rr3p*
(37)
Eq. (36) becomes A =
(nT
- +dp*)gL
+ Qrl-lp*g* + 4rr2a
Referring the availability to the liquid at To,Po
A
- AO = AA
= +rr3p*(g*
- gL)
(A0
(38)
= nTgL),
+ 4rr2a
(39)
Thus at equilibrium,
[a(AA)/ar] I T ~ . P ~ and as before,
=
0 = 47rr2p*(g*- gL)
+ 8rru
(40)
gL - g* = 2u/p*re
re is here defined as the equilibrium cluster radius for given external temperature Toand pressure Po. Substituting Eq. (41) back into Eq. (39) gives the expression for the
ROBERTCOLE
94
availability of a cluster of any size
AA
= 4ur*a[1
- 3(r/re)]
(42)
A graph of this expression is shown in Fig. 4.It is apparent that the condition expressed by Eq. (40)has yielded a state of metastable rather than stable equilibrium; the loss of a molecule from the activated cluster of radius re causing it to collapse, while the addition of a molecule results in spontaneous growth. The cluster of radius re is hence called a vapor nucleus.
B. RATEOF APPEARANCE OF SUCLEI Having considered the condition of stability associated with a vapor nucleus, it is now of interest to determine the rate of formation of such nuclei; a rate of l/hr for example would hardly represent a boiling system in the usual sense. Assuming that activated clusters of all possible sizes exist and that the number of any one size depends upon the degree of difficulty of growth to that particular size in a step by step or bimofecular process such as represented by Eq. (35), the rate of formation of activated clusters containing x molecules is given by the expression J = mf expc- E,/kT]
CLUSTER R A D I U S , r
FIQ.4. Availability of an activated cluster of radius T..
(43)
95
BOILING NUCLEATION
where E, is the activation energy necessary to form the activated cluster of size x. The frequency factor f is estimated from the theory of absolute reaction rates to be f = (kT/h) exp[- E D / ~ T ] (44) where ED is the activation energy for diffusion of a molecule through the liquid. Combining Eqs. (43) and (44) and assuming E, to be equivalent to the availability of the activated cluster as expressed by Eq. (42), then for a vapor nucleus ( r = re),
J
);r
exp
nT
=
(- E D +kT )
+we%
(45)
IV. Superheat Limits A. SIMPLIFIED CLASSICAL TREATMENT Considering the vapor nucleus to represent the lower limit of applicability of the Laplace-Kelvin equation [Eq. (34)], the radius of the vapor nucleus is given by the expression
re =
2u
P,
PL
- PLpL - pv
With the help of the Clausius-Clapeyron equation, -dP = dT
-
hJ9
T(v'
- vL)
hf9PVPL
(47)
T(pL- p v )
which represents the equilibrium vapor pressure curve, one obtains by integration between the limits (PL,Teat)and ( P ,P , ) ,
P, - PL
hf9PVPL
TL
- pV
Taat
= -1npL
where the vapor has been considered incompressible. Substituting for P , - PLfrom Eq. (46) and expanding the logarithmic term, 2~ - pvhf,(TL - TSSt) _ -
re
Tsat
1
[l
-I(
TL - Tsat Tsat
)
>'- ***I
1 TL - Tsat +3( T,,,
ROBERT COLE
96
so that higher order terms may be neglected, yields the expression
One of the conditions associated with the development of the LaplaceKelvin equation is that the vapor is incompressible. Thus an alternate derivation of the superheat limit, which assumes the vapor to be compressible and ideal, should instead use the Kelvin equation P L In ( P J P L ) = 2u/r
(52)
which is obtained from Eq. (31) by the condition p v << pL. The same conditions used in obtaining Eq. ( 5 2 ) should be applied to the Clausius-Clapeyron equation. Namely, pv =
MP/R,T,
pv/pL
<< 1
(53)
thus,
Separating variables and integrating between the same limits as before,
Substituting from Eq. (52) and rearranging,
TL - Tsat
=
2uTm/pVhfgre
(56)
which is identical to Eq. ( 5 1 ) . The superheat limit, i.e., the maximum temperature in excess of the saturation temperature, to which the liquid can be subjected without nudeation occurring, is thus predicted to be inversely proportional to the radius of the vapor nucleus. It should not be overlooked that the equation is applicable only to a system of uniform temperature. 1 . Calculation of the Equilibrium Cluster Radius from Experiment
Indirect measurements of the size of the vapor nucleus have resulted from the experiments of Iienrick et al. [14] and Briggs [15]. Freshly drawn capillary U-tubes, open to the atmosphere were filled with distilled test liquid and the lower part immersed in a bath of liquid at known temperature for a period sufficient for the test liquid to attain the bath temperature ( 5 see in both references). If nucleation did not occur the bath temperature was raised and the process repeated. The equilibrium cluster radius re was calculated from the Laplace-Kelvin equation where P , was
BOILING NUCLEATION
97
TABLE I EQUILIBRIUM CLUSTER RADII FOR LIQUIDSSUPERHEATED CAPILLARY TUBESAT 1 atm Superheat Liquid Ethyl ethero Methanol. Ethanola Benzene” WaterChlorobenzenea Waterb EtherC Isopentanec Ethyl chloridec
-
Kenrick et al. [14].
b
Tkt (“K)
TL-T&$
308 339 351 352 373 405 373 373 373 308 302 286
108 114 123 128 170 118 164 166 167 108 107 113
Briggs [15].
(OK)
IN OPEN GLASS
Estimated equilibrium P,PL cluster radius (kN/m*) (nm)
1430 2580 2930 1390 5390 1000 4860 5060 5160 1460 1350 1930
4.5 4.7 2.5 9.2 7.3 16.7 8.2 7.9 4.7 4.5 -
Wismer [16].
determined as the equilibrium vapor pressure of the test liquid at the bath temperature a t which nucleation occurred. P L was taken as 1 atm. Although the accuracy of the data is somewhat questionable (it is not certain that nucleation could not have been due to cosmic radiation, or the presence of extremely minute dust particles or gas bubbles), they are considered to be of the correct order of magnitude. Some typical caIculated sizes are presented in Table I. Additional measurements result from so-called “cavitation” experiments such as those of Wismer [16]. The test liquid is drawn into a capillary U-tube which is then sealed at one end. The system is pressurized and immersed in a bath at the desired temperature. The pressure is suddenly reduced to atmospheric pressure and if cavitation (nucleation) does not occur within a specified period of time (approximately 5 sec) , the system is repressurized and the bath temperature raised. The equilibrium cluster radius is computed in the same fashion as before. Again there is considerable scatter in the data and the results reported represent the highest attainable superheats. 2. A n Approximate Expression for the Superheat Limit Equation (56) would be more useful for predicting the superheat limit if it did not contain the equilibrium cluster radius. A rather approximate
ROBERT COLE
98
expression for this quantity can be obtained from the rate equation by neglecting the activation energy for diffusion relative to the activation energy for forming the cluster, and assuming that a nucleation rate of 1 vapor nuclei per second per cubic centimeter of liquid could be considered reasonable. To determine the validity of the above approximations, numerical values for re are tabulated in Table I1 for water at a uniform temperature of 543’B. This corresponds to the temperature at which nucleation occurred in the experiments of references [14] and [15]. Other nucleation rates and a second value of E D (equal to E,) are shown for comparison. It is apparent from Table I1 that the equilibrium cluster radii are in order of magnitude agreement with those calculated from experimental measurements and that the assumed values of nucleation rate and activation energy for diffusion are not critical. Hence, takingJ = 1 and E D = 0 in Eq. (45),
Substituting for re into the LaplaceKelvin equation [Eq. (34)] and solving for the superheat vapor pressure difference,
P.-PL=-[
PL pL
- pv
3 k F ln(nTkTL/h)
t 58)
In similar fashion, Eq. (56) becomes (59)
Equation (59) yields fair agreement with experiment when nucleation TABLE I1
EQUILIBRIUM CLUSTER RADII FOR WATER AT
543’K
Equilibrium cluster radii (nm) Nucleation rate (sec-1 cma) 10-6 1 10‘
ED=O
En=E,
2.9 2.7 2.4
2.0 1.9 1.7
BOILINGNUCLEATION
99
TABLE I11 COMPARISON OF THEORETICAL AND EXPERIMENTAL SUPERHEATS FOR LIQUIDS IN OPEN GLASS CAPILLARY TUBESAT 1 atm SUPERHEATED Incipient boiling temp. (OK)
T4
TL
TL
Liquid
(OK)
W/m)
(kg/mP)
(kJ/kg)
Expt1.a
Water Methanol Ethanol Ethyl ether Benzene Chlorobenzene
373 339 351 308 352 405
23.4 8.8 7.9 5.2 7.4 7.5
25.4 20.0 24.5 34.0 35.5 41.7
1635 800 620 248 286 240
543 453 474 416 480 523
a
Vapor density at
Latent heat at !P
Surface tension at
Theoret. Eq. (59) 539 435 444 400 476 534
Kenrick et al. (141.
occurs within the bulk of the liquid. A t atmospheric pressure, Eq. (59) predicts an incipient boiling temperature of 539°K for water with physical properties evaluated at the system temperature. Kenrick et al. [14] found an experimental incipient boiling temperature for water of 543°K. Further comparisons are shown in Table 111.
B. RECENTEXPERIMENTAL OBSERVATIONS In recent years the superheat limit has been investigated extensively, using techniques which involve the use of superheated liquid drops. Trefethen [17] was perhaps one of the first to suggest that such drops might be useful for studying the process of nucleation. In the experimental technique, single drops of either water or carbon disulfide rested on a mercury surface (made concave upward) in contact with mineral oil or water, respectively. The drops were superheated either by reducing the system pressure or by raising the system temperature. The choice of liquids, however, limited the superheats attainable since the maximum superheat could not be greater than the difference in boiling temperature of the two most volatile liquids. The choice of liquids was in turn restricted by: (1) the requirement that all three liquids be immiscible; (2) the one to be superheated must be the most volatile; (3) the one to be superheated must have a density between the density of the other two; and
100
ROBERT COLE
FIG.5. Exploding drop nppnratus of Wakeshima and Takata 118).
(4) the interfacial energies must be such that the drops do not spread over the interface. The maximum superheats attained with the system were 30°K for water and 5OoK for carbon dkulfide. The limitations were due to the system however and not as a result of nucleation. The superheated drops could be exploded for the most part only by mechanical means such as touching the drop with the point of a needle. Even then complete vaporization did not occur and in one instance ten jabs were required to reduce the drop sin?to where it could no longer be easily observed. Wakeshima and Takata [18] devised a technique which overcame many of the limitations encountered by Trefethen. A diagram of the apparatus is shown in Fig. 5 . The vertical container was filled with host liquid ful-
BOILING NUCLEATION
101
filling the requirements of being immiscible with the sample drop, and having both a higher density and a sufficiently higher boiling point. For droplets of saturated hydrocarbons and polymethylenes, the host liquid was sulfuric acid. For ethyl ether, the host liquid was either glycerin or ethylene glycol. The host liquid was heated at the upper end and a stable vertical temperature gradient maintained by mipimizing outward radial heat transport and controlling the temperature of the host liquid at the base of the container. The liquid drops were introduced through a small hole in the bottom of the container from a guide tube which contained a layer of the sample liquid in contact with the host liquid. The drops ranged from 20 to 200 pm in diameter and passed into the heated tube at a rate of approximately 2/min. The drop rises slowly upward through the host liquid (thermal equilibrium being assumed) until the superheat limit is reached, at which time the drop explodes. Thus, knowledge of the position at which the explosion occurs, and the temperature gradient in the liquid, allows a determination to be made of the maximum drop temperature at the moment of vaporization and the presumed superheat limit, i.e., the difference between the drop temperature and its saturation temperature at the system pressure. The experimental results are shown in Table IV and compared with the superheat limit calculated from a rate expression derived by Volmer [ 5 ] : 112
6u =
nT(m(3
A,
- 13'))
-
+ $nr,% kT
TABLE IV COMPARISON
OF
THEORETICAL AND EXPERIMENTAL SUPERHEAT LIMITS" Superheat limit
Material
(OK)
Tkat ( O K )
Explosion temp. (OK)
Expt1.a
Theoret. [Eq. (So)]
309.1 341.7 371.4 300.8 322.3 344.8 354.1 307.6
419 455 484 411 453 473 489 420
109.9 113.3 112.6 110.2 130.7 128.2 134.9 112.4
110.4 111.6 114.4 109.3 128.7 125.2 138.2 109.4
n-Pentane n-Hexane n-Heptane Isopentane Cyclopentane Methylcy clopentane Cyclohexane Ethyl ether Wakeshima and Takata [IS].
ROBERTCOLE
102
where b‘ = ( P , - P L ) / P ,
and X, is the heat of vaporization per molecule. Equations [ S O ] and ( 4 5 ) differ only in the expressions used for the frequency factor. The theoretical superheat limits shown in Table IV were obtained from Eq. (60) by setting J = 1, substituting for re from the Laplace equation (assuming Pv = P,), and basing the total number of molecules on a drop size of 1-mm diam. The agreement is quite good and seems to justify the hypothesis of homogeneous nucleation. Moore [19], while conducting exploratory investigations into the feasibility of using direct contact heat transfer from a hot liquid for spray drying of materials in solution, found that the liquid droplets had to be greatly superheated in order to initiate vaporization. Accordingly, the investigation was modified to a fundamental study of drop vaporization. Basically the superheat limit was determined by spraying drops of Freon 12 into a pressure cell containing degassed, distilled water. At constant temperature, the system pressure was slowly lowered until drops of a predetermined size were simultaneously vaporized. The system pressures so detrrniined are tabulated in Table V along with theoretical values. The latter are calculated as the pressure at which a drop of 0.2-mm diam. should vaporize within 5 sec. Also included are the number of molecules and radius of the critical bubble. The rate expression developed by Moore for predicting the vaporization pressure is
J =
n ~ [ 6 a ( 3- b ’ ) / r n z ~exp( ] ~ ~-~4urC2a/3kT) 3 - b’[l - (a In 2/13 In P ) 1pk]
(62)
TABLE V COMPARISON OF THEORETICAL A N D EXPERIMENTAL VAPORIZATION 12 IN WATER‘ PRESSURES-FREON Vaporization pressure (kN/mz) Temp. (OK) 342.3 344.2 354.2 368.8 379.7 4
Moore [19].
Expt1.a 193 407 1489 2923 3909
Critical Theoret. bubble radius jEq. (62)j re (nm) 22 1 434 1489 2909 3902
4.52 4.67 5.64 8.58 18.2
Number of molecules 206 237 53 1 3000 47,200
BOILING NUCLEATION
103
1. sec
lo** 10’
\
10’
10’
I.#
10.126 ‘
Q
t
134
142
I
FIG.6. Dependence of the mean life of droplets of superheated n-pentane on temperature (Skripov and Sinitsyn [20]).
For z k equal to unity and a In z/d In P equal to zero, Eq. (62) reduces to the Doring-Volmer equation [Eq. (60) J, except for the absence of the term involving the latent heat of vaporization. The rising bubble technique was employed by Skripov and Sinitsyn [20 J to investigate the lifetime of superheated liquid droplets at atmospheric pressure under both normal conditions and under the action of y radiation. Droplets of n-pentane of diameter 0.1-0.5 mm were allowed to rise through a bath of sulfuric acid in which a vertical temperature gradient was maintained. The gradient was approximately O.l”K/mm in the neighborhood of the viewing window. In order to obtain data on droplet lifetime at a given superheat, the drops were brought to rest by impinging on a glass rod which could be positioned vertically in the sulfuric acid. A “snout” on the end of the rod could be rotated either into the path of the rising droplet (for capture of the drop) or to one side, out of the way. Observation indicated that the droplets exploded at the same temperature whether they were held on the “snout” or whether they were freely rising; the droplet possibly being separated from the “snout” by a thin film of acid. The results of the investigation are shown in Fig. 6. Curve 1represents the experimental data under natural conditions and illustrates the very sharp temperature limitation on superheat. The Doring-Volmer equation [Eq. (SO)] predicts a maximum drop temperature of 420°K for a drop of 0.28-mm diam. and a time period of 1 see. Curve 2 represents the experimental data
ROBERTCOLE
104
TABLE VI LIMITING SUPERHEAT
OF
n-PENTbNE, n-HEXANE
AND
Explosion temp.
Material
n-Pentaneb
n-Hexanec
n-Heptaned
Pressure
Saturation
(kN/rn2)
temp. (OK)
Expta
98 490 98 1 1618 2550 98 422 1079 1716 2393 98 490 98 1 1.569 2000
308.7 3G2.7 395.7 422.7 451.2 341.9 396.7 443.2 471.7 492.2 371.2 435.7 474.2 502.7 517.7
417.2 421.7 427.7 438.2 451.2 457.2 461.7 471.7 481.7 496.7 487.2 493.7 502.7 512.7 519.7
Sinitsyn and Skripov [21]. ~ P =c 2736 (kN/m*).
* PC = 3373.5 (kN/m*).
n-HEPTANE“
( O K )
Theory [Eq. (6011 416.7 421.7 428.2 437.7 453.2 -
488.2 494.2 502.7 513.7 523.2
Exptl. superheat
(OK) 108.5 59.0 32.0 15.8 0.0 115.0 65.0 28.5 10.0
4.5 115.0 58.0 28.5 10.0 2.0
PC = 3030.2 (kN/m*)
under the action of y radiation from a “‘Co source. The data are obtained from experiments with 60-160 drops a t each temperature because of the statistical nature of the drop lifetime. These experiments have more recently been extended to higher pressures by the same authors [21]. Skripov and Ermakov [22] extended the experiments of Wakeshima and Takata [lS] to higher pressures. The drops were n-pentane, n-hexane, and n-heptane rising through a sulfuric acid host liquid, pressurized by means of pure inert gas. A portion of the data obtained is presented in Table VI. Theoretical explosion temperatures were calculated from the Doring-Volmer equation [Eq. (SO)] with J = 1; surface tension data was not available for n-hexane at high pressures. The agreement is clearly quite good over the entire pressure range. Kagan [23] has proposed as a criteria for the applicability of the Doring-Volmer equation [Eq. (SO)], the following inequality 2u/reP, << 3 (63) The criteria is increasingly satisfied by the experimental data as the pressure increases. For n-heptane, the value varies from 0.92 a t 98 kN/m2 to 0.03 at 2000 kN/m2.
BOILING NUCLEATION
105
Blander et al. [24] employed the exploding bubble technique to check previous results obtained with one-component systems (n-pentane, nhexane, and water) and to provide new data on a two-component system (n-pentane n-hexadecane) . Data obtained with the single component system were found to be somewhat higher than previous measurements (at least for n-pentane), and are compared with calculations from the steady-state Zeldovich-Kagan theory [23] in Table VII. The expression developed by Kagan is
+
(’>
n PVC J =-2 1 + 6 ~ kT
112
exp( -
%)
4~0r,2
(64)
where P (the condensation coefficient) was taken as unity and
Vt
(8kT/~m)’’~ (65) The parameter is related to the heat flow during bubble growth and involves the latent heat of vaporization and liquid thermal conductivity. For the calculations in Table VII, 6 A was small relative to unity and could be ignored. It is noted that the nucleation rate was taken as lo4 and lo6 ~ m sec-l - ~ rather than unity. These values were estimated as being more realist~icand do result in a slightly higher calculated explosion temperature. Results for the binary system n-pentane, n-hexadecane are presented in Fig. 7. The vaporizat.ion temperature is seen to increase linearly with concentration over the range investigated, presumably as a result of diffusion control. The distinct “nucleation sounds” associated with explosive nucleation (described by Skripov and Sinitsyn [20] as “cracking”) are melodiously described for the binary system as having a high-pitched ((ping” for the pure n-pentane which sinks to a lower pitched ((pang" for =
TABLE VII LIMITING SUPERHEAT OF n-PENTANE
AND
n-HEx.4NEa ~~
Explosion temperature ( O K ) Theoretical, Eq. (64) Material
Exptl.
n-Pentane n-Hexane
421 f 0 . 3 457 f 0 . 5
Blander et al. [24].
J = IO‘cm-asec-’
420.9 (420.4)b 456.8 (456.3)
* Parentheses include compressibility correction.
J = l06cm-Jsec-1
421.5 (421.1) 457.5 (457)
ROBERTCOLE
106
2 0 - \ ~ t 7hexadecane ~ and bottoms out with a lower pitched (‘glub” at 46wtY0 hexadecane. Experiments carried out using pure water drops in a host liquid of Dow Corning No. 710 silicone oil, in general nucleated at temperatures below the maximum nucleation temperature of 571°K. Similar results were obtained by Apfel [25]. Both authors conclude that failure to reach the maximum superheat limit may be a result of heterogeneous nucleation at the liquid-liquid interface. Further experiments by Apfel [26] using a different host liquid (benzyl benzoate) have yielded explosion temperatures to 552.7”K. Skripov and Sinitsyn [20] utilized a mechanical probe to intercept and immobilize rising droplets. Apfel [27, 28) has devised an acoustical technique for achieving the same effect. A schematic of the essential apparatus is shown in Fig. 8. The droplet is superheated as it rises through the host liquid (glycerin). As it reaches the test region an acoustic standing wave field is established, and the resulting acoustic pressure opposes the upward acting buoyant force so that a t a given position the drop is immobilized. If the drop does not explode, the acoustic pressure is increased and a new equilibrium position is achieved. The procedure is continued until some combination of acoustic pressure and superheat results in droplet explosion. The experimental results, using ether and n-hexane droplets, are in good agreement with the classical predictions. Experiments using pulsed heating methods to achieve the superheat limit, and in particular to study the effect of nucleation frequency ( J ) have been reported by Skripov and Pavlov [29] for atmospheric pressure and by Pavlov and Skripov [30] for pressures to the critical value. A platinum wire, immersed in the test liquid was pulse heated a t a rate of
‘4%
to
20
40
30
W T % HEXADECANE
+
FIG.7. Bubble nucleation temperature of n-pentane n-hexadecane mixtures versus weight percent hexadecane (Blander el al. [24], reprinted by permission of the American Chemical Society).
BOILING NUCLEATION
107
NUCLEATION CELL
ACOUSTIC
G - 2
I P
HEATINQ COIL
DROPLET INTRODUCED C A T BOTTOM
FIQ.8. Schematic of essential apparatus (Apfel [28]).
about lo6OK/sec using a single pulse ranging from a low of 20 to a high of 850 psec duration. Under such conditions the liquid in the immediate neighborhood of the wire is strongly heated (by 1O0-20O0K) and the nucleation is explosive in nature. By analysis, the nucleation frequency is related to the number of spontaneous bubbles per unit area (obtained from photomicrographs), the wire temperature (obtained by means of resistance thermometry) , and time. Using this technique nucleation f r e quencies to 101g.5cm-3sec-1 were obtained as compared to frequencies not greater than 106 cm-J sec-1 in previous studies using the exploding drop method. Results from [29] are tabulated in Table VIII. The theoretical values are calculated from the Doring-Volmer equation [Eq. ( S O ) ] using the experimental value of J . It is interesting to note that the nucleation temperature obtained for water is the highest recorded to date, although still 10.5"Kbelow the predicted value.
C. ENGINEERING SIGNIFICANCE Physical explosions resulting from the rapid formation of vapor have for many years represented an unsolved problem of extremely hazardous and destructive consequences. Such explosions have been reported in the paper industry in connection with smelt dissolving tank operations [31, 321, in the metals industry in connection with accidental spillage of molten materials into water [33-351, in the nuclear industry in connection with interactions between water (acting as both coolant and moderator) and
TABLE W I T
MAXIMUM VAPORIZATION TEMPERATURES USING
P U LS E HEATING ' h C H N I Q U E "
Pulse duration (psec) 100
35
Temp. Liquid
(
Temp.
(OK)
log J sec-1)
Expt.
Theory
( cm-a sec-1)
Expt.
19.5 19 .o 18.5 18.5 15.5 18.0 18.5 18.0 18.0 18.0 18.5 18.5
425.7 708.7 462.7 510.2 575.2 466.2 472.2 495.7 518.2 426.2 463.2 493.7
42.5.2
17.5 17 .O 17.0 17.0 17.0 17 .O 16.5 16.5 16.0 16.5 16.5
850
Temp.
(OK)
(OK)
Theory
log J (cm-a sec-I)
Expt.
Theory
423.2 703.2 460.7 505.2
423.7
13.5
420.7
421.7
507.2
13.5 13.5
458.7 505.2
464.7 470.2 493.7 516.2 425.7 459.7 493.2
469.2 473.7
14.0 14.5 13.O 13.O 12.5 12.5 13.O
463.2 465.2 492.2 513.2 423.2 458.7 491.2
log J
!Jj 0
m
Diethy1 ether Iliphenyl ether Acetone Benzene Water Methyl alcohol Ethyl alcohol Propyl alcohol Butyl alcohol n-Pentane n-Hexane n-Heptane Skripov and Pavlov [29].
M
508.7 585.7 470.2 474.7
426.2 461.7 495.2
425.2 460.2 494.2
2 c)
505.2 467.7 465.2
423.2 458.2 492.2
Fm
BOILINGNUCLEATION
109
molten fuel element cladding [36-381, and in the transportation industry in connection with spills of liquid natural gas (LNG) onto water [39]. Explanations of the explosive mechanism require a rate of energy release which can result only if the steam generation is a result of homogeneous nucleation, i.e., vapor release must occur in a matter of microseconds. In considering molten metal-water explosions, Brauer et al. [40] postulated an encapsulation mechanism in which the molten metal drops, upon contact with the quench liquid and rapid initial cooling, form a thin crust entrapping not only the hot molten metal but also some of the quench liquid. The situation is somewhat similar to that of the drop technique for determining the superheat limit. Since there are no natural nucleation sites at the liquid-liquid interface between the molten metal and the entrapped quench liquid, the quench liquid is rapidly heated to the superheat limit. Explosive vaporization occurs in a matter of microseconds, shattering the crust and dispersing small droplets of molten metal throughout the quench bath. Magnified many times, the resulting increase in surface area can account for the rapid generation of vapor required to produce an explosion. A major problem with the encapsulation theory is in accounting for the presence of quench liquid within the crusted drcp of molten metal. Flory et al. [41] have postulated an entrapment mechanism resulting from Helmholtz instability. Katz and Sliepcevich [42] and Katz [43] have proposed a mechanism for explaining the somewhat milder explosions resulting from LNG spills onto water. Their “limit of superheat” theory is explained in terms of the boiling curve reproduced in Fig. 9. When LNG (which consists mostly of methane plus small percentages of higher boiling hydrocarbons) is placed in contact with water at ambient temperature, the temperature difference is such that film boiling results (point A). Continued transfer of heat to the LNG results in vaporization of the more volatile methane and a resulting decrease in the temperature difference toward point B. At this point stable film boiling begins to break down and with a solid-liquid system, vaporization would increasingly occur at nucleation sites on the surface. With the liquid-liquid system however, nucleation does not occur (provided that the LNG wets the surface) and the high rate of heat transfer instead causes rapid superheating until the superheat limit is reached. Explosive vaporization then occurs in a matter of microseconds. In the KatzSliepcevich theory, the superheating is limited to a thin layer of the LNG. A similar mechanism was postulated by Nakanishi and Reid [39] which requires that the surface consist of, or be coated with a material which is chemically similar to the LNG (or other cryogen), and which also has a low freezing point. The chemical similarity of the contacting surfaces insures wettability which is essential to the breakdown of the vapor film,
ROBERT COLE
110 ONVECTION~ AND ONDUCTION,
MODE OF MEAT TRANSFER
~
NUCLEATE BOILING
UNSTABLE
I
VIOLENT BOILING
!
REGION
FILM BOILING
-c
N
L
I
L
L
\ 3
...
m X
3 _1 LL
+ 4
IECREASING, AT
W
1,
I 0
E:
I
1
LIOUID. LIQUID SYSTEMS/
LOG TEMPERATURE DIFFERENCE Mechanisms of Bubble Formation at Interface CONDUCTION AND CoNVECTloN
BOILING BUBBLES FORM
LIQUID
F I L M BOILING
SOLID
FIG.9. Boiling heat transfer mechanisms (Katz [43]).
while a low freezing point seems to be ncccssary to prevent freezing and the consequent introduction of a solid surface into the system which might allow nucleation and prevent superheating. For a water spill, such a coating might be a result of a prior evaporation step leaving a rich C2, Ca, Cd, etc., layer near the surface. Kclson [44] has recently applied the IiatzSliepcevich theory of LNGwater explosions to explain the molten smelt-water and metal-water explosions as an alternative to the encapsulation mechanism [40]. The succession of events is here presented. ( 1 ) The molten globule contacts the quench liquid and is immediately envcloped in a steam blanket due to rapid film boiling. ( 2 ) As the smelt sinks and cools, the Leidenfrost point is reached and the film becomes unstable and breaks down. Due to the absence of nucleation sites at the liquid-liquid interface, vaporization is not possible and
BOILING NUCLEATION
111
direct contact heat transfer to the surrounding water causes a rapid superheating of a thin liquid layer to its superheat limit. (3) Explosive vaporization of the thin liquid layer occurs, the resulting weak shock waves acting as a blasting cap. (4) The shock waves shatter the still hot molten globule, greatly increasing the area of molten material exposed to the quench bath and impelling the small molten particles through the quench at velocity which removes the steam film which would otherwise form. (5) In milliseconds a powerful blast wave develops due to the explosive transformation of a significant part of the sensible heat of the entire mass of molten material into pressure-volume work as a result of the rapidly expanding steam. The small particles may themselves fragment to further propagate the explosive violence, 1700 volumes of steam being created for each volume of water vaporized at 373'K.
V. Heterogeneous Nucleation The liquid superheats predicted by homogeneous nucleation theory are at least an order of magnitude greater than those occurring in many engineering systems. Since in such systems, nucleation is observed to occur on the bounding surfaces rather than in the bulk of the liquid, it seems reasonable to suppose that the surface serves as a catalyst and so reduces the .~ energy requirements for nucleation. The treatment which follows is due to Volmer [S], Fisher [45], Turnbull [46], and Bankoff [47]. A. NUCLEATION FROM PLANESURFACES
A vapor embryo a t a solid-liquid interface is shown in Fig. 10. Assuming the embryo to be a portion of a sphere, the volume and surface areas are given by v = (?rrs/3) (2 - 3m m) (66)
+
where
m = d / r = -cosB
(69)
! FIQ.10. Vapor embryo at a plane interface.
I
LIOUID
ROBERTCOLE
112
The availability of the system, relative to that without the embryo is given by
AA
= (mLgL
+ mVgv + aLvuLv+ asYusv) - (mTgL + asLusL)
(70) Since the surface area covered by vapor was originally covered by liquid prior to the formation of the embryo, &3v =
$L
(71)
and since by a force balance, @V
- $L
= ULV
cos g,
= -m,+V
(72)
Eq. (70) becomes upon some rearrangement,
+4~r*~~~]f~(,g) = $(2 - 3m + m3)= -( :2 + 3 cos 8 - c0s38)
AA where fl(8)
=
[(4rr"/3)pv(gv - gL)
(73) (74)
Since Eq. (73) is of the same form as Eq. (39) ,by analogy,
and
For 0 = 0, the liquid completely wets the surface, fl(0) = 1, and the liquid superheat is the same as for the homogeneous case. A value of 0 = 180" yields fl(8) = 0 and presumably then, no superheat is possible. However, according to Bankoff [47], such a contact angle has never been recorded; the largest found experimentally being approximately 140". Paraffin, which is commonly considered not to be wetted by water exhibits a contact angle of about 95" if smooth. For e = go", fl(0) = 6 and the superheat is reduced by approximately 3001,. This reduction however, is still insufficient to account for the low values observed in practice. Apfel [25] has derived an expression for the activation energy for nucleation at the interface between two immiscible liquids. The lcnticularshaped vapor embryo is shown in Fig. 11. Because of the existence of two different liquid-vapor surface tensions, Eq. (75) is here written as
and
BOILINGNUCLEATION
113
0,
LIQUID A
VAPOR
LIQUID 6
FIG.11. Vapor embryo at a liquid-liquid interface (Apfel [25]).
3 8
- -uAB(QA'
3 + + ~ 2-)16 Q*4
us4
CAB
(78)
where Z may be considered an effective surface tension. For comparison, the effective surface tension for the solid-liquid interface is
-
=
QLv(;
=
QLvfi(e)
- ,,SV)/,,LV]
+ i[(@L
3 113 - @V I/ QLVI)
(79)
B. NUCLEATION FROM SPHERICAL PROJECTIONS AND CAVITIES Vapor embryos are shown in Figs. 12 and 13 on a spherical projection and in a spherical cavity. For the spherical projection, the volume and surface areas are given by
v = (?n.3/3)[(1
- cosp)2(2
+
- (r8/r)3(1 - cosa)2(2 + COS 4 1
COS~)
(80) ULV
=
2*r2(1 - cos p )
asv = 2i?r,2(1
- cos a)
(81) (82)
The availability of the system, relative to that without the embryo is given by M = m V ( g V - gL) ~ L V ~ L V C F ~ L ~cos e (83)
+
+
and assuming that the critical nucleus radius is not affected by the presence of the surface, gL
so that
- gv = 2u/repV
(84)
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114
FIG.12 (left). Vapor embryo 0x1 a spherical projection. FIG.13 ( t i g h t ) . Vapor embryo in a spherical cavity.
where f2jrs/'Te, e) = 4 [ ( ~ ~ / 1 - ~ )~ (cos 1 C - (1
+ cos a)
Y ) ~ ( ~
- cosj3)2(2 + cosp)]
+ +[(rs/Te)'(l
- COSCY) COSB
+ (1 -
(86)
COS~)]
For the spherical cavity, the expression differs from Eq. (86) only in that the sign of the first term on the right-hand side is negative. Values of fz and f3 are shown in Tables IX and X, respectively. For the spherical projection, the f values are again not sufficiently low (except for contact angles >goo) to account for the low superheats obtained in practice. It is interesting to note that for e = 180" (the nonwetting case), fz can either approach zero or unity depending upon the ratio ?-,/re.As T,/T, + 1, fs -+ 0 as might be expected, however as TJr, -+ 0 the spherical surface, around which the nucleus is forming, vanishes and fz -+ 1 since this is again the homogeneous case. TABLE IX VALUESOF
*/2
f2 AS
DETERMINED BY EQ. (86)
0 (Surface disappears)
T/2
U
1
1
s/4
3a/4 n-/2
0.8 1/2
m
(Plane surface)
0
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115
TABLE X
VALUESOF f3
0 (Surface and vapor phase disappear) Vd3
*/2
1 rn
(Plane surface)
r
0
*
1
s/2
0
0
*/3 */4
0
*/6 */4 */2
0.12 0.21 1/2
0
0
0
With the spherical cavity, f3 --+ 1 for the perfectly wetted surface and zero for the nonwetted surface. However, for any value of B between (but excluding) 0 and 180”, f3 will vary from 0 to 3 as r, varies from 0 to 0 0 . Here, as r,/re approaches zero, both the surface and the vapor nucleus must vanish (since the nucleus lies within the surface cavity) ; therefore f3 approaches zero, whereas for the spherical projection it approached unity. Similar results are found for conical cavities [48], where f4
+ 3 (&/re)*sin p cos 01 - +[(1 - C O S C U+) ~coscy) ( ~ + (d’/rJ3sinpcosfl]
= $[ (1 - cos a)
(87)
for the geometry shown in Fig. 14. Superficially, it now appears that the work of forming a vapor nucleus within a surface cavity may be made vanishingly small by simply reducing the size of the cavity toward zero. This can certainly not be correct; the error probably being in the assumption that ratios of cavity radius to critical radius less than unity have any physical meaning. It may be concluded however that nucleation should occur preferentially from surface cavities as opposed to nucleation from within the bulk, from plane surfaces, or from surface projections, and that systems exhibiting poor wetting characteristics should promote nucleation much more easily than well-wetted systems, other factors being similar. Thus poorly wetted surface cavities seem to hold the greatest promise as nucleation sites in most systems.
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I
FIG.14. Vapor embryo in a conical cavity.
C. VAPORTRAPPING The spreading of a liquid over a surface containing grooves and cavities has been considered by Bankoff [49]. For simplicity, only the two-dimensional probltm of a semiinfinite sheet of liquid advancing unidirectiorlally is considered. Figure 15 illustrates the conditions for entrapment of gas in the advance of a semiinfinite liquid sheet across a groove. It is apparent that if the contact angle 0 is greater than the wedge angle r - 24, the advancing liquid front will strike the opposite wall of the cavity before it has completed its advance down the near wall. Hence the condition for
FIG.15 ( l e f t ) . Advance of liquid sheet over a gas-filled groove (Bankoff [491). FIG. 16 (right). Advance of gas-liquid interface over a liquid-filled groove (Bankoff 1491).
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TABLE XI LIMITINQ CAVITYCONDITIONS Case 1 2
3 4
Type of cavity Steep Steep Shallow Shallow
Condition Poorly wetted Well wetted Poorly wetted Well wetted
Trapping ability Traps gas only Traps liquid only Traps gas and liquid Traps neither
entrapment of gas (by the mechanism considered) is
oT--24
(88)
Figure 16 illustrates the condition for displacement of liquid from a groove by an advancing gas-liquid interface. It is apparent that if the contact angle B is less than 24, the gas-liquid interface will contact the opposite side of the cavity before it has completed its advance down the near wall. Thus the condition for failure to displace the liquid is
e < 24
(89)
For convenience, the cavities are divided into 4 classes: (1) those that obey the first inequality but not the second; such cavities will entrap gas only; (2) those that obey the second inequality, but not the first; these cavities will entrap only liquid; (3) those cavities that obey both inequalities; these will entrap both gas and liquid; and (4) those that obey neither inequality; such cavities will entrap neither gas nor liquid.
Thus the limiting conditions shown in Table X I are obtained. Comparison of these results with the conclusions derived from Sect. V,B indicate that those cavities showing the greatest promise of nucleation according to classical nucleation theory (i.e., poorly wetted cavities) , are just those cavities which have the greatest tendency to entrap gases and vapors. Thus it is highly probable that most cases of nucleation on nonwetted surfaces occur from a preexisting gas phase rather than by tearing of the liquid from a portion of the surface.
VI. Nucleation from a Preexisting Gas or Vapor Phase Most real surfaces contain natural or machine-formed pits, scratches, gouges, grooves, etc., of size ranging from the macroscopic to the micro-
118
ROBERT COLE
scopic. If the surface is poorly wetted by the liquid it may be expected that many of the cavities will contain entrapped gas and hence act as bubble initiators. The extent to which this remains true over a period of time depends upon the rate of diffusion of entrapped gas from the cavity into the liquid. Thus the initial bubble population density may also be affected by the initial dissolved gas concentration in the liquid and the time of exposure. It might also be pointed out that a liquid saturated with dissolved gas (say, at room temperature) could activate additional cavities upon being heated to its boiling point as a result of the decrease in solubility with increasing temperature. A. EXPERIMENTAL EVIDENCE An effective procedure for deactivating surface cavities was developed by Harvey et al. [50-53) and by Knapp [54] which seems to confirm that entrapped (undissolved) gases do indeed act as nuclei for vapor bubble formation. The technique involves subjecting the test system (liquid and surface) to high static pressures and then determining the effective tensile strength at atmospheric pressure. One procedure for determining the latter [51, 52) was to simply measure the boiling point at atmospheric pressure; the assumption being that the saturation pressure corresponding to the observed boiling point measured the internal tension of the liquid, and that the difference between this value and atmospheric pressure was the effective tensile strength. The results are quite conclusive; all unpressurized samples experienced nucleation within a few degrees of their normal saturation temperature, while the pressurized samples all boiled at much higher temperatures. In some instances, superheats slightly in excess of 100°K were obtained. Since the effect of increased pressure is to increase the solubility of gases in the liquid (and to force the liquid further into the pores), it is reasonable to conclude that the undissolved gases which had been entrapped in minute surface cavities were absorbed by the liquid, effectively eliminating most of the cavities as nucleation sites. A second procedure [53] involved the use of high speed photography to detect cavitation at the rear end of a blunt glass rod (5-mm diam.) moving rapidly through a narrow (16-mm diam.) glass tube of water. The system was initially prepressurized to 110 MN/m2 for a period of 30-90 min in order to dissolve entrapped gases. If the rod surface contained gas nuclei (i.e., it was not included in the prepressurization treatment) , cavitation occurred at the rear end when the velocity was less than 3 m/sec. When the rod surface was prepressurized, velocities to 37 m/sec were obtained with no indication of cavitation. The static procedure employed by Knapp [54] was similar to that of
BOILING NUCLEATION
119
Harvey. The system was prepressurized to a level in the neighborhood of 100 MN/m2 and boiling point determinations made, with the duration of prepressurization as a parameter. In general, the results completely confirmed those of Harvey. Unpressurized samples always produced bubbles within a degree or two of the normal saturation temperature. The pressurized samples produced superheats ranging from a low of 27°K to a high of 127°K. It is perhaps of interest to note that the liquid was heated by means of resistance wires coiled around the 15-cm long, 1.9-cm diam. glass test tubes, and that the boiling temperature was determined from calibrations based upon the rate of heating. Dynamic cavitation experiments were also conducted by Knapp [54], using precision glass venturi tubes to obtain pressure reduction. The tests were transient in nature, the water being forced through the venturi by sudden application of air pressure. High speed photography was employed to determine the inception of cavitation (which occurred in the throat of the venturi) and the throat pressure calculated from a knowledge of the flow velocity in the upstream section and the fluid pressures in the upstream and downstream reservoirs. In general, the results were similar to the static tests; without prepressurization, cavitation occurred at throat pressures close to the vapor pressure, whereas with prepressurization, definite tensions were found to exist. Additional evidence that entrapped gases act as nuclei for the formation of vapor bubbles has .been obtained by direct measurement and observation of nucleation from prepared surfaces. The first detailed investigation of this type was reported by Cody and Faust [55]. Saturated pool boiling data was obtained on surfaces which had been copper or nickel plated, then roughened by rubbing with emery paper of known grit size. The data indicated a definite effect of roughness on initial superheat and that the rougher surfaces required lower superheats to initiate boiling. Presumably, a greater size range of cavities exists on the coarser surfaces so that it is more likely that cavities of the appropriate size and shape are available for nucleation at the lower superheats. It follows that the effect of polishing is to narrow the size range of available cavities, thus most likely making higher superheats necessary for initiation of boiling. Electron micrographs, photomicrographs, and profilometer roughness measurements were all employed in order to better determine the actual condition of the boiling surface. Clark, Strenge, and Westwater [56] obtained high speed motion pictures of boiling from polished surfaces through a microscope. Twenty nucleation sites were observed: 13 were identified as pits in the surfaces, 3 were scratches, 3 occurred at the boundary between the metal heater and a plastic cement, and 1 was on a shifting speck of unidentified material which appeared briefly on one of the surfaces. The active pits ranged in
120
ROBERTCOLE
size from approximately 10 to 100 pm and were nearly circular, while the active scratches were approximately 10 pm wide.
B. BEHAVIOR OF GAS-FILLED CAVITIES The experimental evidence that nucleation results from undissolved gases, entrapped in surface imperfections of appropriate geometry is quite convincing. If prepressurization techniques are employed and the amount of entrapped gas in any given cavity is reduced to a volume having radius less than the equilibrium cluster value, very high superheats will then be required to activate it. If the system had not been prepressurixed, this same cavity, noxv containing entrapped gas with radius greater than or equal to the equilibrium cluster value, would nucleate spontaneously when the system temperature just exceeds the liquid saturation temperature. In general, once a cavity begins to emit vapor bubbles, a portion of the entrapped gas is carried off with each bubble until eventually the cavity is filled only with vapor; the degree of difficulty (and hence the time for accomplishing this) depending to a great extent on the geometry of the cavity; a reservoir-type cavity, as illustrated in Fig. 17, being extremely stable. Such a cavity represents an outstanding source of extremely low superheat vapor bubbles, remaining available over extended periods of time through many thermal cycles of the heat transfer surface. Most cavities are probably of such a geometry however that over some finite period of time (hours or days) the noncondensible component will have been
GAS
FIG.17. Reservoir-type surface cavity.
