PRESSURE-BASED ALGORITHMS FOR MULTIFLUID FLOW AT ALL SPEEDS—PART I: MASS CONSERVATION FORMULATION

REFERENCES

• Patankar , S. V. and Spalding , D. B. 1972 . A Calculation Procedure for Heat, Mass and Momentum Transfer in Three-Dimensional Parabolic Flows . Int. J. Heat Mass Transfer , vol. 15 : pp. 1787 – 1806 .
   Web of Science ®Google Scholar
• Patankar , S. V. 1981 . Numerical Heat Transfer and Fluid Flow , New York : Hemisphere .
   Google Scholar
• Van Doormaal , J. P. and Raithby , G. D. 1984 . Enhancement of the SIMPLE Method for Predicting Incompressible Fluid Flows . Numer. Heat Transfer , vol. 7 : pp. 147 – 163 .
   Google Scholar
• Acharya , S. and Moukalled , F. 1989 . Improvements to Incompressible Flow Calculation on a Non-staggered Curvilinear Grid . Numer. Heat Transfer, B , vol. 15 : pp. 131 – 152 .
   Web of Science ®Google Scholar
• Van Doormaal , J. P. and Raithby , G. D. An Evaluation of the Segregated Approach for Predicting Incompressible Fluid Flows, ASME Paper 85-HT-9 . Natl. Heat Transfer Conf. August 4–7 , Denver, Co..
   Google Scholar
• Spalding , D. B. 1980 . Mathematical Modelling of Fluid Mechanics, Heat Transfer and Mass Transfer Processes , London, , UK : Imperial College of Science, Technology and Medecine . Mech. Eng. Dept., Rep. HTS/80/1
   Google Scholar
• Issa , R. I. 1982 . Solution of the Implicit Discretized Fluid Flow Equations by Operator Splitting , London, , UK : Imperial College . Mech. Eng. Rep. FS/82/15
   Google Scholar
• Maliska , C. R. and Raithby , G. D. 1983 . “ Calculating 3-D fluid Flows Using Non-orthogonal Grid ” . In Proc. Third Int. Conf. on Numerical Methods in Laminar and Turbulent Flows 656 – 666 . Seattle, WA
   Google Scholar
• Becker , C. , Ferziger , J. H. , Períc , M. and Scheurer , G. 1988 . Finite Volume Multigrid Solutions of the Two-Dimensional Incompressible Navier-Stokes Equations . Notes on Numer. Fluid Mech , vol. 23 : pp. 37 – 47 .
   Google Scholar
• Smith , K. M. , Cope , W. K. and Vanka , S. P. 1993 . Multigrid Procedure for Three Dimensional Flows on Non-orthogonal Collocated Grids . Int. J. Numer. Meth. Fluids , vol. 17 : pp. 887 – 904 .
   Web of Science ®Google Scholar
• Lien , F. S. and Lechziner , M. A. 1994 . Multigrid Acceleration for Recirculating Laminar and Turbulent Flow Computed on a Non-orthogonal, Collocated Finite Volume Scheme . Comput. Meth. Appl. Mech. Eng. , vol. 118 : pp. 351 – 371 .
   Web of Science ®Google Scholar
• Sivaloganathan , S. and Shaw , G. J. 1988 . An Efficient Non-linear Multigrid Procedure for the Incompressible Navier-Stokes Equations . Int. J. Numer. Meth. Fluids , vol. 8 : pp. 417 – 440 .
   Google Scholar
• Ferziger , J. H. and Peric , M. 1996 . Computational Methods for Fluid Dynamics , Berlin Heidelberg : Springer-Verlag .
   Google Scholar
• Gjesdal , T. and Lossius , M. E. H. 1997 . Comparison of Pressure Correction Smoothers for Multigrid Solution of Incompressible Flow . Int. J. Numer. Meth. Fluids , vol. 25 : pp. 393 – 405 .
   Web of Science ®Google Scholar
• Demirdzic , I. , Lilek , Z. and Peric , M. 1993 . A Collocated Finite Volume Method for Predicting Flows at All Speeds . Int. J. Numer. Meth. Fluids , vol. 16 : pp. 1029 – 1050 .
   Web of Science ®Google Scholar
• Marchi , C. H. and Maliska , C. R. 1994 . A Non-orthogonal Finite-Volume Method for the Solution of All Speed Flows Using Co-Located Variables . Numer. Heat Transfer, B , vol. 26 : pp. 293 – 311 .
