Turbulent Buoyant Jets and Plumes. HMT: the Science & Applications of Heat and Mass Transfer. Reports, Reviews & Computer Programs PDF
Preview Turbulent Buoyant Jets and Plumes. HMT: the Science & Applications of Heat and Mass Transfer. Reports, Reviews & Computer Programs
HMT THE SCIENCE & APPLICATIONS OF HEAT AND MASS TRANSFER Reports, Reviews & Computer Programs Editor-in-Chief: D. BRIAN SPAIDING Imperial College of Science and Technology, London, England. ALSO IN THIS SERIES SPALDING GENMIX: A General Computer Program for Two-dimensional Parabolic Phenomena KHALIL Flow, Mixing and Heat Transfer in Furnaces REZK Heat and Fluid Flow in Power System Components CHEN and RODI Vertical Turbulent Buoyant Jets—A Review of Experimental Data JALURIA Natural Convection Heat and Mass Transfer Pergamon Related Journcds CHEMICAL ENGINEERING SCIENCE INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER LETTERS IN HEAT AND MASS TRANSFER PHYSICOCHEMICAL HYDRODYNAMICS TURBULENT BUOYANT JETS AND PLUMES Edited by WOLFGANG RODI Universität Karlsruhe, Karlsruhe, Germany PERGAMON PRESS OXFORD · NEW YORK · TORONTO · SYDNEY · PARIS · FRANKFURT U.K. Pergamon Press Ltd., Headington Hill Hall, Oxford 0X3 OBW, England U.S.A. Pergamon Press Inc., Maxwell House, Fairview Park, Elmsford, New York 10523, U.S.A. CANADA Pergamon Press Canada Ltd., Suite 104, 150 Consumers Rd, Willowdale, Ontario M2J1P9, Canada AUSTRALIA Pergamon Press (Aust.) Pty. Ltd., P.O. Box 544, Potts Point, N.S.W. 2011, Australia FRANCE Pergamon Press SARL, 24 rue des Ecoles, 75240 Paris, Cedex 05, France FEDERAL REPUBLIC Pergamon Press GmbH, 6242 Kronberg-Taunus, OF GERMANY Hammerweg 6, Federal Republic of Germany Copyright © 1982 Pergamon Press Ltd. AJJ flights Reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means: electronic, electrostatic, magnetic tape, mechanical, photocopying, recording or otherwise, without permission in writing from the publishers. First edition 1982 Library of Congress Cataloging in Publication Data Main entry under title: Turbulent buoyant jets and plumes. (HMT : the science & applications of heat and mass transfer ; v. 6) Including bibliographies. Contents: Mechanics of turbulent buoyant jets and plumes/by EJ. List—Turbulent buoyant jets in shallow fluid layers/by G.H. Jirka— A turbulence model for buoyant flows and its application to vertical buoyant jets/by M.S. Hossain and W. Rodi. I. Jets—Fluid dynamics. 2. Plumes (Fluid dynamics) 3. Turbulence. I. Rodi, Wolfgang. II. Series. TA357.T885 1982 628.5 82-5258 British Library Cataloguing in Publication Data Turbulent buoyant jets and plumes. —(HMT, the science & applications of heat and mass transfer; v.6) 1. Jets—Fluid dynamics 2. Plumes (Fluid dynamics) 3. Turbulence I. Rodi, W. II. Series 532'.0527 QC158 ISBN 0-08-026492-1 in order to make this volume available as economically and as rapidly as possible the authors' typescripts have been reproduced in their original forms. This method un fortunately has its typographical limitations but it is hoped that they in no way distract the reader. Printed in Great Britain by A. Wheaton & Co. Ltd., Exeter Preface The discharge of waste fluid from industrial, agricultural or domestic sources into the environment, be it the hydrosphere or the atmosphere, usually leads to the formation of turbulent jets and plumes. The dispersion of the waste and the related dilution of pollutants are governed by the mean-flow and turbulence characteristics of the resulting jets or plumes, which themselves depend on the environmental conditions. In many cases, the density of the discharge fluid is different from that of the environment, either due to different temperature or chemical composi tion or due to suspended particles, and the resulting buoyancy forces can have a great effect on both the mean-flow and mixing ch iracteristics and hence on the dispersion of the rejected pollutants. In order to control and reduce the impact of waste emissions, one needs to understand the basic physical mechanisms governing turbulent buoyant jets and plumes, and one also needs methods to predict these flows. The present volume aims to foster these needs as it discusses the basic mechanisms involved in some detail and also presents formulae to estimate, and a mathematical model to calculate, the behaviour of turbulent buoyant jets and plumes under various conditions. Volume 4 of the HMT-Series is closely related with the present one as it reviews critically experimental data for the subgroup of vertical buoyant jets and plumes. Indeed it was intended to include this work in the present volume, but that review was completed so much earlier than the other contributions that prior publication as a separate volume appeared more opportune. The first contribution to this volume, by List, complements the previously published review by including new experimental data but mainly by using the data as basis for a detailed discussion of the physics of turbulent buoyant jets and plumes, including those in cross flows. The mechanism of jets is described by following from the initial discharge at an orifice with shear layer instability, to the development of large-scale vortices, through to the subsequent fully developed turbulence that ensues. The influence of body forces on the jet development and in particular on the entrain- ment that controls dilution is discussed. The turbulence structure within jets is examined using published experimental data, and the influence of buoyancy on this structure is described.The effects of ambient density stratification and cross flow on the development of turbulent jets and plumes are summarized briefly. With the aid of dimensional analysis, the experimental results are condensed into simple formulae for describing the main integral parameters like jet width and entrain- ment. These formulae are often sufficient for an estimation of jet and plume vu viii Preface behaviour for practical purposes. While J,ist’s contribution is concerned solely with jets and plumes in an infinitely large receiving fluid, Jirka’s article deals specifically with the interaction of jets and plumes with fluid boundaries such as horizontal walls, free surfaces or interfaces. First, the characteristics of horizontal buoyant surface jets jn a semi-confined environment are reviewed, with particular emphasis on thc influence of buoyancy on jet