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A pressure-based framework for the resolution of multi-fluid flow problems
No full textPressure-based methods represent a class of Computational Fluid Dynamics (CFD) algorithms in which pressure, rather than density, is used as a principal variable. This paper presents a review of segregated pressure-based methods and reports on a newly developed fully coupled method for the solution of multi-fluid flow problems. Results indicate the superiority of the coupled solver over the segregated approach. © 2013 AIP Publishing LLC.CARVER MB, 1984, J FLUID ENG-T ASME, V106, P147; Darwish M., 2009, J COMPUT PHYS, V28, P180; Darwish M., 2011, ICNAAM 2011 HALK GRE; HARLOW FH, 1975, J COMPUT PHYS, V17, P19, DOI 10.1016-0021-9991(75)90061-3; Moukalled F, 2004, NUMER HEAT TR B-FUND, V45, P495, DOI 10.1080-10407790490430651; Moukalled F, 2004, NUMER HEAT TR B-FUND, V45, P523, DOI 10.1080-10407790490437997; Moukalled F., 2001, NUMER HEAT TRANSFE B, V40, P99; Moukalled F., 2006, HDB NUMERICAL HEAT T, P325; RHIE CM, 1983, AIAA J, V21, P1525, DOI 10.2514-3.8284; Spalding D.B, 1976, HTS7611 IMP COLL0
Natural-convection heat transfer in channels with isothermally heated convex surfaces
No full textThis article reports on a numerical investigation conducted to study laminar natural-convection heat transfer in channels with convex surfaces that are isothermally heated. Six Grashof number (Gr) values (10≥Gr≥104) and 11 radii of curvature (1≥κ≥∞) are considered. The results are displayed in terms of streamline and isotherm plots, centerline pressure profiles, inlet mass flow rates, and local and average Nusselt number estimates. At the lowest radius of curvature (κ=1), computations reveal the formation of recirculation zones in the exit section for all values of Grashof number considered. As the radius of curvature increases, the Gr value at which recirculation occurs also increases, until it disappears at values greater than 1.5. For all configurations studied, the average Nusselt number [Nu] results indicate an increase in heat transfer with increasing Grashof number values. Moreover, the value of κ at which [Nu] peaks increases with increasing Gr. Inlet volume flow rate and average Nusselt number correlations are presented.Auletta A, 2002, INT J THERM SCI, V41, P1101, DOI 10.1016-S1290-0729(02)01396-0; Auletta A, 2001, INT J HEAT MASS TRAN, V44, P4345, DOI 10.1016-S0017-9310(01)00064-3; AUNG W, 1972, INT J HEAT MASS TRAN, V15, P2293, DOI 10.1016-0017-9310(72)90048-8; Batchelor G.K., 1967, INTRO FLUID DYNAMICS; BODIA JR, 1962, ASME, V84, P40; CHAR MI, 1995, J PHYS D APPL PHYS, V28, P1324, DOI 10.1088-0022-3727-28-7-008; DARWISH MS, 1994, NUMER HEAT TR B-FUND, V26, P79, DOI 10.1080-10407799408914918; Elenbaas W, 1942, PHYSICA, V9, P1, DOI 10.1016-S0031-8914(42)90053-3; Fisher TS, 1999, J HEAT TRANS-T ASME, V121, P603, DOI 10.1115-1.2826022; GASKELL PH, 1988, INT J NUMER METH FL, V8, P617, DOI 10.1002-fld.1650080602; Gordon W. J., 1982, NUMERICAL GRID GENER, P171; Haaland S.E., 1983, NUMERICAL HEAT TRANS, V6, P155, DOI 10.1080-10407798308546980; Magyari E, 2002, Z ANGEW MATH MECH, V82, P142, DOI 10.1002-1521-4001(200202)82:2142::AID-ZAMM1423.0.CO;2-4; MALISKA CR, 1993, P 8 INT C LAM TURB F; Manca O, 2003, INT J THERM SCI, V42, P837, DOI 10.1016-S1290-0729(03)00056-5; Manca O, 2005, J HEAT TRANS-T ASME, V127, P888, DOI 10.1115-1.1928909; MANCA