Kolev Multiphase Flow Dynamics 1 Nikolay I. Kolev Multiphase Flow Dynamics 1 Fundamentals 2nd ed. With 114 Figures and CD-ROM Dr. Kolev Framatome ANP GmbH P. Box 3220 91050 Erlangen Germany ISBN 3-540-22106-9 Springer Berlin Heidelberg New York Library of Congress Control Number: 2004111217 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in other ways, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable to prosecution under German Copyright Law. Springer is a part of Springer Science+Business Media springeronline.com c Springer-Verlag Berlin Heidelberg 2002, 2005 Printed in Germany The use of general descriptive names, registered names, trademarks, etc. in this publi- cation does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting: Digital data supplied by author. Production: PTP-Berlin Protago-TeX-Production GmbH, Germany Cover-Design: medionet AG, Berlin Printed on acid-free paper 62/3020 Yu - 5 4 3 2 1 0 To Iva, Rali and Sonja with love! Silence, Feb. 2004, Nikolay Ivanov Kolev, 36 u 48cm oil on linen A FEW WORDS ABOUT THE SECOND EXTENDED EDITION The reader will find in the second edition the information already included in the first one improved and extended in several places. Chapter 3 of Volume I has been completely rewritten. It now contains the next step in the generalization of the the- ory of the equations of states for arbitrary real mixtures. Now with one and the same formalism a mixture of miscible and immiscible components in arbitrary solid, liquid or gaseous states mixed and/or dissolved can be treated. This is a powerful method towards creating a universal flow analyzer. Chapter 6 has been extended with cases including details of modeling of combustion and detonation of hydrogen by taking into account the equilibrium dissociation. In Chapter 9, dealing with detonation during melt-water interaction, additional introductory in- formation is given for the detonation of hydrogen in closed pipes taking into ac- count the dissociation of the generated steam. A new Chapter 11 is inserted be- tween the former Chapters 10 and 11 giving the mathematical tools for computing eigenvalues and eigenvectors and for determination of the type of systems of par- tial differential equations. The procedure for transformation of a hyperbolic sys- tem into canonical form is also provided. Then the relations between eigenvalues and critical flow and between eigenvalues and propagation velocity of small per- turbation are briefly defined. This is in fact a translation of one chapter of my first book published in German by Springer in 1986. In Chapter 12 about the numerical solution methods, the variation of the volume-porosity with time is systematically incorporated into the numerical formalism. Appendix 2 of Volume I contains some additional information about orthogonal grid generation. Chapter 26 of Vol- ume II, which is included in the accompanying CD, contains some additional ex- periments and movies documenting the performance of the method for fast pres- sure wave propagation in 2D geometry and interesting acoustical problems of melt-water interaction. Of course misprints and some layout deficiencies have also been removed as is usual for a second edition of such voluminous material. The form of the second improved and extended edition has been reached after I received many communications from all over the world from colleagues and friends commenting on different aspects of the two volumes or requesting addi- tional information. I thank all of you who have contributed in this way to improv- ing the two volumes. Erlangen, February 2004 Nikolay Ivanov Kolev INTRODUCTION Multi-phase flows are not only part of our natural environment such as rainy or snowy winds, tornadoes, typhoons, air and water pollution, volcanic activities etc., but also are working processes in a variety of conventional and nuclear power plants, combustion engines, propulsion systems, flows inside the human body, oil and gas production and transport, chemical industry, biological industry, process technology in the metallurgical industry or in food production etc. The list is by far not exhaustive. For instance everything to do with phase changes is associated with multi-phase flows. The industrial use of multi-phase systems requires meth- ods for predicting their behavior. This explains the “explosion” of scientific publi- cations in this field in the last 30 years. Some countries, such as Japan, have de- clared this field to be of strategic importance for future technological development. Probably the first known systematic study on two-phase flow was done during the Second World War by the Soviet scientist Teletov [12] and published in 1958 as “On the problem of fluid dynamics of two-phase mixtures”. Two books that ap- peared in Russia and the USA in 1969 by Mamaev et al. [7] and by Wallis [13] played an important role in educating a generation of scientists in this discipline including me. Both books contain valuable information mainly for steady state flows in pipes. Hewitt and Hall-Taylor published in 1974 “Annular two-phase flow” [5]. The book also considers steady state pipe flows. The usefulness of the idea of a three-fluid description of two-phase flows was clearly demonstrated on annular flows with entrainment and deposition. Ishii [6] published in 1975 the book “Thermo-fluid dynamic theory of two-phase flow”, which contained a rigor- ous derivation of time-averaged conservation equations for the so called two-fluid separated and diffusion momentum equations models. This book founded the ba- sics for new measurement methods appearing on the market later. Nigmatulin published “Fundamentals of mechanics of heterogeneous media” [8] in Russian in 1978. The book mainly considers one-dimensional two-phase flows. Interesting particular wave dynamics solutions are obtaining for specific sets of assumptions for dispersed systems. The book was extended mainly with mechanical interaction constitutive relations and translated into English in 1991 [9]. The next important book [2] for two-phase steam-water flow in turbines was published by Deich and Philipoff in 1981 in Russian. Again mainly steady state, one-dimensional flows are considered. Delhaye et al. published in the same year “Thermohydraulics of two-phase systems for industrial design and