Industrial Safety Series Vol. 1. Safety of Reactive Chemicals (T. Yoshida) Vol. 2. Individual Behaviour in the Control of Danger (A.R. Hale and A.I. Glendon) Vol. 3. Fluid Mechanics for Industrial Safety and Environmental Protection (T. K. Fannelop) Industrial Safety Series, 3 Fluid Mechanics for Industrial Safety and Environmental Protection by Torstein K. Fannelop Institute of Fluid Dynamics, Swiss Federal Institute of Technology, Zurich, Switzerland ELSEVIER, Amsterdam — London — New York — Tokyo 1994 ELSEVIER SCIENCE B.V. Sara Burgerhartstraat 25 P.O. Box 211, 1000 AE Amsterdam, The Netherlands Library of Congress Cata1oging-in-Pub1ication Data Fannelop, Torstein K. Fluid mechanics for industrial safety and environmental protection / by Torstein K. Fannelop. p. cm. -- (Industrial safety series ; 3) Includes bibliographical references and index. ISBN 0-444-89863-8 1. Hazardous substances. 2. Fluid mechanics. I. Title. II. Ser i es. T55.3.H3F36 1994 604.7—dc20 94-10951 CIP ISBN: 0-444-89863-8 © 1994 Elsevier Science B.V. 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 written permission of the Publisher, Elsevier Science B.V., Copyright and Permissions Department, P.O. Box 521, 1000 AM Amsterdam, The Netherlands. Special regulations for readers in the USA. - This publication has been registered with the Copy­ right Clearance Center Inc. (CCC), Salem, Massachusetts. Information can be obtained from the CCC about conditions under which photocopies of parts of this publication may be made in the USA. All other copyright questions, including photocopying outside of the USA, should be referred to the publisher. No responsibility is assumed by the Publisher for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions or ideas contained in the material herein. This book is printed on acid-free paper. Printed in The Netherlands V PREFACE An esteemed colleague once told me he didn't bother to look at new textbooks in fluid mechanics because they bring nothing new. There is considerable truth in this, but for someone less familiar with Lamb, Milne-Thompson and other classical works, textbooks can serve as a useful introduction to new or specialized branches of fluid mechanics. What is "new" is often the application and not the equations or the methods used to solve them. The present book discusses the application of fluid mechanics to the new and growing fields of environmental protection and industrial safety. These fields are often characterized as "interdisciplinary", meaning in practice that considerable research in the library is required to assemble the information needed to solve specific problems. It is my hope that the contents of the eighteen chapters which follow, will make information on methods and means more accessible to students, engineers and consultants concerned with "safety and environment". The problems discussed have been encountered in nearly 25 years of consultancy work for industry and government agencies, and they are believed to represent a typical sample, but not a complete catalogue. A particular problem in writing this book, is how to organize the material in a logical fashion. There are no "basic principles" which can be formulated in the early chapters for further developments and discussions in later parts. The choice made here is to follow the chain of events in real accidents, starting with the loss of containment of hazardous fluids, going on to the spreading and mixing processes in water or air and ending with the damage loads caused by explosions and other critical events. An advantage of this approach is that gaps in knowledge can be easily identified. Where possible, an attempt has been made to fill or reduce such gaps by undertaking new experiments or by theoretical studies. The discussions are limited to the fluid mechanical aspects, and material relevant to other sciences (chemistry, medicine etc.) are considered only perfunctorily (Chapter 18) or not at all. The emphasis is on analytical (and where possible simple) methods, for reasons of understanding and transparency. To someone new to the subject, a fundamental understanding will be more important than the high accuracy possible by "black-box" software. This is not an attempt to downgrade the importance of available computer programs. For certain problems, such as atmospheric vi dispersion, a large and very useful library of free and commercial software exists. But few of these programs are validated, and the inexperienced user could be led, at times, to accept an incorrect answer if he has no way of checking the results. The book is intended for students of fluid mechanics interested in applications outside the traditional engineering fields. The idea of working to protect our environment, is particularly appealing to the present student generation, although some are disappointed to find that environmental fluid mechanics requires just as much study as traditional applications. Another group of potential readers are the scientists and engineers, concerned with safety and environmental flows, who lack formal training in these disciplines. (It is a common experience that in many risk analyses dealing with industrial hazards, the treatment of fluid-mechanical aspects lacks depth and understanding.) Given the broad range of problems considered, it is believed that most readers will find something new or useful. I also have the hope that the book will be useful for selfstudy, in particular for fluid mechanical experts, no longer needed in the aerospace and defense industries, in search of new opportunities. It is written with the perspective of a former aeronautical engineer. The material on which the book is based, has been collected over many years and it is used for a one-year course in applied fluid mechanics. To prepare a book from a set of course notes is a major undertaking, requiring not only personal sacrifice evenings and week-ends, but also the assistance of many colleagues, co-workers and friends. I am indebted to Mrs. M. Ehrismann who typed most of the first draft on her Macintosh and to Ms K. Schlenkert for drawing all the original figures and for converting graphical information to digitized form, suitable for a