O, 2001, P 5 WORLD C EXP HEAT, P645; Marcondes F, 1999, NUMER HEAT TR B-FUND, V35, P317; Moukalled F, 1999, J THERMOPHYS HEAT TR, V13, P508, DOI 10.2514-2.6469; Moukalled F, 2000, NUMER HEAT TR B-FUND, V37, P103; Moukalled F, 2000, INT J HEAT MASS TRAN, V43, P1947, DOI 10.1016-S0017-9310(99)00269-0; Moukalled F., 2006, HDB NUMERICAL HEAT T, P325; NAKAYAMA A, 1989, J HEAT TRANSFER, V111, P807; Naylor D., 1991, ASME, V113, P620; NIECKLE AO, 1987, WINT ANN M ASME BOST, P71; Patankar S. V., 1980, NUMERICAL HEAT TRANS; Peric M., 1985, THESIS IMPERIAL COLL; POP I, 1993, J APPL MATH MECH ZAM, V73, P534; Sparrow E.M., 1984, ASME, V106, P325; STRAATMAN AG, 1993, J HEAT TRANS-T ASME, V115, P395, DOI 10.1115-1.2910691; WIRTZ RA, 1985, 85WAHT14 ASME; Zwart PJ, 1998, NUMER HEAT TR B-FUND, V34, P257, DOI 10.1080-1040779980891505711111
A fully coupled navier-stokes solver for fluid flow at all speeds
No full textThis article deals with the formulation and testing of a newly developed, fully coupled, pressure-based algorithm for the solution of fluid flow at all speeds. The new algorithm is an extension into compressible flows of a fully coupled algorithm developed by the authors for laminar incompressible flows. The implicit velocity-pressure-density coupling is resolved by deriving a pressure equation following a procedure similar to a segregated SIMPLE algorithm using the Rhie-Chow interpolation technique. The coefficients of the momentum and continuity equations are assembled into one matrix and solved simultaneously, with their convergence accelerated via an algebraic multigrid method. The performance of the coupled solver is assessed by solving a number of two-dimensional problems in the subsonic, transsonic, supersonic, and hypersonic regimes over several grid systems of increasing sizes. For a desired level of convergence, results for each problem are presented in the form of convergence history plots, tabulated values of the maximum number of required iterations, the total CPU time, and the CPU time per control volume. © 2014 Taylor and Francis Group, LLC.Abbasi R, 2013, COMPUT FLUIDS, V81, P68, DOI 10.1016-j.compfluid.2013.03.014; Acharya S, 2007, J HEAT TRANS-T ASME, V129, P407, DOI 10.1115-1.2716419; Anderson Jr J.D., 1982, MODERN COMPRESSIBLE; Anjorin V. A. O., 2001, INT J FLUID DYNAM, V5, P59; Barton IE, 1998, INT J NUMER METH FL, V26, P459, DOI 10.1002-(SICI)1097-0363(19980228)26:4459::AID-FLD6453.0.CO;2-U; BATINA JT, 1991, AIAA J, V29, P1836, DOI 10.2514-3.10808; Blokhin AM, 2009, SB MATH+, V200, P157, DOI 10.1070-SM2009v200n02ABEH003990; Cabboussat A., 2005, J COMPUT PHYS, V203, P626; Caretto L. S., 1972, Computer Methods in Applied Mechanics and Engineering, V1, DOI 10.1016-0045-7825(72)90020-5; Darwish M, 2001, NUMER HEAT TR B-FUND, V40, P99; Darwish M, 2007, NUMER HEAT TR B-FUND, V52, P353, DOI 10.1080-10407790701372785; Darwish M, 2004, NUMER HEAT TR B-FUND, V45, P49, DOI 10.1080-1040779049025487; Darwish M, 2009, J COMPUT PHYS, V228, P180, DOI 10.1016-j.jcp.2008.08.027; DEMIRDZIC I, 1993, INT J NUMER METH FL, V16, P1029, DOI 10.1002-fld.1650161202; Deng GB, 2001, COMPUT FLUIDS, V30, P445, DOI 10.1016-S0045-7930(00)00025-6; Dettmer W, 2006, COMPUT METHOD APPL M, V195, P3038, DOI 10.1016-j.cma.2004.07.057; Elling V, 2008, COMMUN PUR APPL MATH, V61, P1347, DOI 10.1002-cpa.20231; Favini B, 1996, INT J NUMER METH FL, V23, P589, DOI 