nuclear engineering” [3]. The book contains the main ideas of local volume averaging, and considers mainly many X INTRODUCTION steady state one-dimensional flows. One year later, in 1982, Hetsroni edited the “Handbook of multi phase systems” [4] containing the state of the art of constitu- tive interfacial relationships for practical use. The book is still a valuable source of empirical information for different disciplines dealing with multi-phase flows. In the monograph “Interfacial transport phenomena” [10] published by Slattery in 1990 complete, rigorous derivations of the local volume-averaged two-fluid con- servation equations are presented together with a variety of aspects of the funda- mentals of the interfacial processes based on his long years of work. Slattery’s first edition appeared in 1978. Some aspects of the heat and mass transfer theory of two-phase flow are now included in modern text books such us “Thermody- namics” by Baer and “Technical thermodynamics” by Stephan and Mayinger, see [1] and [11]. It is noticeable that none of the above mentioned books is devoted in particular to numerical methods of solution of the fundamental systems of partial differential equations describing multi-phase flows. Analytical methods still do not exist. I published in 1986 the book “Transient two-phase flows” with Springer-Verlag in German, discussing several engineering methods and practical examples for inte- grating systems of partial differential equations describing two- and three-fluid flows in pipes. Since 1984 I have worked intensively on creating numerical algorithms for de- scribing complicated multi-phase multi-component flows in pipe networks and complex three-dimensional geometries mainly for nuclear safety applications. Note that the mathematical description of multi-dimensional two- and multi-phase flows is a scientific discipline with considerable activity in the last 30 years. In addition thousands of scientists have collected for years experimental information in this field. But there is still a lack of a systematic presentation of the theory and practice of numerical multi-phase fluid dynamics. This book is intended to fill this gap. Numerical multi-phase fluid dynamics is the science of the derivation and the numerical integration of the conservation equations reflecting the mass momen- tum and energy conservation for multi-phase processes in nature and technology at different scales in time and space. The emphasis of this book is on the generic links within computational predictive models between x fundamentals, x numerical methods, x empirical information for the constitutive interfacial phenomena, and x comparison with experimental data at different levels of complexity. The reader will realize how strong the mutual influence of the four model con- stituencies is. There are still many attempts to attack these problems using single- phase fluid mechanics by simply extending existing single-phase computer codes with additional fields and linking with differential terms outside of the code with- INTRODUCTION XI out increasing the strength of the feedback in the numerical integration methods. The success of this approach in describing low concentration suspensions and dis- persed systems without strong thermal interactions should not confuse the engi- neer about the real limitations of this method. This monograph can be considered also as a handbook on numerical modeling of three strongly interacting fluids with dynamic fragmentation and coalescence representing multi-phase multi-component systems. Some aspects of the author's ideas, such us the three-fluid entropy concept with dynamic fragmentation and coalescence for describing multi-phase, multi-component flows by local volume- averaged and time-averaged conservation equations, have been published previ- ously in separate papers but are collected here in a single context for the first time. An important contribution of this book to the state of the art is also the rigorous thermodynamic treatment of multi-phase systems, consisting of different mixtures. It is also the first time of publishing the basics of the boundary fitted description of multi-phase flows and an appropriate numerical method for integrating them with proven convergence. It is well known in engineering practice that “the devil is hidden in the details”. This book gives many hints and details on how to design computational methods for multi-phase flow analysis and demonstrates the power of the method in the attached compact disc and in the last chapter in Volume 2 by presenting successful comparisons between predictions and experimental data or analytical benchmarks for a class of problems with a complexity not known in the multi-phase literature up to now. It starts with the single-phase U-tube problem and ends with explosive interaction between molten melt and cold water in com- plicated 3D geometry and condensation shocks in complicated pipe networks con- taining acoustically interacting valves and other components. Erlangen, Spring 2002 Nikolay Ivanov Kolev References 1. Baer HD (1996) Thermodynamik, Springer, Berlin Heidelberg New York 2. Deich ME, Philipoff GA (1981) Gas dynamics of two phase flows. Delhaye JM, Giot M, Reithmuller ML (1981) Thermohydraulics of two-phase systems for industrial design and nuclear engineering, Hemisphere, New York, McGraw Hill, New York 4. Hetstroni G (1982) Handbook of multi phase systems. Hemisphere, Washington, McGraw-Hill, New York 5. Hewitt GF and Hall-Taylor NS (1974) Annular two-phase flow, Pergamon, Oxford 6. Ishii M (1975) Thermo-fluid dynamic theory of two-phase flow, Eyrolles, Paris 7. Mamaev WA, Odicharia GS, Semeonov NI, Tociging AA (1969) Gidrodinamika gasogidkostnych smesey w trubach, Moskva 8. Nigmatulin RI (1978) Fundamentals of mechanics of heterogeneous media, Nauka, Mos- cow, 336 pp (in Russian) XII INTRODUCTION 9. Nigmatulin RI (1991) Dynamics of multi-phase media, revised and augmented rdition, Hemisphere, New York 10. Slattery JC (1990) Interfacial transport phenomena, Springer, Berlin Heidelberg New York 11. Stephan K and Mayinger F (1998) Technische Thermodynamik, Bd. Teletov SG (1958) On the problem of fluid dynamics of two-phase mixtures, I. Hydro- dynamic and energy equations, Bulletin of the Moscow University, no 2 p 15 13.