computer-based copy. My colleagues Professors B. Muller and H. Thomann have given useful advice both in general and related to specific topics. Drs. P. Schuhmacher and F. Zumsteg have provided detailed comments on the chapters on atmospheric dispersion and the spreading of dense releases. Many of my former and present assistants have helped me as well, either through their research work or often more directly. Dr. J.P. Kunsch generated new (unpublished) material on underwater explosions. Mr. J. Sesterhenn checked through the complete manuscript and gave invaluable help with regard to unexpected computer and software problems. The contributions of other assistants are evident from the list of references where they appear as authors or co-authors. I am grateful to STATOIL, Norway, for research funding over many vii years on problems related to oil pollution, pipeline rupture and underwater gas releases. I am particularly indebted to Mr. R. Games and Dr. K. Sjoen for their support. Our research on heavy-gas dispersion has been funded in part by the Swiss National Science Foundation. The Swiss Federal Institute of Technology ETHZ has contributed generously to our research over many years. I thank Professor R. Hiitter (Vice-president research) and Dr. C. Holzer, in particular, for their support of this book project. To produce a camera-ready copy, in accord with the Publisher's specifications, requires skills well beyond that available "in house". Dr. M. Bettelini, ably assisted by his wife Anna, has been kind enough to produce the camera-ready script and in the process he has also checked many of the equations and results. Without this dedicated support the book would still be in my desk drawer. I take this opportunity also to thank two friends who over the years have given me much help and stimulation, Professor Inge L. Ryhming and Dr. George D. Waldman. The book could not have been written without help and encouragement from my wife Nanna. I dedicate the book to her with thanks for 36 happy years together. Zurich in December, 1993 Torstein K. Fannelop xvii NOTATION The general notation corresponds to that commonly used in a modern fluid dynamics text in the English language. To avoid problems for readers interested in consulting the original sources, the symbols used in the papers cited have been kept as much as possible. A special list of symbols is included in each chapter to minimize the confusion arising from the differences in notation. The usual cartesian coordinates fx, y, z) and the associated velocity components u, v, w are defined differently in engineering and geophysical fluid dynamics. In problems related to environmental flows, the surface coordinates used herein are x, y and the vertical coordinate z, as is usual in geophysics. Otherwise y is used as the coordinate normal to the bounding surface with v as the corresponding velocity component. English Symbols a speed of sound acceleration thermal diffusivity A flow area surface area constant in power law for front or shock b width radius of jet, plume or thermal B Bond number (nondimensional) scaled radius (plume or jet) c heat capacity velocity speed of sound in liquids wave velocity concentration specific heats at constant pressure or volume constant of integration constant of proportionality C drag coefficient D Cj,C friction coefficient F d depth of layer diameter D diameter xviii molecular diffusion coefficient layer thickness E energy content entrainment function / friction factor similarity variable F buoyancy parameter similarity variable force Fr Froude number (nondimensional) Fd densimetric Froude number (several definitions) F, F components of force (inertia, gravity) t g g gravitational acceleration g g " reduced gravitational accelerations (different definitions) h depth of channel or layer height of object enthalpy H depth of dam, ocean or cloud geometric height i specific impulse s j variable for dimension, j = 0, planar, j = 1 radial J (t) diffusion flux k conductivity empirical constant K velocity lag turbulent eddy-transfer coefficient / length scaling variable 4? > buoyancy length f, £ momentum length m M L thermal lag length of object scaling variable distance to object L buoyancy length (surface plume) B m mass mass fraction of particles momentum flux, mass loss exponent in indicial equation m* apparent mass xix M Mach number, M = u/a M (t) mass of diffusing species n power-law exponent exponent in indicial equation curvilinear coordinate p pressure Po>Ps barometric pressure side-on overpressure P function of pressure probability variable q heat-transfer rate source strength (2D) heat release per unit mass Q volume (liquid) integrated heat flux source strength (3D) r radial coordinate density ratio R radius of object gas constant radial distance Re Reynolds number (several definitions) Ri Richardson number (several definitions) Rh hydraulic radius s length curvilinear coordinate entropy S measure for stratification t time (s) temperature (°C) thickness T period of oscillation temperature (K) scaling variable for time u, v, w velocity components in x, y, z-directions u ', v ', w ' velocity fluctuations in x, y, z-directions u* friction velocity, u* = \ptTp U , V, W external or bulk velocities in x, y, z-directions U wind, current or front velocity V, V volume (gas) g x , y ,z cartesian coordinates, x aligned with wind or main motion, y normal to surface (engineering system), z XX normal to surface (geophysical system) Xfr transition between different flow regimes x stagnation point st X similarity variable Greek Symbols a entrainment rate (plume) constant (3 entrainment rate (heavy-gas cloud) y adiabatic exponent, y = c/c p v constant <5 thickness (viscous layer) e eddy viscosity emissivity r\ similarity variable 6 potential temperature temperature ratio polar coordinate ground slope A wave length scaled dimension or distance ratio of radii; buoyancy and velocity profiles ix viscosity v kinematic viscosity, v = \x/p p density Ap density difference PQ potential density a surface tension normal stress standard deviation r shear stress 0 flow potential depth ratio, <P = h/H X concentration (pollutant, g/m3) W stream function co angular velocity