Proceedings of the International Symposium on Two-Phase Systems. Progress in Heat and Mass Transfer PDF
Preview Proceedings of the International Symposium on Two-Phase Systems. Progress in Heat and Mass Transfer
INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER BOARD OF EDITORS E. A. BRUN, 8 place du Commerce, Paris 15ème, France A. J. EDE, Mechanical Engineering Dept., University of Aston, Gosta Green, Birmingham 4, England CARL GAZLEY, JR., Dept. of Geophysics and Astronomy, The RAND Corporation, 1700 Main Street, Santa Monica, California 90406, U.S.A. U. GRIGULL, Technische Hochschule, Arcisstrasse 21, München, Germany Ε. HAHNE (Associate Editor), Technische Hochschule, Arcisstrasse 21, München, Germany J. P. HARTNETT, Energy Engineering Dept., University of Illinois, Box 4348, Chicago, Illinois 60680, U.S.A. Α. V. LUIKOV, Heat and Mass Transfer Institute, Academy of Science, 25 Podlesnaya, Minsk, B.S.S.R., U.S.S.R. O. G. MARTYNENKO (Associate Editor), Heat and Mass Transfer Institute, Byelorussian Academy of Sciences, 25 Podlesnaya, Minsk, B.S.S.R., U.S.S.R. W. J. MINKOWYCZ (Associate Editor), Energy Engineering Dept., University of Illinois, Box 4348, Chicago, Illinois 60680, U.S.A. TAKASHI SATO, Mechanical Engineering Dept., Kyoto University, Kyoto, Japan D. B. SPALDING, Mechanical Engineering Dept., Imperial College of Science & Technology, Exhibition Road, London S.W.7, England J. H. WHITELAW (Associate Editor), Mechanical Engineering Dept., Imperial College of Science & Technology, Exhibition Road, London S.W.7, England HONORARY EDITORIAL ADVISORY BOARD Chairman: E. R. G. ECKERT, University of Minnesota, Minneapolis, Minnesota 55455, U.S.A. Co-chairman: F. TACHIBANA, Dept. of Nuclear Engineering, University of Tokyo, Bunky-ku, Tokyo, Japan Past-chairman: SIR OWEN SAUNDERS, F.R.S., Imperial College, London, England INTERNATIONAL SYMPOSIUM ON TWO-PHASE SYSTEMS Organized by the TECHNION, ISRAEL INSTITUTE OF TECHNOLOGY and ASSOCIATION OF ENGINEERS AND ARCHITECTS IN ISRAEL Under the auspices of the ISRAEL ACADEMY OF SCIENCES AND HUMANITIES Sponsored jointly by the IIChE, AIChE, ASME PROGRESS IN HEAT A ND MASS TRANSFER VOLUME 6 Proceedings of the International Symposium on TWO-PHASE SYSTEMS EDITED BY G. HETSRONI Department of Mechanical Engineering, Technion, Israel Institute of Technology S. SIDEMAN Department of Chemical Engineering, Technion, Israel Institute of Technology J. P. HARTNETT Department of Energy Engineering, University of Illinois PERGAMON PRESS OXFORD · NEW YORK TORONTO · SYDNEY · BRAUNSCHWEIG Pergamon Press Ltd., Headington Hill Hall, Oxford Pergamon Press Inc., Maxwell House, Fairview Park, Elmsford, New York 10523 Pergamon of Canada Ltd., 207 Queen's Quay West, Toronto 1 Pergamon Press (Aust.) Pty. Ltd., 19a Boundary Street, Rushcutters Bay, N.S.W. 2011, Australia Vieweg & Sohn GmbH, Burgplatz 1, Braunschweig Copyright © 1972 Pergamon Press All Rights Reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of Pergamon Press Ltd. First edition 1972 Library of Congress Cataloging in Publication Data International Symposium on Two-Phase Systems, Haifa, 1971. Proceedings. (Progress in heat and mass transfer, v. 6) Sponsored by the Technion, Israel Institute of Technology and others. 1. Heat—Transmission—Congresses. 2. Two-phase flow—Congresses. I. Hetsroni, G., ed. II. Sideman, S., ed. III. Hartnett, James P., ed. IV. Haifa. Technion, Israel Institute of Technology. V. Series. TJ260.P762 vol. 6 621.4Ό22 72-8471 ISBN 0-08-017035-8 Printed in Great Britain by A. Wheaton & Co., Exeter ISBN 0 08 017035 8 ". ··1nNi1 li'J tJ"JtDi1 tJ":J'~ -.. 9, 1 n"i1i' "Two are better than one ..." Eccles. 