10.1002-(SICI)1097-0363(19960930)23:6589::AID-FLD4443.3.CO;2-R; Grismer M. J., 1994, THESIS NOTRE DAME U; Hirsch C., 1990, NUMERICAL COMPUTATIO; HWANG CJ, 1993, AIAA J, V31, P61, DOI 10.2514-3.11319; Karlci K. C., 1986, THESIS U MINNESOTA; Khalid M. S., 2009, P WORLD C ENG 2009 W; Kissling K., 2010, 5 EUR C COMP FLUID D; Langtry RB, 2005, 2005522 AIAA; LIEN FS, 1993, J FLUID ENG-T ASME, V115, P717, DOI 10.1115-1.2910204; LIEN FS, 1994, COMPUT METHOD APPL M, V114, P123, DOI 10.1016-0045-7825(94)90165-1; MARCHI CH, 1994, NUMER HEAT TR B-FUND, V26, P293, DOI 10.1080-10407799408914931; Menter F, 2003, TURBULENCE HEAT MASS, V4, P2003; Modesto-Madera N. A., 2010, THESIS RENSSELAER PO; Moguen Y, 2013, J COMPUT APPL MATH, V246, P136, DOI 10.1016-j.cam.2012.10.029; Montero R. S., 2000, 200027 NASA ICASE; Moukalled F, 2003, J COMPUT PHYS, V190, P550, DOI 10.1016-S0021-9991(03)00297-3; Moukalled F, 2004, NUMER HEAT TR B-FUND, V45, P343, DOI 10.1080-10407790490268841; Darwish M, 2003, INT J NUMER METH FL, V41, P1221, DOI 10.1002-fld.490; Moukalled F, 2000, NUMER HEAT TR B-FUND, V37, P103; Moukalled F, 2002, NUMER HEAT TR B-FUND, V42, P259, DOI 10.1080-10407790190053941; Moukalled F, 2001, J COMPUT PHYS, V168, P101, DOI 10.1006-jcph.2000.6683; Muzaferija S, 1997, J COMPUT PHYS, V138, P766, DOI 10.1006-jcph.1997.5853; PATANKAR SV, 1972, INT J HEAT MASS TRAN, V15, P1787, DOI 10.1016-0017-9310(72)90054-3; Rhie C., 1983, AIAA J, V17, P1525; Rispoli F., 2009, ASME J APPL MECH, V76, DOI [10.1115-1.3062969, DOI 10.1115-1.3062969]; Rossow CC, 2007, J COMPUT PHYS, V220, P879, DOI 10.1016-j.jcp.2006.05.034; Shapiro A. H., 1953, DYNAMICS THERMODYNAM; Shapiro E, 2005, J COMPUT PHYS, V210, P584, DOI 10.1016-j.jcp.2005.05.001; Shterev KS, 2010, J COMPUT PHYS, V229, P461, DOI 10.1016-j.jcp.2009.09.042; Tao WQ, 2004, NUMER HEAT TR B-FUND, V45, P1, DOI 10.1080-1040779049025485; Tezduyar TE, 2006, COMPUT MECH, V38, P469, DOI 10.1007-s00466-005-0025-6; VANDOORMAAL JP, 1984, NUMER HEAT TRANSFER, V7, P147, DOI 10.1080-10407798408546946; van Wachem B. G. M., 2006, EUR C COMP FLUID DYN; van Wachem B. G. M., 2007, 6 INT C MULT FLOW IC; Yaldin Y., 1991, AIAA J, V29, P712; Yang JY, 2001, AIAA J, V39, P2082, DOI 10.2514-2.1231; ZHANG LX, 2011, J HYDRODYN, V23, P421
Natural-convection heat transfer in channels with isoflux convex surfaces
No full textNumerical solutions are presented for laminar natural convection heat transfer in channels with convex surfaces that are subjected to a uniform heat flux. Simulations are conducted for several values of Grashof number (10 to 104) and radius of curvature (1 to ∞). The governing elliptic conservation equations are solved in a boundary-fitted coordinate system using a collocated control-volume-based numerical procedure. The results are presented in terms of streamline and isotherm plots, inlet mass flow rates, curved wall temperature profiles, maximum hot wall temperature estimates, and average Nusselt number values. At the lowest radius of curvature, computations reveal the formation of recirculation zones in the exit section for all values of Grashof number considered. For a radius of curvature equal to or greater than 2, recirculation does not occur at any Grashof number. For values of radius of curvature between 1 and 2, the value of Grashof number at which recirculation occurs decreases with increasing values of the former. The variation in the buoyancy-induced volume flow