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121
completely carried away and replaced by vapor. Prior to this time however, the pressure-radius relation may be expressed as
Pv
+ PG - PL = 2u/r
(90)
where Pv and Po represent the partial pressures of the vapor and gas, respectively, and T is the radius of the nucleus-liquid interface. Assuming that Pv = P,, and substituting for P , - PLfrom the Clausius-Clapeyron equation, the superheat is given by:
Hence it should be expected that nucleation from such a cavity will begin at a negligibly small superheat, which will then increase to some stable value as the noncondensible is swept out by dilution. Bankoff [57] indicates that this has, in fact, been observed. Ward et al. [58] have presented an analysis on the thermodynamics of homogeneous nucleation in weak gas-liquid solutions which has provoked some controversy on the effect of dissolved gases. Previous experimental studies such as those of Harvey et al. [50-531 and Knapp [54] had indicated that the high tensile strength associated with water was observed regardless of the presence or nonpresence of dissolved gases. The thermodynamic analysis of Ward, however, yields for the equilibrium cluster radius (assuming ideal behavior of the gas and vapor) : re =
V'P,
+
2a PL(cL/c,)
(92)
-PL
where Yl=
exp
["
L P L
(
- P , ) - kTcL kT
1
(93)
cL is the gas concentration in the liquid phase and cmis the concentration in a saturated liquid across a flat interface. Equation (92) predicts a smaller equilibrium cluster radius in a liquid-gas solution than in a pure liquid. The apparent discrepency is (according to Ward, in the discussion to Ward et al. [58]) a result of the use of the single fluid, water, in the above experiments. The same type of calculations which predict that dissolved gas content can affect the nucleation pressure of low surface tension liquids, such as ethyl ether, reveal only a negligible effect for high surface tension liquids such as water at ordinary temperatures, even if they are supersaturated with gas. It seems apparent that additional experimental studies are warranted.
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122
C. BEHAVIOR OF VAPOR-FILLEDCAVITIES We shall now consider only cavities which have either been swept free of entrapped gases as a result of bubble departure, or have been activated as a result of a growing vapor bubble passing over it and displacing the liquid phase. To further simplify the situation, we shall consider the cavities to be conical and that initially, the vapor has a radius equal to or greater than the equilibrium cluster value. Following the analysis of Griffith and Wallis [59], Fig. 18(a) illustrates the vapor-liquid interface in a conical cavity at various stages of time from the initial condition through the time it emerges from the cavity. Figure 18(b) illustrates the variation of the curvature l / r of the interface as a function of vapor volume. For simplicity, the contact angle has been taken as n / 2 rad. It is noted that as the nudeus grows, its volume and radius of curvature both increase, until the mouth of the cavity is reached. The radius of curvature then decreases with increasing volume as the nucleus emerges from the cavity, assuming the shape of a hemisphere. Further growth again yields an increase in the radius of curvature with volume. For the contact angle of r/2 rad, the maximum in the curvature-volume graph occurs at the cavity mouth radius. Since the curvature is directly related to the superheat requirements of the vapor in the cavity, it is the cavity mouth radius which determines the superheat required for the nucleus to %ap” the cavity. Thus modifying Eq. (56) :
TL - T,,t
= 2uTsat/pVhfprm
(94)
where rm is the cavity mouth radius. To distinguish this quantity from the superheat limit associated with homogeneous nucleation, it shall be referred to as the “emergent superheat.”
* VOLUME, V
(a)
(b)
Fro. 18. Curvature of a liquid-vapor interface emerging from a conical cavity.
BOILING NUCLEATION
123
FIQ. 19. Determination of condition for disappearance of maximum curvature.
Curvature-volume lines are also shown in Fig. 18(b) for the identically shaped cavity, but with contact angles of r/12, r/6, u/3, 7?r/12, 2r/3, and 5r/6. It is apparent that there is an effect of contact angle on the maximum curvature, and that a maximum does not exist for all curvatures. The horizontal dashed line in Fig. 18(b) represents the curvature corresponding to the cavity mouth radius. Over a significant range of contact angles, the maximum curvature does not differ too greatly from this value. Hence Eq. (94) may be considered to be approximately valid over the range [ ( r / 4 ) + (p/2)1 < 8 < 7r/12 rad (95) where the upper limit is somewhat arbitrary and the lower limit is obtained as illustrated in Fig. 19. r1 and rz represent the radii of curvature of the interface having contact angle 9 just before and after the interface emerges from the cavity having included angle 2p. The maximum in the curvature will just vanish when r1 = r2. Also at this condition a = e. From the geometry it is found that e = r/2 - e and CY = e - p, therefore:
+
e = (*/4) @/2)
+
(96)
For contact angles less than (r/4) (p/2) (a/4 for cylindrical cavities), no maximum exists in the curvature-volume plots and use of Eq. (94) would overestimate the superheat if such well-wetted cavities remained active. The shape of the curve however indicates the nucleus to be quite unstable and if the superheat is not sufficiently high to allow the vapor to emerge from the cavity, it will condense; causing deactivation. Static contact angles of r / 3 radians have been measured by Griffith and Wallis [59] for water on engineering surfaces. Most cavities which would be expected to contain an entrapped gas phase and thus be initially active would be fairly steep walled; 0 = r/12 rad, for example. For this size cavity, the
124
ROBERTCOLE
minimum contact angle for Eq. (94) to be applicable is 71r/24. Thus the lower limit given by Eq. (96) is probably not too important for this common system, but is of concern where the wettability has been artificially increased by the use of wetting agents or the surfaces are exceptionally clean. Kote that the use of wetting agents might cause cavities, which would normally contain entrapped gases, to fill with liquid and thus be initially inactive. For contact angles greater than 7?r/12 Tad, it is noted that the maximum in the curvature-volume plots decreases and again Eq. (94), which substitutes the cavity mouth radius for the radius of curvature of the interface, will overestimate the emergent superheat. Of equal interest is the behavior of the minimum in the curvature. In the same fashion as the maximum determines the emergent superheat, the minimum determines the extent to which the liquid may be cooled without deactivating the cavity ( k . , by condensation). If the cavity is rounded at the bottom, all of the curves will contain a minimum and approach plus infinity as the vapor volume approaches zero. Thus the liquid may actually be considerably subcooled without causing the cavity to deactivate, provided that the system is highly nonwetting. If the cavity was actually pointed, depending upon the included angle and contact angle, a situation mould be reached where the minimum disappears and the curve approaches minus infinity as the volume approaches zero. Here the cavity could only be deactivated by applying extremely high pressures or low temperatures such that the radius of curvature is reduced below the equilibrium cluster value. From geometrical considerations, the minimum curvature disappears at e = (r/2) /3 rad. Thus, as for the rounded cavity, the effect is observed only under highly nonwetting conditions. Reservoir-type cavities may behave somewhat differently due to the fact that the vapor must first emerge from the reservoir into the cavity neck and, further, that the neck may decrease in size as the surface is approached. Figure 20(a) and (b) for the reservoir cavity is equivalent to Fig. 18(a) and (b) for the conical cavity. The resulting curvature-volume curves are not too different from those in Fig. 18(b). Considering the line for r/2 rad, it is seen that two minimum-maximum combinations exist; one as the vapor enters the neck from the reservoir, and one when the vapor emerges from the neck. The second maximum is equivalent to that considered previously and determines the emergent superheat. The figure indicates that again, Eq. (94) will yield reasonable results over a relatively wide range of contact angles. For the geometry shown, this range is be3 2s/3 rad, where both the upper and lower limits are sometween ~ / and what arbitrary. The minimum curvatures represent conditions of stability. It is noted that the nucleus may achieve a condition of stability within the
+
BOILING NUCLEATION
125
FIG.20. Curvature of a liquid-vapor interface emerging from a reservoir cavity.
neck, within the reservoir, or both, depending upon the specific cavity shape and the contact angle. It is of interest that the minimum curvature coincides with negative values of the superheat even for small contact angles. Thus reservoir-type cavities should be extremely stable, requiring in most instances, a substantial degree of subcooling to cause deactivation. Experimental investigations of the nucleation characteristics of single cavities in uniformly superheated liquids have been conducted by Griffith and Wallis [59] and by Kasturirangan [ S O ] . The latter will be described as they are essentially identical to the pioneering experiments of Griffith and Wallis [59] except for some improvements in the measuring technique. The boiling tank was a large test tube, thoroughly cleaned with chromic acid solution before use and filled with double-distilled water. (As also observed by Griffith and Wallis [59], if the test liquid was deaerated the cavity could not be activated; presumably due to rapid diffusion of air from the cavity into the deaerated water.) The temperature was measured at three axial positions in the test tube by means of calibrated copperconstantan thermocouples contained in an oil-filled glass tube extending down through a stopper in the top of the test tube and into the water. The thermocouples were referenced to the ice point and connected to a multipoint millivolt recorder so that a time record of the system temperature was available for each run, to facilitate interpretation of the data. Also through the stopper (as illustrated in Fig. 21), the test tube was connected,
ROBERTCOLE
126
in turn, to a condensation tank and three U-tubc water manometers in series. A vacuum was drawn on the system by means of a water aspirator and regulated by means of a bleed valve. In order to heat the water in the test tube as uniformly as possible, it was placed in a large, heated oil bath. The test surface was a thin sheet of copper (20 X 20 mm) containing a single artificial nucleation site. Both conical and cylindrical sites were employed, having cavity mouth radii varying from 15 to 150 pm. Griffith and Wallis [59] conducted their experiments using conical and reservoir-type cavities having mouth radii of approximately 25 pm. Hence between the two sets of experiments, a significant number of cavity geometries and cavity mouth radii were studied. The operating procedure was t o place a clean sample of the test material in the water in a steeply inclined position, as shown in Fig. 21, so that the nucleation site and lower thermocouple were at the same horizontal level. The system temperature was raised to the desired value by means of the surrounding oil bath and a vacuum imposed on the entire system causing it to beconir uniformly superheated and simultaneously causing nucleation to occur from the site on the test surface (and anywhere else that a site may exist!). In these tests (as with those of Griffith and Wallis [59]) , the initial superheat (i.e,, the superheat at which thc cavity would first nucleate) was not determined. This was because the cavities would not nucleate unless they contained a preexisting gas phase, and as has been previously discussed, the emergent superheat under such conditions is not the same To Mercury Manometer
To Wote! Manometer
Pressure Reservoir Damper
nof to scale
Silicone Oil Both Bunren Burner
(A) n
Fro. 21. Experimental system for determination of emergent superheat (Griffith and Wallis [59]).
BOILING NUCLEATION
127
1C
I 80
90
100
110
PRESSURE ( k N / r n 2 )
FIG.22. Compnrison of uniform superheat data with Eq. (94)(Kasturirangan 1601).
as would occur if a vapor phase had been present originally. Instead, the cavity was allowed to emit a steady stream of vapor for a period of onehalf hour, at the end of which time it was presumed that the gas had been replaced by vapor. The system temperature was then slowly decreased (at a rate of perhaps 1°K every 5 min). When the bubble frequency had become sufficiently low that it \vm countable, this information was placed directly on the temperature time record. The superheat corresponding to the deactivation of the cavity was then compared with the superheat predicted by Eq. (94). Figure 22 reproduced from Kasturirangan [SO] is typical of the results obtained from both references. Two lines are shown because photomicrographs of the cavity, taken before and after the tests, indicated some apparent corrosion at the cavity mouth. The upper line uses the original T,,, while the lower line uses the apparently increased vaIue. A s concluded by Griffith and Wallis [59), the results show that the bubble nucleation theory leading to Eq. (94) is substantially correct and that a single dimension is sufficient for characterization of a nucleation site; a t Ieast within the contact angle limitations specified.
VII. Size Range of Active Cavities A. EFFECT OF NONUNIFORM SUPERHEAT In all of the previous sections, the system has been assumed to be one of uniform temperature, thus the temperature of the liquid equals the temperature of the wall equals the temperature of the vapor. In practice however, the situation is usually that of heat transfer from a heated surface
128
ROBERTCOLE
to a cooler surrounding fluid. While nucleation and growth occur within the cavity, simultaneous heat exchange exists between the cavity wall, the liquid existing in the cavity, and the expanding nucleus. When the nucleus emerges from the cavity it penetrates into the thermal boundary layer adjacent to the wall and is exposed to a varying temperature over most of its surface. Under conditions of uniform superheat, the criteria for boiling nucleation are that a surface cavity contain entrapped gas or vapor having radius of curvature greater than or equal to the equilibrium cluster value, and that the superheat be sufficient for the nucleus to emerge from the cavity. When the suprrheat varies spatially, the nucleation criteria are not as clear. The criteria specified for uniform temperature are no doubt still necessary, but it is not at all certain that they are sufficient. Since thermal equilibrium no longer exists, the equations describing the shape and motion of the liquid-vapor interface are the coupled momentum and energy equations. The task of predicting the “incipient boiling superheat” thus requires both a hypothesis for the nucleation mechanism and sufficient simplification of the physical problem to allow a mathematical solution.
B. SFCLEATION CRITERIA An engineering surface is characterized not by a single nucleation site, nor by multiple sites of the same size, but rather by a distribution of sites of various sizes and geometries. Experimental observations have indicated that for a given wall superheat, there exists a size range of active cavities. Further, with increasing superheat, the range of active cavities is extended in both directions, i.e., to both larger and smaller cavities. Equation (94) predicts only that smaller cavities should become active. Further, experiments conducted by Griffith and Wallis [59], using artificial conical cavities of approximately 70-pm diam., under conditions of nonuniform superheat, commenced nucleating at a wall superheat of 1l0K rather than the value of 1.6 predicted by Eq. (94). The latter result is of course not unexpected, however it does raise some questions as to the proper interpretation of the superheat term, under conditions where the system temperature is spatially nonuniform. Hsu [Sl] has attempted to provide a theoretical basis for the experimental observations mentioned above, using the nucleation hypothesis developed by Hsu and Graham [SZ]. The nucleus for bubble growth is assumed to sit at the mouth of the cavity and to have been formed by the residual vapor from the preceding bubble. The hypothesis presumes that the cavity meets the geometric requirements for the entrapment of gas or vapor and that the bulk liquid is not sufficiently cold that the nucleus
BOILINGNUCLEATION
129
condenses into the cavity. At time zero, just following the departure of the previous bubble, the nucleus is surrounded by relatively cool liquid a t temperature T,. As time goes on, the liquid is warmed by heat transfer from the surface and the nucleus begins to grow when the liquid temperature exceeds the vapor temperature over the entire liquid-vapor interface. This series of events is depicted in Fig. 23. The “limiting thermal layer thickness” is defined in a fashion similar to the fictitious but useful “laminar sublayer,” i.e., within the limiting thermal layer the transport is a result of molecular action only. Exterior to the thermal layer, turbulent motion is presumed sufficiently strong that the liquid temperature is maintained constant at T,.
C. ANALYSISAND EXPERIMENT The liquid temperature profile is assumed to be determined by the transient one-dimensional conduction equation with appropriate initial and boundary conditions. Thus,
-a e_L eyz, 01 where e L =
aw
I(-=
at ax2 eye, t ) = 0 ,
= 0,
0
(97) eL(6,
t) =
ew
TL - T,. The solution in dimensionless form is n-1
where
.p = eL/ew,
=
x/&,
= Kt/&’
(99)
The vapor temperature (which is as usual assumed uniform) is found from Eq. (94), in terms of 0, 6=
L
t
+ (2aTmt/~~hf,rn)
lirnitin thermal layer tPlickness .I
FIG.23. Model for nucleation hypothesis (Hsu [Sl]).
(100)
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130
where r, is the radius of the nucleus. Several important assumptions have been made in writing Eq. (100) which should be pointed out: (1) I t is assumed that Eq. (94) is a necessary but not sufficient condition for the nucleus to grow, when there are spatial variations in the system temperature. (2) It is assumed that the correct temperature to be used in Eq. (94) xhen the liquid temperature varies from T, to T,, is not T,, but TV. Thus (as pointed out by Hsu [61], the 1.6'K superheat predicted by Eq. (94) for the Griffith and Wallis nonuniform superheat experiments [59] was the vapor superheat TV - T,,,,whereas the measured superheat of 11°K was the wall superheat T , - T,,,.
In order t o apply the growth criterion, it is necessary to specify the relationship between the nucleus radius and the distance 2. For simplicity it is assumed that b = 2 r, = 1.6 rn (101) Thus upon substitution, the dimensionless vapor temperature is = hat
f (A'CdMw) ( 1 - Vb1-I
(102)
where
A' = (2~T,~t)/(p"h/,,) Ca = 1.6 (103) The criterion for growth is that tL = p at q = Vb. Agraphical solution is shown in Fig. 24, where EL is plotted as a function of q from Eq. (98) with
DIMENSIONLESS
DISTANCE.
7
FIQ.24. Temperature profiles for constant surface temperature (Hsu [Sl]).
BOILINQ NIJCLEATION
131
as a parameter. A typical vapor temperature curve as given by Eq. (102) is also shown. It should be noted that different "criterion" curves can be obtained, depending upon the values tsstand (A'C3)/(6ew)specified. The first point that is apparent from Fig. 24 is that for a given dimensionless waiting period, there may be two values of 7lb and hence rc which satisfy the growth criterion. Second, it is apparent that those cavities which require an infinite waiting period (i.e., to the left of &,,in and to the right of are the inactive ones. Hence the size range of active cavities will be determined by the curve for r = co . Under this condition, Eq. (98) reduces to 5"- = tl (104) Combining this with Eq. (102) to obtain the limiting values of 9b* =
[sat
+ ( A ' w e w ) (1 -
tlb*)-'
Vb,
(105)
solving for vb* and then for rc*, To*
= (6/4) { (1
-L
t )
f [(l - FBst)* - (6.4 A'/6ew)]1/2)
(106)
where r,,,sx corresponds to the positive sign and rC,,,,into the negative sign. The condition that rc,min < rc < rc,max is a necessary but not sufficient condition for a cavity to be active. In the event that two favorable cavities are located quite close to each other, the one with the shorter waiting period will always be preferred. Comparison of Eq. (106) with experiment is shown in Figs. 25 and 26. The data of Fig. 25 is that of Clark et al. [56] for n-pentane, and included the wall superheat Ow, the heat flow density q', and the cavity size, but not the incipient boiling superheat, From Fig. 2 of their paper however this was clearly less than 3°F. Accordingly, Eq. (106) is shown for values of Ow0 equal to 1.0, 1.5, and 2.O"F. Most of the sites are found to fall inside the range bounded by the theoretical curve for Bwo = 1.5"F.Similar results are obtained with ether. The data point of Fig. 26 is that of Griffith and Wallis [59] mentioned in Sect. VI1,B. The dashed and solid lines represent Eqs. (94) and (106), respectively. Using the value of 6 rn 76.2 pm, Eq. (106) will pass through the experimental point. The cavities used by Griffith and Wallis [59] were all of the same size. If a size range of active cavities had been available on the surface for nucleation, the solid curve shows that the incipient boiling superheat would have been 5°F instead of the observed value of 20°F (-11°K). The close relationship between 6 and the diameter of the cavity mouth is not unexpected (76.2 and 70 pm, respectively). Defining a thermal layer thickness as
ROBERT COLE
132
PIT 2
0
10
20 30 40 50 60 TEMP DIFFERENCE, e, (OF)
FIG.25. Sizes of effective cavities for boiling of n-pentane (data of Clark et al. [56]), (Hsu [Sl]).
x. = K[(ew- e 8 a t ) / ~ t ~
(107)
Zuber [63] (and also in the discussion to Hsu [Sl]) has shown, using the data of Clark et al. [56], a close agreement between X , and 2rc which is attributed to the cavity diameter being a characteristic of the surface and hence determining the local superheat. Han and Griffith [64] modified the procedure of Hsu by simplifying
FIG.26. Activation of cavities for cavity radius of 35 prn ( 1350 pin.) and limiting thermal layer of 76 pm (3000 pin.). (Data of Griffith and Wallis [59]), (Hsu [61].)
BOILING NUCLEATION
133
the transient thermal analysis (using the 00 boundary condition for the position at which TL = T,) and changing the condition at which nucleation would occur from 2 r, to 1.5 r,. The resulting expression for the size range of active cavities differsfrom [Sl] by a constant and by a difference in definition of the thermal layer thickness.
D. CHARACTERIZATION OF THE BOILING SURFACE With the knowledge that calculations such as those by Zuber [63] indicated the cavity size to be a characteristic of the boiling surface, and having conducted experiments which confirmed that a single dimension was sufficient for characterizing a nucleation site, Griffith and Wallis [59] concluded that a knowledge of the size distribution of active cavities would be sufficient to fix the nucleation characteristics of a surface. More specifically, a plot of the number of active spots per unit area versus the theoretical radius as given by Eq. (94) should remain invariant for a given surface at differing pressures and using different fluids. The results for four different copper surfaces, each of which was finished in the same fashion (3/0 emery paper) are shown in Fig. 27. Water was boiled on two of the surfaces and produced quite similar curves. The surface used for methanol and that
r*- in x 10'
FIG.27 (left). Number of active spots per unit area versus wall superheat: X, methanol on 3/0 finished copper; ethanol on 3/0 finished copper; water on 3/0 finished copper; 0 , water on 3/0 finished copper (Griffith and Wallis [59]). FIQ.28 (right). Same data as Fig. 27 plotted versus radius as calculated from Eq. (94) (GrifIith and Wallis [591).
+,
,n
134
ROBERTCOLE
RADIUS
FIG.29. Distribution of active cavities, according to their radii (Rohsenow [65]).
used for ethanol produced curves which were substantially different from the water surfaces, however. The same data are plotted in Fig. 28 against dimensionless radius as given by Eq. (94). The resulting single curve is a type of cumulative distribution funct,ion which might be obtained by integration from r = rn to r = r of the cavity distribution function shown in Fig. 29. Here n, is the number of cavities having radii in the range r to r f Ar [65].
VIII. Stability of Nucleation Cavities A. THEORETICAL TREATMENT FOR CYLINDRICAL GEOMETRY Bankoff [57} has employed a model for boiling nucleation which assumes that following bubble departure, cold liquid from the bulk penetrates into the heated cavity. If the liquid is sufficiently cool, condensation will cause the liquid-vapor interface to recede. The site is presumed to remain active if the penetrating liquid is heated sufficiently to slow and reverse the motion of the interface. Bankoff’s analysis [57] proceeds as follows: the capillary is assumed to be cylindrical as shown in Fig. 30, and sufficiently deep that it will entrap vapor. The radius of the capillary is R, and the distance traveled by the meniscus at time t is x. The basic assumption of the analysis is that the residual vapor which remains following bubble departure, exists within the cavity, at the pressure of the departed bubble. Since the bubble departs at essentially the liquid pressure, the residual vapor within the cavity must immediately begin to collapse by condensing into the penetrating liquid. Initially then, the meniscus is assumed to be just within the mouth of the cavity, to have zero velocity, and a temperature equal to the saturation temperature corresponding to the pressure of the liquid. As the liquid advances into the capillary (the bulk is assumed to be at its saturation tem-
BOILINGNUCLEATION
135
perature), it receives heat both from the condensation of vapor at the meniscus and by conduction of heat from the capillary walls (the latter is knowingly neglected by Bankoff). The temperature of the liquid at the meniscus (assumed to be at all times in thermal equilibrium with the remaining vapor) increases, and as it approaches the static saturation temperature of the entrapped vapor, causes the collapse velocity of the interface t o decrease rapidly. When the meniscus temperature equals the static saturation temperature of the vapor, condensation stops, the nucleus begins to grow again (here it would seem that conduction from the wall would have to be included in order for the interface to stop within a finite distance) and the capillary remains active. A schematic of the cycle is shown in Fig. 31. Application of the macroscopic mass balance to the liquid in the capillary yields )
where V I is the velocity of the bulk liquid entering the capillary and ax/& is the meniscus velocity. Under most conditions the two velocities are essentially equal.
L
FIG.30. Cylindrical cavity.
ROBERTCOLE
136
:[p/FfT fyfq:m -
5
3
T‘= lT .: lo)
TJ.1
Tm=T’
T”
’*
I
T= .
I b)
fT’ lc)
T,
=f =,.T: ld)
(e)
FIG.31. Iliagram of assumed nucleation cycle for Bankoff model (571: (a) t = 0;(b)
f,
> 0 ; ( c ) t2 > t , ; ( d ) t* > t z ; ( e ) f1 > P.
Employing a quasi-steady-statc approach, application of the macroscopic momentum balance to the liquid in the capillary yields
where inertial effects have been neglected (ie., time rate of change of
total momentum of liquid within the capillary and influx of momentum by virtue of bulk liquid entering thc cavity), gravitational effccts have been neglected, the flow has been assumed laminar, and constant physical properties assumed. P,” and PoLare the vapor and liquid pressures at the meniscus and top of the cavity, respectively. The temperature distribution in the liquid, resulting from a moving plane source of strength,
is
where X is defined in Fig. 30. Equation (111) takes convective transport into account, but incorporates the thin thermal boundary layer assumption, i.e., that the thermal ivave does not penetrate far into the liquid phase. At the interface, X = 0 and Eq. (111) becomes
wherc
T,L
is the temperature of the meniscus. Equation (109) may also
BOILINGNUCLEATION
137
be expressed in terms of the meniscus superheat by means of the ClausiusClapeyron equation
P z v - PoL = hfUPV -(T,L - Th t )
(113)
where it has been assumed that Pv = P,. Eliminating Pzv- PoLbetween Eqs. (109) and (113) and rearranging
By combining Eqs. (112) and (114), a nonlinear integrodifferential equation is obtained for x as a function of t. Rather than attempt to solve this equation, Bankoff instead approximates Eq. (112) by the expression
Before proceeding it is convenient to express Eqs. (114) and (115) in dimensionless form,
where AT, is given by:
Equations (115) and (114) become, respectively, f = Dgr-'/2
where
D= B=
b P V
pLCpLAT, 4w
Rcu cos 6
Equations (120) and (121) can be combined to eliminate f and yield a
ROBERT COLE
138
nonlinear first order differentiai equation dS
Bv ds
+ D ~ T - ~-" 1 = 0,
~ ( 0= )0
(124)
A particular solution which satisfies the differential equation and the initial condition is v =c p (125) where C = [ ( D ' + 2B)"' - D ) / B (126)
This solution is however unsatisfactory in that it does not predict a reversal in the motion of the meniscus and hence contradicts the original hypothesis. Marto and Rohsenow [SS] have modified the Bankoff analysis [57] by assuming that initial condensation is due to the cooling effect associated with microlayer evaporation rather than penetration of cold liquid from the bulk. Following bubble departure, the residual vapor that exists within the cavity is assumed to be at the static saturation temperature and the liquid at the meniscus a t all times in thermal equilibrium with this constant temperature vapor (except at t = 0 ) . The cooled liquid is assumed to have initial temperature To, which is slightly greater than the liquid saturation temperature but less than the static vapor saturation temperature. It is presumed that as a result, condensation begins to occur and the interface recedes into the cavity. (According to the Bankoff model [57], condensation should stop at this condition; compare Figs. 31 and 32.) Heat is received by the liquid from condensation at the interface and conduction from the cavity walls (which initially are presumed to have cooled to a minimum temperature To as a result of microlayer evaporation). As the liquid temperature increases, the interface motion slows and at some point
(C:
(b)
(C)
(d)
(el
FIG. 32. Diagram of assumed nucleation cycle for Marta-Rohsenow model (661: (a) t = 0;(b) ti > 0; (c) t 2 > t, (d) t* > g; (e) t3 > t*.
BOILING NUCLEATION
139
if the bulk liquid temperature equals the saturation temperature, condensation stops, the nucleus begins to grow again, and the cavity remains active. The nucleation cycle is depicted in Fig. 32. Application of the macroscopic momentum balance to the liquid in the cavity yields P,V - POL = (2u cos B)/R, (127) where in addition to neglecting inertial effects and assuming constant physical properties as in reference [57], viscous effects have also been neglected. Note however that these assumptions are all consistent with the physical model; inclusion of the viscous force for example would make the meniscus temperature a function of its velocity and hence time, whereas it has been assumed constant in the model. Application of the ClausiusClapeyron equation then yields
Tk, 2ucos8
(7)
TmL- TLt = PVbP
The temperature distribution in the liquid is obtained by solution of the energy equation. In order to maintain the problem one-dimensional and yet include conduction from the wall, this effect is assumed to be felt directly in the liquid as a time dependent heat source. The assumption is questionable for normal low thermal conductivity liquids, but may be reasonable for liquid metals. In any event, the wall heat flow density must be included if the meniscus velocity is to exhibit a minimum. Thus the energy equation, with initial and boundary conditions is
P ( 0 , t ) = TmL=
TL(a,1 ) = T,(t)
T:,
=
const
(133) (134)
where T, is the waII temperature, amis the surface area of the meniscus, and V is the capillary volume occupied by the liquid. Equation (134)presumes that far from the interface, the liquid temperature within the cavity
ROBERT COLE
140
o,+Aq
-
__ _ _ _ _ _ _
!i
8 ZL
w6a Z Z W
= $E d+z kj:
5;
-_____
I TMAX
ww
Yg
1L
=t 2i 2s 8Y -I
L , N
1
I
equals the variable cavity wall temperature. Thus, as h -+ and Eq. (134) is applied,
Q(l)/
(pLCpL) =
)TIME
00
in Eq. (129),
dTw(t)/dt
(135)
The solution of Eqs. (129)-(135) (for the interface temperature) is
where
The transient response of the wall during the period of interface travel is obtained by considering a semi-infinite body initially at uniform tempera-
BOILING NUCLEATION
141
ture, subjected to a step change in heat flow density for a finite time period. As illustrated in Fig. 33, the time period of the step change corresponds to . period of interface travel begins at bubble the bubble growth period T ~The departure when the wall temperature is a minimum. The solution is
Equation (139) which is the equation of interest is now approximated by a somewhat simpler expression and in order to relate T,,, to TmLand Tminto To,a series of approximations and empirical expressions are introduced. Substituting the resulting expression into Eq. (136),
Combining Eqs. (140) and (128), a linear integral equation is obtained for the interface position as a function of time,
the solution, obtained by use of the Laplace transform, is
When comparing this expression with that of Bankoff [57], it is of interest to note that the second term on the right side is that which is due to the condensation effect. Hence the two expressions are not similar, even though each includes a term proportional to t112. The stability requirement is that dx/dt = 0, and that the value of x for which this condition exists, be less than the cavity depth L.The usefulness of the expression resulting from Eq. (142) is severely restricted however by the empiricisms which have been introduced. The equation is also (as a result) dimensionally incorrect, thus defeating attempts to nondimensionalize it. For the sake of completeness (and to indicate the parameters) ,
where AT- is defined by Eq. (119), qo' is the average surface heat flow
ROBERTCOLE
142
T
FIG.34. Wall surface temperature variations during bubble formation and departure (Shai and Rohsenow [67]).
density, f is the frequency of bubble formation, K is the thermal diffusivity, and superscripts S and L refer to the solid and liquid, respectively. Shai and Rohsenow [67] apparently considered the wall temperature variation employed by Marto and Rohsenow [SS] to be inappropriate for Iiquid metal systems; the proper variation being of the form shown in Fig. 34 for stages 3 and 4. The latter represents the wall temperature variation during the recovery period following bubble departure and for liquid metal systems is perhaps 10-100 times longer than the bubble growth period represented by stages 1 and 2 (used by Jlarto and Rohsenow [SS]) . After the bubble has left, cold liquid from the bulk (at its saturation temperature) is presumed to contact the surface. The resulting initial temperature distribution is shown in Fig. 35. In the solid, the distribution is assumed parabolic up to a distance x = L’ where it becomes equal to the average gradient during a full cycle. The temperature difference at the wall surface (x = 0 ) at t = 0, 6,(0,0), is assumed to be the temperature required to initiate a bubble at the active cavity. The following set of equations describe the problem:
Initial conditions ( t
o ix I L’,
=
0),
e 8 ( ~0) ,
=
es(o, 0) + e,l(o, O ) X
+ e:(o,
0) ( x 2 / 2 ) (146)
BOILINGNUCLEATION
143
U
FIQ.35. Initial temperature distribution in the solid and in the liquid (Shai and Rohsenow [67]). 0
5 Y,
eL(Y,o) = 0
Boundary conditions (x = L', y 3 a),
eL(m,t)
=
o
Interface conditions (x = y = O ) ,
eye, t )
=
e.(o,
t)
The solution for the temperature distribution in the solid is
(147)
ROBERTCOLE
144
-
(t
+
Z) I)&( erfc
where This result is shown graphically in Fig. 36. In order to determine the stability of the cavity, it is assumed that the cavity radius-to-length ratio is such that the resistance to radial heat transport is an order of magnitude less than the resistance to axial transport L / R 10 for liquid metals. For this geometry then, the temperature distribution in the liquid metal (in the cavity) is equivalent to the temperature distribution in the solid. At the same time, the vapor temperature in the cavity is kept constant a t
>
where B1is a constant for a particular fluid. Condensation is presumed to proceed as long as the liquid temperature is less than the vapor temperature. When the two become equal, the meniscus penetration stops (at X , from the surface) and the cavity remains armed. The critical distance is found from the conditions 8, = ev, ae,/at
=
0, at x
=
X,,,
t
=
t,,
(155)
by means of Eqs. (152) and (154). The resulting expression is shown graphically in Fig. 37 as a function of B1. The critical distance is made
TABLE XI1 MAQNITUDE OF PARAMETERS
0.50 1.00 1.92 10.00
0.959 1.OOO
1.035 1.102
1.59 1.58 1.57 1.56
0.005 0.163.5 0.201 0.247
BOILING NUCLEATION
145
FIQ. 36. Temperature variations in the solid, Eq. (152),8, = 1.92 (Shai and Rohsenow [67]).
0.7L
0.60 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 (X/l3
Fro. 37. Maximum meniscus penetration from Eq. (156) (Shai and Rohsenow [67]).
ROBERTCOLE
146
dimensionless by the relaxation length L' (see Fig. 35). The cavity length > X , necessary for a cavity to remain armed is found to be
L
Numerical values of q, E, and F a r e given in Table XII.
B. EXPERIMENTAL FINDINGS Evidence that cavity penetration following bubble departure may indeed occur was first presented by Wei and Preckshot [SS]. High speed photography was used to obtain pictures of bubble nucleation, growth, and departure from heated glass capillaries having a depth of 1 mm and diameters of 1.5, 1.0, and 0.7 mm. A sequence of frames reproduced from the high speed pictures indicated a pocket of vapor in the cavity following bubble departure which produced the succeeding bubble. The vapor pocket grew and eventually emerged from the cavity as a vapor bubble. Interestingly, a liquid film was observed to exist on the capillary walls throughout the entire process. Kosky [69] employed high speed photography for the specific purpose of investigating nucleation site instabilities. Experiments were conducted using a heated glass capillary test cavity of 0.1-mm diam. and 20-mm
5pm,rb, ,
departure
I
/
W M ~ ~ departure
....
0
0 002
0.004 Time b e d
0.006
FIG.38. Motion within capillary nucleation site (Kosky [69]).
BOILINGNUCLEATION
147
FIQ.39. Minimum heat flow densities for stable boiling (Shai and Rohsenow [67]): circles, natural convection; crosses,8 , (0,0 ) ,stable boiling point; squares, Ow (0, 0 ) , stable boiling limiting point; cavity length, 1 = 0.150 in.
depth. Fifteen runs were reported with conditions from 3 X lo2W/m2 to 4.3 X lo4 W/m2 a t pressures ranging from 2.67 to 101 kN/m2 and subcoolhgs to 21°K. A plot of penetration vs. time is shown in Fig. 38 for a bulk water temperature of 295.2"K and saturation temperature of 3122°K. Little penetration occurred a t the lower pressures where the bubbles were hemispherical with an entrapped liquid microlayer under the bubble base. At higher pressures however, where the bubbles tended to be spherical and no microlayer could exist, significant penetration did occur. Thus the Kosky investigation tends to support the Bankoff and Shai models which assume initial condensation as a result of penetration of cool liquid from the bulk. Shai and Rohsenow [67] conducted experimental studies with liquid sodium boiling from a cylindrical cavity having a diameter of 0.27 mm and a depth of 3.8 mm. The limiting points were obtained by decreasing the power, after stable boiling had been achieved at high heat flow density, until boiling stopped. The limiting points shown in Fig. 39, designated by
ROBERT COLE
148
the square symbols were actually stable boiling points which deactivated with further slight decrease in power. Upon deactivation, stable natural convection began and the \Val1 temperature increased. Shown in Fig. 39 is the 3Iarto-Rohsenow equation [Eq. (143)], Eq. (156) solved for go’, and an empirical modification of the latter to take into account presumed convective effects in the liquid. The empirical modification is
With h’ = 1200 Btu/hr ft‘ experimental results.
O F ,
Eq. (157) is in good agreement with the
IX. Minimum Boiling Superheat A. Low THERMAL CONDUCTIVITY LIQUIDS The nucleation hypothesis proposed by Hsu and Graham [62] and desvribed in Sect. VI1,B was the catalyst which generated a scries of papers M hose objc1ctive was the prediction of the minimum superheat required to sustain nucleate boiling. From the analysis of Hsu [Sl] for the size range of active cavities, it is apparent that the discriminant in Eq. (106) must be greater than or equal to zero for the cavity to be active (othern-ise r* is imaginary). The discriminant is zero when
and although the discriminant is actually negative only for values of OW lying betwern the two roots, the lowcr one seems to have little significance. Hence 8,+ greater than the value given by Eq. (158) is predicted to be a necessary (but certainly not sufficient) condition for the existence of sustained bubbling from a surface which contains a spectrum of potentially active cavities. Similar expressions are obtained for the case of constant heat flow density. For that condition, Eqs. (106) and (1%) are still valid, but with 8, everywhere replaced by q’ 6/KL. The actual uses of Eqs. (106) and (1%) arc severcly restricted by a lack of knowledge regarding the proper value to use for 6 in a given system. Since 6 is not really defined, the only way to calculate it is through use of one of the final equations. Thus if incipient superheat data are available under one condition, Eq. (158) may be used to obtain the value of 6, which if assumed constant, may be used to predict the superheat or size range of cavities under other condi-
BOILING NUCLEATION
149
REFERENCE EXPERIMENTAL POINTS IN CALCULATING WC,
1
.
1
, , , 1 , 1
100
u1BCOOLING. 6&
I
l&-&
(OF?
,
I , , , ,
I000
FIQ.40. Effect of subcooling on incipient boiling temperature (Hsu [Sl]).
tions. Application of this procedure by Hsu is shown in Fig. 40 with quite favorable results except at very low values of subcooling. The analysis of Bergles and Rohsenow [70] is very similar to that presented by Hsu [Sl] except that the boundary layer thickness is more precisely defined and a graphical solution was, at least initially, considered to be more convenient. Eq. (94) is presumed to be a necessary condition
TV = T i t
+ 2uTsLst/pVhf4rn
(159)
where as indicated, the temperature is considered to be that of the vapor in the nucleus. The physical properties are to be evaluated at T;,. Thus given the system pressure, the uniform vapor temperature within a nucleus can be represented graphically as a function of nucleus radius as shown in Fig. 41. The size of the bubble nucleus is generally smaller than the thickness of the laminar sublayer in a forced convection flow, hence the temperature distribution near the wall can be approximated by the linear relation
TL = T , - (4’y/KL)
(160)
This distribution for three values of q’ is represented by the dashed lines on Fig. 41. It is postulated that the hemispherical nucleus of radius r, will grow if the liquid temperature at a distance y = r, from the wall is greater than the vapor temperature given by Eq. (159). This criterion requires that all of the liquid surrounding the vapor nucleus be able to transfer heat to the nucleus in order for it to grow. No doubt a nucleus will grow if the liquid temperature at some distance from the wall less than r,, exceeds the vapor temperature. The criterion thus seems to represent an upper limit for the wall superheat required to produce steady bubbling. On the other hand, the means of detection may not be actual observation of the bubble action but rather an observed increase in heat flow density (as on a plot of 4’ vs A T ) . Since the first few bubbles are unlikely to increase the
ROBERT COLE
150
’t
I
BUFFER ZONE
FIQ.41. Initiation of ljubble growth in forced convection (Bergles and Rohsenow 1701).
rate of heat transfer, the wall superheat associated with this indirectly determined appearance of initial bubbling will, most likely, also be higher. The graphical procedure proposed by Bergles and Rohscnow [70] for estimating the inception of boiling is illustrated in Fig. 41. Having plotted Eq. (159),the liquid temperature distribution is obtained from the relations
It is presumed that T W Lis known and that the heat transfer coefficient h’ can bo estimated from standard forced flow nonboiling correlations. Thus for a given q’, Eq. (161) relates the wall temperature and the temperature gradient. According to the criterion, steady bubbling will occur a t thc heat flow density which brings the liquid and vapor temperature curves tangent to each other T L = T’ at y = r, (162)
It is apparent t.hat once tangency occurs, a slight increase in heat flow
BOILING NUCLEATION
151
density (or wall temperature) results in the activation of a wide size range of additional cavities having radii both smaller and larger than that corresponding to the tangency condition. Although agreement with experimental data was quite good, there are two additional conditions which must be fulfilled in order for the method to work. First, a full spectrum of cavity sizes must exist and second, the cavities must contain entrapped gases or vapor. Fortunately, these conditions do exist for many commerically finished surfaces. A similar approach was independently proposed by Sat0 and Matsumura [71]. Rohsenow [65] has more recently indicated a problem which may occur when the heat transfer coefficient h' is low, e.g., low velocity forced flows or in natural circulation flows. The situation then arises where the slope (dTL/dy)y,o as calculated from Eq. (161) may be tangent to the vapor temperature curve, Eq. (159), at a point beyond the maximum existing cavity size. The first liquid temperature profile to intersect the vapor temperature curve at the maximum cavity size would then satisfy condition (162), but not condition (163), and consequently a higher than normal superheat would be required. Under normal conditions, the heat flow density at incipience is given by
obtained from Eqs. (159) and (161) using the conditions specified by Eqs. (162) and (163). For the condition where because of a low heat transfer coefficient, tangency does not result and Eq. (163) can not be satisfied, the heat flow density at incipience is determined by Eqs. (159), (161), and (162) as
Equation (165) is plotted in Fig. 42 for various values of rmax.Rohsenow [65] indicates that although much of the available experimental data is well represented by Eq. (164), another large body of data exists to the right at higher superhe%ts. None however falls to the left. The trend prediced by Eq. (165) is indicated to be difficult to observe. As noted by Davis and Anderson [72], a similar situation may also exist under conditions of normal velocity forced flows if the surface contains only a limited size range of cavities. Again, the tangency condition expressed by Eq. (163) would not be met and the heat flow density at incipience might be as expressed by Eq. (165). As indicated by Davis and Anderson [72] and as is apparent from Eq. (165), specific information on the maximum cavity size is necessary to apply the analysis.
152
ROBERT COLE
Frost and Dzakowic [73] have reported an empirical extension of the Bergles-Ilohsenow analysis [70] to fluids other than water and to natural convection systems. The approach is to modify Eq. (163) t o yield d T L / d y = dT\’/drn
at
1/ =
(Npr)nrn
(166)
The former is rationalized on the basis that y is the depth of superheated liquid adjacent to the heated surface which has temperature in excess of T’, and in single-phase heat transfer, the Prandtl number will dictate the shape of the temperature profile within this boundary layer. As shown in Fig. 13 howver, when compared with experimental data, and with the Berglcs-Rohsenow analysis, the modified approach does not appear to yield substantial improvement except perhaps a t very high and very low reduced pressures. In Fig. 43, X is defined as
Included are data from both forced and natural convection systems. A much different approach has been taken by JIadejski [74]. Having obviously been motivated by the paper of Hsu [Sl], he asks, why must the activation of a riucleus be governed by the superheat at the top of the bubble, rather than that existing at the bubble base (i.e., at the wall)? Further, JIadejski apparently disagrees with both the Hsu [Sl] and Griffiith and Wallis [59] interpretation of Eq. (94).Griffith had assumed that the temperature identified as T L in Eq. (94), which was derived assuming uniform superheat, might be interpreted as T , (the surface temperaturc) in a nonuniformly superheated system. Hsu had assumed that
Fro. 42. Incipient heat flow densities for 10s velocity flons, Eq. (165) (Rohsenon 1651).
BOILINQ NUCLEATION
153
5.0
Hydrogen Water PreonA Benzene X Nitrogen Oxygen 0 Neon Ethanol d-pentane 0 Carbon T e t r a c h l o r i d e 0 Acetone a Kerosene 0
+
0.04 0.002
l
c
n
0.005
t
n
l
0.01
.