4:9 PREFACE THE International Symposium on Two-phase Systems grew out of the desire for closer communication between chemical, civil and mechanical engineers, mathematicians, physicists and chemical-physicists working on the various aspects of this interdisciplinary field. The choice of the title is thus quite deliberate. The purpose of the Symposium was to place relevant recent research in perspective, to elucidate some new research challenges and to relate it to present and future applications. This ambitious goal would not have been realized without the dedicated hard work of many individuals and the financial and moral support of the academic institutions, professional and scientific societies and industry. We gratefully acknowledge the contributions of the Sessions' Chairmen, Professor G. K. Batchelor, Professor H. Brenner, Professor A. E. Dukler, Professor J. P. Hartnett, Dr. G. F. Hewitt, Professor J. O. Hinze, and Professor W. M. Rohsenow. Undertaking the dual task of Keynote Lecturers and Sessions' Chairmen they set the tone of the meeting and deftly conducted the interesting discussions that followed. It is also a pleasure to acknowledge the financial support of the Technion, Israel Institute of Technology, Haifa, that undertook the main financial load (and risked more); the Israel Academy of Sciences and Humanities; the Association of Engineers and Architects in Israel; the Israel Institute of Chemical Engineers; the Ministries of Trade and Commerce, Development, and Defense of the Government of Israel, as well as the various Israeli Industries and Manufacturers Associations. Judging from the participants' response, we gladly report that the conversion of matter into mental energy was highly efficient. Finally, many thanks to the members of the organizing committee of the symposium and the various officials of the ASME and AIChE whose energy and devotion helped make the Symposium a memorable reality; particularly to Professor A. E. Dukler of the University of Houston, who carried the ball from its inception on Mount of Olives in Jerusalem in 1968 to its birth in Haifa in 1971. I humbly dedicate this volume to all those who made its appearance possible. SAMUEL SIDEMAN xi SUPPORTING ORGANIZATIONS OF THE INTERNATIONAL SYMPOSIUM ON TWO-PHASE SYSTEMS Technion — Israel Institute of Technology The Israel Academy of Sciences and Humanities Association of Engineers and Architects in Israel Israel Institute of Chemical Engineers Government of Israel, Ministry of Trade and Commerce Government of Israel, Ministry of Development Government of Israel, Ministry of Defense Government of Israel, Ministry of Defense, Armament Development Authority Israel Electric Corporation Mr. Edgar Astaire, London Haifa Refineries Ltd., Israel Koor Industries Ltd., Israel Israel Mining Industries Alliance Ltd., Hadera, Israel Oil Manufacturers' Research Foundation Committee, Israel Miles Laboratorium Ltd., Haifa, Israel Dead Sea Works, Israel Shemen Ltd., Haifa, Israel xii STATUS OF AND PROBLEMS IN BOILING AND CONDENSATION HEAT TRANSFER! WARREN M. ROHSENOW Massachusetts Institute of Technology, Cambridge, Massachusetts Abstract. Our knowledge of heat transfer associated with boiling and condensation has been advanced considerably in the last two decades from the mysterious experimental data for overall coefficients for special geometrical arrangements to some rather detailed descriptions of mechanisms of various aspects of the processes. Nevertheless, there remain today many unanswered questions. In the following the state of art of various aspects of boiling and condensation will be presented along with some of the significant unanswered questions. BOILING All boiling heat transfer data can be placed on a q/A vs. (T — T ) graph such as the one w sat shown in Fig. 1. For boiling from surfaces in a saturated liquid the basic curve is shown. At low superheat ΔΓ, natural convection or forced convection single-phase heat transfer governs. At some modest ΔΓ, bubble nucleation takes place and the boiling curve rises to a slope in the neighborhood of 3 for most commercial surfaces. As q/A is increased, the number of nucleation sites on the surface increases until at the maximum heat flux an intermittent vapor layer begins to form at the surface. At very high ATs a continuous vapor layer exists over the surface, so-called film boiling. The region between nucleate and film boiling is not well described. It may be an intermittent wet and dry region where liquid occasionally touches the surface. This is an unanswered question. The effect of subcooling of the liquid in pool boiling is not well defined. Increased sub- cooling may move the curve to higher or lower ΔΓίη the nucleate boiling