rate is highly nonlinear with respect to the radius of curvature, and the value of the radius of curvature at which the volume flow rate is maximum increases with increasing Grashof number. The value of radius of curvature at which the maximum hot wall temperature is minimized increases with Grashof number. For all configurations studied, the average Nusselt number increases with increasing Grashof number values. Correlations for maximum wall temperature and average Nusselt number are provided.Andreozzi A, 2008, INT J THERM SCI, V47, P742, DOI 10.1016-j.ijthermalsci.2007.06.013; ANDREOZZI A, 2005, NUMERICAL HEAT TRA A, V47, P74; Auletta A, 2002, INT J THERM SCI, V41, P1101, DOI 10.1016-S1290-0729(02)01396-0; Auletta A, 2001, INT J HEAT MASS TRAN, V44, P4345, DOI 10.1016-S0017-9310(01)00064-3; AUNG W, 1972, INT J HEAT MASS TRAN, V15, P2293, DOI 10.1016-0017-9310(72)90048-8; Batchelor G.K., 1967, INTRO FLUID DYNAMICS; Bodoia J.R., 1962, J HEAT TRANSFER, V84, P40; Campo A, 1999, NUMER HEAT TR A-APPL, V36, P129; CHAR MI, 1995, J PHYS D APPL PHYS, V28, P1324, DOI 10.1088-0022-3727-28-7-008; DARWISH MS, 1994, NUMER HEAT TR B-FUND, V26, P79, DOI 10.1080-10407799408914918; Elenbaas W, 1942, PHYSICA, V9, P1, DOI 10.1016-S0031-8914(42)90053-3; GASKELL PH, 1988, INT J NUMER METH FL, V8, P617, DOI 10.1002-fld.1650080602; Haaland S.E., 1983, NUMERICAL HEAT TRANS, V6, P155, DOI 10.1080-10407798308546980; Kaiser AS, 2004, INT J HEAT FLUID FL, V25, P671, DOI 10.1016-j.ijheatfluidflow.2003.11.022; KIHM KD, 1993, J HEAT TRANS-T ASME, V115, P140, DOI 10.1115-1.2910640; Lakkis I, 2008, NUMER HEAT TR A-APPL, V53, P1176, DOI 10.1080-10407780701852985; Langellotto L, 2007, NUMER HEAT TR A-APPL, V51, P1065, DOI 10.1080-10407790601184355; LEE KT, 1994, NUMER HEAT TR A-APPL, V25, P477, DOI 10.1080-10407789408955961; Magyari E, 2002, Z ANGEW MATH MECH, V82, P142, DOI 10.1002-1521-4001(200202)82:2142::AID-ZAMM1423.0.CO;2-4; Manca O, 2003, INT J THERM SCI, V42, P837, DOI 10.1016-S1290-0729(03)00056-5; Manca O, 2005, J HEAT TRANS-T ASME, V127, P888, DOI 10.1115-1.1928909; MANCA O, 2001, P 5 WORLD C EXP HEAT, P645; Marcondes F, 2006, INT J NUMER METHOD H, V16, P304, DOI 10.1108-09615530610649735; Moukalled F, 1999, J THERMOPHYS HEAT TR, V13, P508, DOI 10.2514-2.6469; Moukalled F, 2000, NUMER HEAT TR B-FUND, V37, P103; Moukalled F, 2000, INT J HEAT MASS TRAN, V43, P1947, DOI 10.1016-S0017-9310(99)00269-0; Moukalled F., 2006, HDB NUMERICAL HEAT T, P325; NAKAYAMA A, 1989, J HEAT TRANSFER, V111, P807; Naylor D., 1991, ASME, V113, P620; NIECKLE AO, 1987, WINT ANN M ASME BOST, P71; Patankar S. V., 1980, NUMERICAL HEAT TRANS; Peric M., 1985, THESIS IMPERIAL COLL; POP I, 1993, J APPL MATH MECH ZAM, V73, P534; Said SAM, 1996, INT J ENERG RES, V20, P559; Shalash J.S., 1997, P 4 INT C EXP HEAT T, P2167; SPARROW EM, 1988, INT J HEAT MASS TRAN, V31, P2197, DOI 10.1016-0017-9310(88)90152-4; Sparrow E.M., 1984, ASME, V106, P325; STRAATMAN AG, 1993, J HEAT TRANS-T ASME, V115, P395, DOI 10.1115-1.2910691; Zwart PJ, 1998, NUMER HEAT TR B-FUND, V34, P257, DOI 10.1080-1040779980891505721
A coupled incompressible flow solver on structured grids