1
I
I I I I I I I
0.05
*
0.1
1
I
L
'
'
0.5
1
1
1
1
1.0
REDUCED PRESSURE, Pr
FIG.43. Dimensionless incipient boiling conditions versus reduced pressure (Frost and Dzakowic [73]).
this same temperature should be interpreted as the vapor temperature for a nonuniformly superheated system. Madejski considers the original interpretation to be correct (i.e., TL).Starting with the Laplace-Kelvin equation [Eq. (34)], generalized to allow for a nonspherical surface, 1 p - P' L (Pa- PL) = .(-1 + -)
RI Rz P , - PLis then approximated by P,' (TL - T,J , where P,' is the slope PL
ROBERT COLE
154
of the equilibriuni vapor pressure curve, to give
where if R1 = Rz, the nucleus is spherical and TLis constant. On the other hand, if TL is a function of position as in the thermal layer adjacent to a heating surface, then the radii of the active nucleus is a function of position and uill depend not only on the wall superheat, but also upon the temperature gradient. The model employed by Nadejski is shown in Fig. 44 and assumes the nucleus to be symmetrical about the y axis, thus resembling a flattened spheroid. Defining a dimensionless temperature difference in terms of the wall superheat,
iL= BL/0w
=
(TL- Tsat)/(Tw.- Tsnt),
tL(O)
=
1
(170)
and noting that for the case of uniform superheat, Eq. (169) becomes AT, =
pL
2a
~pL - pv P,'R,
upon substitut.ing Eqs. (170) and (171) back into Eq. (169) and rearranging
where by definition,
I: FIG.44. Nucleation model (Madejski 1741).
BOILING NUCLEATION
155
To complete the definition of the problem, the temperature distribution is defined to be linear, so that
-
fL(y)= 1
( y / 6 ) for y
5 6,
f L ( y ) = 0 for y
>6
(174)
and the boundary conditions are specified to be
y(Rd
Ir=~c
=
0,
y(0) = b
tan 0 = tan ?r/2 = m, dy/dr =0 (175) In order to obtain an analytical solution to the problem, Eq. (172) is approximated by dyldr
=
AT AT,
and the mean value of R1/R2is obtained by assuming the nucleus to be elliptical in shape and = ?r/2rad,
+
+ (b/RJ2]
(Ri/Rz), = +[I
(177)
The solution to the problem as originally presented by Rfadejski [74] contained a minor error. The corrected solution as presented by Schmidt and Cole [75] is AT AT,
- ‘12 Rc (1 ki2
6
+ ;{I +
5
[l -
( 2 ~ ~ ~ f ) (178) ~ ~ } )
The dimensionless temperature gradient is
RJ6
=
[ 2 ( 2 - k12)]-1’2f ( 2 - ki2)[F(ki,
+T) -
- 2[E(ki, i n ) - E ( h , h ) ] )
F(ki, &a)] (179)
where F and E are elliptic integrals of the first and second kind, defined as
~ ( ke) ~=,
/a
8
(1
- k12 sin2 e)ll2 de
and kl is a parameter varying from 0 to 1. These results are shown graphically in Fig. 45. Unfortunately, there are as yet no experimental data available to compare with the Madejski analysis. The experimental difficulties consist primarily of determining the temperature profile in the liquid at or just prior to the appearance of a vapor bubble. Because of the thinness of the thermal layer (generally measured in micrometers) mechanical prob-
ROBERT COLE
156
i
51 I
0
1
2
I
1
3
1
Rc/b
FIG. 45. Uimensionless superheat versus dinlensionless temperature gradient from Madejski model. Eqs. (178) and (179) (Schmidt and Cole [75]).
ing techniques are questionable. Studies are currently being conducted [76] in which the resistance heating periods are of such short duration (5-50 msec) that the liquid temperature profile is given quite accurately by the conduction equation. Artificial nucleation sites of known size and geometry provide R,, while high speed close-up motion pictures at 16,000 frames/sec provide the time at which nucleation occurs. A technique not yet employed for nucleation inception studies, but one which holds great promise, is laser interferometry combined with high speed photography [77]. Not only can the temperature distribution in the liquid be accurately deterniirird at the moment of nucleation, but provided that the bubble grows symmetrically about a vertical axis, the liquid temperature profile surrounding the gro\ving bubble is revealed. The latter information is of value in determining the relative importance of SIarangoni flows (surface tension driven flows) [78, 79J at the liquid-vapor interface. Kenning and Cooper [SO] describe an experimental investigation of the flow patterns past an air bubble, which they use to formulate expressions for the initiation of boiling during forced convection. The accompanying analysis is based upon the criteria that the nucleus will grow when the
BOILING NUCLEATION
157
bubble surface temperature exceeds the temperature required to maintain the equilibrium value of excess pressure in the nucleus. The latter is expressed by
The bubble surface temperature is obtained for two limiting cases, NRJVpr>> 1 and N d p r << 1. For the former, the temperature profile is approximately linear, and when combined with the experimentally determined position of the dividing streamline (the liquid at this position covered the surface of the air bubble) , yields TB = Tw - 0.54 (q'b/KL)[l
- exp(-
N~e/45)]
(182)
For the latter case,
TB = T,
= (q'YB/KL)
(183)
where Y B = b from the Bergles-Rohsenow analysis [70] or the distance from the surface to the nucleus centroid from the Sato-hfatsumura analysis [71]. The minimum value of wall superheat was found graphically for the condition that the curves for TEand TBshould touch and diverge with TB remaining greater than TE. The following empirical expression was found for the minimum wall superheat necessary to cause the nmleus to grow, for the condition NRYpr>> 1,
Upon comparison with experimental data, the best representation was obtained by changing the multiplying constant (0.93) to 1.33, and the exponent from 0.73 to 0.6, over the range
B. LIQUIDMETALS High thermal conductivity and chemical reduction power cause liquid metal systems to nucleate at higher wall superheats than predicted by the methods of the previous section. In terms of the Bergles-Rohsenow graphical procedure, for a given heat flow density, a high thermal conductivity results in a low liquid temperature gradient which in many cases will be tangent to the vapor temperature curve at cavity radii larger than any existing on the heating surface. Thus the first cavity to nucleate will tend
158
ROBERTCOLE
to be the largest existing cavity. The corresponding superheat is given by Eq. (165), but the maximum cavity radius must be known. The alkali metals, having high chemical reduction powers, tend to remove the oxide coating on a heating surface and consequently wet and penetrate the larger and wider cavities much more readily than do other coolants. The removal of additional existing large cavities as potential nucleation sites increases the incipient superheat even more. Other factors which tend to increase the superheat are the lower slope of the vapor pressure curve in the regions of practical interest and the increase, rather than decrease, in solubility of inert gases with increasing temperature. Holtz [Sl] suggested that the pressure-temperature history of the cavity affected the incipient superheat and proposed an equivalent cavity model to account for the effect. The depth of penetration of liquid into a cavity is presumed to be determined by the maximum liquid pressure PL’ and corresponding liquid temperature TL’ to which the system has been subjected. At this condition, i.e., the point of maximum penetration, the surface is concave toward the liquid (a nonwetting condition) as the oxide coating has not yet been reduced. Once nucleation occurs, the surface flips and becomes convex toward the liquid. This sequence of events is shown in Fig. 46. The equivalent cavity model assumes that nucleations will occur from unwetted cavities having mouth radii less than the cavity radius of the position of greatest penetration. Thus the equivalent cavity radius is given by req =
2a( TL’) PL’
- Pv(TL’)
The pressure difference then required for nucleation is
FIQ.46. Holtz model for cavity nucleation in alkali liquid metal systems: (a) a t initial filling; (b) a t deactivation; (c) at incipient vaporization (Deane and Rohsenow 1871).
BOILING NUCLEATION
159
!
P I (psi01
FIG. 47. Incipient boiling superheats obtained by Chen [85], compared with the Holtz model, Eq. (187) and the Chen model, Eq. (188) (Dwyer [86]). Experimental conditions for potassium: TL’= 1180”F, Pv’= 4.25 psia; Tsst = 1413”F, P L = 16.0 psia.
and the corresponding superheat is obtained by assuming P v = P , and using either the Clausius-Clapeyron equation or vapor pressure data. Comparison of this model with experimental sodium data by Holtz and Singer [82, 831 yielded only qualitative agreement. Heat flow density, in addition to temperature-pressure history was found to influence the incipient superheat. A subsequent paper by Singer and Holtz [84] ascribed the heat flow effect to inert gas diffusion out of the cavities. Chen [85] modified the Holtz model to account for the inert gas entrapped in a cavity. The limiting expression for narrow cavities was
where Go is a measure of the amount of inert gas entrapped. Because of the difficulty of obtaining advance information on this quantity, it is treated as an empirical constant. Equation (188) was compared with experimental potassium data, varying the deactivation pressure PL’, the deactivation temperature TL’,and the boiling pressure PL.Figure 47 is typical of the
ROBERT COLE
160
t
.
0
P l (psi01 Fic. 45. Correlation of Chen's data [85),by the model of Dwyer [SG]. Experimental conditions for potassium: TL' = 1180"F,Pv' = 4.25 psia; TL* = 1413"F, P L = 16.0 psia.
results so obtained, a value of Go equal to 8 X lo-'' in.-lbf/"R being used in all cases. The trend of the data is certainly well predicted and the agreement might even be considered good if it were not for the degree of scatter which is evident. A further modification of the Holtz model has been suggested by Dwyer [SS]. Shown in Fig. 48 are the same data points presented in Fig. 47. The solid line through the data, corresponding to the left ordinate is obtained by assuming a loss of inert gas from the active cavities between the time of maximum boiling suppression and the time of incipient boiling. The solid line corresponding to the right ordinate shows that the assumed loss over the time period of the experiment amounts to approximately one-third of the original gas content. An additional factor incorporated into the Dwyer analysis is the inequality between the bubble radius at maximum boiling suppression r' and that a t incipient boiling r, In Fig. 48, this ratio is taken as 0.7. At maximum boiling suppression the pressure difference is
where the third term on the left represents the partial pressure of inert gas
BOILING NUCLEATION
161
in the cavity and p' incorporates the assumed geometric factors, the mass of inert gas in the cavity, and the gas constant. At incipient boiling,
Equations (189) and (190) are used t o calculate the incipient boiling wall superheat when p', p/p', and r/r' are known or treated as parameters. As indicated earlier, in Fig. 48, @/p' = 1 and r/r' = 0.7, and 0 = p' varies in.-lb,/OR. from an initial value of 3.1 X 10-15 to 2.0 X Dean and Rohsenow [87] obtain essentially the same equations as Dwyer without having to rely upon oxidation and partial reduction of the surface as part of the mechanism. Assuming the existence of reentrant-type cavities on natural surfaces, as shown in Fig. 49, at deactivation the vaporliquid interface hangs at the inner mouth and is concave toward the liquid. For this condition, PL' - Pv' - Po'(t) = (2a' sin +)/Td (191) Cavities having mouth radii greater than rd will deactivate while those having radii less than rd will remain armed. At nucleation
Pv $- PQ(t) -. PL= 2U/rd
(192)
Equations (191) and (192) are essentially equivalent to Eqs. (189) and SODIUM
i 1
VAPOA LIQUID INTERFACE AT DEACTIVATION
FIG. 49. Incipient boiling model for reservoir cavity (Deane and Rohsenow [87]). Deactivation, PL' - Pv' - Po'(t) = (%'sin + ) / r d ; nucleation, PV Po(t) --PL =
+
2u/r4.
162
ROBERTCOLE
(190). The above model was first suggested by Bankoff [SS] in an invited lecture presented a t the International Symposium on Cocurrent GasLiquid Flow, University of Waterloo, Waterloo, Ontario, 1968.
ACKNOWLEDGMENTS Much of this review was presented as a series of lectures during the 1971 Fall Semester at the Technische Hogeschool Eindhoven, Nederland where the author was privileged to spend a full year on sabbatical leave. The author is indebted to Professor Dr. D. A. de Vries for his continued support and encouragement, to the engineers, faculty, and students who took the time to attend his lectures, and to his very good friend Dr. S. J. D. van Stralen without whose advice, encouragement, and kind words, this review might never have been written.
NOMENCLATURE a
A A' b b'
B 3 1
CL
CW
C c 1
CP, c3
Surface area Availability, defined in Eq. (10) Defined by Eq (103) Height of bubble above surface, Fig. 23 Dimensionless pressure, defined by Eq. (61) Constant, defined by Eq. (123) Constant Gas concentration in liquid phase Gas concentration in a saturated liquid across a flat interface Constant, defined by Eq. (126) Constant, defined by Eq, (137) Constants
c4, cs CP
d d'
D
ED E=
f fl
f? f3
14 F 9
G
Specific heat defined in Fig. 10 Defined in Fig. 14 Constant, defined by Eq. (122) -4ctivation energy for diffusion Activation energy for cluster of size x Frequency factor Defined by Eq (74) Defined by Eq. (86) Defined in terms of Eq. (86) Defined by Eq. (87) Force Gibbs function per unit mass or chemical potential Gibbs function, defined by Eq. (11)
Measure of quantity of inert gas entrapped in a cavity Planck constant Heat transfer coefficient Latent heat of vaporization Rate of formation of nuclei per unit volume Boltzmann constant Parameter varying from 0 to 1 Thermal conductivity Depth of cylindrical cavity Relaxation length, Fig. 35 Mass Molecular weight Number of molecules per unit volume Active cavity population density Number of cavities having radii in the range r to T AT Prandtl number Reynolds number Pressure Slope of equilibrium vapor pressure curve Average surface heat flow density Heat flow density Rate of internal hest generation per unit volume Bubble radius Cavity mouth radius Equilibrium cluster radius Nucleus radius
+
BOILING NUCLEATION Radius of spherical projection or spherical cavity Maximum existing cavity radius Radius of curvature Radius of cavity Gm constant Entropy per unit mass Entropy Time Dummy time variable Temperature Bubble surface temperature Equilibrium temperature corresponding to pressure within bubble nucleus Bulk liquid temperature Internal energy per unit mass Internal energy Volume per unit mass Velocity of liquid phase Friction velocity Volume Average thermal velocity of a vapor molecule Coordinate direction Defined by Eq. (167) Thermal layer thickness, defined by Eq. (107) Coordinate direction Compressibility factor Effective surface tension, defined by Eq. (77) Angle defined in Figs. 12-14 Angle defined in Figs. 12-14 Contact coefficient, defined by Eq. (153) Angle defined in Fig. 2 Thermal layer thickness Dimensionless temperature difference Dimensionless distance
e eL K
X A, p V V’
€ P U T 7.
4
+
163
Contact angle measured through liquid phase Temperature difference TL - T m Thermal diff usivity Coordinate direction, defined in Fig. 30 Heat of vaporization per rnolecule Absolute viscosity Kinematic viscosity Defined by Eq. (93) Dimensionless temperature difference Density Surface tension Dimensionless time Bubble growth period Angle defined in Fig. 15 Defined by Eq. (110)
SUBSCRIPTS AND SUPERSCRIFTS 0 Reference state 03 Refers to a flat interface, i.e., an infinite radius of curvature * Refers to an activated state b Refers to value a t top of bubble nucleus 0 GaS 1 Interface k Critical bubble condition L Liquid m Meniscus n Nucleus P Pressure S Solid sat Saturation value S Solid T Total V Vapor W Refers to value at wall U Surface tension
REFERENCES 1. W.M. Rohsenow and J. A. Clark, “Heat Transfer and Fluid Mechanics Institute.” Stanford Univ. Press, Stanford, California, 1951. 2. R. T. Knapp, J. W. Daily, and F. G. Hammitt, “Cavitation.” McGraw-Hill, New York, 1970. 3. W. Nelson and E. H. Kennedy, Paper Trade J . 140, No. 29,50 (1956). 4. R. Becker and W. Doring, Ann. Phys. (Leipzig) 24, 719 (1935).
164
ROBERT COLE
5. 31. Volnier, “Kinetic der Phasenbildung.” Steinkopff, Dresden-Leipzig, 1939. [Engl. transl., “Kinetics of Phase Formation,” Ref. AT1 No. 81935 (F-TS-7068-RE). ti. 7. 8. 9. 10. 11.
12. 13. 14. 1.5. 16. 17. 18. 19. 20.
Clearinghouse Fed. Sci. Tech. Inform., Springfield, Virginia. J. Frenkel, “Kinetic Theory of Liquids.” Dover, New York, 1955. H. Reiss, I d . Eng. Chem. 44, 1284 (1952). J. I a t h e and G. M. Pound, J . Chem. Phys. 36, 2080 (1962). 11. Reiss, J. L. Katz, and E. R. Cohen, J . Chem. Phys. 48, 5553 (1968). Sucleation Phenomena, I d . Eng. Chem. 44, 1269 (1952). .I.S. Michaels, chm., “Symposium on Nucleation Phenomena.” Amer. Chem. SOC., Washington, D.C., 1966. J. P. Hirth and G. M. Pound, Progr. dfater. Sci. 11, 1 (1963). A. C. Zettlemoyer, ed., “Nucleation.” Dekker, New York, 1969. 1:. B. Kenrick. C. Y. Gilbert, and K. L. Wisrner, J. Phys. Chem. 28, 1297 (1924). L. J. Briggs, J . Appl. Phys. 26, 1001 (1955). I<. L. Wisrner, J. Phys. Chem. 26, 301 (1922). L. Trefethen, J . Appl. Ph ys. 28, 923 (1957). H. \%-akeshimaand K. Takata, J . Ph ys. SOC.J a p . 13, 1398 (1958). G.R. Moore, AIChE J. 5, 458 (1959). V. P. Skripov and E. N. Sinitsyn, C,*sp.Fir. Nauk 84, 727 (1964). [Soil.Phys. 1 ; s ~ .
7, 887 (1964-1965).] 21. E. X. Sinitsyn and V. P. Skripov, Zh. Fiz. Khim. 42, 884 (1968). [Russ. J . Phys. C’hern. 42, 440 (1968).] 22. V. P. Skripov and G. V. Ermakov, Zh. Fiz. Khim. 38, 396 (1964). [Russ. J. Phys. (‘hem. 38, 208 (1964).] 23. Y.Kagan, Z h . F i z . Khim. 34,92 (1960). [Russ. J. Phys. Chem. 34, 42 (1960).] 24. M. Blander, D. Hengstenberg, and J. L. Katz, J. Phys. Chem. 7 5 , 3613 (1971). 25. R. E. Apfel, J. Chem. Phys. 54, 62 (1971); also see R. E. Apfel, Acousl. Res. Lab., Iluri~ard(-nil*.Tech. Memo. 62 (1970). 26. K.E. Apfel, Nufure (London), Phys. Sci. 238, 63 (1972). 27. K. E. Apfel, J. Aroust. Sor. Amer. 49, 145 (1971). 28. R. E. Apfei, Suture (London), Phys. Sri. 233, 119 (1971). 29. V. P. Sliripov and P. A. Pavlov, Teplojz. Vys. Temp. 8, 833 (1970). [High Temp. ( C.’SSR) 8, 782 (1970).] 30. P. A. Pnvlov and V. P. Skripov, Teplojz. I’ys. Temp. 8, 579 (1970). [High Temp. (I’SSR) 8. 540 (1970).] 31. J. A. Sallack, Pulp Pap. itfag. Can. 56, 118 (1955). 32. \V. Selson and E. H. Kennedy, Pap. Trade J . 140, 50 (1956). 33. H. G . Lipsett, Fire Technol. 2, 118 (1966). 34. G. Long, Metal Progr. 71, No. 5 , 107 (1957). 35. L. C. Witte, J. E. Cox, and J. E. Bouvier, J. Jfelals 22, No. 2, 39 (1970). 36. J. R. Dietrich, I T S . At. Energy Comm. Rep. ANL-5323 (1957). 37. K. JV. Miller, A. Sola, and Et. K. McCardell, C.S. At. Energy Conun. Rep. IDO16883 (1964). 38. General Electric Co., Z’.’. At. Energy Comm. Rep. IDO-19311 (1962). 89. E. Naknnishi and R. C. Reid, Chem. Eng. Progr. 67, No. 12, 36 (1971). 40. F. E. Brauer, N.W.Green, and R. B. Mesler, Nucl. Sci. Eng. 31, 551 (1968). 41. I<. Flory, R. Paoli, and R. B. Mesler, Chem. Eng. Progr. 65, No. 12 (1969). 42. D. L. Katz aud C. M. Sliepcevich, Hydrocarbon Process. 50, No. 11, 240 (1971). 43. I). L. Katz, Chem. Eng. Progr. 68, No. 5 , 68 (1972).
BOILING NUCLEATION
165
44. W. Nelson, Black Liquor Recovery Boiler Adv. Comm. Meet., Atlanta, Ga., October, 19’72. 45. J. C. Fisher, J . Appl. Phys. 19, 1062 (1948). 46. D. Turnbull, J . Chem. Phys. 18, 198 (1950). 47. S. G. Bankoff, Trans. ASME 79,735 (1957). 48. W. M. Robb, A Study of Boiling Nucleation in Conical Cavities and Wedge-Shaped Grooves. M.S. Thesis, Clarkson Coll. of Technol., Potsdam, New York, 1968. 49. S. G. Bankoff, AIChE J . 4, 24 (1958). 50. E. N. Harvey, D. K. Barnes, W. D. McElroy, A. H. Whiteley, D. C. Pease, and K. W. Cooper, J . Cell. Comp. Physiol. 24, l(l944). 51. E. N. Harvey, A. H. Whiteley, W. D. McElroy, D. C. Pease, and D. K. Barnes, J . Cell. Comp. Physiol. 24, 23 (1944). 52. E. N. Harvey, D. K. Barnes, W. D. McEhSy, A. H. Whiteley, and D. C. Pease, -”c J . Amer. Chem. Soc. 67, 156 (1945). 53. E. N. Harvey, W. D. McElroy, and A. H. Whiteley, J . Appl. Phys. 18, 162 (1947). 54. R. T. Knapp, Trans. ASME 80, 1315 (1958). 55. C. Corty and A. S. Faust, Chem. Eng. Progr., Symp. Ser. No. 17 (Vol. 51), 1 (1955). 56. H. B. Clark, P. S. Strenge and J. W. Westwater, Chem. Eng. Progr., Symp. Ser. No. 29 (Vol. 55), 103 (1959). 57. S. G. Bankoff, Chem. Eng. Progr., Symp. Ser. No. 29 (Vol. 55), 87 (1959). 58. C. A. Ward, A. Balakrishnan, and F. C. Hooper, J . Basic Eng. 85, 695 (1970). 59. P. G r f i t h and J. D. Wallis, Chem. Eng. Progr., Symp. Ser. No. 30 (Vol. 56), 49 (1960). 60. S. Kasturirangan, A Study of Nucleation from Artificial Nucleation Sites. M.S. Thesis, Clarkson Coll. of Technol., Postdam, New York, 1971. 61. Y. Y. Hsu, J . Heat Transfer 84,207 (1962). 62. Y. Y. Hsu and R. W. Graham, NASA Tech. Note NASA TN D-594 (1961). 63. N. Zuber, Hydrodynamic Aspects of Boiling Heat Transfer. U.S. At. Energy Comm. Rep. AECU 4439 (1959); Ph.D. Thesis, Univ. of California, Los Angeles, 1959. 64. C.-Y. Han and P. Griffith, Int. J . Heat Mass Transfer 8, 887 (1965). 65. W. M. Rohsenow, Fluids Eng., Heat Transfer Lubric. Conf., Detroit, Mich. Paper NO. 70-HT-18 (1970). 66. P. J. Marto and W. M. Rohsenow, J . Heat Transfer 88, 183 (1966). 67. I. Shai and W. M. Rohsenow, J . Heat Transfer 91, 315 (1969). 68. C.-C. Wei and G. W. Preckshot, Chem. Eng. Sci. 19, 838 (1964). 69. P. G. Kosky, Int. J . Heat Mass Transfer 11, 929 (1968). 70. A. E. Bergles and W. M. Rohsenow, J . Heat Transfer 86, 365 (1964). 71. T. Sat0 and H. Matsumura, BulZ. JSME (Jap. SOC.Mech. Eng.) 7, 392 (1964). 72. E. J. Davis and G. H. Anderson, AZChE J . 12, 774 (1966). 73, W. Frost and G. S. Dzakowic, ASME-AIChE Heat Transfer Conf., Seattle, Wash. Paper No. 67HT-61 (1967). 74. J. Madejski, Int. J . Heat Mass Transfer 9, 295 (1966). 75. R. J. Schmidt and R. Cole, Int. J . Heat Mass Transfer 13, 443 (1970). 76. R. R. Schultz, Ph.D. Thesis, Dept. of Chem. Eng., Clarkson Coll. of Technol., Potsdam, New York, 1973. 77. F. A. Matekunas and E. R. F. Winter, Int. Symp. Two-Phase Syst., Technion City, Haifa Pap. 1-15 (1971). To be published in “Progress in Heat and Mass Transfer” (G. Hetsroni, S. Sideman and J. P. Hartnett, eds.), Vol. 6, Pergamon, Oxford, 1973. 78. H. Beer, in “Progress in Heat and Mass Transfer” (T. F. Irvine, Jr., W. E. Ibele,
166
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J. P. Hartnett. and R. J. Goldstein, eds.), Vol. 2, pp. 311-370. Pergamon, Oxford, 1969. i 9 . H. Beer, I n f . S y m p . Two-Phase Syst., Technion City, H U I ~Pap. Q 1-7 (1971). To be puldished in “Progress in Heat and Mass Transfer” (G. Hetsroni, S. Sideman and d. P. Hartnett. eds.), Vol. 6, Pergamon, Oxford, 1973. SO. I). B. R. Kenning and M. G . Cooper, Proc. Inst. dfech. Eng. 180, Part 3C (19651966). S1. R. E. Holtz, Argoniie Xaf. Lab. Rep. ANL-7184 (1966). 82. R. E. Holtz and R. M. Singer, A IChE J. 14, 654 (1968). 83. R. E. Holtz and R. M. Singer, Chern. Eng. P r g r . Symp.Ser. No. 92, (Vol. 65), 121 (1969). 84. R. M. Singer, and R. E. Holtz, Id.J. Heal Mass Transfer 12,1045 (1969). 85. J. C . Chen, J . Heal Transfer 90,3V3 (1968). 86. 0. E. Dwyer, Znf. J. Heal .Cfas~’Transfer 12, 1303 (1969). 87. C . W. Dean, IV and W. M. Rohsenon, Mechanism and Behavior of Nucleate Boiling Heat Transfer to the Alkali Liquid Metals. Mass. Inst. Technol., Heat Transfer Lab., Tech. Rep. No. DSR 76303-65 (1969). 88. Y. G. Bankoff, in “Corurrent Gas-Liquid Flow” (D. S. Scott and E. Rhodes, eds.), p. 283. Pleiiiim, S e n York, 1969.
Heat Transfer in Fluidized Beds
CHAIM GUTFINGER AND NESIM ABUAF Laboratory for Coating Technology. Department of Mechanical Engineering. Technion-Israel Institute of Technalogy. Haifa. Israel
I. Introduction . . . . . . . . . . . . . . . . . . I1. General Description of Fluidized Bed Behavior . . . . . . . . A . Flow Properties . . . . . . . . . . . . . . . . B . Bubbles in Fluidized Beds . . . . . . . . . . . . . 111. Heat Transfer between Solid Particles and a Fluid . . . . . . . A. The Problem . . . . . . . . . . . . . . . . . B. Experimental Measurement Techniques . . . . . . . . . C . Experimental Correlations . . . . . . . . . . . . . D. Theoretical Models . . . . . . . . . . . . . . . E . LiquidSolid Fluidized Systems . . . . . . . . . . . IV. Heat Transfer between a Fluidized Bed and a Surface . . . . . . A . Variables Affecting the Heat Transfer Rate . . . . . . . . B Mechanisms Proposed for the Heat Transfer Phenomena between Fluidized Bed and a Surface . . . . . . . . . . . . C. Comparison between theProposedMechanism . . . . . . D. Experimental Results . . . . . . . . . . . . . . E . Immersed Bodies . . . . . . . . . . . . . . . F. Fluidized Bed Coating . . . . . . . . . . . . . . Nomenclature . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . .
.
. .
. . . . . . . . . .
167 169 169 170 171 171 172 173 176 179 180 180
a
.
. . . . . .
181 195 197 206 211 213 214
.
I Introduction Consider a gas flowing upward through a bed of solid particles. If the particles are stationary the process is called flow through a porous medium . If the gas velocity is greatly increased the particles of the bed will be entrained by the gas and the process is called pneumatic conveying. Between these two extremes there exists a state at which the particles are suspended in the flowing fluid. At this state the weight of the particles is counterbalanced by the drag force exerted on them by the fluid. A bed of 167
168
CHAIM GUTFINGER AND NESIM
ABUAF
particles in this state is known as a fluidized bed and the operation of converting a stationary bed of particles into a randomly moving suspended medium is called fluidization. The fluid used to fluidize the particles may be either a gas or a liquid. Basic quantities used in describing a fluidized bed are the minimum fluidization velocity urn!and the minimum fluidization void fraction or voidagc emf which is associated with it. If the velocity of the fluid is increased beyond that of minimum fluidization the bed expands, its density decreases, and its voidage increases. A term called the expansion ratio describes the state of the bed. It is defined as the ratio of the bed height and the bed height at minimum fluidization velocity. There is a basic difference in the dynamic behavior of a gas-fluidized and a liquid-fluidized bed. This is due to the differencein particle to fluid density ratios. In a gas-fluidized bed this ratio is on the order of thousands, whereas in liquid fluidization the particles are only several times heavier than the fluid. Usually liquid-fluidized beds work in a smooth manner. There are no gross instabilities in the flow, and the bed is referred to as a homogeneously fluidized bed or a particulately fluidized bed. Gas-fluidized systems behave differently. The system is usually unstable above minimum fluidization conditions, characterized by violent agitation of solids accompanied by bubbling and channeling of the gas. The gas-fluidized bed is sometimes called an aggregativc or bubbling fluidized bed. Due to the excellent contacting ability between the solid and fluid phase, the fluidized bed has found vast industrial applications in areas involving heterogeneous heat transfer, mass transfer, and chemical reactions. This is particularly true of the gas-fluidized bed. The effectiveness of a multiphase or heterogeneous contacting operation depends strongly on the ability to bring into contact large transfer surfaces in a short time. The fluidized bed system can provide just that. If one also adds to this feature the simple design of the fluidized bed contactor, one can easily understand the high popularity of these systems in industry. The main industrial uses of fluidized beds are in the oil industry. There the fluidized beds serve as reactors for production of high octane gasoline, thermal cracking of petroleum feed stocks, catalytic cracking of heavy hydrocarbons to lower molecular weight compounds, carbonization and gasification of oil shale, coal, and coke, etc. Many chemical reactions are being carried out in fluidized beds due to the favorable economics of these processes. Physical operations being performed in fluidized beds include drying of granular materials or powders, mixing of powders, quenching of hot gases,
HEATTRANSFER IN FLUIDIZED BEDS
169
cooling of powdered solids, cooling of metals in metal treatment operations, and coating of plastic materials on metal surfaces. In the last twenty years a vast body of literature has been accumulated dealing with the fluid dynamics, heat transfer, mass transfer, chemical reactions, and industrial applications of fluidized beds. References 1-10 list the books on the subject of fluidization. Davidson and Harrison [l], who edited the latest compilation on this subject, note in the preface to their work that the volume of literature available on fluidization cannot be read in a lifetime. The present authors, who have attempted a much more modest task of writing only on heat transfer in fluidized systems, share their view on this subject. The present review paper describes the phenomena of heat transfer between the fluidized particles and the fluid, the fluidized bed and the walls of the container or immersed solid objects, and lists some applications of fluidized beds to processes where heat transfer operations are dominant. Chemical reactions and mass transfer in fluidized beds were excluded from this review.
11. General Description of Fluidized Bed Behavior A. FLOWPROPERTIES Figure 1 describes qualitatively the pressure-drop velocity relationship for a fluidized bed. Fluidization starts when the drag force exerted on the particles by the fluid is equal to their weight. This can be put in the following equation form: &/Lrnf = (1 - e m f ) (P. - P f ) g (1)
I
FLUIDIZATION REGION
I ENTRbJNHENT
I
I
A
1.0
I I
10.0 umf
FIG.1. Pressure drop velocity curve for a tluidized bed. (Dashed line is for first fluidization of system showing the effect of particle interlocking.)
170
CHAIMGUTFINGER AND NESIM ABUAF
where L,, and emf are the respective bed height and void fraction at minimum fluidization. The minimum fluidization velocity may be found by assuming at the onset of fluidization a pressure drop equal to that of a packed bed. For the latt>er,several correlations have been proposed. The one by Ergun [ll] is known to give fairly good results C23. It is presented below in terms of minimum fluidization quantities :
Here umfis the superficial velocity, defined as the flow rate per unit crosssectional area of the empty bed, at minimum fluidization conditions; dp is the diameter of the sphere of the same specific area as the particle used. Combining Eqs. ( 1 ) and (2) yields a quadratic expression for umr:
Richardson [12] simplifies this equation by taking Rem[= (660
Emf
as 0.4 to yield:
+ 0.037 Ga)'I2 - 25.7
(4)
where the Galileo number, Ga, is defined as: Ga = C d p 3 ~ ~-( ~~ s~ ) g l / l ~ ~
(5)
Some authors refer to this dimensionless group as the Archimedes number. Another quantity used in describing fluidized beds is the expansion ratio defined as the bed height relative to that at minimum fluidization conditions. It relates to other quantities as follows: L/Lmt
=
(1 - Emf)/(l - E ) = Pmf/Pb
(6)
The range of cxpansion ratios encountered in fluidization is between 1.2 and 3.0.
B. BUBBLES IN
FLUIDIZED
BEDS
We refer now to a gas-fluidized bed. Such a bed has regions of lower density called bubbles or gas pockets. The higher density regions are callcd the emulsion phase. Heat and mass transfer in a fluidized bed are intimately related to the interactions between the emulsion or continuous phase and the bubble, or dispersed phase. The flow of bubbles in a fluidized bed has been treated theoretically by Davidson [5,13], Jackson [14], Murray [15], and others. Jackson [l6] provides an excellent summary on this topic. Experiments on bubble
HEATTRANSFER IN FLUIDIZED BEDS
171
motion in fluidized beds were performed by Park et al. [17], who used a sophisticated electroresistivity probe system. X-ray observations of bubbles were reported in a series of papers by Rowe and co-workers and recently summarized by Rowe in Davidson and Harrison [l]. Davidson’s analysis was used as the basis for a bubbling bed model by Kunii and Levenspiel [lS] who applied it to correlate data on heat and mass transfer and catalytic reactions in fluidized beds [19].
111. Heat Transfer between Solid Particles and a Fluid
A. THE PROBLEM Knowledge of heat transfer rates between solid particles and a fluid is essential in such physical operations as drying of particles or quenching of hot gases as well as in chemical reactions involving large heat effects that occur on and within the fluidized catalyst particles. There is little agreement in reported experimental values of the heat transfer coefficients in the literature. The reasons for this are as follows: Due to the complexity of the contacting pattern between particles and fluid, the approach is to find average heat transfer coefficients for the whole bed rather than local coefficients. This is done mainly by gross measurements of temperature of the entering and leaving stream and the bed temperature. In order to find an averaged heat transfer coefficient over the whole bed, one has to assume a flow model for the fluid and the particles. The favorite models used assume uniform conditions or complete mixing for the solid and either complete mixing or plug flow for the fluid. On a gross scale the temperature of the solids in the bed is nearly uniform, whereas the fluid temperature changes very rapidly in a very short section of the bed close to the distribution grid and very slightly beyond it. Temperature measurements taken in beds with thermocouples were interpreted very differently. Some investigators interpret a bare thermocouple reading as the gas temperature while others as that of the solids. Some use thermocouples protected by a mesh or a cloth and assume the measurement to give the gas temperature, others use suction thermocouple measurements to obtain the gas temperature. Direct measurements of solid particle temperature are even more difficult and unreliable. A novel approach to this problem has been pioneered by Barker [20] who used a heat source, thermistor, and radio transmitter in a l-cm-diam. particle. However, in general solid particle temperatures are being assessed indirectly. Usually the steady state and the unsteady state experimental techniques were used. In the steady state setup the hot gas enters the bed which is kept
172
CHAIM GUTFINGER AND NESIM ABUAF
coo1 either by heat removal or by solid recycling. In the unsteady state sctup the hot gas enters a cold bed which heats up. The exit gas temperature is monitored n-hile the solids temperature is assessed by means of a heat balance. Due to the generally low accuracy of in-bed temperature measurements and oversimplifications in the flow model, heat transfer coefficients reported in the literature show very little agreement. There is 110 complete theory that can predict heat transfer data for fluidiztbd beds, although there are several theorirs that correlate published data. Thus, n-e d l first discuss the experimental data and their correlations and afterward try to explain the data.
B. EXPERIMENTAL MEASUREMENT TECHNIQUES
In this section we describe techniques of study of heat transfer between solid particles and gas under conditions where each particle may be assumed to h at a uniform temperature at any time in the bed. This condition is satisfied when the Biot modulus (Bi = h p d p / k s )based on thc local heat transfer cocfficient h , near the particle is less than unity. Due to the small diameter of the particles this condition is Satisfied in most fluidized beds. 1. Steady State Measurement Techniques
This kind of experiment may be performed either with a fixed amount of solids and heat removal or using a continuous flow of solids. a. Setup with A'o Solid Flow. Typical data of this kind are reported by Heertjes and McKibbins [21), Kettenring et al. [22], Frantz [23], Bradshaw and Myers [24], and Walton et al. [25]. The heat balance performed here states that the heat loss by the gas equals the heat gained by the bed (or solids). This can be written in differentialform as:
uOprcpr dTf = h p a ( T f- T,) dL
(7)
Hcrc u is the specific surface or solid surface per unit bed volume. If one assumes a plug flow model for the gas and complete mixing and uniform tcmpwature for the solid, one may integrate this equation and obtain:
h. Setup with Continuous Solid Flow. Typical data with this setup wcrc reported by Anton [as], Kichardson and Ayers [27], and Sat0 et nl. [ZS].
HEATTRANSFER IN FLUIDIZED BEDS
173
Using identical assumptions to the previous case and performing a heat balance results in:
2. Unsteady State Techniques
Typical data of this kind were reported by Shakhova [29], Fritz [30], Wa.msley and Johanson [31], Donnadieu [32], Ferron [33], and Rosental [34]. The gas is again assumed to be in plug flow and the particles in a uniformly mixed state. A heat balance on a differential bed section of height dL states that heat supplied by the incoming gas to the section should be equal to heat transferred to solids: uoplcp,dTr = h,a(Tr - T s ) dL (7) Here the change in heat content of the gas inside the bed was neglected. This equation may be integrated to yield an expression for the gas temperature as a function of bed height at any instant of time:
Combining this expression with an overall heat balance on the bed yields a timetemperature relationship for the bed:
Here T r is the fluid temperature at bed height L, while Ti is the initial temperature of the bed (fluid and particles). As stated above, this equation neglects the change in heat content of the fluid inside the bed. This neglection is justified when the fluid is a gas. However, for liquid-fluidized beds it is not true and Eq. (11) has to be modified, a point not always realized by researchers in liquid-fluidized beds [35]. c . EXPERIMENTAL CORRELATIONS
A vast body of reported experimental data is available on particle-tofluid heat transfer. In many cases the reported data conflict with one another either due to different measurement techniques, especially of temperature, or due to differences in the fluid-dynamical conditions in the bed stemming from differences in physical construction, size, gas distributor design, or differences in size, shape, and size distribution of the particles. We will not attempt here to list the effect of various parameters on particle
174
CHAIM GUTFIKGER AND NESIM ABUAF
to fluid heat transfer due to lack of space. In the next section dealing with bed-to-surface heat transfer, this topic is attended to in more detail. Let us only note that Barker [36], \vho reviewed the significant literature on particle-to-fluid heat transfer coefficients up to 1964, lists in his review242 refcrenccs. These should be supplemented by a more recent review by Gelperin and Einstein in Davidson and Harrison [l], which adds about 50 rderences on this topic mainly from the Soviet Union. The prrscnt state of the empirical correlations is such that an estimation of a hrat transfer corfficient within a factor of 2 is corisidcred a good one. Frantz [37] and Iiothari [38] have critically reviewed the literature dealing with fluid-to-particle heat transfer correlations based on empirical data. Waltori el nl. [23] have shoivn that bare thermocouples inserted into a fluidized bed indicate neither the true gas nor the true solids temperature, but rather some intrrmcdiate value. Frantz corisidcrs the heat transfer coefficient based on bare therriiocoupIe readings of gas temperature as a n “apparent” coefficient. He proposes a correlation for the apparent Susselt nunibcr based on these coefficients as: = 0.015 lie‘ (12) (Xu,) Hi4 CI )rrrlation for data based on suction thermocouple readings for predict ing the so-called “true” heat transfer cocfficicnt is:
Xu,
=
0.016 Re‘.3Pro67
(13) Thr po\\-tr on Pr wems more like an ornament, since most of the experiments w r e performed in air for which Pr = 0.72. Iiothari [38] has reanalyzed some heat transfer data by assuming a plug flou model for the gas, and complete mixing for the solids, coming up with the correlation,’ that is valid for Re,, < 100:
Xu,
=
0.03 Re’.3
(14)
Figure 2 shon s Iiothari’s correlation together with some experimcntal data as presrnted i n Iiunii and Lcverispiel[19]. For high Reynolds numbers data are expected to fall between the correlation for single spheres [39] and that for fixed beds, both given in Fig. 2. f;eIperin d (11. [-lo, 411, have a diffvrrnt outlook on the particle-to-fluid heat transfer problem. Since heat transfer is known to occur only in a small active section of height L , they treat two separate cases: ( 1 ) total bed height L balance problem”; and
> La; this
case they called the “thermal
1 This correlation has been reported in the literature [2, 191 with the wrong coefficient 0.3 rather than 0.03.
HEATTRANSFER IN FLUIDIZED BEDS
175
FIG.2. Correlation of data for gas-solid heat transfer for Re < 100 (from Kothari [381).
olK1'
O . ~ ' O . l*
V Donnadlou. [32]0 HoortJrrond WKIkblnS. 1211) 0 Wolton st ol.125J A Kottonrlng at 01. c221 ' I0 ' ' loo ' " 1000
'"""I """'
"""'
Re
(2) L < La; here resistance t o heat transfer between gas and solid must be considered.
The height of the active section L , was given for fluidization in air as:
La/d, = 0.18Re/(l
- c)
(15)
As seen from Eq. (15), the height of the active section is of the order of 10-100 particle diameters for most fluidized beds met in practice. For the case of L > La,Gelperin et al. [40] suggested the following correlation: Nu, = BRePr
(16)
which for air simplifies to:
Nu, =
0.24 Re d, Lmt(1 - Emf)
For the case of L < La, Gelperin and Einstein [41] prefer to plot their data in terms of Nu, Pr+.33 vs Re/e. Figure 3 provides such a plot that these authors have prepared from data of many investigators [20, 22, 24, 25,27,32,34,35,37,42-551. In order to keep matters in the right perspective, the present authors have added to Fig. 3 the dotted line which represents Kothari's [38] correlation. This was done by arbitrarily assuming B = 0.5 and Pr = 0.72. The fact that the simple correlation passes through the data only points to the unlimited possibilities of a log-log plot.
176
CHAIM GUTFINGER AND NESIM ABUAF
D. THEORETICAL IfODELS Referring to Fig. 2 one notes that coefficients for fluid-to-particle heat transfer are much lower than one u-ould expect considering the exccllent heat transfer characteristics of fluidized beds. The high heat, transfer rates are mainly due to the large surface area of solids available for the contacting operation rather than high heat transfer coefficients. The minimum heat transfer coefficient for a single sphere in an infinite fluid, for the case where convective heat transfer to the fluid may be neglected, is: as Re+O (18) (Nup)min = 2 As seen in Fig. 2, there are heat transfer coefficients encountered in fluidized beds which are several orders of magnitude lower. 1. The Microbreak Model of Zabrodsky
In this model [56], it is postulated that the true heat transfer coefficient cannot fall below a value given by Rowe [57] as: ~u~~~ = 2 4 1
-
(1 -
4l/31
(19)
Thc solid may be viewed as arranged in horizontal rows. The apparent low Nusselt numbers stem from part of the fluid bypassing several rows of particles and then mixing with the fluid that went through the particles. The gas temperature for the nth mixing after the nth microbreak in the solid is a function of the fluidization velocity. No clue is given to the number of “microbreaks” present in a given bed. In a later paper Zabrodsky [58] developed the idea of low effectivevalues of Xu appearing simultaneously with high true values of Nutr due to the nonuniformity of gas distribution. An expression valid for low Peclet numbers was developed for the calculation of the effective Nu:
For low Pe, Eq. (20) will predict reduced effective Nusselt numbers. 2.