   Web of Science ®Google Scholar
• Lien , F. S. and Leschziner , M. A. 1993 . A Pressure-Velocity Solution Strategy for Compressible Flow and Its Application to Shock/Boundary-Layer Interaction Using Second-Moment Turbulence Closure . J. Fluids Eng. , vol. 115 : pp. 717 – 725 .
   Web of Science ®Google Scholar
• Lien , M. A. and Leschziner , M. A. 1994 . A General Non-Orthogonal Collocated Finite Volume Algorithm for Turbulent Flow at All Speeds Incorporating Second-Moment Turbulence-Transport Closure, Part 1: Computational Implementation . Comput. Meth. Appl. Mech. Eng. , vol. 114 : pp. 123 – 148 .
   Web of Science ®Google Scholar
• Chen , K. H. and Pletcher , R. H. 1991 . Primitive Variable, Strongly Implicit Calculation Procedure for Viscous Flows at All Speeds . AIAA J. , vol. 29 ( no. 8 ) : pp. 1241 – 1249 .
   Google Scholar
• Darbandi , M. and Shneider , G. E. 1997 . Momentum Variable Procedure for Solving Compressible and Incompressible Flows . AIAA J. , vol. 35 ( no. 12 ) : pp. 1801 – 1805 .
   Google Scholar
• Moukalled , F. and Darwish , M. 2001 . A High-Resolution Pressure-Based Algorithm for Fluid Flow at All Speeds . J. Comput. Phys. , vol. 168 : pp. 101 – 133 .
   Web of Science ®Google Scholar
• Moukalled , F. and Darwish , M. 2000 . A Unified Formulation of the Segregated Class of Algorithms for Fluid Flow at All Speeds . Numer. Heat Transfer B , vol. 37 ( no. 1 ) : pp. 103 – 139 .
   Web of Science ®Google Scholar
• Darwish , M. , Asmar , D. and Moukalled , F. 2004 . A Comparative Assessment within a Multi-grid Environment of Segregated Pressure-Based Algorithms for Fluid Flow at All Speeds . Numer. Heat Transfer B , vol. 45 ( no. 1 ) : pp. 49 – 74 .
   Web of Science ®Google Scholar
• Spalding , D. B. 1976 . The Calculation of Free-Convection Phenomena in Gas-Liquid Mixtures , London, , UK : Imperial College . Rep. HTS/76/11 Mech. Eng.
   Google Scholar
• Spalding , D. B. 1980 . “ Numerical Computation of Multi-phase Fluid Flow and Heat Transfer ” . In Recent Advances in Numer. Meth. in Fluids Edited by: Taylor , C. and Morgan , K. pp. 139 – 167 . in
   Google Scholar
• Spalding , D. B. 1981 . A General Purpose Computer Program for Multi-dimensional, One and Two Phase Flow , London, , UK : Imperial College . Mechanical Engineering Department Rep. HTS/81/1
   Google Scholar
• Rivard , W. W. and Torrey , M. D. 1978 . KFIX: A Program for Transient Two Dimensional Two Fluid Flow Rep. Los Alamos Nuclear Regulatory Commission-6623
   Google Scholar
• Amsden , A. A. and Harlow , F. H. 1975 . KACHINA: An Eulerian Computer Program for Multi-field Flows Rep. LA-NUREG-5680
   Google Scholar
• Amsden , A. A. and Harlow , F. H. 1977 . KTIFA Two-Fluid Computer Program for Down Comer Flow Dynamics Rep. LA-NUREG-6994
   Google Scholar
• Darwish , M. , Moukalled , F. and Sekar , B. 2001 . A Unified Formulation of the Segregated Class of Algorithms for Multi-fluid Flow at All Speeds . Numer. Heat Transfer B , vol. 40 ( no. 2 ) : pp. 99 – 137 .
   Web of Science ®Google Scholar
• Moukalled , F. and Darwish , M. A. 2002 . Comparative Assessment of the Performance of Mass Conservation Based Algorithms for Incompressible Multi-phase Flows . Numer. Heat Transfer B , vol. 42 : pp. 259 – 283 .
   Web of Science ®Google Scholar
• Moukalled , F. and Darwish , M. 2004 . The Performance of Geometric Conservation Based Algorithms for Incompressible Multi-fluid Flow . Numer. Heat Transfer B , vol. 45 ( no. 4 ) : pp. 343 – 368 .
   Web of Science ®Google Scholar
• Moukalled , F. , Darwish , M. and Sekar , B. 2003 . A High Resolution Pressure-Based Algorithm for Multi-phase Flow at all Speeds . J. Comput. Phys. , vol. 190 : pp. 550 – 571 .
