WIT PRESS WIT Press publishes leading books in Science and Technology. Visit our website for the current list of titles.

Transcription

1 Water Hammer Simulations WIT PRESS WIT Press publishes leading books in Science and Technology. Visit our website for the current list of titles. WITeLibrary Home of the Transactions of the Wessex Institute, the WIT electronic-library provides the international scientific community with immediate and permanent access to individual papers presented at WIT conferences. Visit the WIT elibrary athttp://library.witpress.com

2

3 Water Hammer Simulations S. Mambretti Universidade Estadual de Campinas, Brazil

4 S. Mambretti Universidade Estadual de Campinas, Brazil Published by WIT Press Ashurst Lodge, Ashurst, Southampton, SO40 7AA, UK Tel: 44 (0) ; Fax: 44 (0) For USA, Canada and Mexico WIT Press 25 Bridge Street, Billerica, MA 01821, USA Tel: ; Fax: British Library Cataloguing-in-Publication Data A Catalogue record for this book is available from the British Library ISBN: eisbn: Library of Congress Catalog Card Number: No responsibility is assumed by the Publisher, the Editors and Authors 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. The Publisher does not necessarily endorse the ideas held, or views expressed by the Editors or Authors of the material contained in its publications. WIT Press 2014 Printed by Lightning Source, UK. 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 written permission of the Publisher.

5 Preface Waterhammer is a pressure surge or wave caused when a fluid (usually a liquid but sometimes also a gas) in motion is forced to change its velocity. It commonly occurs when a valve closes or opens at the end of a pipeline system, or a pump starts or stops; as a consequence, a pressure wave propagates in the pipe. This pressure wave can cause problems, and normally the efforts of the designers are aimed at reducing its effects. However, in some cases the pressure pulses are deliberately caused in order to achieve particular results, such as the pumping of a fluid or the mapping of a network. In all cases, the study of the consequences of this phenomenon is required, and this might be performed with rough formulas as those developed between the end of 19th Century and the beginning of the 20th, or through more advanced models. Nevertheless, all the models have limitations and might be criticized. During the years I spent as a professional consultant and researcher in the field, the need for a reference able to guide through the several models that have been developed and the analysis of their results clearly emerged. Hence the reason to write this book. In the book, chapter 2 presents the governing equations and the hypotheses involved; chapter 3 shows the simplified solutions that have been developed and used before the arrival of computers; in chapters 4 and 5 two numerical integration methods are shown. In chapter 6 a number of devices are presented with the methods that can be used for their modeling. In chapter 7, problems related to the implementation of the model are discussed, giving some suggestions for their solution. In chapter 8 an important phenomenon, the presence of air and cavitation, is analyzed, while in chapter 9 the most advanced models are presented and discussed. Chapter 10 presents some

6 actual hydraulic plants whose behavior has been analyzed and studied with the methods and models presented in the book. Writing a book is always a challenging task, and many people contributed in some way to making this volume a reality. All the case studies have been carried out with the invaluable help of my colleague and friend Dr. Paola Pianta, with whom I discussed many developments and applications of the models presented in this book. Most of my research has been carried out at Politecnico di Milano, where all the experimental tests have been performed, thanks to Prof. Enrico Orsi, head of the Laboratory of Hydraulics, and Prof. Enrico Larcan, head of the Department of Hydraulics. After moving to Brazil, invited by Prof. Paulo Barbosa, head of the Faculty of Civil Engineering, I found an excellent welcome and all the freedom and help I needed to finish the book, thanks to the kindness of Prof. José Geraldo Pena de Andrade, head of the School of Technology, University of Campinas. I cannot forget Prof. Daniele De Wrachien, who has always been a support and a help in my academic life, and Prof. Carlos Brebbia, who not only is the Director of WIT, but he is also an example to be followed both from the scientific and the human point of view. Finally, I have to thank my wife Grazia, both because she allowed me to work overtime and because she drew all the figures for the book. All the mistakes that can be found in the book have to be attributed to my limitations. I would be grateful if the Readers would report any errors and suggest any improvements for the subsequent editions of the book. Stefano Mambretti São Paulo, 2013

7 Contents 1 An old topic still not completely solved An old topic Applications and problems This book The computer programs Compressible flow theory: basic concepts Instantaneous operations Wave celerity Velocity of operations Non-negligible headlosses Governing equations Continuity equation Momentum equation The governing equations Simplified solutions The Allievi s method (1913) The non-elastic hypothesis Governing equations Comparisons Graphical method...36

8 4 Numerical solution of the governing equations: The method of characteristics Numerical solution Initial and boundary conditions Reservoir Valve Junction The computer code First simple application Numerical solution of the governing equations: finite difference methods The Courant Friedrichs Levy stability condition The Lax Wendroff method Solving the governing equations Boundary conditions Asymmetrical schemes Ghost cells The computer code Again the simple application Devices Boundary conditions Surge tanks Simple surge tanks Different types of surge tanks Air chambers Relief valves and rupture disks Centrifugal pumps Other methods for controlling the pressures...84

9 6.6 The computer codes The simple surge tank The simple air chamber Air chamber with headlosses Air chamber and valve Valve modelling: an example Pumps Instabilities Vibrations General remarks Computer program for oscillating velocity Transfer matrix method General remarks Application to hydraulic transients Description of simple system: pipes Description of simple system: valves and effluxes Global matrix of a system A simple application Numerical instabilities Changing CFL number First order methods Flux-limiters Artificial dissipation Effects of air and cavitation Cavities Formation of the cavities Collapse of the cavities Description of the motion in the presence of cavities

10 8.2 Changing of celerity Water column separation Additional resistance terms Models Parameters Laboratory experiments Experimental set-up Experimental tests Computer code Advanced models D models Continuity equation Momentum equation Headlossess Pezzinga s model k ε model Cavitation Release gaseous cavitation model Second viscosity cavitation model Numerical schemes Further problems Case studies Simple pressure pipe for petroleum products in Djibouti Plant characteristics Expected scenarios Case Case Case Conclusions...161

11 10.2 A more complex example for seawater treatment plant in Tanzania Plant characteristics Unsteady flow simulations: existing plant Plant to be designed No air chambers Air chamber 3 m 3 volume Air chamber 5 m 3 volume Conclusions A very complex example for seawater treatment plant in Algeria The plant to be modelled A peculiar device: energy recovery PX Laboratory plant Laboratory tests Model of the seawater plant in Algeria Conclusions Final remarks References 181