The Bubbling Bed Model
Iiunii and Levenspiel [l8, 19) have extended Davidson’s [13] single bubble model to a bed uith a rising crowd of bubbles. According to this model most of the gas rises through the bed as a swarm of bubbles, while a small fraction of it rises through the emulsion phase. Each bubble is surrounded by a thin layer of emulsion called the cloud. Heat and m s interchange occur from the bubble through the cloud and
HEATTRANSFER IN FLUIDIZED BEDS
177
FIG.3. Fluid-to-particle heat transfer as compiled by Celperin and Einstein [41] with Kothari's correlation [38] added. I. Data of Walton et al. [25], Richardson et al. [27], Donnadieu [42], and Juveland et al.
WI.
11. Heertjes et al. [21], Brun et aE. [44], and Lindin et al. [45]. 111. Anton [26]. Line a-a: single sphere, Rowe et al. [59]. 1. Heertjes [46] 9. Kazakova et al. [51] 2. Ravdel et al. [47] 10. Ciborowski et al. [52] 3. Donnadieu [32] 11. Beilin et al. [53] 4. Shimanski [48] 12. Sunkoori et al. [35] 5. Crishin 1491 13. Kettenring et al. [22] 6. Rosental [34] 14. Haruaki [54] 7. Bradshaw et al. [24] 15. Frantz [37] 8. Vasanova [50] 16. Peters et al. [55]
into the bed. When a bubble passes through a bed it is followed by a wake of particles. The solids mix inside the bed by rising to the bed surface in the wake behind the bubble and descending to the bottom through the emulsion phase. A small voIume fraction of solids (less than 2%) is also present within the bubbles. The emulsion phase is maintained a t minimum fluidization velocity, while the bubbles are assumed to rise with a velocity u b > 5umf. If uo and U b are the superficial gas velocity and the bubble velocity respectively, then the fraction of bed consisting of bubbles 6 is given by: 6=
-
(&l U m f ) / U b
=
1 - ( Lm f/ L )
(21)
Heat transfer coefficients may be defined for the bed depending on the temperature used. If the temperature of the leaving gas, consisting mainly of bubble gas, is measured, we have what may be called an overall driving force T f b - T. with a corresponding coefficient hoverall.If the gas temperature inside the bed is measured, say, by a suction thermocouple, an
CHAIM GUTFINGER AND NESIM ABUAF
178
average temperature Trbetween the bubble and emulsion gas will be read. This will result in an apparent driving force T, - T, and a corresponding apparent heat transfer coefficient h.PP. The two coefficients are related by: (22) The heat transfer coefficient is evaluated by equating the heat lost by the gas passing through a bed section to the heat transferred to solids: 6happ
urprcp, dTr
=
=
hoverall
happa(Tr - T,) dL
(23) Now it is assumed that gas enters the bed as hot bubbles. An accounting of heat loss by bubble gas in terms of the flow pattern of the bubbling bed model and the local, or true, heat t-ransfer coefficient, gives : by [ heatinlost bubble
gas
1=I
heat taken up by solids in bubble
1
$-
to [ heat transferred cloud 1 gas
or, in symbols: -PrUbCpf-
dTrb = ?’bhta’(Tfb- Ts) dL
+ H(Tfb - Ts)
(24)
whrrc h , is the local or true heat transfer coefficient between single particle and gas; Y b is the ratio of solids volume in bubble; a’ is the specific surface area of solids, and H is a transfer coefficient between bubble and cloud given by :
Combining Eqs. (22)-(25), one obtains an expression for the apparent heat transfer coefficient : 1 Nuapp= -(ybNut 1--E
+ 6kr
Here Xut is the local Nusselt number for a particle immersed in the bubble far from interfering particles, moving with a terminal particle velocity. One may use the equation of Rowe et al. [59] for its computation: Nu
=
2
+ 0.69 Re’/*Pr*”
(27)
For a given bed of solids Eq. (26) is of the form: Nuapp= A (Re)
+B
(28)
where A is a constant which increases with particle size and B is a very small constant depending on solid content in the bubble.
HEATTRANSFER IN FLUIDIZED BEDS
FIG.4. Comparison of the calculated curves A’ heat transfer in fluidized beds.
-
179
H’ with reported data on gas-solid
Using the bubbling bed model, Kunii and Levenspiel [19] were able to correlate the experimental data of Heertjes and McKibbins [21] and Kettenring et al. [22]. Figure 4 shows the calculated versus the experimental heat transfer coefficients. The excellent fit was possible by adjusting the bubble diameter db. As there are no fluidized beds with single-diameter bubbles, one should view db as an adjustable constant for each particle diameter rather than a measured physical quantity. Still, the seemingly correct power on Re and also the reasonable values required for db show that the bubbling bed model can explain experimental data, including the drastic reduction in A uidized bed heat transfer coefficients as compared to the one for single particles.
E. LIQUIDSOLID FLUIDIZED SYSTEMS Although not as popular as gas-fluidized beds, liquid-fluidized systems lately find important industrial applications such as the design of naturaluranium-water-fluidized nuclear reactors [SO], heat removal from water in desalination processes [Sl], and the use of fluidized particles inside vertical water heat exchangers in order to prevent scale deposition on the heat transfer surfaces [SZ]. Liquid-solid systems generally give rise to particulate fluidization over the whole range of liquid velocities employed. The works of Holman et al. [SO] and Sunkoori and Kaparthi [35] represent typical experimental heat transfer studies in liquid-fluidized beds. Zahavi [Sl] views the heat transfer process as a Wiener process. A more
CHAIM GUTFINGER AND NESIM ABUAF
180
applied aspect of the problem is presented by Trupp [63] who lists 203 references in a review of fluidization relevant to design of a liquid-fluidized bed nuclear reactor. Jfost of the heat transfer studies in liquid-fluidized beds look for similnrities to gas-fluidized bed systems in approach and in the resulting empirical corrclations. As seen from line 12 in Fig. 3, the data of Sunkoori and Kaparthi fall within the range of data for gas-fluidized systems. The present authors believe that due to the more predictable behavior of liquid-fluidized beds a more basic approach to the problem is possible. It seems like the work of Richardson [12] on particulate systems is a step in the right direction.
IV. Heat Transfer between a Fluidized Bed and a Surface The heat transfer rates betwecn a surface and a fluidized bed are much highcr than in single gas flow. In order to explain this phenomenon and predict heat transfer rates for design purposes, several investigators have studied this probleni experimentally and many models have been proposed. The literature in the field is tremendous. The authors have tried to examine, study, and classify this gigantic amount of data, but still it is obvious that they cannot pretend to have covered the whole field. A.
lrARIABLES AFFECTING THE
HEATTRANSFER RATE
In addition to the complexity of the phenomenon, one also realizes that the number of variables affecting the heat transfer rate is very high. A simple consideration of the effect will lead to the following list of the variables involved (one should mention a t this point that all kinds of radiation effects are going to be excluded from the analysis until very high temperature effects will be introduced later) : properties of the fluid, pr, p , cDf, kr ( 2) properties of the granular solid material, d,, p s , cfi, k,, & (3) conditions at minimum fluidization, u,r, t , r (4) fluidization conditions, uo, t ( 5 ) geometric variables, D, D H , LO, LH (1)
A simple dimensional analysis nil1 provide the following nondimensional parameters, relating all the effective variables [2]
With such a large number of nondimensional variables, it is quite easy to visualize the experimental difficulties to be encountered when the effect of
HEATTRANSFER IN FLUIDIZED BEDS
181
only one variable on the heat transfer rate is investigated. The same point also explains the difficulty and, in general, the impossibility of comparing experimental results of different investigators. Any comparison between graphs which represent the variation of the heat transfer coefficient with respect to one variable, without all the others being specified clearly, must be primarily qualitative in nature.
B. MECHANISMS PROPOSED FOR THE HEAT TRANSFER PHENOMENA BETWEEN A FLUIDIZED BED AND A SURFACE Many investigators have tried to model the wall-bed heat transfer phenomena in a fluidized bed and several mechanisms have been proposed. We will try to classify these models in a way similar to that of Kunii and Levenspiel [a], and also present and explain the development of the different ideas through time. After presenting the different models, we will try to relate them, determine the criteria that show which mechanism controls the heat transfer rate, and aid in the selection of a model which will represent a particular experimental or design situation. 1. Steady State Conduction across the Gas Film
In this model heat is conducted through the gas boundary layer near the heat transfer surface. In order to explain the high values of the heat transfer rates obtained experimentally, this gas layer was assumed to be scoured by solids moving along the heat exchange surface, decreasing the boundary layer thickness near the wall. Such a model has been developed by Leva et al. [64-66], Dow and Jakob [67], and Levenspiel and Walton [SS]. Dow and Jakob [67] studied the behavior of the fluidized gas-solid mixtures and classified it as the “dense phase” and the “lean phase” according to the gas velocity. In the “dense phase” fluidization, they observed three types of behavior: bubble formation, slugging, and mechanically smooth fluidization. Their model applied to the mechanically smooth, dense phase fluidization. The motion of the particles in the fluidized bed revealed a pattern as shown in Fig. 5. The motion is primarily upward a t the center of the tube and downward along the tube wall. Temperature measurements showed that the whole bed was at a constant temperature except for a small region a t the bottom (referred to later as the active section [41]) and a narrow layer near the tube wall. Heat is transferred radially through a thin air film to the particles and air moving downward outside this film. The particles carry the heat to the bottom of the bed where thermal equilibrium is attained instantaneously with the incoming cold air. The bombardment with small particles prevents the formation of a laminar boundary layer, and leaves a very thin
182
CHAIMGUTFINGER AND NESIM ABUAF
HEATEI-
COLD AIR IN (Ti) FIG.5. Heat transfer mechanism 1 and motion of the particles.
laminar sublayer and a thicker turbulent layer. Their experimental results are correlated by a simple dimensional analysis as an expression which will be presented in Tables 1-111. Levenspiel and Walton [SS] present a similar model where the resistance to the heat flow is due to a laminar gas layer which is destroyed by solid particles passing through it. Thus the average thickness of the laminar layer is much less than in an empty tube. They assume the particles are of uniform diameter d,, stationary, and arranged in equally spaced horizontal layers. The boundary layer formation at the tube wall is similar to that of a flat plate. At points of contact with the stationary solids, the boundary layer is destroyed and starts once again, Fig. 6. The distance between two successive layers is given as : D, = ~cE,/6(1- E ) 129) As 6f is the average boundary layer thickness between two points, then the
HEATTRANSFER IN FLUIDIZED BEDS
183
FIG.6. Laminar boundary layer thickness between two layers.
heat transfer coefficient is given by:
h, = kJ6+ and ti+ = (10/3) (@J%pr)”y
where = [(I
and
+
m 3 / 2
/3 = 0.041 (1
- 831
- E) (Dr%pr/p)
‘I2
(33)
These models do not take into account the influence o the s o L particles on the heat transfer phenomena. The picture presented and the mechanism proposed cannot be considered to be complete. 2. Unsteady Heat Conduction by Single Particles in Direct Contact with the
Heat Exchange Surface That high heat transfer coefficients are obtained in gas-fluidized beds, that thermal equilibrium is very quickly established between the gas and the particles in the bulk of the bed, that the entire thermal gradient is restricted in the immediate region adjacent to the wall, and that groups of randomly packed particles convey heat from the surface to the bulk of t,he
CHAIMGUTFINGER AND NESIM ABUAF
184
160 FLUID
DISTANCE 100
(P) TW
Tb
DISTANCE (/A
FIG.7. Unsteady heat conduction through a single particle (Botterill et al. [71]).
bed has already been mentioned. Photographic studies near the wall also showed that particles tend to associate in groups, move slowly along the wall, or remain in contact with it a certain time. These observations led Botterill et al. [69, 70, 721, to propose that heat is transferred from the vertical surface to the adjacent layer of particles arriving together at the wall. They confined their theoretical considerations to an isolated solid particle lying in contact with the wall. If the residence time of the particle near the wall is long, heat will penetrate further into the bulk and if the residence time is short, heat exchange calculations can be limited to only one particle, the nearest to the surface. By neglecting conduction through the point of contact, radiation effects, and thermal convection through the surrounding fluid, they solved numerically the unsteady heat conduction between a plane surface and an isolated spherical particle surrounded by static gas, initially a t the temperature of the bed (Fig. 7 ) . Conduciion equation:
where subscript i
=
1 (solid) and i
=
2 (fluid).
Heat exchange across the solid boundary and the fluid phase:
HEATTRANSFER IN FLUIDIZED BEDS
185
This system of equations was solved numerically for a 200-p particle with residence times up to 70 msec. The average rate of heat transfer to a single particle during a given residence time was calculated by integration of the instantaneous rate. The overall heat transfer rates for a given particle residence time was estimated from the average rates, taking into account the number of particles in contact per unit area of the heat exchange surface and scaling it for unit temperature difference. Botterill et a2. [72-751, extended this sample single particle model to different particle sizes and materials. The overall heat transfer coefficient is given by the following expression: h, = (170dp/~)[1 - eXp( -4765/dp2)](~b/~sb)''3
(Btu/hr-ft'-"F)
(37) where r is the residence time expressed in milliseconds. They conducted experiments, where the residence time of the particles at the surface was varied by either stirring the bed or moving the heater at various speeds. Their results showed the validity of their model in their system for short residence times. They also observed that the heat transfer coefficient is a decreasing function of the residence time, the shorter the residence time the higher the heat transfer rate. Botterill et al. [75] also extended their model to the case of heat transfer into two adjacent particles touching the surface in order to clarify experimental results obtained at larger residence times. Couderc et al. [76) studied experimentally the heat transfer rates obtained when the stirrer velocity was kept constant but the flow rate of the air was increased. They observed that the heat transfer coefficient increased with the flow rate at low stirring speeds, but decreased at the high stirring speeds. They reasoned that at constant stirring speed, the residence time is shorter for high flow rates and, therefore, according to Botterill, the heat transfer rate should increase, but in reality they observed that it decreased in some cases. They introduced a new parameter [77], the average distance between the particle and the wall. Although the change in the average distance is small, due to the low thermal conductivity of the gas, the thermal resistance could be considerable. They developed a mathematical model similar to that of Botterill with the addition of the new parameter. The unsteady heat conduction equations were solved numerically and their results were compared with their experimental data. Gabor [78,79) presented two models for the unsteady state heat transfer from a wall to a fluidized bed. One model was based on a string of spheres of indefinite length normal to the heater wall. It seemed geometrically close to reality, but required a large number of computations. The second approxi-
186
CHAIM CUTFINGER AND NESIM ABUAF
FIG.8. Transfer of packet to a wall.
mate model was based on heat transfer through a series of alternating gas and solid slabs. Gabor [80] also compared experimental results measured as a function of residence times, and found them to agree with his calculations based on his approximate alternate slab model. This model can be applied to mechanically smooth, dense phase (particulate) fluidization, but it is obvious that it is far from representing a lean phase fluidization or a fluidized bed with strong agitation and bubbles. 3. Unsteady Transfer of Heat to “Packets” of Particles Which Are Renewed by ?’iolent Disturbances i n the Core of the Fluidized Bed
In an attempt to present a mechanism for the heat transfer in bubbling dense beds, >lickley and Fairbanks [Sl] introduced the picture of a small group of particlm moving as individual units (packets). Their reasoning was based upon previous experimental observations where the void fractions of dense phase bubbling beds were recorded and found to be close to the void fractions of quiescent beds. In a dense fluidized bed, each particle may be expected t o be in contact with several neighbors most of the time. The packets are not permanent, they have a finite persistence in time, their void fraction, density, heat conductivity, and heat capacity are assumed to be the same as those of the quiescent bed. Their model can be seen in Fig. 8. A packet at bed temperature Tt, comes into contact with a flat surface at a temperature T,. Unsteady heat transfer starts upon contact. If A , is the contact area between the packet and the wall, and the packet is homogeneous, the heat transferred after a time t is given by:
HEATTRANSFER IN FLUIDIZED BEDS
187
and the local instantaneous heat transfer coefficient by: Experimentally recorded local heat transfer coefficients will be the time averages of all the local instantaneous coefficientsoccurring during a period of time at a particular location of the surface. If $ ( t ) is the frequency of occurrence in time of packets having an age t, or over a period of time, the fraction of the total time during which the surface is in contact with packets of ages between t and t dt, then the local average coefficient is given by:
+
or
and averaging over an entire isothermal area
h , = A-1
I,
hwLdA
and
h,
=
(kmpmcmS)112 where Slf2= A+
I, Si" d A
(43)
Mickley and Fairbanks [Sl] apply these derivations to the following idealized bed models. a. Slug Flow of Solids Over the Surface. In a fluidized bed with very low gas flow rates, there is no turbulent mixing, and solids are observed to move upward at the center and downward along the outside walls of the bed (Fig. 9). Assuming that the solids move downward with a constant velocity us,the age of all the packets a t a distance 1 from the top is always t = l/u, The calculation for the average heat transfer coefficient for a heater of length LHas presented by Mickley and Fairbanks [Sl] gives:
b. Side Mixing. With large heat transfer surfaces and highly turbulent beds, the sidewise transfer of solids will also have an important effect. To represent this case (Fig. lo), they presented the model that as the solid is
188
CHAIM
GUTFINGER .4ND NESIM ABUAF
FIG.9. Slug flow of solids over a surface,
moving don.nnard some of it is exchanged with some other solid at Tb, brought in sideways from the core of the bed. The average replacement of packets at the wall per unit time by means of side mixing, was defined as s, resulting in: h
w
= ~ (krnprncrns)
(45)
Mickley et al. [82] measured instantaneous and time-averaged heat transfer coefficients in a fluidized bed. The instantaneous values fluctuated sharply, low values being attributed to gas bubbles and high values to the
FIG.10. Downflow with side mixing.
HEATTRANSFER IN FLUIDIZED BEDS
189
sudden appearance of a fresh packet of emulsion. With their data they were able to find the time fraction that the surface was exposed to bubbles and the average bubble frequency near the wall. They also found that the fluctuations in the local heat transfer coefficient can be directly related to the movement of the solids in the vicinity of the surface. One essential deficiency of the model is that the instantaneous heat transfer coefficientis inversely proportional to the square root of the age of the element. If t = 0, the rate is 00 and at infinite age, the heat transfer rate is 0. Baskakov [SS] proposed a similar model with an added contact resistance to the heat transfer, located at the wall, facing the surfaces of the particles in contact with the wall. Thus, the heat transfer coefficient for very small values of age does not become infinite, but is determined by the finite contact resistance at the wall. The contact resistance to be added is given by: 1 h,
--‘v
dP dc,[In(k,/dkt) -
(46)
11
where d is the depth a t which a temperature gradient exists, and he recommends d = 0.1 to be used in Eq. (46). Baskakov’s model [83] still does not solve the problem that for infinitely large values of age, the heat transfer coefficient tends to zero. In all these penetration-type models the residence time of the particle is of fundamental importance. Mickley et al. [Sl, 821 found it by measuring the temperature fluctuations in the heater. Ruckenstein [84] used an instability theory to predict the renewal frequency. Pate1 [85,86], measured heat transfer coefficients and particle residence times at identical wall locations under the same conditions. He also presented two surface renewal models which are essentially extensions of the Toor and Marchello [87] model to describe the heat transfer between the wall and the fluidiaed bed. Model I (Fig. 11). A packet initially at the bed temperature Tb arrives at the wall T, at time t = 0. The packet is assumed to have the same properties as the bed at minimum fluidization. The packet receives heat from the wall through a contact resistance and returns to the bed after a length of time. During the residence time, heat penetrates a distance 2; beyond this distance the temperature is constant and equal to the bed temperature Tb. For an exponential age-density distribution function,
$ ( t ) = 7-l exp(-O/?),
e > 0;
$ ( t ) = 0,
otherwise
(47)
where 0 = a,t/z2 is a dimensionless time and 7 = mean dimensionless residence time of packets at the surface.
190
CHAIM
GUTFINGER AND
XESIM A B U A F
PACKET
T ( x,t) CONTACT
(INITIAL TEMPERATURE Tb
FIG.11. MODELI (Pate1 [%I).
The average heat t,ransfer coefficient is given by:
with asymptotic values for zero and infinite time respectively,
The value of the contact resistance l / h c was taken from Baskakov [SS], Eq. (46).
X o d e l I1 (Fig. 12). The fluidized particles are assumed to be spherical, each possessing the same diameter d,. A particle at the bed temperature TI, arrives at the heating surface T,. I t receives heat from the fluid adjacent to the wall, nhich is assumed to be stagnant and at wall temperature T,. While the particle is a t the surface it also loses heat by conduction to a packet of particles of thickness z situated between the wall particle and the bulk of the bed. The packet was assumed to have the same properties as the bed at minimum fluidization conditions. For an exponential age distribution [Eq. (47)], an average Nusselt number was calculated :
HEATTRANSFER IN FLUIDIZED BEDS
191
I WALL (Tw)
I
I W A U PARTICLE
----
Ttt)
1
INITIAL TEMPERATUR
Tb I
FIG.12. MODELI1 (Patel [85]).
where and
3Pm y=---
x
2 P a d,
and the asymptotic values for zero and infinite time, respectively, are:
kr x Nu(0) = 2 1 - - ~ k m dp
(53)
c = 1 for square packing and c = ($)1’2 for hexagonal packing. Experimental results were compared with the theoretical predictions. The penetration-type model of Toor and Marchello [S7] presented no contact resistance but had a finite characteristic length. The model of Mickley and Fairbanks [Sl] had no contact resistance and assumed the characteristic length to be infinite. Baskakov [ S S ] added the contact resistance, but still its characteristic length was infinite. Patel [SS] included a contact resistance and a finite characteristic length. Agrawal and Ziegler [88] used a similar surface renewal model with a generalized gamma distribution to represent the expected residence times of the particles. Chung et al. [S9] also presented an expression for estimating the heat transfer coefficient in a fluidized bed by using the same concepts.
192
CHAIMGUTFINGER AND NESIM ABUAF
I FLUCTUATION OF
I
I I
I
I Srmyllffi FORCE
I I I
I TIME
FIG.13. Experimental data of Drinkenburg et al. [go].
Employing the concept of a multiple capacitance contact time distribution, they found:
where b = d,/ ( 2a,r)'12and r is the mean residence t,ime. The prtdicted values of the heat transfer rate were compared to the model of Botterill el al. [69] and Dow and Jakob's [67] experimental results. Their model also yielded a maximum value for the Nusselt number for any gas-fluidized system Numax= 13.5
(56)
A long list of references was presented to show that no experimental value above their maximum was yet recorded. To finish this section, the authors a.ould like to present some experimental results obtained b y Drinkenburg el al. [go]. They measured instantaneous temperatures, static pressures, and shear stresses. The experimental results showed that all these properties varied as periodic functions of time. The period could be measured from the recorded fluctuations. From these facts they proposed that the heat transfer is an unsteady phenomenon, and is dependent on the overall bed circulation showing a stick-and-slip flow character, Fig. 13.
HEATTRANSFER IN FLUIDIZED BEDS
193
b;”1 I
I
-t-LATERAL PARTICLE EXCHMGE
FIG.14. Model of Wicke and Fetting [92j.
4. Steady Conduction through the Emulsion Layer Van Heerden et al. [91] observed that the heat capacity of the solid particles per unit volume is about a thousand times greater than that of the gas. The mean particle velocity is much lower than the gas velocity. Therefore, the largest portion of heat will be transferred by the moving particles. They assumed that the interstitial gas between the particles almost immediately follows the temperature of the particles, and the gas only provides the suspension of the particles. They observed that there was almost no radial motion of the particles as they moved downward along the wall. They concluded that the radial heat transfer would be determined by the thermal conductivity of the suspension. They indicated that the heat transfer coefficient would be large for short heat exchange surfaces and smaller for longer sections, and this was verified experimentally. Wicke and Fetting [92] presented a similar model, Fig. 14. Heat (pw) from an exchange surface was first transferred by conduction through a gas layer whose thickness was 6 ~ This . heat was then divided into two components:
194
CHAIM
~
WALL (Tld
\
GUTFINGER tlND
I
XESIM
0 ' 0 0;
ABUAF
FLUIDIZED CORE (Tb)
FIG.15. General description of Kunii and Leverispiel [2]. yz, heat taken by solids flowing parallel to the surfacc in a second zone of emulsion of thickness 6,; and yr, heat transferred into the core portion of the bed by interchange of solids.
Xeglecting y,, their model led to:
2 h w L ~ / K= 1 - CXP( -2LHkr/6&,)
(57)
a-here K = p s ( 1 - emf)c,u,6,. ( u sis the average particle velocity along the heat transfer wall.) In the heat transfer from surfaces to fluidized beds, Gorelik [93] considered the thermal resistance to occur in two layers, along the wall and at the boundary layer. The first layer closer to the wall had a high porosity and the second layer near to the core had the bulk porosity which was assumed to be constant. His numerical results were in agreement with his experimental data. 5 . Geiwral Description of Runii and Levenspiel
The complex picture of the flow field near a heat exchange surface in a fluidized bed can be visualized as prcsented by Iiunii and Levenspicl [ a ] , Fig. 15. In reality four mechanisms operate together: (1
A film of gas 6~ coats the surface. Its thickness 6~ is large or small
HEATTRANSFER IN FLUIDIZED BEDS
195
depending on whether a bubble of air is near the surface or the emulsion is uniform and close to the surface. (2) Some solid particles are in direct contact with the heat exchange surface, (3) There is a layer of emulsion with thickness 6, which flows along the wall. (4) Part of the emulsion layer is replaced occasionally by fresh emulsion coming from the core of the bed or by bubbles rising along the wall. Depending upon the fluidization conditions and the position of the heat exchange surface in the bed, emphasis may be placed upon one or another of these conditions.
C. COMPARISON BETWEEN
THE
PROPOSED MECHANISMS
The heat transfer coefficient between a fluidized bed and a surface is determined by the resistance of the gas-solid emulsion which is near the wall. The total resistance RT can be divided into a film resistance Rfilmand a resistance of either the emulsion or the bed which can involve packets or bubbles R b e d : R t o t a i = R t i l m Rbed. Patel [85, 861, followed a similar approach in his proposed mechanism as presented in the previous section. The film resistance Rfilmnear the heat transfer surface is determined by the steady conduction through a gas film whose thickness is altered by the presence of particles, mechanism ( l ) , and by the unsteady conduction through the solid particles in direct contact with the heat exchange surface, mechanism (2). The contribution of each one will depend on its value as compared to the other one. For dense phase fluidized beds with small particles, the heat transferred by conduction through the particles is quite important. For large particles and high gas velocities the heat transfer can be determined by the gas film near the wall. Now let us compare the heat transferred by thermal conduction through the film Rfilmand the heat picked up by the packets or the emulsion layer with an average residence time ? and sitting near the heat transfer surface
+
Rbed.
If the contact time of the emulsion elements with the surface is very short due to fast circulation, then the film resistance is the controlling mechanism. This short mean contact time is given by Kunii and Levenspiel [2] as:
CHAIMGUTFINGER AND NESIM ABUAF
196
The resistance of the bed R b e d or emulsion packet sitting between the contact film resistance and the bed is mainly determined by the hydrodynamics of the fluidized bed. We can observe two extreme bchaviors of the emulsion layer near the heat exchange surface. The packet of emulsion may contact thc surface for a very short time, all the heat transferred from the wall to the emulsion goes into the heating of the packet, mechanism (3), or the packet can remain a t the surface long enough so that steady state is achieved and the emulsion layer near the wall acts as a resistance to the heat conducted away from the wall. Yoshida et aE. C94) considered a thin layer of emulsion with thickness 6, which suddenly comes in contact with a heat exchange surface. After a time 1 , thr emulsion is replaced by a fresh element from the main body of the bed. The instantaneous heat transfer coefficient is derived as :
h,, =
(kmPmCpJrt)l/2
[
1
w
+ 2 C exp(-mz62/a!t) mil
]
(59)
for short times, and h, = 1
(km/ae)
{ + 2 2 cxp[m2r2(at/6ez) I} 1
(60)
m=l
for long times, where a! = lim/pmcm To calculate the average heat transfer coefficient, they used two surface renewal models.
1. Random Surface Renewal Model
The residence time distribution was given by : $ ( t ) = +p/i
(61)
where T is the mean age of the emulsion elements leaving the surface. This model is representative of the residence time distribution near a heat exchanger in the main core of the bed, which is continuously contacted by rising bubbles. For rapid replacement of the emulsion: 2 = (a?)”*/6e
<1
and
h,
= (kmpm~,/~)l/L
h,
= iLm/Se
For slow replacement of the emulsion: 2
>1
= (a~)”2/6~
These results are shown in Fig. 16.
and
HEATTRANSFER IN FLUIDIZED BEDS
1
3.0[
197
RAPID RENEWAL
SLOW RENEWAL, OF EMULSION MECHANISMl3lAND ( 4 ) TOGETHER
MECHANISM (31 UNSTEADY CONDUCTION THROUGH EMULSW
STEPDl CONDUCTION T W W G H EMULSION
0‘
I
1.0
,
I
4.0
2.0 3.0 2 =(amT)”v6s
FIG.16. Steady and unsteady conduction through emulsion.
2. Uniform Surface Renewal Model The residence time distribution was given by: #(t) = P ) 0
< t < 7.;
# ( t ) = 0,
t
> .T
(62)
All elements stay the sa.me length of time on the surface. This distribution is representative of an emulsion flowing smoothly along a heat exchange surface. With this model Yoshida et al. [94] also derived similar expressions for the heat transfer coefficient: h,
=
( 2 / d ~(kmpmcm/t)1‘*, )
for short contact times
hw
=
km/&,
for long contact times
They also extended these results to a surface immersed in a bubbling bed. They presented expressions for the heat transfer coefficient for the case when the bubble frequency at the surface and the time fraction that the surface is exposed to bubbles are specified.
D. EXPERIMENTAL RESULTS
In this section we will present the influence of the various factors on the heat transfer coefficients as determined from experimental observations. Tables 1-111 present a list of nondimensional correlations reported by different investigators while trying to correlate their experimental findings.
198
cH.4IM
GUTFINGER AND NESIM ABUAF
1. Properties of the Fluid a. Density p r and SpecQic Heat cPf of the Fluid. The dependence of the heat transfer coefficient on the specific heat of the gas is not yet clearly determined. The existing data do not present a common trend. The product pIc, being three orders of magnitude smaller than pat%, one would expect the heat transfer coefficient t o be independent of prep,. The very commonly used ratio of psc,/p~cp,does not have a physical foundation. Gelperin and Einstein [41] and Baskakov [95] have predicted an increase in the heat transfer rate with an increase in the specific heat of the gas or the product of the two properties prcpf, a t high pressures and gas velocities.
b. Gas I'iscosity. Most of the authors agree on the result that the wall heat transfer coefficient decreases with an increase in the gas viscosity. c. Thermal Conductivity of the Gas (kf). The thermal conductivity of the gas is the property which has the greatest influence on the heat transfer coefficient. As reported by Leva [S] in a fixed bed the heat transfer coefficient increases with tho gas thermal conductivity h, a The relation presented by Wen and Leva [96] correlated h, a kf6'. Jacob and Osberg [9T] studied the effect of this parameter on the heat transfer coefficient and their experimental data was correlated b y : hw = hwo(l
- e)[1
- exp(-pkr)l
where h,o and p are empirical constants (values given in Jacob and Osberg ~971). TABLE I
NONDISIENSIONAL CORRELATIONS FOR EXTERNAL WALLP Correlation
Investigator
Remarks
kr h, = 0.64 -Gv
Leva and Grummer [65]
q, fluidization efficiency
c
Leva [a]
Wen and Leva [96]
*
Gelperin and Einstein [41].
kr
e$J =0.16(
i,
1.bp.b
)
0.'
R, bed expansion ratio
HEATTRANSFER IN FLUIDIZED BEDS
199
TABLE I-(continued) NONDIMENSIONAL CORRELATIONS FOR EXTERNAL WALLS“ Investigator Levenspiel and Walton C68 1
Correlation
kr
D, =
r
kr
-hwDc
Remarks
d,G
d,
-lm
- 0.0018(y)(ij)
XdP ~
6(1
= [(I
- c)
+ a*)a/* -
a = 0.041(1
G.
Toomey and Johnstone log El121
Van Heerden et al. [91]
hwD = 0.55 -
ki
(“tp) =
D
0.575 1 o g c F )
+ 0.130
hg =p 0.58 ( B kr
G/c
(): (z) 0.65
Dow and Jakob [67]
=
- c)
0.11
up, particle velocity (ft/sec)
yy.4s
B, shape factor
(continued)
CHAIMGUTFINGER AND NESIM ABUAF
200
TABLE I - - ( ~ ~ t i % ~ e d ) ON DIMENSIONAL
CORRELATIONS FOR
Investigator
Correlation 1.560
-h mc,G
Bartholomew and Katz ~1481
h,
MickIey and Trilling
0.0118-
pm, solid
concentration in fluidized mixture
(y) DIG1
_ h, _--0 . 7 2 CPtG’
.(1 -
hw
-.prt/a
= 2.0
-0.87
G’, mass velocity based on void area D’, effective diam. of free area across bed
$1
Re”.”(l -
,)a
8
CPfG
(-0.44
Huntsinger [152]
2 s
d,”
Brazelton [149]
Das and Sarkar [l51]
+ ln(Re Ga4j3 p,GO
=
Remarks
- 0.0120) -0.227 Prtls Ga0.U
-
Clool
Gamson [150]
EXTERNAL w.4LLW
2)
Ir
_ kt
Nu
=
1.4(Re)@=(Pr)-I
Nu
=
0.055 Re
Kao and Kaparthi Cll.51 Lemlich and Caldas [153] Richardson and hlitson C99 1
h,D - = 119 Pro 4 ( 5 3 ) ( 3 kr
.Rep
(~)o’a””
Ref based on free-fall velocity
N
=
0.020
- (3.45 + :-;)
HEAT TRANSFER IN FLUIDIZED BEDS
201
TABLE I1 NONDIMENSIONAL CORRELATIONS FOR IMMERSED BODIES~ Investigator
Correlation
Remarh
a, const. depends on
orientation of tube Horizontal tubes
Horizontal tubes
Vertical tube
Miller and Logwinuk c98 I
h,,.,
Baerg et al. [lo41
= 49 log
.-0.00037
P8b
dP
nonfluidized bed density
Psb,
h w d p = 0.033(1
Wender and Cooper C1181
-
$(x)
-
Reo.w*cR S t Pr2la= 2.52 Re*,*(l
Gamson [150] Gelperin et al. [154]
Nu
6(1
Gelperin and Einstein [41].
- e)
=
0.73 Reo.**
correction tor location
pfCpf
CR,
- e)-O'
Vertical tube
kt
Horizontal tube
202
CH.4IM
GUTFINGER AND
T\TESIM
ABUAF
TABLE 111 ~0XDIMEXSION.iLCORRELATIONS FOR
THE h h X I M U M
HEATTRANSFER COEFFICIENTSa
-~
Correlation
Investigator Varygin and Martyushin [I561 Baerg el al. [lo41
Zabrodsky
Nu,
hwmar
=
=
0 . 8 6 Gao
ReoDt= 0,118Gap 5.
239.5 log (7.05 X
lO-'p,b)
nonfluidized bed density
Psb,
d,
[a]
Gelperin et 01. [l55]
Remarks
Nu,
=
DH,heater tube diam-
0.64 GaO-"
z,
eter distance between axes of tubes
Sarkits [l57]
Numar= 0.0087 G a o 4 PI0 33 ($45
ReoDt= 0 . 2 Gao 6 (laminar region)
Sarkits [I571
Numnr= 0.019 Gao.8 PrO W
Reopt = 0.66 (turbulent region)
Traber el al. [158)
Numar= 0.021 Gao'PI0"
Reopt = 0.55 GaO
Jacob and Osberg [97]
Itwmax =
ho(l
-Re:
Chechetkin Cl.591
Numax=
Ruckenstein [1601
Numsr = Re$:
a
- t)[1
0.0017 dp0.a
- exp( --pkf)] ho, p, emp. constants
PrO 4
GaO.14 Pr1/3
Reopt = 0.209 Ga0.52 Re,,,
=
0.09 Ga03
Gelperin and Einstein [41].
Additional data of Van Heerden et al. [91], Wicke and Fetting [92], and Jacob and Osberg [97] were correlated by Leva [S J for the heat transfer rates, and h , was found to be proportional to k, to the power 0.60-0.64. Miller and Logwinuk [98) and Richardson and Nitson [99] also agree that h , increases with k r t o the power 0.5-0.66.
HEATTRANSFER IN FLUIDIZED BEDS
203
2. Properties of the Granular Solid Material a. Diameter (d,) and Shape of the Particles (+,-sphericity). Dow and Jakob [67], Wicke and Fetting [92], Jacob and Osberg [97], Mickley and Trilling [loo], Capes et al. [lol], Levenspiel and Walton [SS], and Leva and Grummer [SS], all agree that the heat transfer coefficient decreases when particles with larger diameters are used. The results of Sarkits et al. [102, 1031, as reported by Gelperin and Einstein [41] show that for the laminar flow region the heat transfer coefficient varies inversely with particle diameter, and for the turbulent flow region it has a direct variation. Gelperin and Einstein [41] also present Variggin’s data, where the heat transfer coefficient first decreases rapidly with an increase in the particle diameter, then levels off, and slightly increases once again for very large particle diameters (4.8mm) . The sphericity of the particles & also affects the heat transfer coefficient. Baerg, Klassen, and Gishler [lo41 and Mersmann [lo51 both report higher values for rounder and smoother particles. b. Density of the Solid ( p s ) . Levenspiel and Walton [SS] and Ziegler and Brazelton [lOS] both observed experimentally that the wall heat transfer coefficient increases with the increasing density of the solid ps. Sarkits et al. [102,103, 1071, record that the dependence of the heat transfer coefficient on the solid density becomes weaker as the flow becomes more turbulent. However, in both laminar and turbulent flows h, increases with the density of the solid. c. SpeciJic Heat of the Solid (cps). Dow and Jakob [67], Ziegler and Brazelton [lOS], Sarkits et al. [102, 103, 1071, and several other investigators all agree on the fact that the heat transfer coefficient increases with an increase in the specific heat of the solid, cw.
d. Thermal Conductivity of the Solid (lc,). Campbell and Rumford [lOS], Ziegler et al. [lOS, 1091, Miller and Logwinuk [98], Wicke and Fetting [92], Reed and Fenske [llo], and Bannister [ill], either measured experimentally the heat transfer rates over a wide range of solid thermal conductivities, or reviewed existing results. All found that the effect of the thermal conductivity of the solid k, on the heat transfer coefficient is modest, and thus concluded that h, is independent of k,. Chung et al. [89] developed an expression for the heat transfer coefficient and showed that the latter was independent of the solid thermal conductivity when d,(2a,i)-1’2 was less than 1 (a,is the thermal diffusivityof the solid particle, and 7 is the mean residence time), which is the case for all usual fluidized bed laboratory experiments.
204
CHAIMGUTFINGER AND NESIMABUAF
-
I
f
I
I
I
, I I
Gmf
I
I Gopt
FIG.17. Typical heat. transfer coefficient versus mass velocity.
3. Conditions at Minimum Fluidization (u,f, e m f ) Toomey and Johnstone [112] used a cylindrical fluidization chamber and a centrally located cylindrical heater. Their data was correlated by:
hwdp/k,
3.75[(dp~rn[pf/~)log(G/umt) 7.47
(63) whcrc the gas velocity at minimum fluidization was introduced. This exprmsion should only be used at high gas velocities, because a t minimum fluidization it predicts a zero value for the heat transfer coefficient, a result far from reality. =
4. Fluidization Conditions a. SuperJiciaZ Velocity or Gas M a s s Velocity ( G = p f u o ) . As swn in Fig. 17, where the heat transfer coefficient is plotted versus the gas mass velocity G, the dependencr is not a simple one. If one tries to correlate h , a Gn, the valuf>of the exponent n will depend on the range of the experiments. For this reason n-c have a large number of results with different exponents Dow and Jakob’s data [6T] show that h,,. a: GO.8, van Heerden et al. [91] obtain h , a Go 45, Micklcy and Trilling [loo] correlate as hw a and Bhat and Weingaertner [113] observe th a t h , a One point upon which all researchers agree is the shape of the rising and falling branches of the h,v vs G curve and the fact that there exists a maximum value of the heat transfer coefficient a t a specific superficial gas velocity uo or gas mass velocity, G = pruo.Tables listing the nondiinensional correlations for both the rising and falling sides of the curve, for the maximum heat transfer coefficients, and for the special gas flow rates when the h,,, is attained are presented by Einstein and Gelperin [114]. Gelperin and Einstein [41] show from Variggin’s results that the h, vs G curve is steeper for small particles and flatter for larger particles.
b. Bed Porosity
(E).
It is a commonly observed and accepted fact,
HEAT TRANSFER IN FLUIDIZED BEDS
205
Couderc et al. [76, 771, Rao and Kaparthi [115], etc., that the heat transfer coefficient varies inversely with some function of the bed porosity E. This effect was explained by the film theory: That, as the population of the particles near the wall is decreased, the heat transfer rate mill also decrease. But an increase in the porosity is obtained by an increase in the gas flow rate which under some conditions may have an opposite effect on the heat transfer coefficient.
5. Geometric Variables a. Bed Diameter ( D ) . The experimental results and the different nondimensional correlations do not show a clear and predictable variation of the heat transfer coefficient with the bed diameter. b. Diameter of the Immersed Heater ( D H ) . Jacob and Osberg [97] and several Russian investigators mentioned by Gelperin and Einstein [41], all agree that the wall heat transfer coefficient increases with a decrease in the immersed heater diameter DH, and that the heat transfer rate diminishes as the diameter of the heater is increased; it becomes independent when DH > 10 mm [41]. c. Fluidized Bed Height (L) or Static Bed Height (Lo). Van Heerden et al. [91], Leva [S], Gelperin et al. [ll6], and Xlickley et al. [82] showed that there is no dependence between the heat transfer coefficient and the fluidized bed height or the height at the fixed or static state. This independence is not true if one records its data at a section very close to the air entrance grid, where an active section exists and some entrance effects can be expected. Bibolaru [117] studied experimentally the dependence of the heat transfer coefficient with the height of the fluidized bed and found that at constant air velocity, the heat transfer rate decreases with an increase of the bed height. d. Length of the Heat Exchange Surface (LH). The investigations carried out by Toomey and Johnstone [112], Dow and Jakob [67], and Van Heerden et al. [91] showed that the heat transfer coefficient decreases with an increase in the length of the heat exchange surface LH. Wicke and Fetting [92] presented their results as:
hw
=
(Lmf/L)(K/2LH) { 1 - exp[-2kfL~/(kK)]}
(64)
where K = p , ( l - ~ m r ) ~ p r ~ Mickley s6e. et al. [SZ] used a vertical coaxial cylindrical heater and observed that the heated length had a relatively small effect on the heat transfer coefficient. In correlating different existing data Wender and Cooper [llS] concluded that for a fluidized bed with an external heat transfer surface, the
206
CHAIMGUTFINGER AND NESIMABUAF
condition LH/D > 7, was a good one in order to assume that the heat transfer coefficient is independent of the heater’s length. For internal heat exchange surfaces no effects were observed [llS]. Gelperin et al. [llS] review the work of Wicke and Fetting [92], Zabrodsky [119], Van Heerden et al. [91], Dow and Jakob [67], Baerg et al. [104], concerning the effect of the heat exchange surface height on the heat transfer coefficient. Their experimental investigations showed that if the heat transfer surface is located above the active section of the bed L,, then the heat transfer coefficient is independent of the heater’s height. Immediately near the gas distributing grid, the heat transfer coefficient is higher than the rest of the bed. If the heat exchange surface is located within the stabilization zone of the bed, then the local heat transfer coefficient will decrease from its value a t the bottom, to its constant value of the core of the bed, at a distance of 30-80 mm from the grid.
