Novel Porous Media Formulation for Multiphase Flow Conservation Equations


Novel Porous Media Formulation for Multiphase Flow Conservation Equations

William T. Sha first proposed the novel porous media formulation in an article in Nuclear Engineering and Design in 1980. The novel porous media formulation represented a new, flexible, and unified approach to solve real-world engineering problems. The novel porous media formulation uses the concept of volume porosity, directional surface porosities, distributed resistance, and distributed heat source and sink. Most practical engineering problems involve many complex shapes and sizes of solid internal structures whose distributed resistance is impossible to quantify accurately. The concept of directional surface porosities eliminates the sole reliance on empirical estimation of the distributed resistance of complex-shaped structures often involved in the analysis. The directional surface porosities thus greatly improve the resolution and modeling accuracy and facilitate mock-ups of numerical simulation models of real engineering systems. Both the continuum and conventional porous media formulations are subsets of the novel porous media formulation. Moreover, fluid-structure interactions are explicitly accounted for in this formulation.


 Reviews:

"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. [It] 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 be also recommended as a text for seminars and courses, as well as for independent study. Some chapters of the book present the state-of-the-art reviews, and they provide a solid background for future research." - Ioan Pop, Zentralblatt MATH

A. J. ReynoldsReviews–Thermo-Fluid Dynamic Theory of Two-Phase Flow, by M. IshiiJ. Fluid Mech.786381976
A. K. M. Fazle HussainRole of Coherent Structure in Turbulent Shear FlowProc. Indian Acad. Sci41291981
A. Padilla JrD. S. RoweA Donor Flow Formulation for Momentum Flux DifferencingTrans. Am. Nucl. Sci468511984
B. C-J. ChenB. K. ChaW. T. Sha1984
B. C.-J. ChenT. H. ChienW. T. Sha1985
B. P. LeonardThe QUICK Finite Difference Method for the Convective-Diffusion Equation in AdvancesComputer Methods for Partial Differential Equations, IIIIMACS1979
C. CroweM. SommerfeldY. TsujiMultiphase Flows with Droplets and ParticlesCRC Press, Boca Raton, Florida1998
C. E. BrennenFundamentals of Multiphase FlowCambridge University Press2005
D. A. DrewAveraged Field Equations for Two-Phase MediaStudies Appl. Math.501971
D. R. SpencerJ. WoodcookR. F. WrightJ. E. SchmidtM. PanesD. E. Christenson211993
F. K. LehnerA Derivation of the Field Equations for Slow Viscous Flow through a Porous MediaInd. Eng. Chem. Fundam1811979
G. B. WallisOne-Dimensional Two-Phase FlowMcGraw-HillNew York1969
G. H. CrapisteE. RotsteinS. WhitakerA General Closure Scheme for Method of Volume AveragingChem. Eng. Sci.412271986
H. M. DomanusR. C. SchmittW. T. ShaE. M. PetrillW. L. HoweJ. P. Bass1371986
I. J. CampbellA. S. PitcherShock Waves in Liquid Containing Gas BubblesProc. Roy. Soc. Ser. A2435341958
J. BearDynamics of Fluids in Porous MediaAmerican ElsevierNew York1972
J. C. SlatteryFlow of Viscoelastic Fluids through Porous MediaAIChE J.1310661967
J. C. SlatteryMultiphase Viscoelastic Flow through Porous MediaAIChE J14501968
J. C. SlatteryTwo-Phase Flow through Porous MediaAIChE J163451970
J. G. PatelM. G. HegdeJ. C. SlatteryFurther Discussion of Two-Phase Flow in Porous MediaAIChE J.1810621972
J. J. HaT. Aldemir1986473