No full textThis article deals with the formulation, implementation, and testing of a fully coupled velocity-pressure algorithm for the solution of laminar incompressible flow problems. The tight velocity-pressure coupling is developed within the context of a collocated structured grid, and the systems of equations involving velocity and pressure are solved simultaneously. The pressure and momentum equations are derived in a way similar to a segregated SIMPLE algorithm [1], yielding an extended set of diagonally dominant equations. An algebraic multigrid solver is used to accelerate the solution of the extended system of equations. The performance of the newly developed coupled algorithm is evaluated by solving three test problems showing the effects of grid size, mesh skewness, large pressure gradients, and large source terms on the convergence behavior. Results are presented in the form of convergence history plots and tabulated values of the maximum number of required iterations, the total CPU time, and the CPU time per control volume. This latter performance indicator is shown to be nearly independent of the grid size.Ammara I, 2004, INT J NUMER METH FL, V44, P621, DOI 10.1002-fld.662; BRAATEN ME, 1985, THESIS U MINN MINNEA; Caretto L. S., 1972, Computer Methods in Applied Mechanics and Engineering, V1, DOI 10.1016-0045-7825(72)90020-5; CHOI SK, 1991, 7 INT C NUM METH LAM, V7, P1634; GALPIN PF, 1985, INT J NUMER METH FL, V5, P615, DOI 10.1002-fld.1650050703; Hanby RF, 1996, INT J NUMER METH FL, V22, P353; HSU CF, 1981, THESIS U MINNESOTA M; KARKI KC, 1990, INT J NUMER METH FL, V11, P1, DOI 10.1002-fld.1650110102; LONSDALE RD, 1991, P 7 INT C NUM METH L, P1432; Mazhar Z, 2001, NUMER HEAT TR B-FUND, V39, P91, DOI 10.1080-104077901460704; Moukalled F, 2000, NUMER HEAT TR B-FUND, V37, P103; Moukalled F, 2004, HEAT TRANSFER ENG, V25, P80, DOI 10.1080-01457630490520356; Moukalled F, 2003, NUMER HEAT TR A-APPL, V43, P543, DOI 10.1080-10407780390122808; Pascau A, 1996, COMMUN NUMER METH EN, V12, P617, DOI 10.1002-(SICI)1099-0887(199610)12:10617::AID-CNM103.3.CO;2-A; Patankar S. V., 1981, NUMERICAL HEAT TRANS; PATANKAR SV, 1972, INT J HEAT MASS TRAN, V15, P1787, DOI 10.1016-0017-9310(72)90054-3; PERIC M, 1988, COMPUT FLUIDS, V16, P289; RHIE CM, 1983, AIAA J, V21, P1525, DOI 10.2514-3.8284; RODI W, 1989, COMPUT METHOD APPL M, V75, P369, DOI 10.1016-0045-7825(89)90037-6; SCHNEIDER GE, 1978, NUMERICAL METHODS LA; VANDOORMAAL JP, 1984, NUMER HEAT TRANSFER, V7, P147, DOI 10.1080-10407798408546946; VANDOORMAL JP, 1985, THESIS U WATERLOO WA; VANKA SP, 1983, ANL8387; Webster R, 1996, INT J NUMER METH FL, V22, P1103, DOI 10.1002-(SICI)1097-0363(19960615)22:111103::AID-FLD4063.0.CO;2-K; WEBSTER R, 1994, INT J NUMER METH FL, V18, P761, DOI 10.1002-fld.1650180805; ZEDAN M, 1985, NUMER HEAT TRANSFER, V8, P537, DOI 10.1080-1040779850855216715131
A coupled finite volume solver for the solution of incompressible flows on unstructured grids
No full textThis paper reports on a newly developed fully coupled pressure-based algorithm for the solution of laminar incompressible flow problems on collocated unstructured grids. The implicit pressure-velocity coupling is accomplished by deriving a pressure equation in a procedure similar to a segregated SIMPLE algorithm using the Rhie-Chow interpolation technique and assembling the coefficients of the momentum and continuity equations into one diagonally dominant matrix. The extended systems of continuity and momentum equations are solved simultaneously and their convergence is accelerated by using an algebraic multigrid solver. The performance of the coupled approach as compared to the segregated approach, exemplified