6. Other Factors a. Entrance Efects. Entrance effects as mentioned by Leva [S], Gelperin et al. [ll6], Nickley et al. [82], are common in almost all flow phenomena, and are caused by the sudden modification of the flow pattern. One cannot prevent entrance effects from affecting data. The active section in the fluidized bed is very important and one should take into account its existence when planning experiments. b. Temperature and Pressure of the Fluidized Bed. Levenspiel and Walton [SS] found that the heat transfer coefficient is independent of the temperature of the fluidized bed. Rabinovich and Sechenov [120] found that h , showed an increase with the bed temperature and pressure. A t high temperatures one should remember to take into account the effects of radiation on heat transfer. c. Properties of the Fluidized Bed at Minimum Fluidization (pm, km). Miller and Logwinuk [98] and Nickley et al. [Sl, 821 observed that the heat transfer coefficient increases with the square root of the density or the thermal conductivity of the fixed bed as predicted by the “packet” theory for heat transfer. E. IMMERSED BODIES In the experimental work reported, investigators used external and internal heat transfer surfaces. By external, we mean that the wall of the fluidized bed container itself was used as the heat exchange surface. By internal we mean that bodies with different shapes immersed in the bulk of the fluidized beds were used as the heat exchange surfaces. In order to be able to make a proper comparison between the two, one has to find experiments performed simultaneously a t identical experimental conditions.
HEATTRANSFER IN FLUIDIZED BEDS
207
Toomey and Johnstone El121 reported for the same equipment and similar conditions, heat transfer coefficients for an external wall and an immersed heater. At low gas flow rates, the coefficients for the internal heater were higher than the exterior wall coefficients. As the gas flow rate was increased this ratio approached unity. Raju et al. [121] also made experimental studies and reported that the heat transfer coefficient for an internal surface is higher than that for an external wall. These results cannot be generalized. The important point to keep in mind is that the fluidized bed can exhibit a nonhomogeneous character with regard to the hydrodynamics and heat transfer data. Sometimes with welldeveloped fluidization it may even happen that h,,, > h,,,,. While working with immersed bodies, one has to consider that the heat transfer coefficient may vary with location, first with respect to the air-distributing grid and second at a given plane, if the heater is at the center or not. The results from these variations are sometimes contradictory and one should keep in mind that they depend strongly on the local hydrodynamic conditions in each case. These facts were emphasized by Fritz [122], who investigated the heat transfer between internal surfaces and fluidized beds of various geometrical forms. He found the heat transfer coefficients are affected by the nature and position of the heating surface, the form of the bed, and the flow of the gas. 1. Spheres
Baskakov et al. [123] derived by solving the Laplace equation with the proper boundary conditions, an expression for calculating the local heat transfer coefficient at the outer surface of a hollow spherical heater, from the known temperature distribution on the surface. The latter was determined experimentally,
where 8 is the angle measured from the upstream pole, TI and R1 are the temperature and radius of internal surface, Tz(8) and R2 are the temperature and radius of the outer surface, and Tz,, is the mean integral temperature of the outer surface. Their results show that h, reaches a maximum at the equatorial zones of the sphere (60"-loo"), h, is higher at the pole facing the flow direction than at the pole situated downstream. As the gas flow rate is increased, the maximum h, shifts to smaller values of 8, and tends to equalize over the surface. Use of larger particles tends to equalize the h, over the surface. The distribution of h , is more pronounced for the immersed heater with the larger diameter.
208
CHAIM GUTFINGER AND NESIM
ABUAF
Galloway and Sage [124) and Ziegler and Brazelton [lo61 also used spherical probes and made heat transfer measurements. Ilchenko and Sfakhorin [125] also studied experimentally the heat transfer from a spherical probe. The wall heat transfer Coefficient increased linearly when the fluidized bed temperature was raised from 300" to 650°C, above that, the dependence was nonlinear. This effect was attributed by the authors to radiative effects. 2. Flat Plates
Iiorolev and Syromyatnikov [1261 studied experimentally the hydrodynamics of a fluidized bed in the vicinity of a plate submerged into it. The local porosity xvas measured by an x-ray apparatus, and the velocity of the gas phase was determined by a pitot tube. Their results showed that the iocal porosity a t the plate is higher than thc average value in the bed, and the gas velocity near the surface is higher than within the bed. They performed exprriments where a plate was cooled in a fluidized bed with and without a metal mesh surrounding it. Higher heat transfer rates were obtained when the plate was without the net. Raskakov and Fillipovskiy [127] built a flat plate calorimeter consisting of different heating elements. Thcy determined thc relationship between the average rate of heat trarisfcr and thv size and orientation of the plate and also thc variation of the local heat transfer coefficient along the plate for different parameters. They observed that the maximum heat transfer rates were obtained when the plate was in the vertical position, h , decreased when they used larger plates. When the plate thickness was increased, the rate of hcat transferrcd was affwtcd by the shape of the bottom. The local heat transfcr coefficients decreased from the bottom of the plate upward. Fillipovskiy and Baskaliov [1281 published a second experimental investigation where temperature distributions were measured near the heated plate. When the heated surface was turned upmud, a. layer was formed on the plate and the heat transfer coefficient decreased. 3. Small Cylinders
Kirk and Hudson [129] used two small immersed cylinders for both heat and mass transfer studies in fluidized beds. They observed that the Reynolds analogy between hcat and mass transfer does not apply for transfer processes in fluidized beds. The extra increase of the heat transfer coefficient as compared to the mass transfer was attributed to the role of the particles themselves in the transfer phenomena. This led them to conclude that a model like that of Botterill was more realistic.
HEATTRANSFER IN FLUIDIZED BEDS
209
4. Immersed Tubes
a. Vertical Tubes. Vreedenberg [130, 1311, placed a tube in various positions in a fluidized bed and determined the heat transfer coefficients. His experimental data were correlated by: h, dp/kr = a(Gv/Gmfvmt)0'35 (66) where v is the kinematic gas viscosity and a is a constant depending on location and orientation of the tube. Miller and Logwinuk [98] determined the heat transfer coefficient between two concentric vertical cylinders. Their data were correlated by:
Baerg et al. [lo41 also reported heat transfer data for an immersed vertical tube. Their results are 25% higher than the heat transfer coefficients for an external wall. Their data were correlated by: h,
=
- 55 exp[-O.O12(G - 0.71psb)l
h,
(68)
where hw,,,
= 49 10g(O.O0037p,~/d,)
and Psb is the nonfluidized bed density. Wender and Cooper [ll8] correlated experimental data of several investigators by using an internal vertical tube as the heat exchange surface and came up with the following expression :
where CR is a correction factor for nonaxial tube location [llS]. Berg, Baskakov, and Sereeterin [132, 1331, found that the heat transfer coefficient changed along the height of the vertical cylindrical heater. Genetti et al. [134] studied the heat transfer from internal bare and finned vertical tubes. b. Horizontal Tubes. Yreedenberg's [135] data for horizontal tubes covering a large range of particle diameters and solid density were correlated by:
(
hw -dp - 0.66 GDps(l kr PfLt-c and
">"""
Pr0.3
for
r?) k)
< 2050
(70)
210
CHAIM
GUTFINGER AND
NESIM
ABUAF
For the values in between, he suggested to use the arithmetic average of the tn-o values. Gelperin and Einstein [41] presented measurements of t>helocal heat transfer coefficients around the perimeter of horizontal tubes. The heat transfer rate is largest a t the equatorial lateral zones and smallest a t the upstream and downstream poles. This nonhomogeneity was related to the motion of the particles near the surface. Bartell el al. [136] once again compared heat transfer data between bare and finnrd horizontal tubes. c.
Tube Bundles.
i. Bundles of vertical tubes. Gelperin and Einstein [41] summarize the results obtained with bundles of vertical tubes. The value of the heat transfer coefficirnt increases for tubes located at the center line, slight deviations are obtained for the peripheral tubes. As the number of the tubes in thp bundle is increased the gas flow is more uniform and the heat transfer rate tends to be equal for each tube. The bed height and the distance to the gas inlet grid have little effect. When the ratio of the distance between tvio adjacrnt center lines and of the tube diameter is smaller than 2, the heat transfer coefficient is observed to decrease. Thry report the following correlation [41] for vertical bundles: h, d,/kr
=
0.75 Ga0.**[1 - (&/Z)]0'14,
Z / D T= 1.25-5.0
(72)
\there DT is the tube diameter and z is the horizontal distance between two adjacent center lines. ii. Bundles of horizonla1 tubes. Lese and Iiermode [137] studied the heat transfer from a horizontal tube in the presence of other unheated tubes. They also studied the effect of the number, size, and configuration of the other tubes on the heat transfer coefficients. The heat transfer from bundles of horizontal tubes placed in line and in staggered arrangement was investigated by Dahlhoff and Von Brachel [138] and also b y Gelperin et al. [139]. Correlations are presented by Gelperin and Einstein [41] as: In line tube arrangement,
Z / D T= 2-9,
h, d,/kr
=
0.79 GaO.**[l- (DT/Z)]0'25
(73)
in staggered tube arrangement, (74)
HEATTRANSFER IN FLUIDIZED BEDS
21 1
F. FLUIDIZED BED COATING As an application of heat transfer between a fluidized bed and an immersed surface we will describe here the problem of fluidized bed coating. When a hot object is dipped in a bed of fluidized plastic powder, a film of fused plastic coating will be formed on its surface. The coating thickness depends on the object temperature, the fusion temperature of the powder, the immersion time in the bed, the physical properties of the object and the powder, as well as on the heat content of the object. If the object possesses a very large heat content, it can be considered as an infinite heat source, and its temperature could be taken as constant during the coating process. The case of constant-wall-temperature fluidized bed coating was analyzed by Gutfinger and Chen [140,141]. Recently their analysis was extended to the case of variable object temperature [142,143]. Experimental data on coating are reported in the literature by Pettigrew [144] and Richart [145], while some industrial applications are described by Landrock [146]. Consider a flat plate with an area A , and halfwidth w , which is dipped vertically in a fluidized bed. The object is initially at a temperature, TlVo, which is higher than the softening temperature of the coating material, T,. The plastic coating material in contact with the object surface will melt and begin to form a layer on the plate. The process now involves the transfer of heat from the plate to the continuously growing film, and then into the fluidized bed. Usually the object is metallic, possessing a high thermal conductivity and a finite heat capacity, and therefore its temperature will remain uniform but decrease with time, i.e., the body is treated as a lumped parameter system. Heat from the plate is transferred through the coating film whose properties, pc, c,, k,, are assumed to remain constant during the process. The surface temperature of the coating film is assumed to be constant and equal to the melting or softening temperature of the coating polymer T,. Although the rate of heat convected from the coating surface into the bed is obviously dependent on the fluidization conditions and the temperature gradient, in this analysis the heat transfer coefficient between the plate and the fluidized bed is assumed to be independent of location and direction, and is taken to be constant during the coating. The temperature within the fluidized bed Tb is assumed to be uniform and constant. With these assumptions, the one-dimensional heat conduction problem with a moving boundary, describing the coating process, is given by the following set of equations:
CHAIMGUTFINGER AND
212
NESIM ABU.4F
---___ -----_
--- Af I
0
1
1.0
2.0
1
3.0
4.0
2
FIG.18. Plot of final dimensionless coating thickness A( and final dimensionless wall temperature 8, I versus dimensionless parameter 2 for various dimensionless melting temperatures em.
The boundary and initial conditions are:
T(0,O) =
Two
T ( 0 ,t )
=
Tw(t)
T(6, t j
=
T,
+
[~scfi(
Trn - Tbj
+ A] 6
(80)
and 6(0)
=
0
(811
Equation (79) is the heat balance at the surface of the coating film. It equstcs the heat conduction to the surface with the heat convected into the fluidized bed, plus the heat absorbed b y the coating material which sticks to the plate and forms the film. Equation (80) expresses the fact that the heat loss by the body during the time interval (0, t ) is equal to the heat transferred to the fluidized bed, plus the heat consumed in bringing the coating film temperature from its initial value Tb to its final value T. Equations (75)-(81) were solved [142] by a heat-balance integral technique similar to one used by Goodman [147], for the special case of negligible latent heat, of fusion A. This case corresponds t o noncrystalline
HEATTRANSFER IN FLUIDIZED BEDS
213
polymers usually used in coating. Good agreement was obtained between theoretical predictions and experimental results. Figure 18 provides a plot of dimensionless final coating thickness and object temperature as a function of a coating parameter 2:
The final coating thickness 6f is the one at which the coating terminates. In dimensionless form it is defined as :
Dimensionless final object temperature is: Bwf =
(Twf -
/( TWO- Tb)
(84) Figure 18 is the illustration the practicing coating technologist will be most interested in, as it shows the highest coating thickness possible for a given set of coating parameters as well as the drop in wall temperature at the point where the final thickness is achieved. Tb)
NOMENCLATURE Specific surface, surface of solid per unit volume of bed Specific surface of solid, 6/dp Heat exchange area Contact area of packet and surface Area of immersed surface Biot modulus, h,d,/k. Specific heat of packet, specific heat of quiescent bed Specific heat of coating Specific heat of fluid Specific heat of solid Bubble diameter Diameter of sphere of same specific area as that of the particle Diameter of the fluidized bed Diameter of the immersed heater Distance between two successive layers Time fraction that surface is exposed to bubbles Acceleration of gravity Fluid mass velocity, udf Galileo number (also called Archimedes number), dp3m (ps--Pt) g/P2
Heat transfer coefficient for the contact resistance at the wall Heat transfer coefficient between fluid and particle Local or true heat transfer coefficient between particle and fluid Heat transfer coefficient between fluidized bed and surface Local average heat transfer coefficient Instantaneous local heat transfer coefficient Bubble-to-cloud heat transfer coefficient Tube diameter Thermal conductivity of coating Fluid thermal conductivity Thermal conductivity of packet., thermal conductivity of quiescent bed Thermal conductivity of the solid Length Bed height Active bed section Length of heat exchange surface
CHAIM GUTFINGERAND SESIM ABUAF Bed height a t minimum fluidization conditions Static fluidized bed height Bubble frequency a t the surface Particle Nusselt number, hdP/lzi Xusselt number, h d P / k r Pressure Pressure drop Peclet number, d,u,/mr Prandtl number, c,,p/kr Heat flow rate from the wall into the packet Instantaneous heat transfer rate Radius of sphere Reynolds number, dpu@pr/p Reynolds number at minimum fluidization, dou,cpf/p Average replacement of packets a t wall by side mixing Time Temperature Fluidized bed temperature Temperature of fluid Temperature of gas in bubble Initial bed temperature Melting or softening temperature Solid temperature Wall temperature Initial wall temperature Bubble velocity Superficial velocity of minimum fluidization Superficial velocity at fluidization conditions Solid velocity Halfwidth of plate Coordinate system Penetration distance Coordinate system Vertical distance between two adjacent tube center lines
z
2
Horizontal distance between two adjacent tube center lines Coating parameter, Eq. 82
GREEKSYMBOLS Thermal diffusivity of fluid Thermal diffusivity of solid Solids volume fraction inside bubble Coating thickness, volume fraction of bed occupied by bubbles Final coating thickness Thickness of gas layer Thickness of emulsion layer Average boundary layer thickness near the wall Dimensionless final coating thickness Void fraction at fluidization conditions Void fraction at minimum fluidization Angle ( T m - Tb)/(Two - Tb) Dimensionless wall temperature Heat, of fusion Fluid viscosity Fluid kinematic viscosity Bulk density at fluidization conditions Density of coating Fluid density Density of packet Bed density at minimum fluidiaation conditions Density of the solid Settled bed density Residence time Mean residence time Sphericity of solid particles Residence time distribution function
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HEATTRANSFER IN FLUIDIZED BEDS
215
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R. D. Patel, U.S. At. Energy Comm. ANL-7353 (1967). L. B. Koppel, R. D. Patel, and J. T. Holmes, AZChE J. 16,456 (1970). H. L. Toor and J. M. Marchello, AZChE J . 4, 97 (1958). S. Agrawal and E. N. Ziegler, Chem. Eng. Sci. 24, 1235 (1969). B. T. F. Chung, L. T. Fan, and C. L. Hwang, J. Heat Transfer 94, 105 (1972). A. A. H. Drinkenburg, N. J. J. Huige, and K. Rietema, Proc. Znt. Heat Transfer Conf., Srd, Chicugo 4, 271 (1966). 91. G. Van Heerden, A. P. P. Nobel, and D. W. ‘Van Krevelen, Znd. Eng. Chem. 45,
85. 86. 87. 88. 89. 90.
1237 (1953). E. Wicke and F. Fetting, Chem.-Zng.-Tech.26, 301 (1954). A. G. Gorelik, Znth.-Fiz. Zh. 13, 931 (1967). K. Yoshida, D. Kunii, and 0. Levenspiel, Znt. J. Heat Mass Transfer 12,529 (1969). A. P. Baskakov, “High Speed Non-Oxidative Heating and Heat Treatment In a Fluidized Bed.” Izd. Metallurgia, Moscow, 1968. 96. C. Y. Wen and M. Leva, AZChE J. 2,482 (1956). 97. A. Jacob and G. L. Osberg, Can. J. Chem. Eng. 35, 5 (1957). 98. C. 0. Miller and A. K. Logwinuk, Znd. Eng. Chem. 43, 1220 (1951). 99. J. F. Richardson and A. E. Mitson, Trans. Znst. Chem. Eng. 36,270 (1958). 100. H. S. Mickley and T. A. Trilling, Znd. Eng. Chem. 41, 1135 (1949). 101. C. E. Capes, J. P. Sutherland, and A. E. McIlhinney, Can. J. Chem. Eng. 46,473 (1968). 102. V. B. Sarkits, D. G. Traber, and I. P. Mukhlenov, Zh. Prikl. Khim. (Leningrad) 32, 2218 (1959). 103. V. B. Sarkits, D. G. Traber, and I. P. Mukhlenov, Zh. Prikl. Khim. (Leningrad) 33, 2197 (1960). 104. A. Baerg, J. Klassen, and P. E. Gishler, Can. J. Res. Sect. F 28,287 (1950). 105. A. Mersmann, Chem.-1ng.-Techn. 39, 349 (1967). 106. E. N. Ziegler and W. T. Brazelton, Znd. Eng. Chem., Fundam. 3,324 (1964). 107. I. P. Mukhlenov, D. G. Traber, V. B. Sarkits, and T. P. Bondarchuk, Zh. Prikl. Khim. (Leningrad) 32, 1291 (1959). 108. J. R. Campbell and F. Rumford, J. SOC.Chem. Znd., London 69,373 (1950). 109. E. N. Ziegler, L. P. Koppel, and W. T. Brazelton, Znd. Eng. Chem., Fundam. 3,304 (1964). 110. T. M. Reed and R. M. Fenske, Znd. Eng. Chem. 47, 275 (1955). 111. J. Bannister, Z n d . Chem. 36, 331 (1960). 112. R. D. Toomey and H. F. Johnstone, Chem. Eng. Prop., Symp. Ser. 49,51 (1953). 113. G. N. Bhat and E. Weingaertner, Brit. Chem. Eng. 10,615 (1965). 114. V. G. Einstein and N. I. Gelperin, Znt. Chem. Eng. 6, 67 (1966). 115. S. P. Rao and R. Kaparthi, Trans. Indian Znst. Chem. Eng. p. 43 (1969). 116. N. I. Gelperin, V. G. Einstein, and N. A. Romanova, Znt. Chem. Eng. 4,502 (1964). 117. V. Bibolaru, Bul. Stiint. Teh. Znst. Politeh. Timisoara 12,413 (1967). 118. L. Wenderand G. T. Cooper, AZChE J. 4, 15 (1958). 119. S. S. Zabrodsky, Tr. ENZN A N BSSR No. 8 (1959). 120. L. B. Rabinovich and G. P. Sechenov, Znzh.-Fiz. Zh. 22, 789 (1972). 121. K. S. Raju, G. J. V. J. Raju, and C. V. Rao, Indian J. Technol. 5 , 237 (1967). 122. W. Fritz, Chem.-Zng.-Tech.41,435 (1969). 123. A. P. Baskakov, B. V. Berg, B. Vandantseveeniy, T. S. Zunduggiyn, and L. G. Gelperin, Heat Transfer, Sou. Res. 4, 127 (1972). 124. T. R. Galloway and B. H. Sage, Chem. Eng. Sci. 25, 495 (1970). 125. A. I. Ilchenko and K. E. Makhorin, Khim. Prom. (Moscow) 43,443 (1967). 92. 93. 94. 95.
218
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V. N. Korolev and N. I. Syromyatnikov, Heat Transfer, Sou. Res. 3, 112 (1971). A. P. Baskakov and N. F. Fillipovskiy, Heal Transfer, Sou. Res. 3, 176 (1971). N. F. Fillipovskiy and A. P. Baskakov, Znzh.-Fit. Zh. 22, 234 (1972). L. A. Kirk and F. L. Hudson, Trans. Znst. Chem. Eng. 44, T7 (1966). H. A. Vreedenberg, J . Appl. Chem. 2, 26 (1952). H. A. Vreedenberg, Chem. Eng. Sci. 11, 274 (1960). B. V. Berg, A. P. Baskakov, and B. Sereeterin, Znzh.-Fiz. Zh. 21,985 (1971). B. V. Berg and A. P. Baskakov, Khim. Prom. (Moscow) 43,439 (1967). W. E. Genetti, R. A. Schmall, and E. S. Grimmett, AZChE Annu. Meet., 63rd, Chicago Paper 15h (1970). 135. H. A. Vreedenberg, Chem. Eng. Sci. 9, 52 (1958). 136. W. J. Bartell, W. E. Genetti, and E. S. Grimmett, AZChE Annu. Meet., GSrd, Chicago Paper 1.5 (1970). 137. H. K. Lese and R. I. Kermode, Can. J . Chem. Eng. 50,44 (1972). 135. B. Dahlhoff and H. Von Brachel, Chon.-Zng.-Tech. 40,372 (1968). 139. N. I. Gelperin, V. G. Einstein, and L. A. Korotyanskaya, Znt. Chem. Eng. 9, 137 (1969). 140. C. Gutfinger and W. H. Chen, Znt. J. Heat Mass Transfer 12, 1097 (1969). 141. C. Gutfinger and W. H. Chen, Chem. Eng. Progr. Symp. Ser. 101,91 (1970). 142. N. Abuaf and C. Gutfinger, Znt. J . Heat Mass Transfer 16,213 (1973). 143. M. Elmm, Znt. J. Heat Mass Transfer 13, 1625 (1970). 144. C. K. Pettigrew, Mod. P h t . 44, August, 150 (1966). 145. D. S. Richart, Plast. Des. Techno2. 2, July, 26 (1962). 146. A. H. Landrock, Chem. Eng. Prop. 63, No. 2, 67 (1967). 147. T. R. Goodman, Trans. ASME 80, 335 (1958). 148, R. N. Bartholomew and D. L. Katz, Chem. Eng. Progr., Symp. Ser. 48, 3 (1952). 149. W. T. Brazelton, Ph.D. Thesis, Northwestern University, Evanston, Illinois, 1951. 150. B. W. Gamson, Chem. Eng. Progr. 47, 19 (1951). 151. C. N. Das and S. Sarkar, Indian J. Technol. 5, 276 (1967). 152. R. C. Huntsinger, Proc. S. Dak. Acad. Sci. 46, 185 (1967). 153. R. Lemlich and J. Caldas, AZChE J . 4, 376 (1958). 154. N. I. Gelperin, V. Y. Kruglikov, and V. G. Einstein, Khim. Prom. Moscow 6 , 358 (1958). 185. N. I. Gelperin, V. G. Einstein, and N. A. Romanova, Khim. Prom. Moscow 11,823 (1963). 156. N. N. Varygin and I. G. Martyushin, Khim. Mashinoslr. MOSCOW, 5 , 6 (1959). 157. V. B. Sarkits, Dissertation, LTI im Lensoveta, 1959. 158. D. G. Traber, V. M. Pomarentsev, I. P. Mukhlenov, and V. B. Sarkits, Zh. PrikE. Khim. (Leningrad) 35, 2386 (1962). 159. A. V. Chechetkin, “Vysokotemperaturnye Teplonositeli” (High Temperature Carriers).” Gosenergoizdat, Moscow 1962. 160. E. Ruckenstein, Zh. Prikl. Khim. (Leningrad) 35, 71 (1962).
126. 127. 128. 129. 130. 131. 132. 133. 134.
Heat and Mass Transfer in Fire Research
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S L LEE Department of Mechanics. State University of New York at Stony Brook Stony Brook. New York
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J M HELLMAN Power Systems. Westinghouse Electric Cmporation Pittsburgh. Pennsylvania
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I. Introduction
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A . The Phenomena of Fire B. Fire Classification C. Thechemical Natureof Wood I1. Pyrolysis A. Experimental Methods of Studying Pyrolysis B. Interpretation of Experimental Results C . Mathematical Models of the Pyrolysis Process . D. Relation of Pyrolysis Testing to Fire Protection I11. Ignition A . Ignition Sources B. Fire-Safety Oriented Ignition Tests C . Ignition-Radiation Induced D . Ignition-Wildland Fires I V . The Plume A . Plume Phenomena B. Analytical Plume Studies C. Experimental Fire Plume Studies V . Firespread A. Firebrand Spotting B. Evaluationof FuelLoadof Fire C. Theories for Fire Spread D. Experimental Determination of Fire Spread Rates E. Large-Scale Fire Spread Studies 219
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VI. Instrumentation in Fire Research A. Exhaust Hoods B. Wind Tunnels C. Fuels D. FabricTesting Methods E. Flow Visualization F. Temperature Measurement G. Velocity Measurement. VII. Fire Research and the Fire Fighter A. Equipment Designed for the Fire Fighter B. Building Codes. C. Product Testing VIII. Concluding Remarks References
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I. Introduction Ever since primitive man discovered that controlled fire was useful and uncontrolled fire deadly, the combustion of liquid and solid fuels has been subjected to intensive investigation. Much time and effort has gone into the study of determining the most favorable burning conditions for commonly used fuels such as coal and oil, but relatively little technical effort, until recently, has been devoted to a study of the burning of materials not usually considered fuels, such as furnishings, homes, and forests. The need for research in this area is great. In the last decade in the United States alone, fire took an annual toll of more than 11,000 lives, and the direct fire losses from just fires in buildings exceeded one and onehalf billion dollars. These losses, coupled with a worldwide effort to encourage scientists and engineers to look a t human-oriented problems, nurtured the recognition of a relatively new discipline, $re research. This discipline is different from the more established ones in that even most of the elementary problems therein still elude the possibility of a fundamental treatment, no matter how crude. Another difference is the broad spectrum of technical and technological areas that are encompassed by the title of fire research. The reason for the inclusion of so many diverse areas is that for hundreds of years fires have occurred in many diverse places and from many diverse causes. Over this span of time, cells of expertise have grown with direct application intended in each of these areas; firemen have learned the “best” way to fight house fires, foresters have learned the “best” way to prevent and fight forest fires, and insurance company researchers have determined “acceptable” (at least from a claims point of view) limits of fire danger for the various buildings, installations, devices, and industrial practices.
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To these and other similar groups have now been added fluid mechanics and heat transfer scientists and engineers among others interested in applying their knowledge and method of approach to the problem of unwanted fires. As a result of the varied interests of the people involved in fire research, there is often considerable interplay among the various groups; the inputs to one problem often come directly from the outputs of many other problems, and subsequently its outputs may very often find their way back to serve as inputs to the same other problems. The aim of this article is to present a review of recent technological advances in the field of fire research, along with some of the basics of the fire problem. It is hoped that this broad approach will enable researchers unfamiliar with the various aspects of fire research to obtain an overview of the subject, some of the problems and presently available methods of solution, and to permit those researchers working within one branch of fire research to visualize their work within an overall framework and possibly see new applications for their experimental and analytical expertise. Review papers on more specialized aspects of fire research have been written by Emmons [l], Lee [a], Thomas [ 3 ] , Lawson [4], and Berl [ 5 ] .
A. THE PHENOMENA OF FIRE The study of a single small burning candle illustrates many of the significant processes going on in a larger fire as well as showing, by comparison with the phenomena occurring in larger fires, how inadequate simple scaling procedure can be. For the candle flame shown in Fig. 1, heat from the combustion zone is transmitted to the solid wax and melts an exposed portion of it. The melted wax is then gradually drawn by capillary action into the wick where further absorption of heat transforms it into a volatile fuel vapor. This vapor is oxidized in the diffusion flame, producing combustion products and heat. Part of the generated heat is transmitted back to the candle to melt additional wax for the continued supply of fuel vapor for the sustained burning of the flame. The resulting hot gas mixture is driven upward by buoyancy, forming a natural convection plume above the flame. This upward motion constitutes part of a recirculation flow field around the flame both to provide fresh air needed for combustion and to help shape the geometry of the flame. Figure 2 illustrates the transfer mechanisms in a large fire. Note that a large-scale fire can contain a special spread mechanism, often dominant, which is not present in a candle flame. This process, known as spotting, occurs when burning pieces of fuel material (firebrands), such as leaves,
S. L. LEE A K D J. 3'1. HELLMAN
222
HOT
PLUME
A
"
. L
\ 4
DIFFUSION FLAME
'
MOLTEN WAX
SOLID WAX
FIG.1. Candle flame and associated phenomena.
-
AMBIENT WIND
--
4BURNED I
1 I
y'i {
I \
\',, k , '
RADIATIVELY HEATED AREA (PYRQYSIS L DEHYDRATION OCCUR)
HEAT CONDUCTION
FIG.2. Wildland fire and associated phenomena.
HEATAND MASSTRANSFER IN FIRERESEARCH
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tree branches, or partially burning pieces of paper, are carried by the wind, either ambient or fire induced or a combination of the two, to a new location. If ground fuel conditions are right, these firebrands can ignite a new fire. From this reasoning, the study of a simple free burning fire should cover three main interrelated disciplinary areas : (a) The generation of combustible fuel vapors from the fuel bed material and the ignition process; (b) the diffusion controlled flame; and (c) the natural convection plume, including its interaction with the ambient wind and firebrands, if any.
B. FIRECLASSIFICATION In fire literature, various types of fires have been identified and given names. The National Fire Protection Association has established the following classificationsfor building and industrial fires [S] :
Class A : Fires involving ordinary combustible materials (such as wood, cloth, paper, rubber, and many plastics), requiring the heat absorbing (cooling) effectsof water, water solutions, or the coating effects of certain dry chemicals which retard combustion. Class B : Fires involving flammable or combustible liquids, flammable gases, greases, and similar materials where extinguishment is most readily secured by excluding air (oxygen), inhibiting the release of combustible vapors, or interrupting the combustion chain reaction. Class C: Fires involving energized electrical equipment where safety to the operator requires the use of electrically nonconductive extinguishing agents. Class D : Fires involving certain combustible metals, such as magnesium, titanium, zirconium, sodium, potassium, etc., requiring a heat absorbing extinguishing medium not reactive with the burning metals. These classifications have been primarily used for the specification of suitable extinguishment materials for the various types of fires. Another set of fire classifications delineating different types of very large-scale, or mass, fires has been recognized. A conflagration is a fire that develops moving fronts under the influence of wind or topography, and the hot, burning area is usually confined to a relatively narrow depth. A fire storm is defined as a fire in which many parts of the entire fire area are burning simultaneously. Such a fire is essentially stationary, with little outward spread. It is usually identified with a towering convection column, extending to heights of the order of up to a few miles. Feeding the convection column
arc. intense ground level winds drawn inward toward the fire. This airflow is believed to be a major reason for the lack of significant outward spread of the flaming region. In the Hamburg fire storm, witnesses recalled seeing automobiles being tossed about by the winds generated near the fire storm. A mouiny fire storm, so named by Countryman [7] for a wind-driven fire storm, is a fire storm that spreads under the influencc of wind or topography. Under certain conditions of fuel, wind, and topography, numerous firebrands can spot-ignite large areas ahead of a large fire, and the resulting developing fire can take on many of the characteristics of a fire storm, yet continue to move rapidly into unburned areas. This type of fire has been observed in u-ildland mass fires, and because of the very large areas that can be ignited in such natural and man-made disasters as carthquakes and nuclear attacks, it is possible that fire storms can also flare up in urban areas. Of the three types of mass fires, the conflagration is at least conceptually understandable, while the fire storm and moving fire storm are potentially the most dangerous and a t present least predictable. -1graphic description of the fire storm phenomena, for a relatively small-scale fire storm, has been given by Pirsko el al. [ S ] : About 1230 P.S.T. a high voltage transformer shorted a t an irrigation pump house, rreating a very hot ignition source. The resulting brush fire spread uphill against the gradient wind but under the influence of eddies on the lee side. Near the top of the hill, the fire began to turn east. Major forward progress was by spot fires that jumped as much as a quarter mile ahead of the front. rin experienced fire control officer on the scene estimated that because of the spotting, forward spread to the east aas about 10 times faster than normal for this area. The fire approached Arroyo Paredori one mile east from the pump house around 1400 to 1430 P.S.T. As the main fire and spot fires joined near the Arroyo, many small whirl-winds were seen to start. Wind sweeping southward down Arroyo Paredon whirled rlnckwise to the west where the slope flattened out. In the unstable air vertical development was unhindered. Many more spot fires started as entire Inirnirig bushes, 5 to 10 feet tall, were carried aloft and dropped into unburned vegitation. These fires built up great quantities of heat. Whirls continued to form, rise, and break off at the top. Firefighters could hear the roar of shock waves from the intensely burning brush. Then many of the small \vhirls seemed to coalesce, arid the whole fire area started to rotate clockwise. This massive fire-bearing whirlwind built up in height and started to roll downslope to the south. It plucked brush and small oak trees from the ground and carried them aloft. The intense whirl continued its vertical growth. The southward movement steered the fire into the area of homes, a chicken ranch, arid avocado orchards. That the whirl carried fire for about 200 feet after leaving the wildland fuel was shown by scorched and burned avocado trees and burned chickens a t the ranch. .4s it passed the ranch, the fire whirl ignited some walls. Eggs stacked for shipment were cooked in their crates. The Hhirlwind then sheared off the roof of a 7-rOOIn house, blew many windows inward, and lifted venetian blinds over the tops of the remaining walls. Streaking through the avocado orchard, the whirl tore some trees
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out of the ground, broke tops of some, and smashed others. Limbs and trunks in its path pointed in the direction the lire whirl traveled. A 4-foot diameter oak tree was uprooted and twisted toward the center of the path. Four people were injured by flying material and falling debris. Two houses were destroyed-one of two stores and 10 rooms; three automobiles aere smashed; and a garage and part (section) of the chicken ranch were blown apart. A barn filled with hay was hoisted in the air, pulled apart, and never found again. Boards, plaster, corrugated sheet metal, and other building parts were scattered over an extensive area. The fringe of the fire whirl passed over a Carpenteria fire department tanker and sucked out the rear window of the truck cab. A fireman standing on the rear platform was pulled up vertically so that his feet were pointed to the sky while his hands clasped the safety bar. Continuing south through the avocado orchard to a two lane road, the whirlwind turned at a right angle to the east for about 250 feet and then made another right angle turn to the south down an orchard lane. I t rammed a 3 by 6 by f inch piece of plywood 3 inches deep into an oak tree, then lifted and moved overland to the south toward the Pacific Ocean. At the main fire, the ridgetop fuel break and the direction of the prevailing wind made control of the north fire perimeter comparatively easy. Two spot fires on the next ridge to the east were controlled by 2200 the same day.
C. THECHEMICAL NATUREOF WOOD
A description of the material wood, which is involved in many unwanted fires, is given by Murty Kanury and Blackshear [9]. Wood is the name given to the main tissue of the stems, roots, and branches of the so-called “woody plants.” It consists of “cells” or “fibers” which can be isolated by chemical means. Some of these cells (prosenchyma) are vessels, tracheids, and libriform fibers for transport of water and air and for giving mechanical strength. The diameter of these cells varies from 0.02 to 0.5 mm. Other cells (parenchyma) contain living protoplasm, cell nuclei, metabolites, and reserve food such as starch, fats, dyestuffs, and resins. These cell fibers range in length from 0.5 to 1.5 mm and in width from 0.07 to 0.1 mm. The porosity 4 (ratio of the volume of the pores to the volume by the cell walls) of real woods lies somewhere in the range 40-75%. The specific gravity of the actual woody substance is approximately 1.5. The influence of the porosity and the moisture content M (percent based on the oven dried weight) on the specific gravity of real wood is: = 1
+
1.5(1 - +/loo) 0.0135 M ( l - #1/100)
Chemically, wood is composed (by weight) of 50% C, 6% H, 0.10% N, 0.40% ash, and the rest oxygen. Wood is basically a combination of three
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s. L. LEE .4ND J. Jf. HELLMAN
main components-about 20y0 lignin, 40% hemicellulose, and 40y0 cellulose and other carbohydrates. Cellulose is a polymeric residue, attacked neither by alkalides nor acids, its fiber diameter being about 60 A. The molecular weight of cellulose is found to be about lo6.The nondissolving residues of wood (which are later identified as cellulose) have a formula somewhat like CsHlOOswhich is isometric with starch. That this residue is enclosed within the cells has been shown. From the chemical formula, it can be seen that the degree of polymerization of cellulose is approximately 104. Hemicellulose consists of certain wood polyoses and carbohydrates which accompany many celluloses in nature. It is soluble in alkalies and easily saccharized by dilute mineral acids. While Gay-Lussac’s (1839) work on the elementary composition of wood gave the impression that wood is a homogeneous substance, Payen (1838) showed that membranes from wood fail to contain cellulose. By treating whole wood with nitric acid and alkali, he separated cellulose from some “incrusting” substances. Lignin, along with hemicellulose, is easily destroyed by acidic reagents. Lignin is that substance which cannot be converted into sugar. The “incrusting substance” Payen found was a mixture of polyoses and lignin. Lignified membranes were discovered to take place in color reactions with certain organic reagents. Colorimetric methods are extensively used to study lignin. Lignin is found to be of relatively lower molecular weight (about 1OOO). The elementary composition of lignin is found to be C47H52016 or C,,H3,0,(OH)j(CH30)j. It has a refractive index of about 1.6. Further information on the chemical nature of wood can be found in the books by Browning [lo].
11. Pyrolysis When a solid or liquid fuel burns, the molecular structure of the fuel is modified by the action of the heat reaching the fuel. The net result of this chemical change is to produce a combustible vapor. This process, called pyrolysis, has been under intensive investigation, since one possible method of control of fires is to eliminate or reduce the intensity of the sources of the flammable vapors. The pyrolysis process is often treated as a “wave” traveling through the material. I n a coordinate system affixed to the wave, density and temperature profiles would appear as in Fig. 3. If a more complete understanding of the heat and mass transfer within the pyrolyzing fuel can be achieved, it will be possible to better control the burning process. Theoretical work in this area is closely associated with available experi-
HEATAND MASSTRANSFER IN FIRERESEARCH -V*
227
VELOCITY OF PYROLYSIS WAVE
RAW
WOOD
WAVE FRONT I
I
"r"
DENSITY
"VVY
OLWIITY
FIG.3. A pyrolysis wave in a coordinate system moving with the wave.
mental findings, and there is much discussion in the literature as to the validity of various experimental procedures.
A. EXPERIMENTAL METHODS OF STUDYING PYROLYSIS 1. Digerential Thermal Analysis and Thermogravimetric Analysis
In differential thermal analysis (DTA) a sample of the material under test is instrumented with a thermocouple and placed in a controlled environment (i.e., nitrogen or air) along with a similarly instrumented and sized inert block. The assembly is then placed in an oven, and the temperature increased at a predetermined rate. The temperature difference between the sample and the inert material is recorded. Chemical reactions occurring within the sample as the raw material undergoes chemical changes a t the various ambient temperatures are either exothermic or endothermic, and show up as spikes on the differential temperature readout. The location and magnitude of these spikes can then be used to obtain information as to the identification of the reactants. Sample DTA plots are shown in Fig. 4. In thermogravimetric analysis (TGA), the sample is attached to a sensitive electronic balance, the assembly placed in a controlled environment, and the temperature raised at a predetermined rate. The rate of loss of weight is recorded, and the rate of generation of vapors as a function of
S. L. LEEAND J. M. HELLMAN
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I-
0
YI
1
I,
-u 0
w
so
200
I00
300
Te WfWh(*c) %
TGA
-----------\
f x 0
w
f
U 0
IP'C
w
-
100
-
60
-
I
. I
I
1
80
100
I
I 200
I
I
300
60
40
20
1
4 0
Temptratur ('C)
FIG.4. Differential thermal analysis of cellulose treated with 5% zinc chloride by weight (top) and of pure cellulose (bottom) [ll].
temperature can be obtained. Figure 5 illustrates a TGA thermogram for cellulose both with and without a fire retardant. 2. Mass Spectrometry and Gas Chromatography When mass spectrometry and gas chromatography are used to study pyrolysis, the sample is placed in a controlled environment, heated at a known rate, and the vapors injected into the instrument. The pyrolysis gases can then be identified by reference to standard tables. Experimental
HEaT AND MASS TRANSFER I N FIRERESEARCH
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work in this area has been done using both cellulosic materials [14] and a simulated heated char [lS]. 3. Densometric Analysis
In this type of analysis, the sample is instrumented with thermocouples to provide temperature profiles within the sample as a function of time as the sample is burned from the outside in. Right circular cylinders of cellulose have been used in this type of experiment with reasonable success. The cylinders are ignited around the periphery, and x-rays or gamma rays (from a 13'Cs source) used to take a picture along the axis of the cylinder at progressive times during the burning. From measurements of the optical density variations of the resulting negatives, it is possible to correlate the physical density of the cellulose inside the sample with the temperature profiles for various times, producing a time history of the pyrolysis occurring within the sample. Blackshear and Murty Kanury [lS] originated this method using x-rays, and Nolan et al. [17] and Brown [lS] have obtained results with the I3'Cs source. OF EXPERIMENTAL RESULTS B. INTERPRETATION
There is considerable variation in the reported results for the heat of reaction during pyrolysis, a key element in any theory of fire spread. 100
I0
t
\1\'\'\\\ vvll---
omo*
'I-
20
0
FIG.5. TGA thermograms of cellulose and (NH4)ZHPOI treated cellulose heated at 25"C/min in a flow of 100 cm3/min air [12].
230
S. L. LEE AND J. M. HELLMAN
Roberts has reviewed the literature on wood pyrolysis [19, 203, and points out that published experimental estimates of the heat of reaction range from an endothermic value of 370 J/gm (for cellulose) to an exothermic value of - 1700 J/gm (for wood). He concludesthat the following factors caused variations in the reported kinetics of the wood pyrolysis reactions. (a) The rate and course of the pyrolysis reactions in cellulose are very sensitive to catalytic and autocatalytic effects. Values for the apparent activation energy of the pyrolysis reactions have been obtained over the range E = 40-230 kJ/mole; a reaction with E = 125 kJ/mole appears to be the most important one during the pyrolysis of cellulose in bulk samples of wood. (b) Lignin pyrolyzes appreciably more slowly than does cellulose a t temperatures greater than 340°C. Its pyrolysis does not appear to be sensitive to catalytic or autocatalytic effects. (c) The physical structure of wood restricts the free movement of volatile products of pyrolysis until it suffers macroscopic changes, such as fissuring, which generally occur a t temperatures of 300-320°C. Before the local occurrence of such changes, conditions strongly favor autocatalysis. Subsequently the products can escape relatively easily, and the importance of this effect is reduced. (d) If the rate of temperature rise in a slab of wood is low or if it is heated only to temperatures of the order 300-320°C, it is to be expected that the kinetics of the pyrolysis reactions will be highly dependent on experimental conditions because the effects of the low pressure region will predominate. Conversely, if this low temperature region is passed through quickly, the kinetics will be more consistent. With regard to the overall pyrolysis of wood, Roberts reaches the following conclusions.
(a) Under some conditions, such as reduced pressure, the primary process of pyrolyzation can be endothermic. (b) Under normal conditions, a t atmospheric pressure in continuous slabs of wood, the primary pyrolysis of wood is exothermic. The difference may be caused by a change in the reaction mechanism of cellulose due to autocatalytic or catalytic effects. (c) If wood is heated to temperatures in excess of 320'33, the heat of reaction is approximately constant a t - 160 to - 240 J/gm of products evolved. It is estimated that 65% of this heat generation is due to the pyrolysis of lignin and 35% to the pyrolysis of cellulose. This heat of reaction originates in the primary pyrolysis of the wood materials and does not require the assumption of secondary reactions for explanation. (d) If wood is heated to temperatures not in excess of 320"C, the heat
HEATAND MASSTRANSFER IN FIRERESEARCH
231
of reaction is highly dependent on experimental conditions and may rise to -1600 J/gm. This change is due to secondary reactions; as the wood structure is progressively degraded with increasing temperature, the escape of volatile products is facilitated and the contribution of secondary reactions is reduced. Secondary reactions can contribute an extra - 1200 J/gm to the heat generated by the primary reactions. These conclusions are far from universal acceptance. At this time, much further research is needed into the chemistry of pyrolysis to permit a more basic understanding of the process and obtain more reliable values of the heat of reaction, either exothermic or endothermic, at the various locations in the structure of the pyrolysis wave.
