7R18. Multiphase Flow Dynamics, Volume 1: Fundamentals; Volume 2: Thermal and Mechanical Interactions. - NI Kolev (Framatome ANP GmbH, PO Box 3220, Erlangen, 91050, Germany). Springer-Verlag, Berlin. 2002. 699 pp. CD-Rom included. ISBN 3-540-42984-0. $139.00. Volume 2 ISBN 3-540-43017-2, 692 pp,$139.00.

Reviewed by RW Lyczkowski (Energy Syst Div, Argonne Natl Lab, Bldg 362, Rm C348D, 9700 S Cass Ave, Argonne IL 60439-4815).

This is a dual review, so it will be longer than normal. There are 13 Chapters in Volume 1 (98 figures) and 26 Chapters in Volume 2 (77 figures) as listed below. Chapter 13 of Volume 1 and Chapter 26 of Volume 2 are available on an attached CD-ROM in pdf format. The system requirements are Windows 98 and higher. Both pdf files contain links to the computer animations. To see the animations, one double clicks on the active links contained inside the pdf documents. The animations are then displayed in an internet browser, such as Microsoft Internet Explorer or Netscape. Alternatively, gif-file animations are also provided. The books are described as a monograph in the Table of Contents. They are not textbooks, as there are no problems. There are a few examples scattered throughout the text, but most of them are contained on the CD-ROM attached to Volume 1.

The author is identified as being with Framatome ANP Gmbh in Erlangen, Germany, a large multinational company second in size to GE. The monograph is the result of 20 years of research and experience and is claimed to be a handbook of three-dimensional multiphase numerical modeling (at least in the context of nuclear safety analysis). The author is to be commended for gathering and updating his research and reviewing that of a great many others together in one place and attempting to make a cohesive whole.

Reading the Introduction and Summary, one gets the impression that a very general multiphase local volume-averaging approach is going to be adopted in Volume 1, Fundamentals, using what is referred to as the Slattery-Whittaker theorem together with the Leibnitz rule. In fact, the theoretical framework adopted is that of Sha, Soo, and Chao (Nuclear Eng Design, Vol 82, pp 93–106, 1984), and not that of Slattery (Advanced Transport Phenomena, Cambridge Univ Press, 1999), Soo (Multiphase Fluid Dynamics, Science Press, distributed by Gower Technical, 1990, a revision of Soo’s landmark Fluid Dynamics of Multiphase Systems, 1967), or Gidaspow (Multiphase Flow and Fluidization Continuum and Kinetic Theory Descriptions, Academic Press, 1994), for example, (none of which are referred to) or the references cited. The Sha, Soo, and Chao approach is in fact an artifice, which justified the numerical construct of surface permeabilities, sometimes called area factors, in thermal hydraulics and nuclear safety computer programs resulting from the control volume approach. A single parameter, the porosity, results from rigorous local volume averaging. The approach is immediately reduced to the case of only three fluids, ie fields or phases. A novel feature is the treatment of multi-component three-field flow. Fluid-solids systems, per se, ie, fluidized beds, pneumatic conveying, etc, are not to be found here and this literature is not referred to except indirectly in the context of correlations for particle fragmentation and coalescence. This is understandable as the author’s background is in nuclear safety analysis.

The author rightly points out that none of the above references, nor his, treat the numerical aspects of multiphase flow, and this is correct. Gidaspow’s book presents the results of many numerical simulations and comparisons with experiment, but fails to describe the numerical methods. Such numerical methods are scattered throughout the literature. Again the author maintains that there remains a lack of a systematic presentation of theory and numerical multiphase fluid dynamics. To address this deficiency, the author states that the emphasis of the book is the generic links of the computational predictions with 1) fundamentals, 2) numerical methods, 3) empirical or constitutive interfacial phenomena, and 4) comparisons with experimental data. The author’s collected research on the three-fluid entropy and exergy concept, the rigorous thermodynamic treatment of multi-component systems, and an exposition of boundary fitted description and numerical treatment in Cartesian, cylindrical and curvilinear coordinates for three fields are claimed to be presented in this monograph for the first time.

The monograph is intended for applied scientists, practicing engineers, graduate students, and doctoral research programs. Does in fact the monograph achieve its claimed objectives? So-called modeling hints and details are given on the CD-ROM using many comparisons of predictions with experimental data. With these hints, the author claims that the reader can write his own computer programs. The incredible detail and confusing nomenclature in Volume 1 offered this reviewer a serious impediment to understanding and progress through the fundamentals development. A lot more of the details could have been relegated to Appendices, either at the end of the chapters or at the end. If an expert has problems following the development of fundamentals, then what chance does the novice applied scientist, practicing engineer, or graduate student have in digesting the great magnitude effort?