   Web of Science ®Google Scholar
• Darwish , M. , Moukalled , F. and Sekar , B. 2003 . A Robust Multi-grid Algorithm for Multifluid Flow at All Speeds . Int. J. Numer. Meth. Fluids , vol. 41 : pp. 1221 – 1251 .
   Web of Science ®Google Scholar
• Moukalled , F. and Darwish , M. 2004 . Pressure Based Algorithms for Multi-fluid Flow at All Speeds—Part II: Geometric Conservation Formulation . Numer. Heat Transfer B , vol. 45 : pp. 523 – 540 .
   Web of Science ®Google Scholar
• Baldwin , B. S. and Lomax , H. 1978 . Thin Layer Approximation and Algebraic Model for Separated Turbulent Flows AIAA Paper 78–257
   Google Scholar
• Sotiropoulos , F. and Patel , V. C. 1995 . Application of Reynolds-Stress Transport Models to Stern and Wake Flow . J. Ship Res. , vol. 39 : p. 263
   Web of Science ®Google Scholar
• Cokljat , D. , Ivanov , V. A. , Srasola , F. J. and Vasquez , S. A. 2000 . Multiphase K-Epsilon Models for Unstructured Meshes Boston, MA June 11–15
   Google Scholar
• Pourahmadi , F. and Humphrey , J. A. C. 1983 . Modeling Solid-Fluid Turbulent Flows with Application to Predicting Erosive Wear . Int. J. Phys. Chem. Hydrodynamic , vol. 4 : pp. 191 – 219 .
   Google Scholar
• Elghobashi , S. E. and Abou-Arab , T. W. 1983 . A Two-Equation Turbulence Model for Two-Phase Flows . Phys. Fluids , vol. 26 ( no. 4 ) : pp. 931 – 938 .
   Web of Science ®Google Scholar
• Chen , C. P. and Wood , P. E. 1986 . Turbulence Closure Modeling of the Dilute Gas-Particle Axisymmetric Jet . AICHE J. , vol. 32 ( no. 1 ) : pp. 163 – 166 .
   Web of Science ®Google Scholar
• Mostafa , A. A. and Mongia , H. C. 1988 . On the Interaction of Particles and Turbulent Fluid Flow . Int. J. Heat Mass Transfer , vol. 31 : pp. 2063 – 2075 .
   Web of Science ®Google Scholar
• Lopez de Bertodano , M. , Lee , S. J. , Lahey , R. T. Jr. and Drew , D. A. 1990 . The Prediction of Two-Phase Turbulence and Phase Distribution Phenomena Using a Reynolds Stress Model . ASME J. Fluids Eng. , vol. 112 : pp. 107 – 113 .
   Web of Science ®Google Scholar
• Lopez de Bertodano , M. , Lahey , R. T. Jr. and Jones , O. C. 1994 . Development of a k-ε Model for Bubbly Two-Phase Flow . ASME J. Fluids Eng. , 116 : 128 – 134 .
   Web of Science ®Google Scholar
• Lopez de Bertodano , M. , Lahey , R. T. Jr. and Jones , O. C. 1994 . Phase Distribution in Bubbly Two-Phase Flow in Vertical Ducts . Int. J. Multiphase Flow , vol. 20 ( no. 5 ) : pp. 805 – 818 .
   Web of Science ®Google Scholar
• Zwart , P. J. , Raithby , G. D. and Raw , M. J. 1998 . An Integrated Space-Time Finite-Volume Method for Moving-Boundary Problems . Numer. Heat Transfer B , vol. 34 : pp. 257 – 270 .
   Web of Science ®Google Scholar
• Gaskell , P. H. and Lau , A. K. C. 1988 . Curvature Compensated Convective Transport: SMART, a New Boundedness Preserving Transport Algorithm . Int. J. Numer. Meth. Fluids , vol. 8 : pp. 617 – 641 .
   Web of Science ®Google Scholar
• Darwish , M. S. and Moukalled , F. 1994 . Normalized Variable and Space Formulation Methodology for High-Resolution Schemes . Numer. Heat Transfer B , vol. 26 : pp. 79 – 96 .
   Web of Science ®Google Scholar
• Cornelius , C. , Volgmann , W. and Stoff , H. 1999 . Calculation of Three-Dimensional Turbulent Flow with a Finite Volume Multigrid Method . Int. J. Numer. Meth. Fluids , vol. 31 : pp. 703 – 720 .