region, depending on the natural convection geometry, horizontal tubes [1] or vertical plates [2]. The maximum heat flux in nucleate boiling increases with increasing subcooling and the curves in the film boiling region are higher for increased subcooling. In forced convection at various velocities and liquid subcoolings the data is as shown in Fig. 1. The asymptotes at (T — T ) = 0 are given by w sai — ^conv (^sat ~~ ^liq) 0) asymp where A depends on the velocity for given fluid conditions. As q/A is increased, the boil- covn ing becomes more vigorous and the boiling curves seem to merge into a single "fully t Keynote Lecture. 1 2 W. M. ROHSENOW log (T -T ) w 8 FIG. 1. Regimes in boiling heat transfer. developed" boiling curve at high heat flux. The maximum heat flux becomes a complex function of quality, pressure, heat flux distribution and flow geometry. INCIPIENT BOILING Boiling is believed to take place at cavities on the solid surface. It is presumed that a distribution function of cavity sizes as shown in Fig. 2 exists where J n dr (2) R FIG. 2. Nucleation on a heated horizontal surface immersed in various liquids. The distribution of active cavities according to their radii is shown. PROBLEMS IN BOILING AND CONDENSATION HEAT TRANSFER 3 a b e d FIG. 3. The formation of bubbles of vapour over cavities in a heated surface. FIG. 3a. Re-entrant cavity. is the number of cavities between r and r . Figure 3 shows a liquid-vapor interface emerg- x 2 ing from a cavity. If the reciprocal of radius of curvature (1/r) is plotted versus vapor volume there is a maximum in the curve (Fig. 4) which for most cavities is l/r . cavity At equilibrium at a spherical interface 2σ Ρν-Ρι= — . (3) It is shown [3], [4] that the vapor at a curved interface is very nearly at the saturation pressure and temperature of a flat interface. For bubble growth the liquid temperature must be at least greater than the vapor temperature. Since the liquid pressure is smaller, it must be superheated. Therefore, using the Claussius-Clapeyron equation for conditions along the saturation curve, dTTVf_ = g (4) dp h fg 4 W. M. ROHSENOW VOLUME FIG. 4. Radius of curvature vs. vapour volume in a cavity. the amount of superheat in the liquid for bubble growth to begin may be expressed as fol- lows by combining eqns. (3) and (4): (5) The various forms of this equation obtained by integrating along the saturation curves are compared in reference 4. The effect of any gas in the vapor space is to reduce p — p and ΔΓ by replacing 2a/r v t 5Η by (2a/r — p) in eqns. (3) and (4). g A system including a liquid and a solid surface with cavity size distribution as shown in Fig. 2 if heated slowly so that its temperature is essentially uniform throughout should nucleate at the largest cavity present [5]. This is the temperature or ΔΤ required for 8Η incipient boiling. In convection systems (liquid non-metals) the temperature gradient in the liquid just before incipient boiling occurs can be quite large: (6) Here h is the heat transfer coefficient which is a function of the geometry, the fluid properties and the flow rate; k is the liquid thermal conductivity. For a given liquid temperature, x both the temperature gradient (dT/8y) and the wall temperature T increase as the heat y=0 w flux increases. A series of curves representing the temperature distribution very near the heated wall is shown for increasing heat flux in Fig. 5. Also shown in Fig. 5 is a curve labeled T*, which is a plot of eqn. (5) with the radius of the cavity plotted as the distance g from the heated surface. A possible theory [6], [7]: Nucleation takes place when the tem- perature curve in the liquid is tangent to the curve representing eqn. (5). The implication is that the surface contains cavities of various sizes (Fig. 2) and when the temperature at the outer surface of the bubble reaches the critical value given by eqn. (5), the bubble grows at the cavity whose radius is represented by the distance between the wall and the point of intersection. At the point of tangency, the radius of the first cavity to nucleate, by solving eqns. (5) and (6) simultaneously, is (7)
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