Volume 1 has a global Nomenclature section, but Volume 2 has a separate Nomenclature section in each and every chapter. Therefore, there is little likelihood that the Nomenclature for the fundamentals and numerical method in Volume 1 is consistent with the correlations and models contained in Volume 2. This reviewer admits to have not checked for consistency. Key superscript and subscript notations in Volume 1 are missing in the Notation section. These include, but are not limited to the following: Superscripts

e defined by Eq. 1.11 as “heterogeneous”

l defined by Eq. 1.15 as “intrinsic” field average

$le$ defined by Eq. 1.17 as intrinsic surface average (for field l)

$lσ$ defined implicitly on page 13 in $Vlστ$ instantaneous interfacial

τ implicitly defined by $Vlτ$ means “instantaneous” in Nomenclature Subscripts

$DTN$ defined on page 204.

The grammar is a little awkward in places, and there are typographical errors scattered throughout both Volumes 1 and 2. A little more editorial assistance could have been used. Some examples are: Hetsroni is consistently misspelled as Hetsrony; the subheading 1.4 on page 10 is corrupted; Eq. (1) and Eq. (28) in Fig. 2.4 should be Eq. (2.1) and Eq. (2.28). In a book of this complexity, such things are to be expected in the first printing.

There are very few explanations as to how the correlations in Volume 2 are to be meshed with Volume 1. There is no clear discussion of how the energy is to be partitioned for the various heat transfer mechanisms eg, bubble growth in a superheated liquid, condensation in a subcooled liquid, etc. One of the first attempts to derive a consistent methodology to do so was published by Solbrig, Hocevar, and Hughes (Preprints of AIChE Papers 17th National Heat Transfer Conference, Salt Lake City Aug, 14–17, 1977, AIChE, New York, 1977). The IVA series of codes developed by the author and colleagues embody this linkage. Why not make a generic version of this code available with the monograph, or maybe a few templates?

Each chapter has its own Reference section. There is a general Index section at the end of each volume. SI units are used exclusively. The figures (some of which are in color), tables, and equations are of extremely high quality. The book is sturdily bound with an attractive matte cover and is printed on acid free paper. The monograph will be of use as a general reference to specialists in the area of thermal hydraulics and nuclear reactor safety. The preponderance of references by the author (most chapters are mostly references to the author’s works) in technical reports and conference proceedings will make it difficult to obtain the original sources of the revisions contained in the monograph. Can the monograph be used to write computer programs using the fundamentals and correlations? This reviewer seriously doubts that anyone could write their own code based on this monograph. The correlations from Volume 2 might be programmed into existing computer programs.

The chapters in the two volumes are organized as follows with brief descriptions or highlights. Subtitles are not listed as the length would be excessive.

The chapters of Volume 1, Fundamentals, include the following:

Mass conservation (44 pp)—Fig. 1.1 is pretty, but meaningless and confusing, also appears as Fig. 1.1 in Volume 2.

Momentum conservation (70 pp)

Derivatives for the equations of state (52 pp)—Thermodynamic derivatives are derived for several planes for multi-component mixtures. The two appendices present derivatives for steam/air and solid and liquid uranium dioxide. The entire chapter could have been relegated to an Appendix.

Variety of notations of the energy conservation for single-phase flow (36 pp)—This chapter serves as an introduction to Chapter 5. The energy equation is expressed in terms of internal energy, temperature, entropy, and enthalpy without conduction. The one-dimensional equations are transformed into canonical form using the method of characteristics (MOC) and solved for a shock tube simulation and an error analysis is performed. An appendix analyzes the accuracy of the donor-cell differencing compared with the MOC.

First and second laws of the thermodynamics for multi-phase multi-component flows (70 pp)—This chapter continues Chapters 1 and 2. The “general” energy equation for three fluids in a porous medium is expressed in terms of internal energy, temperature, entropy and enthalpy.

Some simple applications of the mass and energy conservation for multi-component single-phase systems (18 pp)—Several analytical solutions are obtained which can serve as benchmarks for computer codes.

Exergy of multi-phase multi-component systems (16 pp)—Exergy is defined in accordance with several investigators and applied to a three-fluid multi-component system.

One-dimensional three-fluid flow (86 pp)—The mass, momentum, and entropy equations summarized in Chapters 1, 2, and 5 are simplified and cast into canonical form using the MOC. Transient and steady-state flow equations are derived using the slip ratio model.

Detonation waves in melt-coolant interaction (34 pp)—Shock wave relations are derived for water in contact with molten iron or uranium dioxide and a numerical solution is presented.