C. MATHEMATICAL MODELSOF
THE
PYROLYSIS PROCESS
The typical model for analytical study of the pyrolysis process is a slab of wood exposed to heating on one side and insulated and impermeable to gas flow on the other. Assumptions are made as to the chemical reactions occurring within the porous, pyrolyzing wood, and for the various thermal properties of the material. Vapor generation rates, temperature profiles, and other pyrolysis related quantities can then be determined. Panton and Rittmann [Zl] have studied the case of a plane slab initially a t a uniform temperature suddenly heated on one side. Two cases are investigated, both assuming first order reactions with an Arrhenius rate equation. In one case, a single reaction, in which a virgin solid goes to a second solid plus a gas, is considered. The second case looks at a more complicated kinetic scheme: solidl + solidz solidl --f gasz solidz--f solidr
+ gasl + gass
They assume that the thermal conductivity is proportional to the density, and that the flow of vapors produced has no effect on the energy balance of the pyrolysis process. Figures 6(a)-6(c) illustrate some of the results of this study. Kung [22] uses a plane slab geometry and assumes transient conduction, internal heat convection of volatiles, Arrhenius decomposition of virgin material into volatiles and residual char, endothermicity of the decomposition process, and density, specific heat, and thermal conductivity of the char determined from a linear interpolation between values of the virgin wood and solid char. Murty Kanury [23] assunies linear temperature profiles in the interior of a wood-like solid, a critical temperature for pyrolysis, instant removal of the pyrolysis products upon their formation, and that
232
TIME(t1
(0)
FIG.6a. Total gas generation rate vs time for various values of the heat of reaction, R: E = 40; dimensionless frequency factor, F = 10-8; dimensionless radiation absorption boundary condition, CR = 1. Maxima occur a t approximately the same time, however, the duration of the reaction is markedly changed [21].
(b)
DISTANCEW
FIG.6b. Profiles of reaction rate a t various times for an exothermic reaction; E = 40, F = 10-8, R = -0.3, GR = 1. The front surface is X = 1. The maximum reaction rate a t the back wall is above 9, while at the surface it is about 4 1211.
HEATAND MASSTRANSFER IN FIRERESEARCH
233
W I4
a ; I
0 IV 4 W
K
(C)
DISTANCE I X )
FIG.6c. Profiles of reaction rate at various times for an endothermic reaction; E = 40, F = R = +0.3, GR = 1. The maximum reaction rate occurs at the surface [21].
the thermal properties of char and wood are dependent only upon the solid density and not temperature. A major difficulty in interpreting the results of this type of analysis is that there is not sufficient experimental data on the thermal properties of wood in the various stages of pyrolysis to provide a good check of the results or the validity of the assumptions made in obtaining the results. Many of the theoretical analyses performed when using the types of assumptions outlined in this section will provide good agreement with one set of experimental data but not with another. Assuming an exothermic heat of reaction where, in reality, it is endothermic, or vice versa, should be one of the obvious causes for noncorrelation of any theory with a certain set of experimental data.
D. RELATION OF PYROLYSIS TESTING TO FIREPROTECTION In an attempt to reduce damage from fires that do start, various chemical additives have been developed over the years to slow the spread of fire.
S. L. LEEAND J. 31. HELLMAN
234 2000
r
rControl
4
0
8
12
16
20
24
28
32
36
24
28
32
36
Elapsed time (min )
2000
1
r
/-Control
800
0
4
8
I2
16
20
Clapred time (min )
FIG.7. Effect of fire retardants AS (top) and DAP (bottom) on the weight loss rate of pine cribs (131.
One of the testing methods used to determine the effectiveness of a proposed fire retardant is by DTA and TGA. The rationale of the rating procedure is based on the observation that fires can burn either by glowing or flaming. Due to its slower rate of spread, the glowing burning fire is usually preferable from the traditional fire fighting point of view. Pyrolysis studies have indicated that wood can undergo two types of thermal degradation [13]. One, occurring at temperatures lower than 270°C, produces char, carbon dioxide, water vapor, and little combustible gas. The second type, occurring at temperatures above 340°C,produces little char and a large amount of combustible gases. This high energy path produces burning with flames. For a fire retardant to be effective,it must act to decrease the
HEAT AND hIASS
TRANSFER I N FIRERESEARCH
235
activation energy associated with the glowing burning process, causing this type of burning, rather than the flaming burning, to predominate in a fire. Typical chemicals used against forest fires for this purpose are diammonium phosphate (DAP), ammonium sulfate (AS) , and monoammonium phosphate (MAP). The phosphate-based chemicals have the added advantage of also acting as a fertilizer to the remaining vegetation, speeding the recovery time of the forest from the ravages of a fire. Figure 7 illustrates the weight loss rate of pine cribs as a function of the amount of DAP and AS used. Note the strong suppression of the rate of weight loss. This results in a smaller quantity of combustible gases produced, and hence a slower fire spread. 111. Ignition
A.
IGNITION SOURCES
I n almost every location where some type of fuel for a fire exists, ignition sources are quite often present. These sources can be in the form of lightning in a forest, a spark from an automotive ignition system, or a lit cigarette dropped from the hands of a smoker as he falls asleep. At times there is no fire as a result of an ignition source, while at other times a deadly fire may result. Another type of ignition is possible without an ignition source [24, 251. This process, known as spontaneous generation or self-ignition, can be explained by thermal explosion theory, Fig. 8. In usual exothermic reactions of interest to the fire problem, the rate of the reaction approximately doubles for every 10°C increase in temperature. If the heat generated by the reaction cannot be transmitted away fast enough, the rate of the reaction and the temperature will continue to increase until flaming burning occurs. This type of reaction can occur in many materials, as listed in Table I. Some of these reactions are thought to be initiated by the heat generated by biological decay of organic material. Since the rate of pyrolysis of a material is a function of the type of heating as well as the chemical nature of any impurities present, i t is not possible to precisely determine the ignition temperature of a type of material. Representative figures for various materials have been published and are listed in Table 11. In general, the ignition temperature of wood is of the order of 400"F, and 150°F is the highest temperature to which wood can be continuously exposed without risk of ignition. At temperatures intermediate to these values it is possible for pyrolysis to occur over an extended period of time, producing charcoal, a material which can undergo
TABLE I
MATERIALSSUWECT fro SPONTANEOUS HEATING'
Msterinl
Tendency to spontaneous henting
Usual shipping container or storage method
Precautions against spontaneous heating
Remarks
Charcoal
High
Bulk, bags
Keep dry. Supply ventilntion
Coal, bituminous
Moderate
Bulk
Store in small piles. Avoid high temperatures
Corn-meal feeds
High
Burlap bags, paper bags, bulk
Fertilizers: organic, inorganic, combination of both
Moderate
Bulk, bags
Fish meal
High
Bags, bulk
Linseed oil
High
Tank cars, drums, cans, glass
Manure
Moderate
Bulk
Mnterinl should be processed carefully to maintain safe moisture content and to cure before storage Avoid extremely low or high mois- Organic fertilizers containing nitrates must be carefully preture content pared to avoid combinations that might initiate heating Keep moisture 6 1 2 % . Avoid ex- Dangerous if overdried or packposure to heat aged over 100°F Avoid contact of leakage from con- Rags or fabrics impregnated with this oil are extremely dangerous. tainers with rags, cotton, or Avoid piles, etc. Store in closed other fibrous combustible materials containers, preferably metal Avoid extremes of low or high Avoid storing or loading uncooled moisture contents. Ventilate the manures piles
Hardwood charcoal must be carefully prepared and aged. Avoid wetting and subsequent drying Tendency to heat depends upon origin and nature of coals. High volatile coals are particularly Iiable to heat Usually contains an appreciable quantity of oil which has rather severe tendency to heat
Oiled fabrics
High
Rolls
Tung nut meals
High
Paper bags, Bulk
Varnished fabrics
High
Boxes
Waste paper
Moderate
Bales
Wool wastes
Moderate
Bulk, bales, etc.
0
National Fire Protection Association [26].
Keep ventilated. Dry thoroughly Improperly dried fabrics extremely before packing dangerous. Tight rolls are comparatively safe. Material must be very carefully These meals contain residual oil processed and cooled thoroughly which has high tendency t o heat. before storage Material also susceptible t o heating if over-dried Process carefully. Keep cool and Thoroughly dried varnished fabventilated rics are comparatively safe Keep dry and ventilated Wet paper occasionally heats in storage in warm locations Keep cool and ventilated or store Most wool wastes contain oil, etc., in closed containers. Avoid high from the weaving and spinning moisture and are liable t o heat in storage. Wet wool wastes are very liable to spontaneous heating and possible ignition
h-
z
tr
z
hm m
S. L. LEEAND J. 11. HELLMAN
238
GENERATION
X 3 J
u.
2 w
I
LOSSES
<
QENERATION
TEMPERATURE
FIG. 8. Thermal explosion theory-the rate of an Arrhenius reaction approximately doubles with a 10°C increase in temperature. If system heat losses cannot transmit away this increased heat, “spontaneous generation” of fire may occur.
self-ignition. The time for ignition of wood is strongly dependent upon the intensity of heating and the moisture content, as illustrated in Fig. 9.
B. FIRE-SAFETY ORIENTEDIGNITION TESTS Researchers engaged in determining the fire safety of various materials approach the problem of ignition from the viewpoint of: “Given a credible -2.00 0
0
O X IQX-MOISTURE CONTENT
10
20
T I M TO 16NITE
30
40
50
(SEC)
FIG.9. Effect of moisture content on the ignition of wood [28]. -Oak, - - - Western Red Cedar.
HEATAND MASS TRANSFER IN FIRERESEARCH
239
TABLE I1
IGNITION TEMPERATURES FOR VARIOUSMATERIALS~
Material
Type of specimen
Paper, newsprint Paper, filter Cotton, absorbent Cotton, batting Cotton, sheeting Woolen blanket Viscose rayon (parachute) Wood fiberboard Cane fiberboard
cuts cuts Roll Roll Roll Roll Roll Piece Piece
Wood Western Red Cedar White Pine Long Leaf Pine White Oak Paper Birch a
Self-ignition Temp. (OF) 378 406 428 410 399
Self-ignition temp. (OF)
Wood Short Leaf Pine Long Leaf Pine Douglas Fir Spruce White Pine
446 450 511 446 464 401 536 421444 464 Self-ignition Temp. ( O F ) 442 446
500 502 507
National Fire Protection Association [27].
ignition source, will this item burn?” Testing for fire danger is usually done full-scale with the actual materials submitted for test. In testing fabrics for flammability, the National Bureau of Standards (NBS) has established a testing procedure [29] where a standard-size piece of the material is held vertically in a frame, and a small flame is directed at its base for a specified period of time (see Fig. 10). If the smolder or flame propagates upward from the ignition point to a given height, or if burning pieces of fabric drop from the main piece, the fabric fails the test. For testing bed mattresses and upholstered chairs [30], lit cigarettes or other sources of ignition are placed at various points on the item under test, and the spread of the smoldering zone is determined. If it exceeds a specified value, the item fails the test. As can be seen from Tables IIIAIIIC, which describe a set of tests done on bedding and chairs, many of the test items would produce a lethal hazard to a person sleeping in a room with the item. Note also that in addition to carbon monoxide, there are measureable quantities of other poisonous gases produced by the combustion process.
Test no. 1 2
3 4 5 6 7 8 B 10 11 12 13 14 15
ID 17 18 19 20 21 22
Materials
Ignition sour‘ce
IM-R, S-M Cigarette IM-R, S-M Match (flat) IM-R, S-M Match (edge) IM-R, S-P Cigarette IM-R, S P O / C Cigarette IM-C, S-M Cigarette M-Pu, S-M Pill M-L, S-M Pill IM-R, S-M, B-R/A Cigarette IM-R, S-M, B-C Cigarette IM-R, 8-M, B-Po Cigarette IM-R, S-M, B-.4 Match (flat) IM-R, S-M, B-W Cigarette* IM-R, MC-Ac/V, S-M Match (flat) IM-R, MC-V, 8-M Cigarette Match (flat) IM-R, MP-C/R, S-M IM-R, MP-C/N, S-M Match (flat) IM-R, 8-M( l ) , B-A( 1) Cigarette IM-R(FR), S-M(FR), B-W(FR) Cigarette Match (flat) IM-R, MC-C(FR), 8-M TM-R, ELM, P-F Cigarette* Match (flat) IM-R, S-M, P-P
Max temp.
Max CO
Max CO,
Min 01
Test duration
(OF)
(%I
(%I
(70)
(min)
220 200 150 195 315 240 360 455 265 27.5 280 250 205 265 220 240 220 380 75 190 135 250
0.470 0.510 0.665 0.420 0.413 0.375 0.173 0.495 0.495 0.413 0.300 0.495 0.387 0.550 0.340 0.620 0.530 0.360 0.043 0.310 0.223 0.673
4.8 3.7 3.8 3.3 5.5 3.9 5.0 6.75 4.15 5.55 2.7 3.35 2.75 3 .0 3 .0 3.5 3.8 4.5 0.2 1.75 1.15 4.15
17.0 17 .O 18.0 18 .0 16.2 17.7 16.6 13.1 17.4 16.7 18.2 18.2 18.4 18.1 18.4 17.7 17.7 18.6 20.7 19.4 20.1 17.1
185 127 120 1!)5 227 204 74 45 165 180 215
m
90 235 105 285 95 95 165 190 110 180 90
r
s
n
Materials
Test no.
Cushion
Fabric
Weave
R C R
wo Pr wo Fr Do Do Em Ve
Ignition source
Max temp. (OF?
Max CO
Max COz
Min Oz
(%)
( %?
(%I
Test duration (min)
0.113 0.195 0.405 0.180 0.375 0.290 0.215 0.105
1.70 4.15 4.35 4.95 4.10 4.75 3.25 4.30
17.6 17.3 16.9 15.9 17.0 15.4 17.8 16.3
189 180 161 190 197 140 53 35
~
23 24 25 26 27 28 29 30
N Ac PP V R
Cigarette Cigarette Cigarette Cigarette Cigarette Cigarette Match (edge) Match
335 330 360 400 330 435 335 395
Hafer and Yuill 1311. Key to abbreviations: B-A Blanket, acrylic B-C Blanket, cotton B-Po Blanket, polyester B-R/A Blanket, rayon acrylic B-W Blanket, wool Fire retardant treated (FR) Innerspring mattress, with cotton ticking IM-C Innerspring mattress, with rayon ticking IM-R MC-V Mattress cover, vinyl MC-Ac/V Mattress cover, acetate on vinyl
MP-C/N MP-C/R M-L M-Pu N P-F P-Po S-M
Cushion and fabric
Weave
a
b
U L R
Urethane Latex Rubber Rayon C Cotton N Nylon P p Polypropylene V Vinyl (with thin foam and cloth backings) Ac Acetate
s-P S-Po/C
Matress pad, cotton-nylon filled Mattress pad, cotton-rayon filled Matress, latex rubber Mattress, polyurethane Nylon Pillow, feather Pillow, polyester Sheets, cotton muslin Sheets, cotton percale Sheets, polyester/cotton
2 t?
Wo Woven P r Print F r Frieze Do Dobby Em Embossed (plastic) Ve Velvet (1) Laundered * Cigarette placed on sheet after initial attempts failed
N F
S. L. LEEAND J. Ri. HELLMAN
242
TABLE IIIb
TIMETO REACHTOLERANCE LEVELSO 30 min
5 inin
Test XO.
Temp 284'F
CO 0.30%
Temp
212°F
CO 0.15%
1 hr Temp 150°F
2 hr CO 0.045%
Smoke density 0% L.T.
Cigarette Ignition-Bedding
1 4 5
2:43
6 9
10 11 13 15
2:s
I8
2:18 2:12 2:50 2:18 1 :46 1 :45 3:22 3:10 4:32 2:36 -
19
21
4:30 1:53
2:10 1:53 1:45 2:02 1:40 1:32 3:10 1 :40 4:16 2:oo
2:02 2:14 2:39 1 :33 1:40 1:37 2:51 3:lO 4:12 1 :53
2:oo 1:18 1:40 1:20 1:03 0:42 2:20 0:20 3:lO 1 :20
1:52 2:15 2:57 1 :58 1:43 2:22 2:42 1:20 3:54 1 :58
__
-
2:57
-
1 :20
1:43
0 : 10 0 : 12
2:20
-
2:20 2:06 1:47 1:38 2:52
-
-
-
-
Match or Pill Ignition-Bedding
2 3 7 8
2:21 0:37
1:06
0:09
-
0:08
0:Oi
0 : 14 0:34 0:53 0:22 0:25 0:75 0:38
0:05
12 14 16 17 20 22
-
0:05
1 :22 0:42 0:46
-
0:55
0 : 15
0:51
0:08
0:25 0:32 0 : 11 0:12 0:36 0:16 0 : 16 0:41 0:26
1 :OF, 0:05 0:03
0:07 0:06 0:06 0:04
0:02 0 : 10
0:08
>0:05 0:10
0 :10
0 :17
0:09
0:06
0:06 0:51 0 : 18
0:05 0:09
0 : 16
0:11 0:12 0:13 0:20
2:24 1 :20 1:05 2:3i 2:03 0:25
2:18 1:15 0:45 2:37 1:09 0:25
1:58 1 :30 0:34 2:11 1:20 0:26
0:17 0:07
0:18 0:06
Cigarette Ignition-Chairs
23 24 25 26 27 28
2:25 1 :21 1 :06 2:38 2:05 0:26
-
2:25 1:20
1:47
1:05
-
2:37
2:38
2:04
-
0:26
-
1:28 1 :25 2:40 2:05 0:29
Match or Pill Ignition-Chairs
29 30
0:19 0:06
-
Hafer and Yuill 1311.
0 : 18 0:06
0:20
-
0 : 18 0:05
HEATAND MASSTRANSFER IN FIRERESEARCH
243
TABLE IIIc
LEVELSFOR VARIOUSEXPOSURE TIMES" TOLERANCE ~-
~
Time Environmental factor Temp ( O F ) CO (%I
coz (%I (%I
0 2
5
b
5 sec
5 min
30 min
2 hr
300
284 0.3 5.0 9.0
212 0.15 4.0 11.0
150b 0.045 3.5 14.0
1.5 12.0 7.0
Hafer and Yuill [31]. Temperature limit is for a 1-hr exposure.
There is as yet no worldwide standard for flammability safety limits or test methods. Emmons [l] has plotted the order of flammability of 24 wall-covering materials as measured in round-robin tests by six different European countries, Fig. 11. He points out that material # l S has been rated the best of the 24 tested by Germany, and the worst of those tested by Denmark.
C. IGNITION-RADIATION INDUCED Since intense thermal radiation fields are often present in the vicinity of a fire [32], experimentation has been performed to determine the effect of radiation on the ignition of wood. In typical experiments, standardized samples are exposed to a specified radiative flux until ignition occurs. Often, a small pilot flame is used as an additional ignition source in these tests to further simulate the fire environment. Bamford et al. [33] used this method of experimentation to obtain information about the burning of wood in their pioneering paper of 1946. This method has been used by Simms and Law [34] on wet and dry wood to determine the maximum acceptable level of radiation for buildingspacing regulation purposes. For their analytical correlation, they modeled the wood as inert and having a fixed ignition temperature. They found that the moisture content increased the energy required for self-ignition and also increased the minimum intensity needed, though with pilot ignition they found that its effect was only marked for moisture contents above 40%. At the lowest likely moisture content of 10% they determined that it would take 10 min. for a radiation level of 0.4 cal/cm2-sec to cause ignition. Other workers have also performed experiments in this area [35-391.
S. L. LEE AND J. h l . HELLMAN
244
D. IGNITION-WILDLAND FIRES One source of ignition that is often dominant in wildland fires is due to firebrand activity. This spread mechanism is most effective when the ambient wind speed is great. This wind also tilts the hot convection column generated by the fire, radiatively heating the area ahead of the flames. If there is fuel present in this area, it will be dried out and the pyrolysis process started. This is then fertile ground for firebrand ignition of secondary fires which grow and merge into the main fire front. A common source of forest fires is lightning. In addition to the instantaneous ignition source presented by a lightning stroke, it now appears that there is also a possibility of the lightning creating a fuse, for later ignition of a forest fire [40]. If lightning strikes a rotted tree, glowing burning can be established within the hollowed-out trunk. After a period of time, perhaps several days after the storm has passed, enough heat can be generated to cause the fire to break out into flaming burning and possibly start a forest fire. VENTILATION
GUIDE FOR SPECIMEN HOLDER
VENTILATION PORTS
FIG.10. Vertical test cabinet for fabric ignition tests [29].
HEATAND h h s s TRANSFER IN FIRERESEARCH
22 21 20 I9 18 -
245
24
23
17
*
-
A
n
A V E R N RATING
FIG. 11. Flammability ratings of 24 wall-covering materials by 6 different national Germany, X Belgium; 0 Denmark, 0 France, A Netherlands, standard tests: England [l].
*
IV. The Plume The behavior of the hot air plume rising above a burning zone has received much attention in recent years. Since the plume sometimes plays an important role in the spread of fire, knowledge of its behavior will contribute heavily in any comprehensive fire spread theory. A knowledge of plume behavior is also important from a fire prevention and extinguishment point of view. One commonly used type of fire extinguishment system uses heat sensors and sprinklers located near the ceiling of a room. The heat from a fire at floor level must be convected upward to the sensors to activate the sprinkler system. Reaction time for this type of device is dependent upon the dynamics of the plume. In addition, the action of the sprinkler system itself can be strongly dependent upon the behavior of the plume. If a very strong upflow of hot air is generated by an intense fire, the water distributed by the sprinkler head may be slowed down in its fall and evaporated before it gets to the actual fire, nullifying much of the potential it may have for extinguishing the fire.
A. PLUMEPHENOMENA One of the most interesting aspects of plume studies is the interaction of a plume with the ambient air. This interaction can be through the vorticity present in relatively still air, or the effect of an ambient wind on the plume. -4mechanism for the generation of fire storms can be obtained from a study of the effect of local vorticity on an intense plume. As water draining from a bathtub concentrates ambient vorticity into a funnel-like pattern, a fire plume from a strong heat source can also develop into a rapidly swirling vortes. It has been postulated that the fire storm that occurred in Hamburg during World War I1 was formed in this way, and the conditions which led to the intense plume were both climatic and atmospheric [41]: The weeks preceding the air raids were unusually hot, due in part to a temperature inversion that concentrated smoke particles in the region close to the ground, preventing radiative cooling of the area by night. The day of the raids, the ground temperature was 86"F, and the temperature decreased 15" within the first 2000 ft. of elevntion, and averaged 4.8" per 1000 ft. between the 1000 and 12,500 ft. levels. This extreme temperature gradient, coupled with almost nonexistent winds in the city a t the time of the raids produced favorable conditions for B strong, nearly vertical plume. The heat source for the generation of the plume was supplied by the total burning of approximately five square miles of the city. Aircraft reported the plume height to be approximately 30,000 ft. with a cumuloninibus cloud, complete with anvil head top, a t this level. Ground observers reported a definite counterclockwise swirl to the winds generated by the plume. dlthough no windspread measurements were made near the center of the burning, observations of wind damage indicated that speeds of over 100 miles per hour were attained.
Small scale vortices are often observed in the neighborhood of wildland fires. Some of these are akin to dust devils that occur frequently in hot, arid areas. An ambient shear field interacting with a plume has been shown to produce this type of phenomenon. In nature, the shear field can be gencrated by either the ambient or fire-generated wind interacting with the topography in the area of the fire. Hills, edges of forested areas, and city streets betwen large buildings can all help produce such shear fields. Larger vortices can be created by the interaction of an intense plume with a strong ambient wind. This phenomenon will be discussed in Section V on fire spread.
B.
~ ~ A L ~ T I C CPLUME AL STUDIES
Various types of fire-generated plumes have been analyzed. This section present,s a representative sampling of methods of analysis for several
HEATAND MASSTRANSFER IN FIRERESEARCH
247
different types of plumes. The diffusion flame, the primary type of combustion in fires is discussed by Lewis and von Elbe [42]. 1. The Axisymmelric Swirling Turbulent Plume
A similarity assumption has enabled Lee [43] to obtain solutions for the characteristic size and the fields of buoyancy (or temperature) and the axial and swirling velocities, in an axisymmetric swirling turbulent plume. The flow is assumed fuliy turbulent and of such proportions that the boundary-layer type of assumptions are valid. Fluid density variations are neglected in the governing continuity and energy equations and in the inertial and viscous terms of the governing momentum equations, but are retained in the buoyancy force term in the momentum equation. (This is the Boussinesq approximation.) The following similar profiles are assumed for the axial and swirling velocities and the local buoyancy at all axial stations : u(z, r ) = u ( 2 ) exp( - r2/b2)
AT (2,r )
=
AT (z)exp ( - r2/X2b2)
where u and w are the components of the x (axial) and 0 (tangential) directions, respectively, of the timemean velocity of the fluid at a point inside the plume flow field; r is the radial coordinate; b y X g Ap X g(p1 - p ) is the local buoyancy; p1 is the density of the undisturbed ambient fluid; p is the local time-mean density; b = b ( t ) is the value of r at which the magnitude of the axial velocity u(x) is l / e of that of the maximum axial velocity along the axis u ( z ) ; f ( r / b ) is the profile distribution of the swirling velocity w(x, r) which assumes the maximum values w(z) at the maximum of f ( r / b ) which has the magnitude of unity; this function is determined experimentally; and is a universal constant relating the length scale of the axial velocity profile to the length scale of the local buoyancy profile.
Taylor’s entrainment assumption is used to relate the horizontal entrainment velocity at the edge of the plume to the axial velocity within the plume at the same height. The equations are then nondimensionalized
S. L. LEEA K D J. l f . HELLMAN
243
and solved, using a series solution developed around the origin for small values of the nondimensional axial distance, or numerical solutions for arbitrarj. values of position along the axis. Two nondimensional parameters govern the form of the solution, a source Froude number F and a source swirling velocity parameter G which has the form of the reciprocal of a source Rosshy number. F = 0 corresponds to a pure buoyancy source, while F = m indicates a pure momentum source. G describes the relative amount of wirling- of fluid at the source. This solution is valid for small to moderate swirl, G 5 1. Representative solutions appear in Figs. 12a and 1%.
> V
30 3
& 3 m
>
t V
s
I 25
w
>
5
J
Q X a
X
a 20
b
I 3
EX
i
r
u)
m w A
2
s-m? 2 w
In 3
DlMENSiONLESS AXIAL DISTANCE ABOVE SOURCE, X
FIG.12a. Results of maximum axial velocity and maximum buoyancy: F = 10; solid line, U ; dashed line, 1 / P [43].
HEAT.4ND
blASS
TRANSFER I N FIRERESEARCH
249
m v)
3
a a a W
f
J
n
0 I-
v,
a W I-
V
a a a r
0 0) v)
W _I
z
0
?E
z W
z
0
DIMENSIONLESS AXIAL DISTANCE ABOVE SOURCE, X
FIG.12b. Results of maximum swirling velocity and characteristic plume radius: F = 10; solid line, W ; dashed line, B ; long and short dashed line, 10 W [43].
The coordinates are nondimensionaliaed by
U
=
B=
UF6l7G’”/~o,
W
b F4”G3”bo,
P=
=
WF~/’G’”/WO ( A Y / Y ~F2I7G5l7 ) (AYo/Yi)
where
F=
Ly%O
Xg11Zb~’2 (Ayo/y~)
G = 2k’/’~o/~o and k is a swirling velocity profile constant dependent upon the shape of
S. L. LEE AND J. 81. HELLMAN
230
the swirling velocity profile f ( r / b ) ; a is the entrainment coefficient, a constant for the case under study; subscript 0 is the value a t x = 0 ; and subscript 1 is the value in the ambient undisturbed fluid. 2. -Yatural Conrection aboce a Line Fire
Lee and Emmons [44] have studied the two-dimensional plume rising from a line fire of finite width. The pressure is assumed to be constant in the horizontal plane and the boundary layer, and Boussinesq approximations are invoked. As in the swirling plume described earlier, Taylor’s entrainment assumption is used to obtain the horizontal velocity at the edge of the plume. Based on the experimental work of Rouse et al. [45], Gaussian profiles of time-mean vertical velocity and time-mean buoyancy are utilized. The length scale for the time-mean vertical velocity is b, related to the width of the plume, and the length scale for the time-mean buoyancy is Xb with X a universal constant. The behavior of the solution is governed by a single parameter, a source Froude number,
F = (2/n)1/4(ayl/~ ~r,)l/?~,/(gb,)1/2 (The notation, except where explicitly stated differently, is the same as that used in Section IV,B,l.) For the case F = 1, the velocity u = constant, the plume (kidth’’ b is proportional to x , and the buoyancy A y l y is inversely proportional to I . With F < 1 , the actual plume may be regarded as a section of a plume arising from a virtual line source a t a distance
[ F Z (~ ~2)11/31~(~~) below the real source, where
I+) =
[”
cv/(.3
-
1)1/31dv,
= (1 -
~2)--1/3
For a real source with F < 1, the plume width first decreases and then increases again. For F > 1, the plume g r o w in size rapidly a t first and then more and more slowly. In this case, the virtual source is located a t a distance I,[(P - 1 y 3 1 below the real source, where
I+) Both cases for which F
=
i”
cv/(2
+ 1)1/31av
< 1 and F > 1 approach the case F
= 1 as the
HEATAND MASSTRANSFER I N F I R E RESEARCH
25 1
height increases. F = 1 corresponds to a balance between inducted mass increase and buoyancy which just maintains the vertical velocity constant. If the original plume velocity is relatively too low, i.e., F < 1, the plume first grows slowly or even contracts to raise the local Froude number. If, on the other hand, the original plume velocity is too high, as in a heat jet., i.e., F > 1, the plume grows first more rapidly, decreasing the velocity. 3. Natural Convection in an En.closure with Localized Heatin.9 from Below
Torrance and Rockett [46] have obtained numerical solutions for the flow field within an enclosure generated by a heat source at the bottom. This type of study has direct application to the design and pIacement of fire detectors. The room model used in this study is a vertical cylinder of height a and radius b, with the fire simulated by a small heat source in the center of the floor. The problem is assumed to be two-dimensional and axisymmetric and totally laminar, which eliminates the possibility of the inclusion of any turbulent flow in their computation. The Boussinesq approximation is used for the density, and other fluid properties are assumed constant. The fluid is considered initially motionless and a t a uniform temperature To. The enclosure walls are also a t this temperature, except for the heat source which, for times greater than zero, is activated. This heat source is of radius c and at a temperature Th, which is greater than To.The temperature of the heat source is considered to be independent of the flow fieId. The solution of the problem consists of the time-dependent velocities, temperatures, and rate of heat transfer to the enclosure, as well as the fully developed solution. The method of solution is to satisfy the continuity equation by introducing a stream function, and then take the curl of the momentum equation, eliminating the pressure as a variable and obtaining vorticity transport equations. These equations, coupled with the energy equation and boundary conditions, form a complete system. Two dimensionless parameters enter into the problem through the boundary conditions; the aspect ratio of the enclosure (radius/height), Rb = b/a, and the relative size of the heat source, (heat source radius/enclosure height), R, = c/a. Two other dimensionless parameters enter when the equations are nondimensionalized, a Grashof number, Gr
=
gp( Th - To)a3/v2
and the Prandtl number,
Pr
=
v/k
where g is the acceleration of gravity, /3 is the volumetric expansion coeffi-
cient, Y is the kinematic viscosity, and k is the thermal diffusivity. The equations are made dimensionless in the following way: time
T
vrrtical and radial coordinates X
= (k/a2)t =
x/a,
R
r/a
=
vertical and radial velocity components
U
=
(a/lc) u, V
temperature
6
=
( T - To)/ (Th - To)
=
( a / k )u
A finite difference scheme [47] is used to numerically solve the equations. Steady state streamline fields for various Grashof numbers are shown in Fig. 13, and transient streamlincs are shown in Fig. 14.
4
R
(d)
(el
R (f
l
FIG.13. Steady state streamline fields for various Grashof numbers, Gr; the streamlines correspond to specified fractions of the maximum value of stream function $,mnx: (a) Gr = 4 X lo4, hax X 0.719; (b) Gr = 4 X105, X 3.29; (c) Gr = 4 X 106, Jlmnl X 8.23; (d) Gr = 4 X lo7, $msr X 16.7; (e) Gr = 4 X lo*, $ma. X 37.0; (f) Gr = 4 X los, X 103.7 [46].
HEATAND MASSTRANSFER IN FIRERESEARCH
R
R
R
(0)
(b)
(C)
R (d )
253
R
R
(e)
(f)
FIG.14. Transient streamline fields for Cr = 4 X 106 at various times T ; the streamlines correspond to $ values of :, $, %,and f of (a) T = 0.002, $,,,ax = 0.80; (b) T = 0.004, Jlmsx = 3.62; (c) r = 0.006, = 6.46; (d) T = 0.01, = 7.97; (e) T = 0.02, $msx = 8.24, $,,,in = -0.00063; (f) 7 = 0.1, qmax= 8.23 [46].
4. Shear-Induced Instability of the Plume above a Line Fire-the
Generation
of Multiple Fire Whirls Garris and Lee [48] have performed a stability analysis of the plume arising from a line source of heat. Given the proper balance between buoyant and shear forces, the plume will break up into a string of uniformly spaced vertical vorticies. Since fires in nature can be considered to approximate line sources of heat, particularly in wildfires where a welldeveloped line fire is often formed, and since some level of ambient shear is usually present in the ambient wind, this mechanism can explain the formation of the numerous multiple fire whirls observed near some fire locations [S, 491. The mathematical model employed in this study [48] is shown in Fig. 15. An infinite line source of heat is placed between two infinite vertical parallel screens separated by a distance 2 L. The screens are set in motion parallel to the heat source with velocities equal in magnitude, U., but opposite in direction. The screens are assumed to provide negligible resistance to the influx of fluid, while being able to impart shear to the fluid with no slip in the tangential direction. The screens are assumed far enough apart so that they will have no direct influence upon the vertical velocity component of flow in the plume. For values of the Prandtl number of 5/9 and 2, closed-form solutions can be obtained for the undisturbed flow system. A regular perturbation analysis is performed on this solution, and the equations linearized. A stream function is introduced into the problem for the perturbed velocities and is assumed to have as one of its Fourier components the form
JI
=
RY)expCi(s/c.> - P ~ I
where 5 is a complex amplitude function; a is the inverse wave number of
S. L. LEE AND J. M.HELLMAN
254
Using a similarity transform, the equations of motion can be reached to an analog of the Orr-Summerfield equation. Solution of this linear homogeneous equation with homogeneous boundary conditions is an eigenvalue problem such that for specified values of any two of the three parameters CU
( = a/6),
6
(= ap/US),
and
Re,(= U 8 8 / v )
a solution exists if and only if the third parameter takes on a specific = 0 for the discrete value. The stability criterion is that pr = 0 or entire range of disturbances studied. Physically this means that the solution predicts a standing wave type of phenomenon which typically develops into a flow exhibiting stationary vorticies. Figure 16 shows the results of the numerical solution to the problem for the two chosen values of Prandtl number, and Fig. 17 shows a typical set
c,
2
f
Source
I
}------>
, L
,'
u
Velocity Components
V
Fro. 15. Mathematical model of line fireshear field interaction [48].
+
the component of disturbance; p = Br i p i ; pr is the circular frequency of the component of disturbance; and 8%is the amplitude factor.
HEATAND R ~ A S S TRANSFER IN FIRERESEARCH 1000
100
I
I
=
I
IIIII
I
I
I
I I 1 1 1 1
I
I
I
255
I I I l l
R- 2
STABLE 10 :
M \ I3 II
F3
1.0
r Invlrcid Limits
0. I
I
I
I
I
I
I , ,
I
I
I
,
,
,
,
,
0. I
FIQ.16. Stability diagram for line fire-shear field interaction [48].
of streamline patterns for the perturbed flow. The parameter values are
ci = 0,
&=
2.0,
and
Pr
=
5/9
Based on a study of the most unstable case, a technique used successfully in predicting the spacing of water droplets suspended from a water film around a cylinder [50], the most probable vortex spacing distance can be predicted. 5. Survey of Other Analytical Plume Studies
Plume studies in general, and fire-generated plumes in particular, have been studied by Morton [51-541. In a review article on fire whirls, he demonstrates the theory of vorticity concentration by fire-generated plumes. Other papers have analyzed the modeling of fire plumes and forced plumes. Murgai and Emmons [55] have investigated the effect of an arbitrary lapse rate variation on the plume from an arbitrary-size fire. Rlurgai et al. [56] have analyzed two axisymmetric fires and found that the plumes interact and draw together to form a single plume at a suitable distance above the sources. This analysis has application to the merging of several fires in a city or forest to form a single large fire, with the associated possibility of developing into a firestorm. A spreading fire can take on the appearance of a ring, as it spreads out in all directions. The plume generated by this type of fire has been studied by Lee and Ling [57]. Nielsen and
S. L. LEEAND 3. 11.HELLMAN
256
8 6 4
2
a
0
\
x ,I
-2
(=
-4
-6 -8 -4
-2
0
0.2
0.4
0.6
0.0
.92lrz=x / x FIG.17. Streamlines of perturbed flow (481: Pr = $, G = 2.0, ?i = 0.0, Re8 = 2.982.
Tao [58] have included the effects of combustion and composition variation within the plume in their analytical model. Smith [ 5 S ] has included radiation effects in his study of large plumes. Plume studies are by no means limited to fire-generated plumes. Particulate deposition studies from emanations from smokestacks, a pullutionoriented problem, is intimately tied in with the dynaniics of the attendant plume from the stack. Recent moves by the Atomic Energy Commission calling for cooling towers to be installed at inland nuclear power generation stations should maintain the interest in this field, as t8hebehavior of the plume rising from the tower will effect both its effectiveness and acceptability by the local populace.
C. EXPERIMENTAL FIRE PLUYESTUDIES Experimental studies of the plume generated by fire have been performed on fires ranging in size from candles to full-scale forest fires extrnding over many square miles. This section is devoted to small, laboratory-size fires. The larger plumes are covered in Sections IV, B and V.
HEATAND MASSTRANSFER IN FIRERESEARCH
257
1. The Turbulent Swirling Natural Convection Plume
In conjunction with his theoretical analysis, Lee [SO] has measured the velocity and temperature field above a turbulent swirling natural convection plume. The flow field was generated by the impingement of several air jets directed tangentially against a Bunsen burner flame. A specially designated hot wire probe was used to measure the time-mean directional velocity, and the time-mean temperature was measured with a thermocouple. From the measurements, the swirling velocity distribution could be obtained, and the selection of an appropriate zero level (origin of the coordinate system used for analysis) produces close agreement of the experimental data points with the theory, as illustrated in Fig. 18. 2. Multiple Fire Whirl Formation
Extending the work of Emmons and Ying [Sl], Lee and Garris [S2] have constructed an apparatus that places a line fire in a controllable
I
0
0.5
I
1 .o
I
1.5
I
2.0
I
I
2.5
3.0
FIG.18. Comparison of theoretical and experimental results on an axisymmetrical swirling turbulent natural convection plume [60]. Theoretical results are shown by solid curves. Experimental results: 0 , U ; A, 10 W ; X, t(l/P); 0, B ; F = 9.5; G = 0.107. B is characteristic plume radius; l/P is reciprocal of maximum buoyancy; W is maximum swirling velocity; U is maximum axial velocity; X is axial distance above selected swirling plume source; F is the source Froude number; G is the source swirling-velocity parameter.
258
S. L. LEE A N D J. 11. HELLMAN
shear field, closely modeling their mathematical representation. With no shear field applied, the propane-air diffusion flame is usually quite smooth and uniform along the length of the channel burner and a few inches in height. U’hcn the shear field generated by a pair of countermoving screens reaches a critical value, the line fire breaks up into a number of regularly spaced fire whirls with hardly any burning taking place in between. Increasing the applied shear in the flow field increases both the whirl spacing and the whirl height. The fuel dependence of the visible whirl behavior can be classified into two regimes: a. Small Fuel Supply. Whirl height is determined by the effectiveness of the fuel-air mixing, which is governed by the whirl vortex strength. The whirl height then increases with available vorticity, but decreases with increased furl supply due to reduced circulation associated with a reduction in the characteristic spacing. b. Large Fuel Supply. The whirl height is governed by the quantity of fuel available to it. The whirl height then increases with both increased vorticity and with increased fuel supply.
3. Satural Conrectioti br au Enclosure with Localized Heatitty from Betorc Torrance el al. [63] have conducted an experiment to verify their numerical calculations for the flow pattern in a n enclosure with localized heating from below. An electrically heated disc was placed in the center of the floor of rectangular and circular cylindrical chambers. The flow was visualized by use of light, highly reflective metaldehyde particles injected into the flow field and illuminated by a narrow sheet of light. Photographs were taken of the particle streaks to determine the flow pattern. Good qualitative agreement with the numerically predicted streamlines was achieved . 4. Ellclosure Fire Studies
Practical interest in the behavior of fires within roomlike enclosures has spurred intensive experimental investigations of this type of combustion. Gross and Robertson [64] measured the mass rate of burning, teniperature, and gas composition for fully developed fires in three model enclosures. The rate of burning during this period is limited b y the size and shape of the ventilation opening (window). In general, the burning rate was found to he proportional to the area of the window opening times the square root of the height of the opening. They noted a transition zone within the range of this ventilation parameter where this proportionality did not hold. This can be associated with a characteristic change in the
HEAT AND hIASS
TRANSFER IN FIRERESEARCH
259
position of flaming from predominantly within and directly above the array of wood sticks (crib) to locations of more ready access to air, and an increase in the fraction of window height used for exhaust gases. They conclude that for a ventilation-limited enclosure, the major portion of the heat generated is transferred by radiation from the flames and glowing fuel. Other work on fires in enclosures has been done by Thomas et al. [SS]. Based on burning rate data from experiments where the flow of air was measured during the burning of a wood crib in an enclosure, they note two distinct burning regimes.
Regime I (applicable to small ventilation openings): (a) The burning rate is almost independent of the amount of fuel and its surface area. (b) The burning rate is almost proportional to the air supply through the windows. This may not be the whole of the air involved in combustion if there is flaming out of the window. Regime 11 (large ventilation openings): (a) The burning rate is determined by the type of fuel and the design of the fuel bed. (b) The burning rate is largely independent of air supply through the windows. They made the subsequent conclusions. (a) As the window area increases, the processes by which air is drawn into a fire in a compartment change from being predominantly the pressure difference caused by a stagnant stack of hot gases to those smaller pressure differences associated with entrainment of air into moving streams of gas. (b) While the window is small, an increase in window area or height leads to an increased burning rate and consequently a decrease in the duration of the fire. For a narrow range of window height, this duration is proportional to the fire load per unit window area. When the window becomes sufficiently large in relation to the fire load, the burning rate becomes virtually independent of the window area but depends on the fuel itself, so that the amount of fuel, particularly the surface area and its thickness have a n important influence on the burning rate. This may result in the burning rate increasing with the amount of fuel, and the duration being largely determined by the fuel thickness. (c) A high correlation appears to exist between the burning rate per unit window area and the intensity of radiation emitted from the window. Tsuchiya and Sumi [SS] have numerically solved the equations governing the behavior of fire in an enclosure. They have assumed that the rate of combustion and the composition of the fire atmosphere are functions of the temperature and fuel composition. The rate of combustion was calcu-
260
S. L. LEE A N D J. 31. HELLMAN
lated using two controlling factors, the air supply and the fuel surface. The more restrictive rate was used. 5 . Surrey of Other Experimental Plume Studies
Huang and Lee [67] have conducted an experimental investigation of the effects of two parallel line fires. They found that a small fire in close proximity to a largr fire can play a dominant role in determining the direction of inclination of the plume arising from the larger fire. Wood and Blackshear [68] have made a motion picture study of the various modes of burning of a pan of fuel, observing fire plume profiles, spontaneously developed fire whirls, and mechanically initiated fire whirls. Sand particles, picked up from the fuel bed, were observed moving within the fire whirls, indicating a potential for firebrand spotting. Corlett [ S O ] has made a systematic study of the energy feedback from fire to fuel source as a function of fuel properties, using a circular upward facing burner to simulate the pool. A downward facing burner has been used to simulate a ceiling fire studied by Orloff and De Ris [70]. Welker and Sliepcevich [71) present a correlation of data taken from liquid pool fires to permit prediction of an effective drag coefficient for flames, and of the degree of flame bending and trailing due to an ambient wind interacting with a largr fire. Putnam [72] has measured the effect of crosswind on flame height and horizontal extension.