by SIMPLE, is tested by solving five laminar flow problems using both methodologies and comparing their computational costs. Results indicate that the number of iterations needed by the coupled solver for the solution to converge to a desired level on both structured and unstructured meshes is grid independent. For relatively coarse meshes, the CPU time required by the coupled solver on structured grid is lower than the CPU time required on unstructured grid. On dense meshes however, this is no longer true. For low and moderate values of the grid aspect ratio, the number of iterations required by the coupled solver remains unchanged, while the computational cost slightly increases. For structured and unstructured grid systems, the required number of iterations is almost independent of the grid size at any value of the grid expansion ratio. Recorded CPU time values show that the coupled approach substantially reduces the computational cost as compared to the segregated approach with the reduction rate increasing as the grid size increases. © 2008 Elsevier Inc. All rights reserved.Ammara I, 2004, INT J NUMER METH FL, V44, P621, DOI 10.1002-fld.662; Brufau P, 2003, J COMPUT PHYS, V186, P503, DOI 10.1016-S0021-9991(03)00072-X; BRAATEN ME, 1985, THESIS U MINNESOTA; Brandt A., 1977, Mathematics of Computation, V31, DOI 10.2307-2006422; Caretto L. S., 1972, Computer Methods in Applied Mechanics and Engineering, V1, DOI 10.1016-0045-7825(72)90020-5; CHORIN AJ, 1968, MATH COMPUT, V22, P745, DOI 10.2307-2004575; Darwish M, 2001, NUMER HEAT TR B-FUND, V40, P99; Darwish M, 2007, NUMER HEAT TR B-FUND, V52, P353, DOI 10.1080-10407790701372785; Darwish MS, 1996, NUMER HEAT TR B-FUND, V30, P217, DOI 10.1080-10407799608915080; DARWISH MS, 1994, NUMER HEAT TR B-FUND, V26, P79, DOI 10.1080-10407799408914918; Deng GB, 2001, COMPUT FLUIDS, V30, P445, DOI 10.1016-S0045-7930(00)00025-6; Elias SR, 1997, INT J NUMER METH ENG, V40, P887; Fedorenko R P, 1962, USSR COMP MATH MATH, V1, P1092, DOI 10.1016-0041-5553(62)90031-9; GALPIN PF, 1986, NUMER HEAT TRANSFER, V10, P105, DOI 10.1080-10407798608552499; Hanby RF, 1996, INT J NUMER METH FL, V22, P353; HARLOW FH, 1965, PHYS FLUIDS, V8, P2182, DOI 10.1063-1.1761178; HAYES RE, 1989, COMPUT FLUIDS, V17, P537, DOI 10.1016-0045-7930(89)90027-3; HUTCHINSON BR, 1986, NUMER HEAT TRANSFER, V9, P511, DOI 10.1080-10407798608552152; KARKI KC, 1990, INT J NUMER METH FL, V11, P1, DOI 10.1002-fld.1650110102; LANSDALE RD, 1991, NUMERICAL METHOD L 2, V7, P1432; Mazhar Z, 2001, NUMER HEAT TR B-FUND, V39, P91, DOI 10.1080-104077901460704; Moukalled F, 2003, J COMPUT PHYS, V190, P550, DOI 10.1016-S0021-9991(03)00297-3; Darwish M, 2003, INT J NUMER METH FL, V41, P1221, DOI 10.1002-fld.490; Moukalled F, 2000, NUMER HEAT TR B-FUND, V37, P103; Moukalled F, 2001, J COMPUT PHYS, V168, P101, DOI 10.1006-jcph.2000.6683; Moukalled F., 2006, HDB NUMERICAL HEAT T, P325; Moukalled F, 2003, NUMER HEAT TR A-APPL, V43, P543, DOI 10.1080-10407780390122808; Pascau A, 1996, COMMUN NUMER METH EN, V12, P617, DOI 10.1002-(SICI)1099-0887(199610)12:10617::AID-CNM103.3.CO;2-A; Patankar S. V., 1981, NUMERICAL HEAT TRANS; PATANKAR SV, 1972, INT J HEAT MASS TRAN, V15, P1787, DOI 10.1016-0017-9310(72)90054-3; POMMERELL C, 1994, SIAM J SCI COMPUT, V15, P460, DOI 10.1137-0915031; POUSSIN FD, 1968, SIAM J NUMER ANAL, V5, P340; RHIE CM, 1983, AIAA J, V21, P1525, DOI 10.2514-3.8284; RODI W, 1989, COMPUT METHOD APPL M, V75, P369, DOI 10.1016-0045-7825(89)90037-6; Rubin S., 1982, J COMPUT PHYS, V27, P153; SCHNEIDER GE, 1978, NUMERICAL METHODS LA; VANDOORMAL JP, 1985, THESIS U WATERLOO ON; VANKA SP, 1986, J COMPUT PHYS, V65, P138, DOI 10.1016-0021-9991(86)90008-2; WEBSTER R, 1994, INT J NUMER METH FL, V18, P761, DOI 10.1002-fld.165018080525191