development. An entrainment relationship is derived and compared with experimental data, and the possible formation of hydraulic jumps is discussed. The main portion of Jirka’s contribution is concerned with the development of buoyant jets discharging into shallow, vertically confined fluid layers. Various configurations of practical importance are considered like submerged discharges interacting with the surface as well as discharges at the surface or at a density interface. Of major concern is the development of stable or unstable flow in the confined layer, the former being associated with buoyant spreading motion along the bounding surface and the latter with the formation of a recirculation cell. Integral analysis for different flow regimes leads to simple formulae for describ- ing the flow development, including stability criteria for the layer flow. The formulae also allow the calculation of dilution and are often sufficient for estimating the main parameters of practical interest. In the last contribution, by Hossain and Rodi, a significantly more complex mathematical model is described which allows detailed calculations of the flow, including not only the integral parameters but also the distributions of velocities, temperature, etc. These distributions are governed by basic differential equations like the time-averaged Navier-Stokes and temperature equations, which contain turbulent transport terms. The latter may be influenced strongly by buoyancy and require the introduction of a suitable turbulence model before the equations can be solved. Hossain and Rodi describe such a model, which is derived by simplification of a second-order model involving differential transport equations for the turbulent transport terms (Reynolds stresses and turbulent heat or mass fluxes). The resulting algebraic stress/flux model is suitable for general buoyant flows, except those with extended regions in which the turbulent transport is against the gradient of the transported quantity (counter gradient transport). The model is tested by application to those vertical-buoyant-jet cases for which data were reviewed in HMT-Volume 4, while the application to the horizontal surface jet discussed in Jirka’s contribution is described elsewhere. Judging from these verifications, the model appears to simulate realistically the most important characteristics of turbulent buoyant jets and plumes and should be a useful tool for simulating in detail flows of this type. Karlsruhe, January 1982 W. Rodi Mechanics of Turbulent Buoyant Jets and Plumes E. J. LIST California Institute of Technology Pasadena, California 91125 1 Acknowledgements This article was written at the California Institute of Technology in Pasadena, California. Without the support of Caltech, faculty colleagues, students, and staff it could not have appeared. Over a period of years many sponsors have supported the research program in the W. M. Keck Laboratories and this article has drawn substantially on work performed under those research grants. In particular, the support of the U.S. National Science Foundation, the Southern California Edison Company, and the Ford Energy Program at Caltech are gratefully acknowledged. The author is particularly appreciative of the assistance received from Joan Mathews and Melinda Hendrix-Werts in the preparation of this article. 2 List of Symbols A jet orifice cross-sectional area a non-dimensional constant B specific buoyancy flux b(x) jet lateral dimension at boundary b* jet lateral dimension where heat flux is 37% of maximum mean b jet lateral dimension where velocity is 37% of maximum mean u b jet lateral dimension where concentration is 37% of maximum mean n Θ J C-JCLJC^JC, non-dimensional constants in jet trajectory equations C ,C. plume and jet invariants P J c specific heat at constant pressure P D jet dimension at orifice D-,D non-dimensional constants in jet dilution equations ? E energy released from heat source F^ buoyancy Gr Grashof number g gravitational acceleration H energy release rate h^ length scale for jet in density-stratified environment h length scale for plume in density-stratified environment 4 Turbulent Buoyant Jets and Plumes non-dimensional constants horizontal length scale in density-stratified crossflows buoyant jet length scale RM R jet orifice scale (= A’/’) Q M specific momentum flux of jet at the orifice m local specific momentum flux N Brunt-VBiskIlkI frequency - P mean pressure inside jet mean pressure in environment Q jet specific mass flux at the orifice q2 turbulent kinetic energy/unit mass R local buoyant jet Richardson number autocorrelation function R plume Richardson number (invariant) P r lateral dimension in cylindrical polar coordinates lateral position in jet or plume where velocity is half maximum velocity S dimensionless buoyant jet parameter in stratified environment t time reference time T’ temperature fluctuation maximum mean temperature on jet axis Tm tempera t ure in the environment U mean crossflow velocity mean velocity at jet orifice uO maximum mean velocity on jet axis - U mean velocities in axial direction on jet or plume U’ local velocity fluctuation from mean in x-direction - V transverse mean velocity V’ local velocity fluctuation from mean in transverse direction Mechanics of Turbulent Buoyant Jets and Plumes 5 mean vertical velocity on jet axis in a crossflow m' X streamwise Cartesian coordinate Y tracer mass flux in jet or plume Y transverse coordinate in plane jet or plume lateral position in plane jet or plume at which velocity is y4 half maximum velocity vertical coordinate jet trajectory function in crossflow characteristic length scale for plume in crossflow characteristic length scale for transition in jet in crossflow characteristic length scale for jet in crossflow Greek Symbols a entrainment coefficient non-dimensional constants jet and plume entrainment coefficients local specific buoyancy flux turbulent momentum flux coefficient pressure force coefficient E specific turbulent kinetic energy dissipation rate dimensionless coordinate Ic thermal diffusivity e species concentration maximum mean species concentration mean species concentration 8 flux-weighted mean concentration local deviation from mean species concentratiou ratio of b e /b dimensionless constant U' microscales integral scales
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