   Web of Science ®Google Scholar
• Serizawa , A. , Kataoka , I. and Michiyoshi , I. 1986 . “ Phase Distribution in Bubbly Flow ” . In Proc. Second Int. Workshop on Two-Phase Flow Fundamentals , Troy, NY : Rensselaer Polytechnic Institute . Data Set No. 24
   Google Scholar
• Nakoryakov , V. E. , Kashinsky , O. N. , Randin , V. V. and Timkin , L. S. 1996 . Gas-Liquid Bubbly Flow in Vertical Pipes . J. of Fluids Eng. , vol. 118 : pp. 377 – 382 .
   Web of Science ®Google Scholar
• Lahey , R. T. , Lopez de Bertodano , M. and Jones , O. C. 1993 . Phase Distribution in Complex Geometry Ducts . Nuclear. Eng. Design , vol. 141 : p. 177
   Web of Science ®Google Scholar
• Boisson , N. and Malin , M. R. 1996 . Numerical Prediction of Two-Phase Flow in Bubble Columns . Int. J. Numer. Meth. Fluids , vol. 23 : pp. 1289 – 1310 .
   Web of Science ®Google Scholar
• Tsuji , Y. , Morikawa , Y. and Shiomi , H. 1984 . LDV Measurements of an Air-Solid Two-Phase Flow in a Vertival Pipe . J. Fluid Mech. , vol. 139 : pp. 417 – 434 .
   Web of Science ®Google Scholar
• Adeniji-Fashola , A. and Chen , C. P. 1990 . Modeling of Confined Turbulent Fluid-Particle Flows Using Eulerian and Lagrangian Schemes . Int. J. Heat Mass Transfer , vol. 33 : pp. 691 – 701 .
   Web of Science ®Google Scholar
• Naik , S. and Bryden , I. G. 1999 . Prediction of Turbulent Gas-Solids Flow in Curved Ducts Using the Eulerian-Lagrangian Method . Int. J. Numer. Meth. Fluids , vol. 31 : pp. 579 – 600 .
   Web of Science ®Google Scholar
• Osiptsov , A. N. 1980 . Structure of the Laminar Boundary Layer of a Disperse Medium on a Flat Plate . Fluid Dynam. , vol. 15 : pp. 512 – 517 .
   Google Scholar
• Wang , B. Y. and Glass , I. I. 1988 . Compressible Laminar Boundary Layer Flows of a Dusty Gas over a Semi-infinite Flat Plate . J. Fluid Mech. , vol. 186 : pp. 223 – 241 .
   Web of Science ®Google Scholar
• Thevand , N. , Daniel , E. and Loraud , J. C. 1999 . On High-Resolution Schemes for Solving Unsteady Compressible Two-Phase Dilute Viscous Flows . Int. J. Numer. Meth. Fluids , vol. 31 : pp. 681 – 702 .
   Web of Science ®Google Scholar
• Chang , I. S. 1980 . One and Two-Phase Nozzle Flows . AIAA J. , vol. 18 : pp. 1455 – 1461 .
   Google Scholar
• Ishii , R. , Umeda , Y. and Kawasaki , K. 1987 . Nozzle Flows of Gas-Particle Mixtures . Phys. Fluids , vol. 30 ( no. 3 ) : pp. 752 – 760 .
   Web of Science ®Google Scholar
• Chang , H. T. , Hourng , L. W. and Chien , L. E. 1996 . Application of Flux-Vector-Splitting Scheme to a Dilute Gas-Particle JPL Nozzle Flow . Int. J. Numer. Meth. Fluids , vol. 22 : pp. 921 – 935 .
   Web of Science ®Google Scholar
• Back , L. H. and Cuffel , R. F. 1966 . Detection of Oblique Shocks in a Conical Nozzle with a Circular-Arc Throat . AIAA J. , vol. 4 : pp. 2219 – 2221 .
   Google Scholar
• Back , L. H. , Massier , P. F. and Cuffel , R. F. 1967 . Flow Phenomena and Convective Heat Transfer in a Conical Supersonic Nozzle . J. Spacecraft , vol. 4 : pp. 1040 – 1047 .
   Web of Science ®Google Scholar
• Cuffel , R. F. , Back , L. H. and Massier , P. F. 1969 . Transonic Flowfield in a Supersonic Nozzle with Small Throat Radius of Curvature . AIAA J. , vol. 7 : pp. 1364 – 1366 .
   Google Scholar