Double diffusive natural convection in a porous rhombic annulus
No full textThis article reports on an investigation performed to study laminar steady state double diffusive natural convection in a two-dimensional porous enclosure of rhombic cross-section. Solutions are obtained numerically using a finite volume method for the case when the inner wall is uniformly heated to a temperature Th while subjected to a high solute concentration S h, and the outer wall is evenly cooled to a temperature Tc while exposed to a low solute concentration Sc. Simulations are conducted for several values of Rayleigh number (Ra), Darcy number (Da), Prandtl number (Pr), porosity (ε), and enclosure gap (Eg) for fixed values of Lewis number (Le = 10) and buoyancy ratio (N = 10). The results are displayed in terms of streamlines, isotherms, isoconcentrations, mid-height velocity, temperature, concentration profiles, and local and average Nusselt and Sherwood number values. Predictions indicate that for the Lewis number and buoyancy ratio considered, the flow field is more affected by mass transfer than by heat transfer. Moreover, convection effects increase with an increase in Ra, Da, Eg, and-or ε. The porosity of the porous matrix has no effect on the flow, temperature, and concentration fields at low values of Darcy number. Furthermore, the total heat and mass transfer increases as Pr increases and-or as the enclosure gap decreases due to an increase in the wall area over which heat and mass transfer occur. Values of and indicate dominant diffusion at low Ra number values with convection affecting the total heat and mass transfer at high Ra values. © 2013 Copyright Taylor and Francis Group, LLC.AMIRI A, 1994, INT J HEAT MASS TRAN, V37, P939, DOI 10.1016-0017-9310(94)90219-4; Basak T, 2009, INT J HEAT MASS TRAN, V52, P4612, DOI 10.1016-j.ijheatmasstransfer.2009.01.050; Basak T, 2008, INT J HEAT MASS TRAN, V51, P2733, DOI 10.1016-j.ijheatmasstransfer.2007.10.009; Beji H, 1999, NUMER HEAT TR A-APPL, V36, P153; Bennacer R., 2001, Numerical Heat Transfer, Part A (Applications), V39, DOI 10.1080-104077801750178860; BERGMAN TL, 1986, J HEAT TRANS-T ASME, V108, P206; Borjini MN, 2005, NUMER HEAT TR A-APPL, V48, P483, DOI 10.1080-10407780590959907; Borjini MN, 2006, INT J HEAT MASS TRAN, V49, P3984, DOI 10.1016-j.ijheatmasstransfer.2006.03.041; Brinkman H. 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Mixing and evaporation of liquid droplets injected into an air stream flowing at all speeds
No full textThis paper deals with the formulation, implementation, and testing of three numerical techniques based on (i) a full multiphase approach, (ii) a multisize-group (MUSIG) approach, and (iii) a heterogeneous MUSIG (H-MUSIG) approach for the prediction of mixing and evaporation of liquid droplets injected into a stream of air. The numerical procedures are formulated following an Eulerian approach, within a pressure-based fully conservative finite volume method equally applicable in the subsonic, transonic, and supersonic regimes, for