V. Fire Spread One of the prime goals of fire research is an understanding of the proccsses by which fires spread. If this knowledge can be attained, then the problem of stopping unwanted fires will become much easier. Many studies, both analytical and experimental, have bern performed to gain insight into the mcchanisms of spread of fires. Great emphasis has been placed in three arcas: the spread of fires in wildland, the spread of fires in buildings, and the spread of fires in fabrics. Studies in the latter two areas have often bten initiated with the aim of establishing realistic and reproducible safety standards and building codes.
A. FIREBRAND SPOTTING The ignition of unburned areas of firebrands is a major fire spread mechanism in wildland fires. Two classes of firebrand trajectories have been observed: one is responsible for short range spot fires ahead of the main fire zone (typically up to about half a mile from the fire front), and
HEATAND MASSTRANSFER IN FIRERESEARCH
261
a long range spotting mechanism that can ignite fires a t distances of approximately 7-20 miles from the main fire. The driving force for short range spotting is a relatively mild combination of the upward currents due to the heat generated by the fire, and the ambient wind. Using experimentally determined values of the drag coefficient of firebrand materials, it is possible to write the equations of motion for the firebrand particle, and then trace its position as a function of time. If some burning law is used to compute the mass loss in time, it is possible to determine the point of burnout of the firebrand. If burnout occurs before landing, no threat of ignition occurs. Tarifa et al. [73] have computed trajectories of cylindrical firebrands carried aloft in a vertical convection column of constant speed. The firebrands left the column a t random heights and then were carried by a constant horizontal wind. Also investigated was the case of spherical firebrands in an inclined convection column of given width; the (constant) velocity within the convection column was the vectorial sum of a constant vertical convective and horizontal wind. The firebrands were picked up from the ground and left the convection column a t a point determined by the initial position of the firebrand. A limiting case, a t which the firebrand just burned out upon grounding, was determined. Lee and Hellman [74] have determined the trajectories of firebrands in the flow field above a fire whirl, a swirling, turbulent natural convection plume. The rate of burning of the firebrand played a vital role in determining whether the centrifugal forces would be great enough to eject the particle from the flow field before it had gone any significant radiaI distance. I n these trajectory studies, the presence of the particle is assumed to have no significant influence on the surrounding flow field. In an area where firebrand concentration is high, this condition is violated, and a complete two-phase treatment of the problem will become necessary. Another method of transport of firebrands is within a moving vortex. As in a tornado or waterspout, it is possible for material to become stabilized near the core of the vortex. As the vortex moves, this material, possibly burning, is transported together with the vortex. When this burning material drops to the ground along the path of movement of the vortex, it can ignite secondary fires. Long range spotting is closely associated with the so-called moving fire storms. Berlad and Lee [75] suggest that in a large, intense fire, an extremely strong convection column is formed which can reach a high altitude. A strong ambient wind can then interact with this column, a situation very similar to a cross stream interacting with a solid rod. As in the formation of a typical vortex street, vorticies can be regularly shed from the convection column. However, since the convection column does not have
262
S. L. LEE AXD J. 11. HELLMAN
rigid sides, some of the hot gases, along with convectcd burning solid material, can be entrained into the vorticics, which are then carried downstream. In the Sundance forest fire (sec Section V,E), this mechanism has been credited with igniting secondary fires approximately 7 miles downstream from the fire's primary convection column. Other material traveled even much further, but did not ignite any large spot fires. The time span between the rapid buildup of the intense 4-mile tall convection column virtually straight up above a deep river valley and the ignition of the spot fires closely niatches the time needed for a vortex to travel thc distance betwcrn the points. A corroborating piece of evidence for this suggestion is that fire fighters manning the fire lines noticed distinctively periodic high velocity wind gusts during the time that the vortex street was thought to havr occurred. In the proposed path of the vorticies many large totally unscorched trees were uprooted and felled by the high winds. Recently Lee and Chan [76] confirmed that this mechanism of vortex street formation does, in fact, occur. A round water jet was directed across the flow in a water channel, and the resulting flow pattern observed. Periodic vorticies were clearly evident, generated by the interaction of the channel flow and the jet. The presence of the injected dye particles suspended in the vorticies lends credence to the theory of mass transfer of particulate matters stabilized in moving vortices. Certain characteristics are necessary for a material to become a long range firebrand. Since the times of travel can be on the order of 10-20 min., it is necessary that the material burn very slonly. The remaining mass and drag coefficient must be of the right proportion so that the drag produced by the surrounding flow can carry it and place it, still burning, onto the ground a t the required distances. Experiments have shown that glowing burning is the most probable type of combustion that firebrands undergo while in flight. Table IV lists some typical firebrand materials and their characteristics.
B. EVALUATION OF FUELLOADOF FIRE One of the dominant factors in determining the rate of spread of a fire is the quantity and distribution of fuel in the neighborhood of the ignition source. A planar intersect method can be used to measure the fuel volume and surface area of a wooded region [78]. Here, a sampling plane is established in a typical forest zone, the dimensions of the plane increasing with fuel element size. A plane used for analyzing logging slash can be from 1 to 30 meters long, while only a 30-cm-long plane is needed for analysis of forest floor litter. The orientation of the plane should be such that most of the fuel element-plane intersections are perpendicular. The
TABLE IVa OF FIREBRAND MATERIALS IN FREEFALL TESTS" BURNINGCHARACTERISTICS
In flight Species Black Jack Oak Red Oak Willow Oak Water Oak sweetgum Black Cherry Florida Maple Black Willow Yellow Poplar Southern Magnolia Sycamore Mockernut Hickory Winged Elmb Slash Pine Birch Bark Spanish Moss Deer Moss Pine branch tips Dead Semi Green Clements [77]. Ulmus ahia Michx.
On ground
No. samples
No. flaming
No. glowing
No. out
No. flaming
No. glowing
No. out
100 100 100 100 100 100 100 100 100 100 100 100 100 50 40 30 100
21 56 1 0 14
79 44 99 100 86 96 84 96 38 57 37 18 79 49 0 0
0 0 0 0 0 0 12 4 0 0 0 0 21 1 0 0 0
6 29 0 0 7 2 1 0 51 34 40 57 0 0 39 28 85
4.4 71 99 98 92 98 21 87 45 65 57 43 59 36 1 2 8
50 0 1 2 1 0 78 13 4 1 3 0 41 14 0 0 7
50 50 50
32 32 17
0 0
16 20 7
33 30 43
1 0 0
4
4 0 62 43 63 82 0 0 40 30 94
6
18 18 32
1
t.3
8
S. I,. LEE AND J. 11. HELLMAN
264
TriRLE IVb TERNIN.41,
VELOCITIES
OF
FIREBRAND MATERIALS~ Velocity (ft/sec)
Material Spring leaves Black Jack Oak Srigarhrrry Sycamore Cottonn-ootl Mockernut Hickory Fall leaves Red Oak Sweetgum Cottotin ood Black Jack Oak Black Cherry Florida Maple Killow Oak Blnrk Willow Yellow Poplar Southern Magnolia Water Oak Sycamore Mockernut IIickory Pine neeclies Slash Pine Shortleaf Pine Loblolly Pine Cones Loblolly Pine Slash Pine Longleaf Pine Shortleaf Pine Jack Pine Florida Sand Pine Palmetto Fronds
(Quercus mnrz2andica bluench.) (Celfis Laet*igataKilld.) (Pla/anits occidentalis L.) (Popitlus deltoides Bartr.) (Carya tornentosn Sutt.)
0.12 6.87 6. A9 .5.86 5.77
(I)uercus falcata Blichx.) (Liquidambar styracijua L.) (Populus deltoides Bartr.) (C)itercus marilandica hluench.) ( P r u n u s serotina Ehrh.) (Acer barbalum Michx.) (Querors phellos T,.) (Saliz nzgra Marsh.) (Liriotlendron tulipzfern L.) (Magnolia grandijora L.) ( Q i ~ c nigra ~ s L.) (Planlanus OccidPnlaZis L.) (Carya tonienioso Xiitt.)
5.88 7.35 7.04 4.25 4.78 4.39 5.03 5.58 5.61 5.52 5.12 5.30 6.72
(Pinits elliottii Engelm.) (Pinus echinata Mill.) ( Pinus taeqa L.)
13.09 9.49 13.54
(Pznus taeda L.) (Pinus elliottii Engelm.) (Pinus palrislris hlill.) (Pinus eclrinafa Mill.) (Pinits hnnksiana Lamb) (Pinus claicsa ( C h a p . ) vasey) (Serenon repens (Barti-.) Small)
35.16 44.04 41.35 28.36 35.38 54.29 15.1.5
Clements 1771.
various fuel clenients that compose the fuel bed are classified according to size and shape, and each element that intersects the sampling plane is grouped according to class and counted. Correction can be made for nonperpendicular intersection of fuel elements with the sampling plane. The
HEATAND MASSTRANSFER IN FIRERESEARCH
265
fuel volume and surface area can be calculated from the following equations
k
z
i=l
j=1
where
v
is the fuel volume (cubic meters) in a forest volume equal to the area of the sampling plane A multiplied by the height L ; ni is the number of particle intersections for the ith cylinder-size class; di is the average diameter of the ith cylindrical class (meters) ; k is the number of classes for cylinders; S is the fuel surface area (meters squared) ; mj is the number of particle intersections for the j t h parallelepipedsize class; is the average thickness of the jth-size class (meters); is the average width of the jth-size class (meters) ; is the number of classes for parallelepipeds. is the particle surface area-to-volume ratio (meters-') ; = 4 / d for cylinders; and = 2 / t for thin parallelepipeds, such as hardwood leaves. Another type of wildland fuel analysis has been performed by Countryman and Philpot [79] who analyzed 16 randomly selected chamise shrubs. This plant is found in southern California, and is a predominant fuel in range fires in that area. They measured and tabulated the parameters which have been found to have a bearing on the fire spread rate: size-class distribution of fuel elements, amount and distribution of dead fuel, fuel loading, fuel density, surface-to-volume ratio, fuel bed porosity, fuel moisture content, heat content, and chemical composition of the fuel. The flammability of the leaves of some Australian forest species has been the subject of a paper by King and Vines [ S O ] . They concluded that the flammability of the leaves under study is related to the sum of the concentrations of all the mineral elements in the leaves. Philpot [ll] has also investigated the effect of mineral content on leaf flammability and also found a good correlation. Bryson and Gross [Sl] have reported on the initial findings of a program to determine the live floor loads and fire loads in modern office buildings. Two buildings in the Washington, D.C. area were selected and the live floor loads (occupants, floor covering, movable partitions, furniture, etc.) weighed and the placement in the room noted. The fire load, including movable contents and the interior-finish
266
S. L. LEEAXD J. 11.HELLMAN
fire load mere weighted and the weights converted to equivalent weights of combustibles of a specified calorific value. The movable contents fire load was further divided into free movable contents, those materials readily available for combustion, and those materials enclosed in steel shelving, steel file cabinets and desks, and insulated files and safes. The latter were derated by a specified factor before entering into the computations. The information obtained from this type of field work is essential if the rate of fire spread in buildings is to be calculated, and suppressive steps taken. For example, guidelines already exist specifying the appropriate spacing distance between sprinklers in a sprinkler system for fire extinguishment.
C. THEORIES FOR FIRE SPREAD Attempts have been made to quantify, in a fairly general sense, the fire spread process. Berlad [82] has taken the approach that from a fairly large distance a large fire containing individual trees can be “smeared” into a continuum. Using some of the techniques found useful in the analysis of the combustion of premixed gas systems, he has brought up the importance of certain fire related parameters. These include the ignition delay, which is the time between the landing of a firebrand in a fuel bed and the ignition of a new fire; an autoignition temperature for the fuel; the fuel gasification kinetics; and the flame interface shape and penetration depth. Using this type of approach, it is possible to analyze the preflame region of spreading forest fires [83]. Albini [84] has broken the process of the spread of fire through brush into a multistep process, each step of which can be analyzed separately, but which are joined by common physical parameters. The regions he has delineated are:
(a) (b) (c) (d)
preheating and outgassing region, region of intermittent deflagration, flame attachment region, and steady burning region.
The coupled equations for the various regions are then solved numerically to yield spread rate, flame depth, and flame length. Frandsen [85] analyzes the rate of spread through a porous fuel bed using a quasi-steady approximation. He evaluates the energy equation for a volume element in the preignition phase of the fuel as it closes with the fuel-combustion zone interface, and finds that the vertical gradient of the vertical component of the overall forward heat flux plays an important role in the rate of fire spread.
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De Ris [SS] has formulated a theoretical description of a laminar diffusion flame spreading against an airstream over a solid or liquid fuel bed, and finds that the flame spread rate is strongly influenced by the adiabatic stoichiometric flame temperature and the fuel bed thermal properties, except for the fuel bed conductivity parallel to the propagation direction. In another study [87], he has examined the spread of flames in a duct with combustible walls, as occurs in the ductwork from kitchen range hoods, mine roadways, and air spaces between piles of stored materials. For a fuel-rich fire in a duct, he is able to write an energy balance for the system and calculate the temperature distribution in the gas and walls. Sirignano and Glassman [SS] have shown that under certain conditions, the change in surface tension of a liquid fuel due to heating by the fire can be the dominant factor in determining the rate of spread. D. EXPERIMENTAL DETERMINATION OF FIRESPREAD RATES Many experiments have been performed to determine the effects of different parameters on fire spread rates. Small-scale test fires have been used to determine the effectiveness of various fire retardant chemicals, obtain information about the chemical kinetics of the burning process, and provide information about the mechanisms involved in fire spread. Great care must be used in extrapolating results from small to large fires. Modeling laws for fires are far from complete, and until the phenomenon of fire is better understood, no accurate generalizations can be made. 1. crib Burning
A reproducible fuel for the study of fire spread in wildla.nds or enclosures can be constructed by careful packing of uniformly sized fuel elements into an array. By varying the spacing between elements, the array fuel loading can be set to a predetermined value. Byram et al. [SS] examined the burning of cribs of white fir of various sizes and loading both with and without an ambient wind. Rothermel and Anderson [go] used pine needles as fuel and, in addition to measuring fire spread rates, instrumented individual pine needles with thermocouples to measure heat transfer rates within the fuel bed. They concluded that the rate of spread increased with wind speed, flame depth increased and vertical depth of burn decreased with increase of wind speed, and in the absence of wind, the rate of spread decreased linearly as fuel moisture increased. It was also concluded that the fire was carried in the surface fuel particles. With ambient wind, measurements indicated that the air temperature was higher than the needle temperature, causing both the radiative and convective heating of the fuel. Both this study, and the earlier one by Byram et aE. point out
S. L. LEEAND J. 31. HELLMAN
268
that in the presence of wind, combustible gases, the exact source of which is unknown, may form on the surface of the fuel bed ahead of the main fire front. These are ignited periodically by the fir(: and sweep ahead of the main firc front along the surface of the fuel, and can possibly play a major role in the mechanism of fire spread in the presence of wind. Rotherme1 and Anderson have produced a correlation of thc rate of spread of thcir test fires with a n ryuivalcnt unit energy release, drfined by weight loss rate X energy equivalent of fuel (Btu/ft2 niiri)
ER =
rombustion area
From their experimental results, they determined that 3240
E -
- (1
ER =
for ponderosa pine
+ 0.0069 li) 2740
(1
for white pine
+ 0.0088 Cr)
whew C' is the ambient wind velocity. As shown in Fig. 19, one limiting case produces fire storms (no spread), while the other limiting case is that of a runa\\-ay fire. Gross [Sl] and, more recently, Block [92] have dctermined that the burning rates of cribs can be grouped into two regions. In a densely packed crib, the spccific burning rate depends strongly upon th r packing density 2s-
-c 20 E -
\
-! -
R U W Y
FIRES
=IsQ
3
Y
: 10 AD
i_ -
PONDEROSA PINE
WHITE
A I R VELOCITY
(ft/min)
PINE
0.0
0
a A 0
0
I32
A
-
264
J
440
G
704
Y
0
TRANSITIOU
W
2 50
I
0
\f L , , iooo
1500 zoo0 EQUIWLEW WIT ENLWY RELEASE
FIRE SloRMr
, o - , 2500 aoo
En
3500 (Btu/min/ft2)
FIG.19. Fire characteristic curve relating rate of spread and equivalent unit energy release rate [ER,extrapolated from Eqs. (19)] [SO].
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and crib height. I n a loosely packed region, the burning rate becomes independent of these factors. 2. Burnin.g of Materials Other Than Wood
Numerous materials have been burned in an effort to gain an understanding of the combustion process for solid, wood-like materials. Parker [93] has studied the flame spread down a vertically supported index card. Kinbara et al. [94] measured the downward propagation of smoldering combustion in circular rods of rolled paper, circular incense sticks, strips of cardboard, and tightly bound piles of carbdoard. Emmons and Shen [95] have investigated the burning of strips of paper. Hottel et al. [96] have measured the effects of artificial irradiation and of humidity on the propagation of a line fire through beds of torn newsprint and computer card punchings. Tinney [97] placed wooden dowels in a furnace and measured center temperature, weight loss, and internal pressure histories. 3. Other Fire Spread Studies As noted in Section III,B various types of fabrics have been burned in fire spread tests to determine their safety for use in clothing, bedding, upholstery, and as floor coverings. Vogel and Williams [98] have studied flame propagation along arrays of (headless) match sticks, and conclude that convective effects are of primary importance in flame propagation for fuel elements of the tested scale. Berlad et al. [99] have analyzed the fire spread through a pine needle crib in terms of a quasi-steady fire spread wave.
E. LARGE-SCALE FIRESPREADSTUDIES Studies of full-scale fires often reveal fire phenomena that do not occur in laboratory-sized studies. When possible, fire departments, forest services, and other fire researchers go to the sites of naturally occurring fires in an attempt to observe the phenomena with an educated eye. One of the best documented forest fires occurred in northern Idaho during the summer of 1967 [loo]. In only nine hours, this fire traveled 16 miles and engulfed more than 50,000 acres of timberland. Data obtained from this fire included the weather history in the area of the fire, a topographical survey of the area, descriptions of the fire activity from various personnel in aircraft and on the ground, fuel distribution, and photographic data on the position of the fire a t various times, and the aftereffects of the fire. This data was pivotal in the formulation of a theory to explain long range spotting [75].
Large fires have been set in a controlled manner to measure various fire paranietws. In Project Flambeau [loll, designed to investigate mass fircs, fuel beds ranging in size up to 170,000 ft2 and having a fuel loading of about 3.5 113s f t 2 w r e burned. Other tests simulated a suburban housing area, with niany smallrr fuel beds designed to match fuel-loading charactcristics of individual homes. Instrumentation included cup anemometers, tracer smoke, pressurc transducers, aspirated thermocouples, weighing platforms, and cameras. The instruments were located on towers in the fire arca. Data was recorded on strip chart recorders and on punched tape for ease of automatic data processing. A similar set of tests were performed in Australia under the name Project Euroka [l02]. From thew tests, several fire phenomena have been clearly demonstrated. All of thc high intensity fires produced plumes which spawned vortices and, in some cases, fire whirls. In the Flambeau tests, firebrand spotting x a s much more intense than prcviously anticipated; one fuel bed sct up for later tcsting was ignited by firebrands from a test under way. The Flambeau test series produced a set of sufficient, but not necessary, conditions for a mass fire. These are listed in Table V. Other conclusions from the test series were:
(a) Fuel characteristics are the major controlling factors in fire behavior. (h) Ilate of thermal energy production is of primary importance in determining fire characteristics and behavior. (c) Strong turbulence and airflow develop within the fire boundaries. (d) Radiation is of minor importance in fire spread outside the boundaries. (e) For multiple fuel bed fires, the position of a fuel bed in the array has only a minor effect on its thermal pulse (the rate of heat output per unit area and time) pattern. (f) Wildland fuels may be used to simulate urban fires. (g) Lethal Concentrations of noxious gases occur within and adjacent to fires. (h) The folloiving model has been established for a stationary mass fire. (i) Fuel bed zone-extmds from the ground to the top of the fuel brd. The vertical dimension may vary from less than one inch to many feet, depending on the type of fuel involved. (ii) Combustion zone-the actively flaming area in and above the fuel zone. Vertical height varies, hut is usually less than 100 ft above the fuel bed. (iii) Transition (turbulence) zone-lies between the combustion zone and the more organized flow of the main convection column. Both upper
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TABLE V SPECIFICATIONS FOR Items Fuel bed (wood fuel) Surface to volume ratio (a) Porosity ( 7 ) Fuel loading Kindling fuel Fuel bed area Ignition points Fuel moisture Fire Fire area Fuel bed spacing Terrain Weather Ambient wind 10 ft level Ambient wind 5000 f t level Relative humidity Temperature Lapse rate
A
MASS FIRE’ Specifications
25.11 ft2/ft3 23.85 = lo-* f t 3 / f t 2 > 17 lb/ft2 10 x 10-2 lb/fts >1700 ftZ 1/300 f t 2 of fuel bed area
100,000 f t 2 <25 ft Level (approx.) < 10 ft/sec <20 ft/sec <30% >50°F Neutral to unstable
Countryman [7].
and lower boundaries are indefinite. In most fires, this zone probably does not extend more than 100 to 200 ft above the combustion zone. (iv) Fire (thermal) convection zone-the area between the top of the transition zone and the base of the convection column gap. Energy for the convection in this zone comes chiefly from the fire, although some condensation of water vapor is also likely. Vertical height of this zone may vary from less than 1000 ft in some fires to more than 15,000 ft in others. (v) Smoke fallout zone-a relatively thin zone a t the base of the convection cap. This thin layer of smoke spreading out from the convection column is characteristic of towering convection columns. (vi) Condensation convection zone-the area from the smoke fallout zone to the top of the convection column. The column usually widens abruptly to form a “cap.” It is usually light in color as a result of the condensed water vapor of ice crystals. Heat from condensation is likely the chief source of energy for convection in this zone. This zone is not found in all fires. Its formation depends upon air mass characteristics as well as on size and energy output of the fire. The vertical length of this zone is variable. At times it may approach the length of the fire convection zone.
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S. L. LEE AND J. fir. HELLMAN VI. Instrumentation in Fire Research
As research in fire has progressed, methods of making the necessary measurements have been developed. This section describes some of the experimental techniques that have proven useful.
A. EXHAUST HOODS Due to the large quantities of noxious gases produced by fires, experimental or otherwise, it is essential that fire research laboratories be equipped with an effective exhaust hood. The size of the hood will, to a large extent, govern the scale of the experiments performed. Typical exhaust hoods for laboratory-scale fire research have an opening of a linear dimension of length scale of 12 f t [103, 104). The interior surfaces of the hood should be able to withstand a maximum temperature of 2200'F. Variable height and blower speed, while not essential, add to the versatility of an exhaust hood installation. Placement of the exhaust hood in the laboratory is important; an asymmetric location can generate shear in the inflow and convection column that cannot be controlled. Curtains can be used to alleviate this problem. Care must be taken in the design of the air inlet to the room; it should not be placed so that air is drawn over the experimental apparatus.
B. WIND TUNNELS Both vertical and horizontal wind tunnels are used in fire research. The Northern Forest Firc Laboratory of the U.S. Forest Service has an elaborate facility with both high and low speed horizontal tunnels. These have been used in measuring the rate of spread over cribs of various fuel types, both with and without fire retardants. Tarifa et al. [73] has used a small horizontal wind tunnel to measure the drag, mass loss, and rate of decrease of size of firebrand materials. The vertical wind tunnrl has seen use primarily in the determination of the terminal velocity of firebrand materials. A conical test section is used and from the inlet conditions, the gcometry of the tunnel, and the axial location of the material under test, the terminal velocity can be computed. This is an important quantity because in theoretical analysis of the spotting phenomenon, it is often assumed that the firebrand travels horizontally a t its terminal velocity.
C. FUELS I n fire studies where the nature of the combustion is not considered a critical part of the investigation, such as in experiments in upper plume
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dynamics, gas-air flames can be used as the heat source. This fuel has the advantage of uniformity and precise control over flow rate and placement. Both bottled and city gas have been used. When it is important that the pyrolysis process be controlled, pure cellulose can be molded into the desired shape and burned. For more true to life studies, the wood crib has been used extensively as a fuel source. In using both cellulose and wood as fuels, careful control must be placed on moisture content, packing density, and element size.
D. FABRIC TESTING METHODS The National Bureau of Standards, in association with other testing organizations, has developed standardized procedures for establishing the fire danger from various types of commonly used fabrics. One type of faLric tester has been described in Section II1,B. Other testers, holding the fabric sample at angles other than vertical have also been used. Carpeting is tested by applying an ignition source and watching for fire spread. A full-size corridor, modeled after a hallway in a nursing home or hospital has been set up as a laboratory to investigate the effect of typical airflow patterns on the spread of fire. Flammable carpeting has been established as the means of spread of several nursing home fires. It is hoped that tests such as these will permit establishment of a standard of flammability of carpeting for this type of use.
E. FLOWVISUALIZATION To obtain a visual indication of the flow pattern in the neighborhood of a fire, various tracer materials have been used. The smoke produced in a fire is often sufficient to delineate major flow patterns, including vortices. Very light materials have been injected into plumes in the hope that the path they trace will closely approximate the fluid streamlines. Metaldehyde, a commercial insecticide sublimes fairly easily and when the vapor recondenses, it forms a very light, highly reflective particle. Thistledown has been scattered in a plume to visualize the flow pattern. In large outdoor fire tests, balloons weighted to neutral buoyancy can be released to trace the streamlines. Rockets trailing titanium tetrachloride or aluminum powder tracers have been used in the Flambeau series of tests. In very large fires, after-the-fact information is often useful in establishing approximately the nature of the fire. The pattern in which debris is scattered, the direction in which felled trees are pointing, and the rate and method of spread of the fire provide clues as to the flow pattern generated by the fire.
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S. L. LEE AXD J. 34. HELLMAN
F. TEMPERATERE MEASUREMENT Thermocouples and radiation thermometers are the primary instruments used to measure temperatures in fire environments. I n using thermocouples, it is essential that they be radiation shielded. I n a very intense radiation environment, i t may be necessary to use an aspirated thermocouple; the sensing element is placed in a tube and air from the surrounding region is drawn over it. Limits on maximum temperatures occurring in a region can be obtained by using temperature-sensitive paints. This type of instrumentation is very useful in locations where other types of temperature-measuring devices cannot be easily placed, such as at the top of a ladder used by a fire department. This type of reading can be important if the mechanical strength of the Iadder is a strong function of the maximum temperature to which it has been exposed. Radiation thermometers have the advantage of not requiring any physical contact with the object whose temperature is desired. This method must be used with care, for the temperature readings are strongly dependent upon the emissivity of the object and the transmission characteristics of the air between the source and the thermometer. Project Fire Scan is a n attempt by the U. S. Forest Service to adapt an airborne radiation thermometer for use in detecting forest fires over a large region of timberland. In experimental work, the choice of fuel can, to some extent, control the radiation losses from the flaming zone, where temperatures are highest. As an example, methyl alcohol produces a nonluminous flame, with little radiation loss, and acetone produces a luminous flame with significant radiation losses. I n wood-fueled fires, the radiation losses are less easily controlled, and can be significant. It has been postulated that radiation losses are a n extinction mechanism for fires.
G. VELOCITYMEASUREMENT The greatest difficulty in measuring wind velocities in a fire environment derives from the high temperature. Commonly used hot wire anemometers have a very short life span. A temperature-calibrated hot wire probe using a 0.002-in. nickel wire has proven useful in measuring time-mean velocities in a plume [60]. Optical interferometric methods such as the Schlerin or Mach-Zender interferometers have had use in the experimental study of the plumes above small flames. I n large experimental fires, stainless steel cup anemometers and wind vane directional indicators have been used, albeit heavily insulated. The laser-doppler anemometer, already in use in rocket exhaust plume
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studies, can be used to great advantage in fire research. No physical contact with the area under investigation is needed, density variation of the air does not affect the readings, and the soot contained in the plume provides ample scattering sites. The method would probably not be useful for readings of the interior of dense smoke-filled plumes.
VII. Fire Research and the Fire Fighter One of the direct beneficiaries of fire research should be the fireman. The methods used to fight fires today are quite similar to those used hundreds of years ago. Firemen now used motorized vehicles instead of horse-drawn ones to get to the scene of the fire, but men still have to unroll the hose, drag it into the burning building, breaking down any walls or obstacles in their way, pour hundreds of gallons of water on the fire until it is extinguished, drag the hose out of the building, clean it, reroll it, store it on the truck, and then return to the station house. Due to the hostile environment in a burning structure and the premium on speedy operation, it is almost inevitable that frequent injuries make fire fighting one of the most dangerous occupations. Any application of modern technology that will serve to make the job of extinguishing fires less time consuming or dangerous, will increase the level of fire safety in the community. Since salaries now consume approximately 90y0 of a department’s budget, any increase in efficiency can lower fire protection costs.
A. EQUIPMENT DESIGNED FOR
THE
FIREFIGHTER
1. Fire Station Location
Ideally, when an alarm box is pulled, the local fire brigade mill respond quickly. This can be achieved only if the fire station is a short travel time span away from the location of the fire. Unfortunately, fire station locations are often dictated by population patterns of fifty or a hundred years ago, and do little to serve present-day needs. For lack of a better criterion for judging the adequacy of fire protection, insurance company ratings are often used to determine the need for new station locations. In a n effort to put the location and relocation of fire stations on a more rational basis, a systems analysis approach [105, 1061 has been applied. After gathering data on frequency of fires from various areas in a fire district, the types of fires, geographic and political divisions in the area, false aIarm frequency, and travel times from the station houses to the fire locations, a statistical analysis can be performed. This can determine the
276
S.L. LEEAXD J. A I . HELLMAN
effect of adding or removing a station house a t a certain location. Manpower and equipment at the various locations can also be varied analytically to obtain an optimal configuration for the given financial allocation. 2. Fire Deparfmetit Vehicles
The red firc truck may soon be only a memory. Visibility testing of diff erclnt colors under nonideal viewing conditions has shown that lime yellow is much more visible than the traditional red under all lighting conditions. Nore substantial changes have taken place on both the pumpers and the hook and ladder; more powerful pumps are now being used to throw streams of water, and the ladder is being replaced, in niany instances, by a snorkel, an open cab on an articulated arm. This design has been shonn to have a more rapid response time than the conventional ladder. Attacks on firemen responding to calls during urban disturbances have led to the adoption of closed, rather than open, cabs for the trucks. The hose used in fire fighting has proven adequate, but has several serious drawbacks. After use, the wet-through hose is quite heavy, which increases turnaround time for the brigade due to handling problems. In subfreezing weather, the hose freezes after usr, making retrieval very difficult and time consuming. A nonflammable, light hose material would alleviate some of these problems.
3. Firemeti’s Clothing and Gear
Thr Bureau of Labor Statistics, based on a study of fire fighter’s injuries, has identified the five major hazards faced by firemen [107]. These are: (a) (b) (c) (d) (e)
contact ivith caustic, toxic, and noxious substances; striking and being struck by objects; overexertion; falls; contact with high temperatures and hot objects.
Since the fireman is working in an unfriendly environment, it is essential that he be properly clothed. An ideal outfit would enable him to work with ease, yet be protected from the above-listed hazards. A major piece of clothing worn by firemen is the turnout coat, a n outer garment that covers the upper torso. In an attempt to provide fire departments with a rational basis for choice of turnout coat, the NBS has recently embarked on a study of available coats and of materials that might be useful in such coats [lOS]. One of the more remarkable findings of this study was that on all of the commercially available coats tested, a t least
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one of the layers of the multilayer coats (inner lining, interlining, outer shell) was quite flammable. This presents a clear and present danger if the coat rips during a fire. I n addition to flammability testing, the turnout coats were subjected to tests of fabric weight, breaking strength, tear strength, stiffness, water penetration, abrasion resistance, shrinkage, and seam strength. These tests have resulted in a performance-oriented specification for turnout coats to be used by fire departments when they are requesting bids from manufacturers [l09]. Rather than specifying the various materials of which the coat is to be composed, the specification states the technical specifications which the coat must meet. The basic procedure applied to the turnout coats can also be applied to other pieces of fire apparatus. Boots, helmets, gloves, fire hoses, and ladders all need to be evaluated from an objective viewpoint with the goal of improving the device’s response to the fireman’s needs. Application of technology gathered in other fields can make a great improvement in the usefulness of fire apparatus. Light, compact portable breathing units designed for use by NASA for use in space are being modified for use as fire equipment. Present-day breathing apparatus weighs approximately 30 lbs. A 10-lb unit of equivalent capacity would enable the firemen to do their job more quickly and effectively. Some fireproof fabrics developed after the disastrous Apollo fire are now being tried for use in the construction of firemen’s clothing. Miniaturized communications gear now permits the fire chief on the scene of a fire to keep in contact with his men inside the building. A frequent cause of loss of life at fires is the collapse of the structure on the firemen. To avoid this danger, collapsing walls are frequently brought down by the fire company, often with axes and sledge hammers. Technology has provided more efficient ways of doing this job. Shaped explosive charges can be carefully controlled to accomplish the job with a minimum of damage to the surrounding areas and a minimum of exposure to danger by the firemen. New, more powerful pumpers can throw streams of water powerful enough to break down endangering walls. High-intensity strobe lights have been redesigned to work in a fire environment to serve as beacons, indicating stairwells, windows, or other exit ports that might become obscured by heavy smoke in a building.
B. BUILDINGCODES Attempts to legislate losses from fire out of existence usually come in the form of fire codes for communities. The basis for many of these codes has been practical experience and testing done a t government and insurance
278
S.L. LEE AND J. X.HELLMAN
company laboratories. Many of these codes are now obsolete due to changing building materials and building styles. There has been a large growth in the number of high-rise buildings in the past 20 years as the population density has groivn in various areas. Many of the new skyscrapers are essentially scaled boxes; windows are permanently shut to permit year round air-conditioning. In case of fire, it becomes almost impossible to evacuate the hundreds of occupants in an orderly manner in a short period of time. This has brought about some drastic rethinking in ways to obtain fire safety in this type of building [llO]. One thought is to build heavily fireproofed “islands of safety’’ a t various locations throughout the building. Occupants from the surrounding areas would go to these locations in case of fir(.. In addition to providing a shorter transit time for the people to get to safety, this method also Xvould clear the stairs and elevators for use by fire department personnel. Another possible way to increase fire safety in tall buildings is through selective ventilation [ill]. Most fire codes now call for all air-conditioning to be shut off automatically when a fire is discovered, preventing increased air travel to the fire, and preventing smoke from the fire from traveling throughout the building. With greater use of plastic in modern buildings, there is an increased danger that the poisonous products of pyrolysis may become heavily enough concentrated in the fire area to become lethal. Selective ventilation can be achieved by increasing the strength of the return air system on the floor of the fire and exhausting smoke through emergency outlets in the building return ductwork. Another way is to increase the supply of fresh air so a s to keep the smoke dilute. Pressurization of such areas as elevator shafts and stairwells can curtail air movement and prevent the ingestion of smoke into these areas. Modern elevators have proven to be vulnerable in fires. Heat actuated call aud dircction buttons can direct the cab to the floor with the fire. Door opening mechanisms based on interruption of a light-photocell circuit by entering passengers can be fooled into staying open by dense smoke. Occupants are now instructed to avoid using the elevators in case of fire, and it is possible to arrange the elevator controls so that when the alarm rings, the cab is directed automatically to the ground floor where it can be put under manual control for use by firemen. Recent developments in instrumentation are being applied to the problem of fire detection in buildings. In addition to sensitive temperature indicators, smoke detectors, some using laser beams [ l l Z ] have been developed for use in fire alarm systems. A performance-based firc alarm rating criterion, when achieved, will be a useful addition to present fire codes. This will depend on progress in the related areas of fire spread and plume dynamics.
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One way that many codes try to prevent the gross spread of fires is through legislating the minimum spatial separation between buildings. The point of view often taken in establishing these codes is that the primary fire spread mechanism that will cause danger is radiation heat transfer. This is a prime motive for the work done on piloted ignition of radiatively heated materials (Section II1,C). An ideal code would keep buildings spaced so that the intensity of radiation from a burning building to a second building would be less than 0.3 cal/cm*-sec, the threshold level for piloted ignition of many building materials C1131. Unfortunately, this criterion usually results in unfeasibly large spacings between buildings. A less conservative rationale can be based on data from experimental burnings of typical dwellings. Two types of buildings were burned: one with a highly flammable interior and the other with a noncombustible interior. The highly flammable case produced a radiation intensity twice that of the noncombustible case (40 vs 20 cal/cm2-sec). It was noted that the peak radiation levels did not occur until at least 16 min. had elapsed from the ignition of the fire. Prior to this time, levels were approximately 20% of the peak values. Since this is usually sufficient time to permit a fire brigade to get to the scene, a standard case can be established at these lower levels. A method of quantifying this procedure involves a conJguration factor, defined as the ratio of the radiant intensity at the receiving surface to that at the radiating surface. This can be calculated from geometric considerations if the radiation is assumed t o be from a blackbody at uniform temperature. The critical values for the configuration factor can be calculated from 0.3 F --- 0.035 - (40/5)
F
0.3 - 0.07 - (20/5)
for hazardous cases
for normal cases
To establish a better basis for a code, it will be necessary to establish more precisely the nature of radiation transfer from burning buildings with windows, and research is continuing in this area [114, 1151.
C. PRODUCT TESTING Testing products for fire hazard before they are used in buildings can eliminate many dangerous ignition and smoke sources. Insurance company laboratories have been doing this type of testing for many years, and Congress has recently made the National Bureau of Standards responsible for overseeing specifications of flammability in fabrics [l 161. As electronic
280
S. L. LEE AXD J. 31. HELLMAN
equipment bccomes more complex and widespread and new building materials come into use, different types of testing are needed. Several plastics, upon heating, have been shown to produce poisonous gases. Products made from these types of materials become extremely dangerous during a fire. Some building materials have been shown to produce an inordinate amount of smoke upon burning. Others produce great quantities of heat. Instrumentation has been devised to determine the extent of these dangers from various materials. Chemical analysis can be performed on the products of pyrolysis to determine its character. A method of measuring the ‘(amount of heat available for release” by materials in building materials, called “potential heat,” has been devised by Loftus et al. [117]. Gross et al. [118] have established a method of measuring the smoke from burning materials using the incrcase in optical density across a standardized path. To establish standards for structural soundness in a fire environment, it is first necessary to determine what a typical fire environment is, and then specify the loading that the structural members must withstand for the given time period. Tests on full-scale beams in instrumented rooms are used to establish the effectiveness of various coatings and construction practices [119]. To establish a typical fire environment it is necessary to determine typical fire loading, ventilation, and room size conditions. Testing of less than full-scale samples can lead to nonconservative ratings; fireproofing materials applied to scaled-down beams often prove adequate. On large, full-scale beams, increased thermal expansion can lead to the cracking and shedding of large chunks of the fireproofing material, exposing the bare metal to the flames.
VIII. Concluding Remarks Fire research is a rapidly growing field with workers from many allied disciplines. Many of the aspects of fire have been investigated, but except for plume dynamics, few areas are well enough quantitatively understood. The overall question of fire spread is closely linked with the problem of fire extinguishment. Advances in one area xi11 lead to advances in the other, with the associated reduction in life and property losses to fire. ACKNOWLEDGMENT The authors wish to express their sincerest appreciation to the RANN (Research Applied t o National Needs) Program of the National Science Foundation for its generous SUPPOI% that has made this work possible.
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Author Index
Numbers in parentheses are reference numbers and indicate that an author's work is referred to although his name is not cited in the text. Numbers in italics show the page on whioh the complete reference is listed.
