Novel porous media formulation for multiphase flow conservation equations. With forewords by Alan Schriesheim, Wm. Howard Arnold and Charles Kelber (Q2880137)

The study of flow through a porous medium is relevant in many practical fields, e.g. in the petroleum technology and in agriculture engineering. These flows have attracted the interest of many researchers because of their possible applications in many branches of science and technology. Some of the direct technological examples of flow in porous media are drying processes, powder metallurgy, transpiration cooling, insulation of buildings and pipes, chemical catalytic reactors, geothermal energy, fiber and granular insulations, design of packed bed reactors, underground disposal of nuclear waste materials and many others. Many new approaches have been developed that make it possible to compute various flows and transport properties of porous media with considerable precision.NEWLINENEWLINEThe main scope of this book is to make novel porous medium formulations for multiphase flow conservation equations equivalent to Navier-Stokes equations for a single phase. ``The work presents a very careful and detailed introduction to the modern methodology in porous media and opens a new challenging area, and encourages many promising young engineers and scientists to further advance the state-of-the-art in thermal hydraulics, in general, and in the novel porous media formulation for multiphase flows, in particular '' (from the author's preface).NEWLINENEWLINE The book consists of 8 chapters, contents, figures and tables, three forewords, nomenclature, preface, acknowledgement, two appendices, references and an index. The description of these chapters is, in short, as follows:NEWLINENEWLINEChapter 1: Introduction, describes the background information about multiphase flow, and illustrates the significance of phase configurations in multiphase flow needed for universally accepted formulation of multiphase flow conservation equations. It is pointed out that the time-volume-averaged multiphase conservation equations are derived in a region that contains stationary and solid internal structures.NEWLINENEWLINE Chapter 2: Averaging relations, presents preliminaries, local volume average and intrinsic volume average, local area average and intrinsic area average, local volume average theorems and their length-scale restrictions and conservative criterion of minimum size of characteristic length of local averaging volume.NEWLINENEWLINEChapter 3: Phasic conservation equations and interfacial balance equations, gives the phasic conservation equations and interfacial balance equations. It is mentioned that, in principle, the coupled phasic equations should be solved for given initial conditions together with boundary conditions at the phase interfaces. Because the configuration and location of fluid-fluid interfaces are not generally known, their detailed solutions are next impossible.NEWLINENEWLINEChapter 4: Local volume-averaged conservation equations and interfacial balance equations, is devoted to the description of local-volume averaged mass conservation equation of a phase and its interfacial balance equation, local volume-averaged linear momentum equation and its interfacial balance equation, local volume-averaged total energy equation and its interfacial balance equation, and finally local volume-averaged internal energy equation and its interfacial balance equation. This chapter presents also a summary of local volume-averaged conservation equations and a summary of local volume-averaged interfacial balance equations.NEWLINENEWLINEChapter 5: Time averaging of local volume-averaged conservation equations or time-volume-averaged conservation equations and interfacial balance equations, is a rather long chapter which presents the basic postulates, useful observation without assuming \({\mathbf v}'{}_k= 0\), time-volume-averaged mass conservation equation, time-volume-averaged interfacial mass balance equation, time-volume-averaged linear momentum conservation equation, time-volume-averaged interfacial linear momentum balance equation, time-volume-averaged total energy conservation equation, time-volume-averaged enthalpy conservation equation, time-volume-averaged enthalpy balance equation (capillary energy ignored) and summary of time-volume-averaged conservation equations.NEWLINENEWLINEChapter 6: Time averaging in relation to local volume averaging and time-volume averaging versus volume-time averaging, discusses (1) time averaging in relation to local volume averaging, and (2) a proper order of time-volume averaging versus volume-time averaging. It contains time averaging in relation to local volume averaging and time-volume averaging versus volume-time averaging.NEWLINENEWLINEChapter 7: Novel porous media formulation for single phase and single phase wth multicomponent applications, develops a genetic three-dimensional, time-dependent family of COMMIX codes for single phase with multicomponents based on the novel porous media formulation. It contains a description of COMMIX code capable of computing detailed microflow fields with fine computational mesh and high-order differencing schemes, and a COMMIX code capable of capturing both macroflow field and macrotemperature distributions with a coarse computational mesh. The author has mentioned that he has successfully modelled the complex AP-600 PCCS, which uses phase change to remove the heat generation during a DBA from the containment vessel to the environmental via natural convection.NEWLINENEWLINEChapter 8: Discussion and concluding remarks, refers to time averaging of local volume-averaged phase conservation equations, novel porous media formulation, future research and summary. A set of rigorously derived multiphase flow conservation equations in a region containing stationary and dispersed solid structures via time-volume-averaging has been presented. This set of conservation equations is in differential-integral form, in contracts to a set of partial differential equations used currently.NEWLINENEWLINEThere are two appendices: (A) Staggered-grid computational system, and (B) Physical interpretation of \(\triangledown \alpha_k= -\mathbf v^{-1} \int \underline{\mathbf n}_k {\mathbf{dA}}\) with \(\gamma_\nu =1\).NEWLINENEWLINE In the reviewer`s opinion, this book provides a fundamental and comprehensive presentation of the mathematical and physical theory of multiphase flow, pointing out several important practical applications. The book is excellently written and readable. Numerical solutions are given graphically and in tabular form. A large list of 66 papers and books is included at the end of the book. The book will be useful to a wide range of specialists working in the area of flows in porous media, such as design engineers, physicists, chemical engineers, and also to researchers interested in the applied mathematical theory of flows in porous media. It can also be recommended as a text for seminars and courses, as well as for independent study. Some chapters of the book present state-of-the-art reviews, and they provide a solid background for future research.