Conservation equations in general curvilinear coordinate systems (34 pp)

Numerical solution methods for multi-phase flow problems (92 pp)—Discretizations of the equations presented in Chapters 1, 2, and 5 are given using donor cell differencing for low-order terms and central differencing for second-order terms as programmed in the IVA series of computer codes (IVA2 through IVA6). The Newton-Raphson iteration scheme and higher order discretizations schemes are discussed. A section on pipe flow network definitions is included. Eight appendices give details of the discretizations definitions and one simple iterative method. The IMF (Harlow and Amsden, J Comp. Phys, Vol 17, 1975) and K-FIX (Rivard and Torrey, LA-NREG-6623, 1977) numerical solution schemes developed at Los Alamos National Laboratory, for example, are not discussed.

Numerical solution method for multi-phase flow problems in curvilinear coordinate systems (54 pp)—This chapter is parallel in construction to Chapter 11. The reader is urged to read Appendices 1 and 2 before reading this chapter. Four appendices give details of the discretization definitions.

Appendix 1 offers a Brief introduction to vector analysis (28 pp) and Appendix 2 covers Basics of the coordinate transformation theory (56 pp). Also included is Visual demonstration of the method (40 pp on CD-ROM), as well as a seven-page Index.

The chapters of Volume 2, Mechanical and Thermal Interactions, include the following:

Flow regime transition criteria (26 pp); Drag forces (42 pp); Friction pressure drop (16 pp) [Govier and Aziz, “The Flow of Complex Mixtures in Pipes, Van Nostrand Reinhold Co., New York, 1972 contains much more information covering Chapters 1 through 3; however it is not up to date and is long out of print]. Diffusion velocities for algebraic slip models (46 pp); Entrainment in annular two-phase flow (18 pp); Deposition in annular two-phase flow (14 pp); Introduction to fragmentation and coalescence (22 pp); Acceleration induced droplet and bubble fragmentation (48 pp); Turbulence induced particle fragmentation and coalescence (26 pp); Liquid and gas jet disintegration (26 pp); Nucleation in liquids (32 pp); Bubble growth in superheated liquid (24 pp); and Condensation of a pure steam bubble in a subcooled liquid (22 pp). Chapters 7 through 10 are a review of the subjects of fragmentation and coalescence. Fragmentation of melt in coolant (52 pp)—The major portion addresses thermo-mechanical fragmentation of liquid metals in water with additional sections on particle production, thermal fragmentation and oxidation. Chapters 12 through 14 are reviews of the subjects of nucleation, bubble growth, and condensation.

Continuing on with the chapters: Bubble departure diameter (18 pp)—A new model is developed and compared with experimental data.

How accurately can we predict nucleate boiling? (28 pp)—This chapter is a revised version of a new theory previously published by the author. An Appendix reviews the state of the art of modeling nucleate pool boiling.

Heterogeneous nucleation and flashing in adiabatic pipes (22 pp)—A new model is developed for heat and mass transfer for bubble fragmentation and coalescence and compared with data.

Boiling of subcooled liquid (10 pp)—Heat and mass transfer correlations are presented.

Natural convection film boiling (6 pp)

Forced convection boiling (22 pp)—A collection of heat and mass transfer correlations is presented for convection boiling, transition boiling, and critical heat flux.

Film boiling on vertical plates and spheres (42 pp)—A closed form analytical solution is presented for mixed-convection film boiling on vertical walls and on a sphere and compared with experimental data. There are two short appendices on natural and force convection.

Liquid droplets (36 pp)—The chapter presents correlations for nucleation of condensing subcooled steam, interfacial heat transfer without mass transfer, direct contact condensation of steam on a subcooled droplet, flashing of superheated droplets, evaporation of saturated droplets into superheated gas and gas mixture containing an inert.

Heat and mass transfer at the film-gas interface (26 pp)—The chapter presents correlations for convective heat transfer, flashing of superheated films, evaporation of saturated films in a superheated gas, condensation of pure steam on subcooled films and the effect of noncondensibles.

Condensation at cooled walls (14 pp)

Implementation of the discrete ordinate method for radiation transport in multi-phase computer codes (46 pp)—A summary of the method is presented and the development of the radiation transport model for the IVA computer code initially developed without obstacles is extended to handle internal obstacles.

Validation of multi-phase flow models by comparison with experimental data and analytical benchmarks (92 pp on CD-ROM attached to Vol 1)

The first volume, Multiphase Flow Dynamics 1: Fundamentals, should be purchased by libraries for reference and by researchers in the field of thermal hydraulics in the nuclear safety industry. Volume 2, Thermal and Mechanical Interactions could be of use in other fields of research for the wealth of correlations contained therein.