A
I
Abdulkadir, A., 34(47), 37 Abuaf, N., 211, 212, 218 Adams, J. B., 7, 8041, 9, 21, 22(14), 24 (32, 37, 41), 25(32, 371, 36 Adams, J. S., 270(102), 683 Ade, P. A., 34, S7, 53, 68, 81 Agrawal, I).K., 21, 23, 36 Agrawal, S., 191, 617 Aizawa, M., 172(28), 815 Albini, F. A., 266, 28s Alvares, N. J., 243(39), 286 Anwtassakis, E., 21, 23, 36 Anderson, D., 55(43), 88 Anderson, G. H., 151,166 Anderson, H.E., 267, 268(90) 269, $83 Anfimov, N. A., 53(34), 58(34), 64(34), 70 (34), 71(34), 82 Angehno, H., 185(76,77) 205(76,77), 616 Anton, J. R., 172, 177, El5 Apfel, R. E., 106(26, 27, 28), 107, 112, 113, 164 Aronson, R. B., 278(110), 684 Avduevskii, V. S., 53,58(34) 64,7O, 71, 89 Ayers, P., 172, 175, 177(27), 615
Bankoff, S. G., 111, 112, 116, 121, 134, 136, 138, 139, 141, 162, 166, 166 Bannister, J., 203, 617 Barker, J. J., 171, 174, 615 Barnes, D. K., 118(50, 51, 52), 121(50, 51, 521, 165 Bartell, W. J., 210, 218 Bartholomew, R. N., 200,618 Baskakov, A. P., 189, 190, 191, 198, 207, 208,209, 216, 617, Bastin, J. A., 2(7), 34, 35, S7, 44, 45, 46 (20), 48,53(31), 57(20), 62,68(18,31), 81
Batten, J. J., 270(102), 683 Becker, R., 92, 163 Beer, H., 156(79), 165, 166 Beilin, M. I., 177, 216 Berg, B. V., 207(123), 209,217,218 Bergles, A. E., 149, 150, 152, 157, 165 Berl, W. G., 221,281 Berlad, A. L., 261, 266(83), 269(75), 686, 283
Bernett, E. C., 50, 51, 59, 68, 81 Bhat, G. N., 204, 217 Bilson, E., 27, 37, 57(47), 82 Bibolaru, V., 205, 217 Birkebak, R. C . , 2(4, 5, 6), 12, 13, 16(22), 17, 19(24), 20, 21, 23(6, 29,38, 39,401, B 24, 28, 29(40), 30(24, 381, 31(4, 61, 32 (40), 34(4, 6, 47), 36, 36, 37, 52, 53 Baerg, A., 201, 202, 203, 206, 209, 617 (32,37), 54(32,37, 39), 69(32, 37), 70 Baker, M., 75(69), 83 (37,39), 75(39, 70,71),76(70), 77(39), Bahl, S. K., 255(56), 682 78(39, 70, 71), 80(39, 701, 81, 86, 83 Balakrishnan, A., 121(58), 166 Blackshear, P. L., 225,229, 243(39), 260, Baldridge, S., 65(52), 67(52), 82 281, 682 Bamford, C. H., 243, 681 285
AUTHORINDEX
286
Blackwell, J. H., 48, 81 Blakely, A. D., 234(13), 281 Blander, >I 10.5, ., 106, 164 Block, J. -4., 268, 283 Bolsamo, S.R., 32, 37 Bondarchuk, T. P., 203(107), 217 Botterill, J. S. bl., 181(70, 72), 185(72, 73, 74, 733, 192, 216 Bouvier, J . E., 107(35), 164 Bowell, E. L. C., 2(7), 35 Bradshaw, K. D., 172, 177, 215 Brauer, F. E., 109, 164 Brazelton, W. T., 183, 200, 203(109), 208, 217, 218
Briggs, F., 19, 21, 24(30), 36 Briggs, L. J., 96, 97, 98(1>), 164 Brown, U. J., 229(17, 18),281 Brown, J. K., 262, 283 Browning, B. L., 226, 281 Brun, E. A., 177,216 Brundrett, G. W., 184(71), 216 Bryson, J. O., 263, 283 Butler, J. C., 57(46), 82 Butt, XI. H. D., 185(75), 216 Byram, G. &I., 267, 283
C Cain, G. L., 184(71), 185(75), 216 Caldas, J., 200, 218 Campbell, J. R., 203, 217 Campbell, hi. J., .5(8), 19, 20, 24(27), 35, 36, *57(45),73(39), 82 Capes, C. E., 203, 217 Carman, M. F., 37(46), 82 Carrier, W. D., 111, 53(43), 56, 82 Carslaw, H. S., 48, 81 Cassidy, W. A., 19(25), 24(25), 36 Charette, M. P., 7, 8, 9, 36 Chechetkin, A. V., 202, 218 Chen, J. C., 1.59, 160, 166 Chen, W. H., 211(140, 141), 218 Chung, B. T. F., 191, 203, 217 Chute, J., Jr., 53(35), 74(35, 36), 82 Ciborowski, J., 177, 216 Clark, H. B., 119, 131, 132, 165 Clark, J. A., 86, 163 Clark, K. K., 229(15), 281 Clark, S. P., Jr., 53(35), 54(36), 74(35,36), 82
Claxton, K. T., 177(59), 178(-59), 216 Clegg, P. E., 34, 37, 44(18), 45(18), 46, 48 (18), 33(18), 57, 62(18), 68(18), 81 Clements, H. B., 263, 264, 267(89), 283 Cohen, A. J., 19(25), 24(25), 36 Cohen, E. R., 92, 164 Cole, R., 153, 156, 165 Colner, D., 275(105), 284 Conel, J. E., 11, 21, 22, 24(32, 33, 34), 36, 71(63), 73(63), 82 Cooper, G. T., 200, 201, 205, 209, 217 Cooper, K. W., 118(50), 165 Cooper, hi. G., 136, 166 Copes, C. E., 171(17), 215 Corlett, R. C., 260, 282 Corty, C., 119, 165 Couderc, J. P., 185(77), 205, 216 Countryman, C. M., 224, 265, 270, 271, 281, 283
Cox, J. E., 107(35), 164 Crank, J., 243(33), 281 Cremers, C. J., 2, 4, 5, 6, 12, 13, 16(22), 17, 19, 20, 21, 23(6, 26), 31(46), 34, (4, 6), 35, 36, 48, 52, 53(37), 54(37 38, 39, 40, 41, 42), 57, 58(38, 41), 69 (32, 37, 38, 39, 40, 41), 70(37, 38, 39, 40, 41), 71, 75(39, 71), 76(41, 70), 77, 78, 79(41), 80(38, 39, 701, 81, 82, 83
D Dahlhoff, B., 210, 218 Daily, J. W., 87(2), 163 Das, C. N., 200,218 Davidson, J. F., 169(1, 5), 170(13), 171, 174, 176, 214, 215 Davis, E. J., 151, 165 Dawson, J. R., 19, 20, 21, 23(26, 29, 40), 24, 28, 29(40), 31, 36, 53(32), 54(32), 69(32), 81 Dean, C. W., 158, 161, 166 Deinken, H. P., 177(43), 216 Del Notario, P. P., 261(73), 272(73), 283 Denega, A. I., 177(51), 216 De Ris, J., 260, 267(87), 282,283 Dietrick, J. R., 109(36), 164 Doring, W., 92, 163 Dollfus, A., 19(28), 36 Donnadieu, G. A., 173, 175, 177(44), 215, 216
AUTHORINDEX Dougherti, J. E., 177(43), 216 Dow, W. M., 181, 192, 199, 203, 204, 205, 206, 216 Drake, E. M., 54(36), 74(36), 82 Drinkenburg, A. A. H., 192,217 Drbohlav, R., 169(4), 215 Dwyer, 0. E., 159, 160, 166 Dzakowic, G. S., 152, 153, 165
E Ebert, C. H. V., 246(41), 282 Einstein, V. G., 174(40, 41), 175(40), 177, 181(41), 198, 200, 201(154), 202(155), 203, 204(41), 205(116), 206, 210(139), 215, 217, 218 Ekonomov, S. P., 53(34), 58(34), 64(34), 70(34), 71(34), 82 Elliott, D. E., 189(71), 216 Elliott, E. R., 267(89), 283 Elliott, T. C., 278(111), 284 Elmas, M., 211, 218 Emelianov, D. S., 177(53), 216 Emmons, H. W., 221, 243, 245(1), 250, 255, 257, 269, 281, 282, 283 Endo, H., 269(94), 283 Enjalbert,, M., 185(76, 77), 205(76, 77), 216
Epstein, P., 40, 80 Ergun, S., 170, 215 Ermakov, G. V., 104, 164
F Fairbanks, D. F., 186, 187, 188(82), 189(81,82), 191,205(82), 206(82), 216 Fan, L. T., 196(89), 203(89), 217 Faust, A. S., 119, 165 Fenske, R. M., 203, d l 7 Ferron, J. R., 173, 216 Fetting, F., 193, 202, 203, 205, 206, 217 Fielder, G., 34, 37, 44(18), 45(18), 48(18), 53(18), 62(18), 68(18), 81 Fillipovskiy, N. F., 208, 218 Fisher, J. C., 111, 165 Flory, K., 109, 164 Fountain, J. A., 48, 51, 52, 56, 57, 81 Frandsen, W. H., 244(40), 266, 269(99), 282, 283 Frantz, J. F., 172, 174, 177, 215
287
Frenkel, J., 92, 164 Fritz, J. C., 173, 215 Fritz, W., 207, 217 Frost, W., 152, 153, 165 Fryxell, D., 55, 82 Fugii, N., 64(50, 51), 67(51, 53), 82
G Gabor, J. D., 185, 186, 116 Galloway, T. R., 208, 217 Gamson, B. W., 200, 201, 218 Garg, D. R., 243(36), 282 Garipay, R. R., 73(65, 66), 82, 83 Garlick, G. F. J., 19(28), 36 Garris, C. A., 253, 254(48), 255(48), 256 (48), 257, 282 Gear, A. E., 46(20), 57(20), 81 Geake, J. E., 19(28), 36 Gelperin, L. G., 207(123), 217 Gelperin, N. I., 174(40, 41), 175, 177, 181 (41), 198, 200, 201, 202, 203,204(41), 20$(116), 206, 210(139), 216,217, 218 Genetti, W. E., 209, 210(136), 218 George, C. W., 234(13), 281 George, P. M., 267(89), 28.3 Gilbert,, C. S., 96(14), 97(14), 98(14), 99 (14), 164 Gilsinn, D., 275(105), 284 Gishler, P. E., 201(104), 202(104), 203,206 (104), 209(104), 217 Glaser, P, E., 42, 43, 45, 48, 50, 58(22), 59 (22), 64, 68, 81 Glass, B., 25,36 Glassman, I., 267, 283 Gold, T., 5(8), 19, 21, 24(27), 27, 36, 37, 57, 82 Goodman, T. R., 212, 218 Gorelik, A. G., 194, 217 Graham, R. W., 128, 148(61), 149, 165 Gray, V. E., 280(118), 284 Green, N. W., 109(40), 164 Greenwood, W., 55(43), 82 Griffth, P., 122, 123, 125, 126, 127, 128, 130, 131, 132(59), 133, 152, 166 Grimmett, E. S., 209(134), 210(136), 218 Grishin, M. A., 177, 216 Gross, D., 235(25), 258, 265, 268, 280 (117, 118), 281, 282, 283, 284 Grummer, M., lSl(64, 65) 189, 203, 216
ACTHORINDEX
288
Guiglion, C., 185(77), 216 Gutfinger, C., 211(140, 141, 142), 212, 218
J
Jackson, R., 170(16), 215 Jacob, A., 187, 189, 199,202,203,205, 217 Jaeger, J. C.,40, 70, 71, 72, 78, 81,82 Hafer, C. A., 31, 281 Jaeger, J. S., 48, 76, 81 Hagemeyer, W-.A,, 71(63), 73(63, 64,65), Jaffee, L. D., 50(30). 51(30), 59(30), 6s 82, 83 (30~ 81 Haiajian, J. D., 73(58), 82 Jakob, hl., 181, 184, 192, 203, 204, 206, Hamano, Y., 67(33), 82 216 Rammitt, I?. G., 57(2), 163 Johanson, L. N..173, 21/i Han, C.-Y., 132, 265 Johnson, F. S., 29, 37, 75(68), 83 Hapke, B., 2(1), 7(1), 9, 10, 19(25),21(31), Johnson, G. M., 234( 13), 281 24(%3},35, 36 Johnson, S. W., 56(44), 82 Harrison, I)., 169(1, 21, 170, 171, 174, 814, Johnson, T. V., 7, 8, 9, 35, 36 215 Johnstone, H. F., 199. 204, 205, 207, 217 liaruaki, F., 177, 216 Jones, B. P., 73(66), 83 Harvey, E. K , llS(51, 32, 53), 121(.50, 51, Jones, R. L., 24(41), 36 62, 531, 165 Jueland, A. C., 177, 216 Hawthorn, 11. D., 188(82), 189(82), 205 ( 8 3 , 206(82), 216 Heertjes, P. XI., 172, 175, 177(46), 179, K
H
215,216
Heiken, G., 55(43), 82 Kagan, Y., 104, 105, 164 Hellman, J. AX., 261, 272, 283, 284 Kang, W. K., 171(17), 215 Hemingway, B. S.,44(17), 59(17), 60(16, Kanomori, H., 43(15), 44(15), 45(15), 60 17,49),61, 63(17), 64(17, 49), 69(17), (1.5), 62(15), 64(15,50,51), 65(15), 67, 70(17), 81, 82 81, 82 Hengstenberg, D., 105(24), 106(24), 164 Kaparthi, R., 173, 177(35), 179, 200, 205, Heselden, A. J., 259(65), 282 215, zir Hickerson, C. W., 224(8), 253(8), 281 Kasturirangan, S., 125, 127, 166 Ilirth, J . P., 92(92), 164 Katz, D. L., 109(43), 110, 164,200, 218 Holman, J. P., 179(60), 193(86), 216 Katz, J. L., 92, 105(24), 106(24), 164 Holtz, 11. E., 138, 159(83, 84), 166 Kazakova, E. A., 177(45, .51),116 Hooper, F. C.,121(38), 165 Kennedy, E. H., 87(3), 107(32), 164, 169 Hoori, Z., 179(62), 216 Kenning, I).B. R., 156, 166 Horai. K., 43, 44(13), 4.5, 60(15), 62, 64, Kenrick, F. B., 96, 97, 98(14), 99, lG4 65(lq5,X), 67, 81,81 Kerhm, S., 53(35), 74(35), 82 Hottel, II. C., 269, 283 Kermode, K.I., 210, 218 Hsu, Y. Y,,128(62), 129, 130, 132, 133, Kettenring, K. N., 172, 175, 177, 179, 115 148, 1.52, 165 Khitrin, L. N., 233(24), 281 Huang, W. C., 260,282 Kinbara, T., 269, 283 Hudson, F. L., 208, 218 King, I?. A., Jr., 57, 82 Huige, S. J. J., 192(90), 217 King, N. K., 265,283 Humphreys, H. W., 250(45), 282 Kirk, L. A,, 208, 218 Hunt, G. It., 11, 32, 36, 37 Klassen, J., 201(104), 202(104), 203, 206 Huntsinger, H C., 200, 218 (104), 209(104), zir I-fwang, C. L , 196(89), 203(89), 227 Knapp, R. T., 87, 118, 119, 121, 163, 165 Koppel, L. B.,193, 203(109), 217 I Korolev, V. N., 208, 218 ?. Korotyanskaya, L. A,, 210(139), 218 Ilchenko, A. I., 208, 217 Kosky, P. G., 146, 165 Ingrao, H. C., 76, 78, 83
AUTHORINDEX Kothari, A. K., 174, 175, 177(38), 216 Kritz, M. A., 48, 81 Krotikov, V. D., 41, 71, 81 Kruglikov, V. Y., 201(154), 218 Kung, H. C., 231, 281 Kunii, D., 169(2, 6), 170(2), 171(19), 174 (2, 19), 176(19),179, 180(2), 181, 194, 195, 196(94), 197(94), 214, 216, 217
L Lamb, W., 19(28), 36 Landrock, A. H., 211, 218 Langseth, M. G., Jr., 53, 54, 74(35), 82 Law, M., 243, 259(65), 279(114), 281, 282, $84 Lawson, D. I., 221, 278(112),281, 284 Lebedev, P. D., 174(40), 175(40),215 Lebofsky, L. A., 7, 8, 9, 36 Lee, S. L., 221, 247,248(43), 249,250,253, 254(48), 255(48, 50, 57), 256(48), 257, (62), 260, 261(75), 262, 269(75), 272 274(60), 281, 282, 283, 284 Lee, T. G., 280(118), 284 Lemlich, R., 200, 218 Lese, H. K., 210, 218 Leva, M., 169(8), 181(65, 66), 189, 202, 203, 205, 206, 215, 216, 217 Levenspiel, O., 169(2), 170(2), 171(19), 172(25), 174(2, 19, 25), 176(19), 175(25), 177(25),179,180(2), 181(68), 182, 194, 195, 196(94), 197(94), 199, 203, 206,2l4, 215, 217 Lewis, B., 247, 282 Lewis, J. B., 177(59), 178(59),216 Linan, A., 243(37), 282 Lindin, V. M., 177, 216 Ling, C. H., 255, 282 Linsky, J. L., 41, 47, 57, 71, 73(7), 76(73), 78(73), 81, 83 Lipsett, S. G., 107(33), 164 Lipska, A. E., 229(14), 281 Loftus, J. J., 280(117, 118), 284 Logan, L. M., 11, 32, 36, 37 Logwinuk, A. K., 201, 202, 203, 206, 209, 217 Lohneiss, W. H., 253(49), 282 Long, G., 107(34), 164 Lothe, J., 92, 164 Low, J. W., 71, 73(62), 76, 78, 82 Lowndes, R. P., 21, 23, 36
289
Lucas, J. W., 71,73(63,64,65,66,67), 76, 82, 83 Lyons, W. E., 16(22), 36
M McBirey, A. R., 43, 81 McCardell, R. K., 107(37), 164 McCord, T. B., 7,8(14), 9, 21, 22(14), 24, (32, 37), 25(32, 37), 36,36 McElroy, W. D., 118(50, 51, 52, 53), 121 (50, 51, 52, 53), 165 McGuire, J. H., 279(113), 284 McIlhinney, A. E., 203(101), 217 McKibbins, S. W., 172, 175, 177(21), 179, 215 Madejski, J., 152, 154, 155, 166 Makhorin, K. E., 208, 2f7 Malan, D. H., 243(33), 282 Manderfield, E. L., 172(22), 175(22), 177 (22), 179(22),216 Marchello, J. M., 189, 191, 217 Markvart, M., 169(4), 616 Marov, M. Y., 53(34), 58(34), 64(34), 70 (34), 71(34), 82 Marshall, W. R., Jr., 174(39),215 Marston, A. C., 34, 37, 53(31), 68(31), 81 Martens, H. E., 50(30), 51(30), 59(30), 68(30), 81 Marto, P. J., 138, 140, 142, 166 Martyushin, I. G., 202, 218 Matekunas, F. A., 156, 166 Matsumura, H., 151, 157(71), 165 Mersmann, A., 203, 217 Mesler, R. B., 109(40, 41), 164 Michaels, A. S., 92, 164 Mickley, H. S., 186, 187, 188, 189, 191, 200, 203, 204, 205, 206(8l), 216, 21 7 Miller, C. O., 201, 202, 203, 206, 209, 217 Miller, R. W., 109(37), 164 Mitson, A. E., 200, 202, 2f7 Miautani, H., 64(50, 51), 67(51), 86 Mlodinski, B., 177(52), 216 Moore, G. R., 102, 164 Moore, T. W., 179(60), 216 Moreno, G. F., 261(73), 272(73), 28.9 Morozhenko, A. V., 10,36 Morton, B. R., 255(51, 52, 53, 541, 282 Mukhlenov, I. P., 202(158), 203(102, 103, 107), 817, 218 Mulligan, J. C., 48, 81
AUTHORINDEX
290
Muncey, R. W., 71, 72(56), 82 Murase, T., 43, 81 Murcray, D. G., 11, 36 Murcray, F. H., 11, 36 Murgai, M. P., 255(56), 282 Murray, B. C., 71, 73(61), 82 Murray, J. D., 170, 215 Murty Kanury, A,, 225, 229, 231, 243(39), 281, 282 Muzichenko, L. B., 177(51), 216 Myers, J. E., 172, 177(24), 215
N Nakanishi, E., 109(39), 164 Napalkov, G. N., 174(40), 175(40), 215 Nash, I). B., 21, 23, 24(32, 33, 34), 36 Nelson, W., 87(3), 107(32), 111, 163, 164,
Perry, C. H., 21, 23, 36 Peters, K., 177, 216 Petitt, E., 40, 73(2), 76, 78, 80 Pettigrew, C. K., 211, 218 Philpot, C. W., 228(11), 234(13), 265(11), 281, 283 Pieters, C., 7, 8, 9, 36 Pirsko, A. R., 224, 253(8), 281 Plitt, K. F., 276(108), 284 Pomarentsev, V. M., 202(158), 218 Pound, G. M., 92(12), 164 Prasad, C., 266(83), 283 Preckshot, G. W., 146, 165 Puplett, E., 34, 3r, 53(31), 68(31), 81 Putman, A. A., 260, 283
16.5
Nicholson, S. B., 40, 73(2), 76, 78, 80 Nielsen, H. J., 255, 275(106), 282 Nilsson, E. K., 275(106), 284 Nobel, A. P. P., 193(91), 199(91), 202(91), 204(91), 205(91), 206(91), 217 Nolan, P. F., 229, 281
0 O’Leary, B. T., 3(8), 19, 21, 24(27,30), 35, 36, *57(45),82 Olson, R. L., 172(25), 174(25), 175(25), 177(25), 215 Orlichek, A., 177(55), 216 Orloff, L., 258(63), 260, 282 Osako, hl., 67(<53),82 Osberg, G. L., 171(17), 189, 202, 203, 205, 215, 21’7 Othmer, 1). F., 169(7, lo), 215
P Pandya, S. J., 34, 37, 53(31), 68(31), 81 Panton, I<. L., 231, 232(21), 233(21), 281 Paoli, R., 109(41), 164 Park, W. H., 171, 215 Parker, W. J., 269, 283 Patel, R. D., 189, 190, 191, 195, 217 Pavlov, P. A., 106(30), 107(30), 108, 264 Pease, I). C., 118(50, 51, 52), 121(.50, 51, 52), 165
Rabinovich, L. B., 206, 217 Raju, G. J. V. J., 207(121), 217 Raju, K. S., 207, 817 Ranz, W. E., 174(39), 216 Rao, C. V., 207(121), 217 Rao, S. P., 200, 205, 217 Rastogi, A., 21, 23, 36 Ravdel, A. A., 177, 216 Redish, K. A., 184(69), 185(75), 192(69), 216 Reed, T. hl., 203, 217 Reichman, J., 73(.57, 58), 82 Reid, R. C., 109(39), 164 Reiss, H., 92, 164 Richardson, G. T., 270(102), 282 Richardson, J. F., 170, 172, 175, 177, 180, 200, 202, 215, 217 Richart, I).S., 211, 218 Rietema, K., 192(90), 217 Rittmann, J. C., 231, 232(21), 233(21), 281 Robb, W. M., 115(48), 165 Roberts, A. F., 230(19, 20), 281 Robertson, A. F., 230(19, 20), 235(25), 2.33, 280(117, 1191, 281, 282, 284 Robie, R. A., 44(17), 59, 60(16), 61,63(17), 64(49), 69, 70, 81, 82 Rockett, J. A., 251, 258(63), 282 Rohsenow, W. If., 86, 134, 138, 140, 142 (66, 67), 143, 145, 147, 149, 150, 151, 152165), 157, 158, 161, 163, 165, 166
AUTHORINDEX Romanova, N. A., 202(155), 205(116), 206, 217,218 Rosental, E. O., 173, 177, 216 Ross, D. K., 184(69), 192(69), 216 Rosse, Earl of, 73(60), 82 Rothermel, R. C.,267, 268, 269(99), 272 (103), 283, 284 Rothwell, E., 229(17), 281 Rougier, M., 9, 36 Rouse, H., 250, 282 Rowe, P. N., 176, 177, 178, 216 Ruckenstein, E., 189, 202, 816,218 Rumford, F., 203, dl7 Ryan, J. V.,280(119), 284
S Saari, J. M., 47, 57, 59,60(48), 62, 72(54), 73(64, 65), 76, 78, 82,83 Sage, B. H., 208,217 Salisbury, J. W., 11, 32, 36,37 Sallack, J. A., 107(31), 164 Sarkar, S., 200, 218 Sarkits, V. B., 202(158), 203(102, 103, 107), 217,218 Sato, S.,172, 216 Sato, T., 151, 157(71), 166 Schmali, R. A., 209(134), 218 Schmidt, A., 177(55), 216 Schmidt, R., 56(44), 82 Schmidt, R. J., 155, 156, 166 Scholz, C., 43(14), 62, 81 Schreiber, E., 43(14), 62, 81 Schultz, R. R., 156, 166 Sechenov, G. P., 206, 217 Sega, S., 269(94), 283 Sereeterin, B., 209, 218 Sergius, L. M., 224(8), 253(8), 281 Shai, I., 142, 143, 14.5, 147, 166 Shakhova, N. A., 173, 816 Shalaev, S. P., 53(34), 58(34), 64(34), 70 (34), 71(34), 82 Sharikov, J. V., 177(47), 816 Shen, T., 269, 283 Shimanski, J. N., 177, 216 Shirai, T., 169(9), 172(28), 216 Simmons, G., 43(15), 44(15), 45(15), 54 (36), 60(15), 62(15), 64(15), 65(15, 52), 67(52), 74(36), 8f, 82 Simms, D. L., 243(35), 281, 282
291
Simon, I., 48, 51, 52, 81 Singer, R. M., 159(83, 84), 166 Sinitsyn, E. N., 103, 104, 105(20), 106, 164 Sinton, W. M., 76, 78, 82 Sirignano, W. A., 267, 283 Skripov, V. P., 103, 104(22), 105, 106(30), 107(29), 108, 164 Sliepcevich, C. M., 109, 164, 260, 282 Smith, J. M., 172(22), 17,5(22), 177(22), 179(22), 216 Smith, R. K., 256, 282 Sola, A., 107(37), 164 Steigmann, G. A., 19(28), 36 Stephens, D. R., 43, 44(12), 45(12), 81 Stewart, F. R., 243(36), 269(96), 282, 283 Stimpson, L. D., 73(67), 76, 83 Strenge, P. S., 119, 131(56), 132(56), 166 Sumi, K., 259, 282 Sunkoori, N. R., 173, 177, 179, 816 Susott, R. A., 229(12), 281 Sutherland, J. P., 203(101), 217 Swartz, J. A., 275(106), 284 Syromyatnikov, N. I., 208, 218
T Takata, K., 100, 101, 104, 164 Tao, L. N.,256, 289 Tarifa, S. C.,261, 272, 883 Thomas, P. H.,221, 243, 2.59. Z81, 282 Tinney, E. R., 269,283 Titulaer, C., 19(28), 36 Tornberg, N. E., 21, 23,36 Toomey, R. D., 199, 204,205, 207, 817 Toor, H. L., 189, 191, 217 Torrance, K. E., 251, 252(46), 253(46), 258,282 Traber, D. G., 202,203(102,103,107), 217, 218 Trefethen, L., 99, 164 Trilling, T. A., 200, 203, 204, 217 Troitsky, V. S., 41, 71, 81 Trupp, A. C.,180, 216 Tsuchiya, Y., 259, 282 Turnbull, D., 111, 166
U Ulrichs, J., 73(59), 82 Utech, H. P.,276(107, log), 284
AUTHORINDEX
292
White, J. E., 2(4, 5, 6), 12, 13, 23(6), 31 (4, 6), 34(4, 6), 56, 54(39), 70(39), Vandantseveeiy, B., 207(123), 217 75(39, 70, 71), 76(70), 77(39), 78(39, Vanecek, V., 169(4), 215 70, 71), 80(39, 70), 82, 83 Van Heerden, G., 193, 199, 202, 204, 205, Whiteley, A. H., 118(50, 51, 52, 53), 121 206, 21: (50, 51, 52, 53), 165 Van Krevelen, D. W., 193(91), 199(91), Whitty, G. F., 270(102), 883 z o 2 ~ 9 1 ~ , 2 0 4 ~ 9 1 2~ , ~ 0 5 6~ $17 ~~i ~ ~, Wicke, E., 193, 202,203,205,206,217 Varma, R. K., 255(56), 282 Wildey, R. L., 46, 71 (611, 73(62), 88 Varygin, N. N., 202,218 William, D. W., 270, 283 Vsanova, L. K., 177, 216 Williams, F. A., 243(37), 269, 282, 283 Vattierra, hf. L., 243(38), 882 Williams, G. C., 269(93), 283 Vincent, R. K., 11, S6 Williams, J. R., 184(69, 70), 192(69), 216 Vines, R. G., 265, 283 Williams-Leir, G., 279(115), 284 Vinogradov, A. P., 53, 64,70, 81 Williams, W. J., 11, S6 Vitkus, G., 73, 82 Wilson, W. H., 44(17), 59(17), 60(17), 63 Vogel, M., 269, 283 (17), 64(17), 69(17), 70(17), 81 Volmer, M., 92, 101, 111, 164 Winter, D. F., 47, 57, 59, 60(48), 72, Von Brachel, H., 210,218 73(48), 82 Von Elbe, G., 247, 282 Winter, E. R. F., 156, 165 Vreedenberg, H. A,, 201, 209(131, 1351, Wismer, K. L., 96, 97(14, 16), 98(14), 99 218 (141, 164 Witte, L. C., 107(33), 164 W Wodley, F. A., 229(14), 281 Wong, V. M., 179(60), 216 Wakeshima, I-X., 100, 101, 104, 164 Wones, D., 43(15), 44(15), 45(15), 60(15), Walker, G., 19(28), S6 62(15), 64(15), 65(15), 81 Wallis, J. D., 122, 123, 125, 126, 127, 128, Wood, B. D., 260, 282 130, 131, 132, 133, 152, 166 Wood, H. L., 50(30), 51(30), 59(30), 68(30) Walton, J. S., 172, 174, 175, 177, 181, 182, 81 199, 203, 206, 216, 216 Wamley, W. W., 173, 216 Y Ward, C. A., 121, 165 Warren, X.,43, 62, 81 Yanovitskii, E. G., 10,36 Watson, K., 46, 48, 50, 51, 52, 73(19), 81 Yerbury, M., 27, 37, 57(47), 82 Weatherford, W. A., 243(38), 282 Yih, C. S., 250(45), 282 Wechsler, A. E., 42, 43, 45, 48, 50, 51, 52, Ying, S. J., 257, g88 54(36), 58(22), 59(22), 64,68, 74(36) Yoshida, K., 195, 196, 817 81, 82 Young, A. T., 76(73), 78(73), 83 Wei, C.-C., 146, 166 Yuill, C. H., 242, 243, 281 Weingsertner, E., 204, 21 7 Weintraub, M., 181(64), 216 2 Welker, J. R., 260, 282 Zabrodsky, S. S., 169(3), 176, 202, 206, Wells, E. N., 19(25), 24(25), 36 214,216, 217 Wen, C. Y., 189, 217 Zahavi, E., 179(61), 816 Wender, L., 200, 201, 205, 209, 217 Zenz, F. A,, 169(7), 816 Werner, R. A., 56(44), 82 Wesselink, A. J., 40, 46, 71, 72, 75, 78, 81 Zettlemoyer, A. C., 92, 164 Ziegler, E. N., 191, 203(109), 208, 217 West, E. A., 48, 51, 52, 56,57, 81 Westwater, 3. W., 119, 131(56), 132(56), Zuber, N., 132, 133, 166 Zunduggiyn, T.S., 207(123), 817 166
V
Subject Index A
Bubble growth criteria for, 128-129 high-speed photography and, 146-147 local surface heat flow and temperature in, 140 in nucleation studies, 100-105 wall surface temperature in, 142 Building codes, fire research and, 277-279 Bulk density, spectral directional reflectance and, 26-27
Activated molecules, stability of, 93-94 Active cavities, nonuniform superheat of, 127-128
Age-density distribution function, 189 Albedo bond, 13 geometric, 13-14 of moon, 7 normal, 14 Angle of illumination, 28-30 Apollo 11, 3-6, 20, 23-26, 29-31, 33-34,
C
49, 53-55, 59, 67-69, 74, 76, 78
Candle flame, combustion in, 221-222 Cavities active, 127-128 nucleation criteria for, 129 stability of in nucleation, 134-148 Cellulose, fire and, 225-226 Clausius-Clapeyron equation, 95-96, 159 Clinopyroxine, in lunar fines and rocks, 7 Conflagration, defined, 223 Core-tube densities, of lunar fines, 55-56
Ap0110 12, 3, 5, 21-27, 29-34, 49, 54-55, 57, 59, 67, 70, 72, 74, 76
Apollo 13, 2, 41, 73 Apollo 14, 3, 6, 23-34, 54-55 Apollo 15, 2-3, 23-25, 32, 41, 74-75 Apollo 16, 25, 41 Apollo 17, 41
B Basalt lunar, 44-45, 59-60, 62 thermal conductivity of, 57 Bidirectional reflectance, 19-21 Blackbody radiation, 11, 15-16 Boiling heat transfer, 110 Boiling nucleation, 85-162 see also Nucleation engineering significance of, 107-111 heat flow densities in, 147 Madejski analysis in, 152-156 model of, 134 Boiling superheat, 148-162 Boiling surface, in nucleation, 133-134 Bond albedo, 13 Breccia, lunar, 59, 61
D Directional emittance, lunar, 15-16 Directionalreflectance apparatus, for lunar materials, 16-17 Directional reflectance coefficients, for lunar materials, 31 Directional reflectance equation, 31 Directional spectral emittance, 15-10 Drop vaporization, 101-102
E Emergent superheat, 122 determination of, 126 Emulsion packet, 186-188, 196 293
SCBJECT INDEX
294
Equilibrium condition, Kelvin equation and, 89 Equilibrinni vapor pressure, 87 Exploding hubble technique, 105 Exploding drop method, in nucleation studies, 100-101
F Fabrics, ignition tests for, 24Cb241, 244, 273, 279-280
Fire classification of, 223-223 convection above line type of, 230-2.51 denwmetric analysis of, 229 enclosed, %;&-2(iO firebrand spotting in, 260-262 fuel load evaluation in, 262-266 heat and mms transfer in, 221-222 hot air plume in, 24rv260 ignition in, 23.i-245 losses from, 220 m a s spectrometry and gas chroniatography in, 228-239 riaturd convection in, 2.3-252, 258 o ~ h e materials r than wood in, 269 phenoineria of, 221-223 reaction rates in, 232-233 spontaneous heating in, 236-237 spread of, 260-275 sprinkler system in, 245 thermal explosion theory in, 238 tolerance levels in, 243-243 wildland, 222 wood chemistry in, 225-226 Fi rebra rids burning characteristics and terminal velocities of, 2G3-2ti4 sptrt t ing of, 262-262 Fire depnrtment vehicles, 276 Fire fighter, equipment for, 275-277 Fire iiisurance, 920 Fire pl unie, 245-260 w e crlso Plunic Fire protection, pyrolysis testing and, 2X-23 .i Fire research building codes and, 277-279 defined, 220-221 exhaust hoods and, 272 fabric testing methods in, 273
fire fighter and, 275-280 flow visualization in, 273 fuels in, 272--273 heat and mass transfer in, 219-280 instrumentation in, 272-280 product testing in, 279-280 pyrolysis products and, 280 tall buildings and, 278 temperature measurement in, 274 velocity measurement in, 274-275 wind tunnels in, 272 Fire retardants, 234 Fire-safet y oriented ignition tests, 238-243 Fire spread fuel characteristics in, 262-270 large-scale studies of, 269-271 rates of, 267-269 theories of, 266-267 Fire st at ion locat ions, 27.5276 Fire storm, 223-22.3 plume in, 246 Flammability tests and ratings, 240-241, 245 see atso Ignition
Fluid, heat transfer between solid particles and, 171-180 Fluidization defined, 168 initiation of, 169-170 Fluidized bed behavior of, 169-171 coating for, 211-213 conduction through emulsion layer of, 193-194
defined, 168 emulsion layer in, 194-195 emulsion packet in, 186-188, 196 entrance effects in, 206 experiniental heat transfer results in, 202-206
flat plates in, 208 flow field near heat exchange surface of, 191-195
flow properties in, 169-171 fluidization conditions in, 204-205 fluid properties in, 198 gas or liquid, 168 geometric variables in, 205-206 granular solid material properties in, 203
heat balance in, 212
SUBJECT INDEX heat transfer in, 167-213 heat transfer between surface and, 180-213 heat transfer coefficients for, 177-178 height and length of, 205 immersed bodies in, 206-207 immersed tubes in, 209-210 minimum fluidization in, 203-204 random surface renewal model of, 196 small cylinders in, 208 spheres in, 207-208 temperature and pressure in, 206 tube bundles in, 210 tubes in, 209-210 uniform surface renewal model of, 197 Fluidized systems, liquid-solid, 179-180 Forest fires, 220 see also Fire Fra Mauro crater, moon, 5 Fuel, ignition of, 235
G Gas, in fluidized bed, 167-168 Gas chromatography, 228-229 Gas-filled cavities, nucleation and, 120-121 Gas film, steady state conduction across, 181-188 Gas-fluidized bed, 168 Gas-solid heat transfer, 175 Geometric albedo, lunar, 13-14 Gibbs function, 90
H Hadley-Apennine lunar region, 6 Hadley Rille, 2 Heat balance, in fluidized beds, 212-213 Heat conduction Fourier law of, 39 unsteady, through single particle, 185 Heat exchange surface, 184-185 Heat flux equation for, 47 Fourier’s law and, 46 Heating, spontaneous, 236-237 Heat transfer age-density distribution function and, 189-190 bubbling bed model of, 176-177
295
downflow with side mixing in, 189 through emulsion layer, 193-194 experimental correlations in, 173-175 experimental measurement techniques in, 172-173 external walls in, 184-185 in fire research, 219-280 in fluidized beds, 167-213 between fluidized beds and surface, 180-213 gas-solid, 175 laminar boundary layer thickness and, 183 in lunar surface layer, 72-79 mechanism for, 181-199 from packet to wall, 191 particle motion and, 182 phonon conduction in, 43, 45 through “packets” of particles, 186 between solid particles and fluid, 171180 steady state measurement techniques in, 172-173 theoretical models of, 176 unsteady state techniques in, 173 Zabrodsky microbreak model of, 176 Heat transfer coefficients for fluidized beds, 177 local instantaneous, 187 nondimensional correlations for, 202 in nucleation, 150-151 Heat transfer rate, variables in, 180-181 Heat transfer systems, nucleation and, 86-87 Hemicellulose, fire and, 226 n-Heptane, limiting superheat of, 104 Hewlett-Packard minicomputer, 19 n-Hexane, limiting superheat of, 104 Holtz model, of trapped inert gas, 159-160 Homogeneous nucleation, liquid superheats in, 111 1
Ignition fire and, 235-245 radiation induced, 243 in wildland fires, 244-245 Ignition temperatures, for various materials, 239 Ignition tests
SUBJECT INDEX
296
fire-safety oriented, 238-243 for various fabrics, 240-241 Immersed bodies in fluidized bed, 206-207 nondimensional correlations for, 201 Inert gas, in nucleation model, 159-160 Integrating sphere, theory of, 16
K Kelvin equation, 87-92
L Laplace equation, 87-92 LaplaceKelvin equation, 87, 92, 95 Line fire convection above, 250-251 mathematical model of, 2.54 plume instability in, 2.53-254 Line heat-source method, 48-49 Liquid drop, equilibrium vapor pressure of, 87 Liquid-fluidized bed, 168 see also Fluidized bed Liquid metals, nucleation of, 157-162 Liquids ebullition and cavitation in, 92-95 low thermal conductivity, 148-157 superheated, see Superheated liquids temperature distribution in, 136-139 Liquid-solid fluidized systems, 179-180 Liquid-vapor interface, curvature of, 12212.5 Low thermal conductivity liquids, 148162 Luna missions, 1, 10, 41, 53,58 Lunar basalt see also Moon specific heat of, 60, 62 thermal conductivity of, 4 4 4 5 , 57 thema1 diffusivity of, 64 Lunar breccia, specific heat of, 61 Lunar fines see also Lunar materials average composition of, 2.5 core-tube density and, 55-56 line-heat-source method for, 49 in mare regions, 42
properties of, 23-24 simulated, 50 solar albedo for, 28 specific heat of, 63-64 spectral directional reflectance for, 2329 thermal conductivity of, 45-59 thermal diffusivity of, 68-70 Lunar materials see also Lunar fines; Lunar rocks backscattering from, 20-21 bidirectional reflectance apparatus for, 17 bidirectional reflectance results for, 1921 directional reflectance apparatus for, 16-17 directional reflectance results for, 21-30 directional spectral emittance for, 15-16 experimental results for, 19-34 “fairy castle structure’’ of, 10 fines properties in, 23-24 heat transfer within lunar surface layer in, 39-80 line heat-source method for, 4 8 4 9 measuring techniques for, 16-19 oldest, 6-7 specific heat of, 3 9 4 0 spectral emittance of, 18-19, 30-34 thermal conductivity of, 3 9 4 0 thermal diffusivity of, 40 thermal parameter of, 40 thermophysical properties of, 1-77 Lunar olivine dolerite, specific heat of, 61 Lunar reflectances, defined, 13 Lunar rock chips, directional spectral reflectance of, 22 Lunar rocks clinopyrosene, 47 specific heat of, 59-63 thermal conductivity of, 4 2 4 5 thermal diffusivity of, 64-68 Lunar Sample Analysis Program, 3 Lunar samples, numbering of, 4 Lunar surface temperatures of, 76 variable vs. constant properties for, 77 Lunar surface layer heat transfer in, 39-80 thermal parameter of, 70-72
SUBJECT INDEX M Madejski analysis, in boiling nucleation, 152-156 Manned Spacecraft Center, Houston, 42 Marangoni flows, 156 Mare Imbrium, spectral emittance from, 11 Mare Tranquilitatis, 4, 8-10 Mass spectrometry, fire and, 228-229 Mass transfer, in fire research, 219-280 Molecules, activation energy for, 92, 112 Moon see also Lunar (adj.) absorption band on, 7 albedo of, 7, 13-14 backscattering from, 7 bidirectional spectral reflectance of, 8, 15 blackbody radiation from, 11, 15-16 bond albedo of, 13 directional reflectance of, 14-15 fines on, see Lunar fines Fra Mauro area on, 5, 9 infrared radiation from, 40 landings on, 1 Le Monnier area on, 9 Ocean of Storms on, 5 Oceanus Procellarum of, 6 oldest materials from, 6-7 origin of, 1 Plato crater on, 9 reflected light phase disbribution function of, 9 remote sensing data for, 7-11 Sea of Cold on, 8 Sea of Moisture on, 8-9 Sea of Serenity on, 8 Sea of Showers on, 11 Sea of Tranquility on, 4-6, 8-10 specific heat of, 3 9 4 1 surface composition of, 40-41 surface temperature of, 13 surface polarization of, 7 temperature variation on, 77 thermal conductivity of, 39-59 thermal radiation measurements for, 1235 thermophysical property reference values for, 79-80
297
Tycho crater on, 8 variable surface temperature comparisons for, 13 Moon rocks, see Lunar rocks
N National Aeronautics and Space Administration, 4, 42, 277 National Bureau of Standards, 276, 279280 Nucleation activated molecules in, 92-94 activation energy for, 112 active cavities size range in, 127-134 analysis and experiment in, 129-133 Bergles-Rohsen ow graphical procedure and, 157-158 boiling, 85-162 boiling superheat in, 148-162 boiling surface characterization in, 133134 bubble growth in, 100-105 cavity activation in, 132-134 cavity stability in, 134-148 constant surface temperature profilns in, 130 criteria in, 128-129 cycle in, 136-138 dimensionless superheat vs. dimensionless temperature gradient in, 156 equilibrium cluster radius in, 96-97 experimental findings in, 146-148 experimental observations in, 99-107 exploding drop method in, 1OQ-101 explosive, 87, 105, 107-108 gas-filled cavities in, 120-121 heat flow densities in, 147 heat transfer coefficient in, 150-151 heterogeneous, 111-1 17 homogeneous, 92-95, 111 liquid metals in, 157-162 low thermal conductivity liquids in, 148-157 Madejski model in, 154-156 Marangoni flows in, 156 nuclei appearance in, 94-96 from plane surfaces, 111-113 from preexisting gas or vapor phase, 117-127
SUBJECT INDEX
298
pulsed heating methods in, 106 ring bubble technique in, 103 sounds of, 87, 105 from spherical projections and cavities, 113-117 superheat limits and, 95-111 vapor embryo and, 1 1 2-1 13 vapor-filled cavities and, 122-127
Reservoir cavities, liquid-vapor interface in, 124-125 Rising bubble technique, in nucleation studies, 103 Rocks, lunar, see Lunar rocks; see also Terrestrial rocks Rossby number, in plume studies, 248 Rossland mean absorption coefficient, 47
0 Oeem of Storms, 5
Oceanus Procellarum, 6 Olivine dolerite, lunar, 59-61
P Paper industry, explosions in, 107 n-Pentane, limiting superheat in, 104 Perkin-Elmer spectrometer, 17-18 Phonon conduction heat flux and, 46 heat transfer and, 45 temperature and, 43 Plume axisymmetric swirling turbulent, 247250 enclosed fire and, 258-260 experimental studies of, 266-260 in fire studies, 245-246 multiple fire whirl formation in, 257-258 stability of in line fire, 253-256 Pulse heating technique, vaporization temperatures in, 108 Pyrolysis, 226-235 experimental studies of, 227-229 fire protection and, 23d-235 interpretation of results in, 229-231 mathematical models of, 231-233 products of, 280
R Radiant energy flux, heat flux and, 47 Radiation, ignition and, 243 Reflectance defined, 13 directional, 14-15 Remote sensing, lunar data from, 7-11
S Seas, lunar, see Moon Slug flow, of solids over surface, 187 Smelt dissolving tank operations, 107 Solar reflectance, for lunar fines, 28-30 Solid particles, heat transfer between fluid and, 171-180 Solids slug flow of over surface, 187 temperature distribution in, 144 Specific heat of lunar fines, 63-64 of lunar materials, 39-40, 59-63 Spectral directional reflectance angle of illumination and, 28-30 bulk density and, 26-27 for iunar fines, 23-29 Spectral emittance vs. bulk density, 32 for lunar materials, 31-34 Spherical projections and cavities, nucleation from, 113-117 Spontaneous heating, materials subject to, 236-237 Subcooling, incipient boiling temperature and, 149 Superheat dimensionless, in Madejski nucleation model, 156 emergent, 122, 126 minimum boiling, 148-162 nonuniform, 127-128 Superheated liquid drops, 99 Superheated liquids equilibrium cluster radii for, 97 theoretical vs. experimental values for, 99
Superheat limits classical treatment in, 95-99
SUBJECT INDEX expression for, 97-98 studies of, 99-100 Surface science, fundamental equations of, 87-92 Surveyor missions, 1, 7, 10, 41, 73, 78
T
299
V Vapor, physical explosions from, 107-108 Vapor bubble equilibrium vapor pressure and, 87 formation of, 119 Vapor embryo in conical cavity, 116 in nucleation, 112-113 Vapor-filled cavities, nucleation and, 122127 Vapor formation, explosive, 87 Vaporization temperature, pulse heating technique in, 108 Vapor phase, nucleation from, 117-127 Vapor temperature, dimensionless, 130
Tall buildings, fire safety in, 278 Terrestrial fines, thermal conductivity of, 50 Terrestrial rock powders, thermal conductivity of, 52 Terrestrial rocks, thermal properties of, 43-44 Thermal conductivity heat flux and, 46-47 of lunar fines, 45-59 W of lunar materials, 3940, 42-59 measurement of, 48 Walls, nondimensional correlations for in parameters for, 48 heat transfer, 199-200 pressure effects in, 58 Wall superheat,, in boiling nucleation, 154 temperature dependence in, 51 Wall surface temperature, in bubble forfor terrestrial fines, 50 mation, 142 Thermal diffusivity Wavy gas-liquid int,erface, 88 of lunar fines, 68-70 Wildland fires of lunar materials, 40 fuel analysis in, 262-266 of lunar rocks, 64-68 ignition in, 244 Thermal explosion theory, fire and, 238 vortices in, 246 Thermal parameter Wood of lunar materials, 40, 70-72 chemical nature of, 225-226 of simulated lunar fines, 68 pyrolysis of, 228-231 Thermal radiation measurements, lunar, 12-35 Thermophysical properties, reference valZ ues for lunar studies of, 79-80 Zabrodsky microbreak heat transfer Trapped gases, vapor bubbles and, 119 model, 176 Tubes, in fluidized beds, 209-210
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