Turbulent Jets and Plumes A Lagrangian Approach
Jets and plumes are shear flows produced by momentum and buoyancy forces. Examples include smokestack emissions, fires and volcano eruptions, deep sea vents, thermals, sewage discharges, thermal effluents from power stations, and ocean dumping of sludge.
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TURBULENT JETSAND PLUMES - A LAGRANGIAN APPROACH
JOSEPH H. W. LEE
Department of Civil Engineering The University of Hong Kong Hong Kong, China
VINCENT H. CHU
Department of Civil Engineering and Applied Mechanics McGill University Montreal, Canada
Springer Science+Business Media, LLC
Library of Congress Cataloging-in-Publication Data Lee, J. H. W. (Joseph H. W.) Turbulentjetsand plumes: a Lagrangian approach I by Joseph H.W. Lee, Vincent Chu. p.cm. Includes bibliographical references and index. Additional material to this book can be downloaded from http://extras.springer.com ISBN 978-1-4613-5061-3 ISBN 978-1-4615-0407-8 (eBook) DOI 10.1007/978-1-4615-0407-8
1. Turbulence. 2. Jets--Fluid dynamics. 3. Plumes (Fluid dynamics) 4. Lagrange equations. I. Chu, Vincent, 1942- II. Title. TA357.5.T87L44 2003 620.1 '064--dc21 2003047599
Copyright © 2003 Springer Science+Business Media New York Originally published by Kluwer Academic Publishers in 2003 Softcoverreprint ofthe hardcover 1st edition 2003 All rights reserved. No part of this work may be reproduced, stored in a retrieval system, or transrnitted in any form or by any means, electronic, mechanical, photocopying, rnicrofilrning, recording, or otherwise, without the written perrnission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Permission for books published in Europe: [email protected] Permissions tor books published in the United States of America: [email protected]
Printedon acid-free paper.
To Winnie and Alice
Contents
Preface 1. INTRODUCTION
xi 1
2. TURBULENT JETS 1. Plane Jet 1.1 Governing Equations 1.2 Integral Equations 1.3 Eulerian Integral Model 1.4 Entrainment Hypothesis 2. Round Jet 2.1 Mean Flow Structure 2.2 Additional Remarks on 3D Jet: 3. Theory vs Experiment 3.1 Mean Properties 3.2 Turbulence Properties 4. The Top-hat Profile 5. Prediction of Potential Core Length 6. Summary
21 26 28 29 30 33 34 34 37 39 39 41 46 47 49
3. TURBULENT BUOYANT PLUMES 1. Buoyancy and Reduced Gravity 2. Turbulent Round Plume 2.1 Dimensional Considerations 2.2 Eulerian Integral Model 2.2.1 Governing Equations 2.2.2 Integral Model Equations 2.2.3 Entrainment Hypothesis 2.2.4 Asymptotic Solution 2.2.5 Densimetric Froude number 2.2.6 Experiments 2.3 Effect of Initial Momentum: Vertical Buoyant Jet 2.4 Buoyancy Reduction due to Density-temperature Nonlinearity
55 56 60 60 64 64 65 66 66 70 72 75 79
TURBULENT JETS AND PLUMES - A LAGRANGIAN APPROACH
V1ll
3. 4. 5. 6.
Lagrangian Approach for Plume Modelling Negatively Buoyant Jets Turbulent Line Plume Summary
80 86 89 94
4. INCLINED BUOYANT JET IN STAGNANT ENVIRONMENT103 1. Lagrangian Model for Buoyant Jet in Stagnant Fluid 107 1.1 Zone of Established Flow (ZEF) 108 1.2 The Potential Core (ZFE) 110 2. Numerical Solution 113 2.1 Jet Trajectory and Potential Core Development 113 2.2 Dilution 119 2.3 Boundary effects 121 3. Application Examples 123 4. Summa