J. M. DelhayeInstantaneous Space-Averaged EquationsTwo-Phase Flows and Heat TransferS. KakacF. Mayinger81HemisphereWashington, DC1977
J. M. DelhayeJ. L. Archard31976
J. M. DelhayeLocal Time-Averaged EquationsTwo-Phase Flows and Heat TransferS. KakacF. Mayinger101HemisphereWashington, DC1977
J. P. HinzTurbulenceMcGraw-Hill1978
J. R. HullK. V. LiuW. T. ShaJ. KomalC. E. NielsonDependence of Ground Heat Loss upon the Solar Pond Size and Parameter Insulation: Calculation and Experimental ResultsJ. Solar Energy33251984
K. SakaiJ. G. SunW. T. Sha1994
M. ChapmanFRAM-Nonlinear Damping Algorithm for the Continuity EquationJ. Comp. Phys44841981
M. IshiiT. HibikiThermo-Fluid Dynamics of Two-Phase FlowSpringer ScienceNew York2006
M. IshiiThermo-Fluid Dynamic Theory of Two-Phase FlowEyrollesParis1975
N. I. KolevMultiphase Flow DynamicsSpringer2007
R. McGriffJ. ChaoB. ChexalW. Layman1984
R. W. DavisE. F. MooreL. P. PurtellA Numerical-Experiment Study of Confined Flow around Rectangular CylindersPhys. Fluids27461984
S. L. SooDynamics of Multiphase FlowI&EC Fundam.44251965
S. L. SooEquations of Multiphase-Multidomain MechanicsMultiphase TransportT. VezirogluHemisphereWashington, DC1980
S. W. HopkeJ. C. SlatteryBounding Principles for Two-Phase Flow SystemsInt. J. Multiphase Flow11975
S. WhitakerAdvances in Theory of Fluid Motion in Porous MediaInd. Eng. Chem61141969
S. WhitakerDiffusion and Dispersion in Porous MediaAIChE J.134201967
S. WhitakerThe Transport Equations for Multiphase SystemsChem. Eng. Sci281391973
S. WinnikowB. T. ChaoDroplet Motion in Purified SystemsPhys. Fluids9501966
T. B. AndersonR. JacksonA Fluid Mechanical Description of Fluidized BedsI&EC Fundam.65271967
U. GhiaK. N. GhiaC. T. ShinHigh- Solutions for Incompressible Flow Using the Navier-Stokes Equations and a Multigrid MethodJ. Compu. Phys483871982
W. A. StewartA. T. PirvzynskiV. Svinivas851985
W. G. GrayA Derivation of the Equations for Multiphase TransportChem. Eng. Sci302291975
W. G. GrayK. O’NeillOn the General Equations for Flow in Porous Media and Their Reduction to Darcy's LawWater Resour. Res121481976
W. G. GrayP. C. Y. LeeOn the Theorems for Local Volume Averaging of Multiphase SystemsInt. J. Multiphase Flow33331977
W. L. BaumannH. M. DomanusW. T. ShaEBR-II In-Vessel Thermal-Hydraulic Transient Simulation Using the COMMIX-1A Computer CodeTrans. Am. Nucl. Soc434991982
W. T. ShaAn Overview on Rod-Bundle Thermal-Hydraulic AnalysisNucl. Engi. Design6211980
W. T. ShaB. T. ChaoNovel Porous Media Formulation for Multiphase Flow Conservation EquationsNucl. Eng. Design2379182007
W. T. ShaB. T. ChaoS. L. Soo1983
W. T. ShaB. T. ChaoS. L. Soo841984
W. T. ShaB. T. ChaoS. L. SooPorous Media Formulation for Multiphase Flow with Heat TransferNucl. Eng. Design82931984
W. T. ShaB. T. ChaoS. L. SooTime Averaging of Volume Averaged Conservation Equations of Multiphase FlowAIChE Symposium Series2554201983
W. T. ShaC. I. YangT. T. KaoS. M. ChoMulti-Dimensional Numerical Modeling of Heat ExchangersJ. Heat Transfer1044171982
W. T. ShaH. M. DomanusR. C. SchmittJ. J. OrasE. J. H. Lin1978
W. T. ShaJ. C. Slattery801980
W. T. ShaJoe F. Thompson1979
W. T. ShaNumerical Modeling of Heat ExchangersHandbook for Heat and Mass Transfer8151986
W. T. ShaS. L. Soo1990
W. T. ShaS. L. SooOn the Effect of Term in Multiphase MechanicsInt. J. Multiphase Flow51531979
W. T. ShaT. H. ChienJ. G. SunB. T. ChaoAnalysis of Large-Scale Tests for AP-600 Passive Containment Cooling SystemNucl. Eng. and Design2321972004
W. T. ShaV. L. Shah1994
Y. BachmatSpatial Macroscopization of Processes in Heterogeneous SystemsISR. J. Technol103911972