the discrete and continuous phases. The k-ε two-equation turbulence model is used to account for the droplet and gas turbulence with modifications to account for compressibility at high speeds. The performances of the various methods are compared by solving for two configurations involving streamwise and cross-stream sprayings into subsonic and supersonic streams. Results, which are displayed in the form of droplet velocity vectors, contour plots, and axial profiles, indicate that solutions obtained by the various techniques exhibit a similar behavior. Differences in values are relatively small with the largest being associated with droplet volume fractions and vapor mass fraction in the gas phase. This is attributed to the fact that with MUSIG and H-MUSIG, no droplet diameter equation is solved and the diameter of the various droplet phases is held constant, as opposed to the full multiphase approach. © 2008 American Institute of Physics.ABRAMZON B, 1989, INT J HEAT MASS TRAN, V32, P1605, DOI 10.1016-0017-9310(89)90043-4; AGGARWAL SK, 1995, J ENG GAS TURB POWER, V117, P453, DOI 10.1115-1.2814117; AGGARWAL SK, 1984, AIAA J, V22, P1448, DOI 10.2514-3.8802; Bertoli C, 1999, INT J HEAT FLUID FL, V20, P552, DOI 10.1016-S0142-727X(99)00044-2; BOGDANOFF DW, 1994, J PROPUL POWER, V10, P183, DOI 10.2514-3.23728; Brown DP, 2006, COMPUT FLUIDS, V35, P762, DOI 10.1016-j.compfluid.2006.01.012; Burger M, 2002, J ENG GAS TURB POWER, V124, P481, DOI 10.1115-1.1473153; CHEN XQ, 1995, NUMER HEAT TR A-APPL, V27, P143, DOI 10.1080-10407789508913693; Chen XQ, 1996, INT J HEAT MASS TRAN, V39, P441, DOI 10.1016-0017-9310(95)00162-3; Darwish M, 2001, NUMER HEAT TR B-FUND, V40, P99; FAETH GM, 1983, PROG ENERG COMBUST, V9, P1, DOI 10.1016-0360-1285(83)90005-9; Founti MA, 2007, NUMER HEAT TR B-FUND, V52, P51, DOI 10.1080-10407790701225496; Fox RO, 2008, J COMPUT PHYS, V227, P3058, DOI 10.1016-j.jcp.2007.10.028; Frossling N., 1938, Gerlands Beitrage zur Geophysik, V52; Gharaibah E, 2004, HEAT MASS TRANSF, P295; Godsave G.A.E., 1953, P 4 S INT COMB COMB, P818; GREENBERG JB, 1993, COMBUST FLAME, V93, P90, DOI 10.1016-0010-2180(93)90085-H; Hagessaether L., 2002, THESIS NORWEGIAN U S; HALLMANN M, 1995, J ENG GAS TURB POWER, V117, P112, DOI 10.1115-1.2812758; Hassanizadeh M, 1979, ADV WATER RESOUR, V2, P191, DOI 10.1016-0309-1708(79)90035-6; Hassanizadeh M, 1979, ADV WATER RESOUR, V2, P131, DOI 10.1016-0309-1708(79)90025-3; HUBBARD GL, 1975, INT J HEAT MASS TRAN, V18, P1003, DOI 10.1016-0017-9310(75)90217-3; JIN JD, 1985, COMBUSTION EMISSION, P213; Jones I., 2003, P 3 INT C CFD MIN PR, P13; KAY IW, 1992, J PROPUL POWER, V8, P507, DOI 10.2514-3.23505; Klose G, 2001, J ENG GAS TURB POWER, V123, P817, DOI 10.1115-1.1377010; KRAMER M, 1988, THESIS U KARLSRUHE; Krepper E, 2005, NUCL ENG DES, V235, P597, DOI 10.1016-j.nucengdes.2004.09.006; Launder B. E., 1974, Computer Methods in Applied Mechanics and Engineering, V3, DOI 10.1016-0045-7825(74)90029-2; LAURENT F, 2002, THESIS U CLAUDE BERN; Laurent F, 2004, J COMPUT PHYS, V194, P505, DOI 10.1016-j.jcp.2003.08.026; Luo H, 1996, AICHE J, V42, P1225, DOI 10.1002-aic.690420505; MASSOT M, 2003, THESIS U CLAUDE BERN; MELVILLE WK, 1979, INT J HEAT MASS TRAN, V22, P647, DOI 10.1016-0017-9310(79)90113-3; Miller RS, 1998, INT J MULTIPHAS FLOW, V24, P1025, DOI 10.1016-S0301-9322(98)00028-7; MOUKALLED F, 2003, P 12 IASTED INT C A, P1; Moukalled F, 2000, NUMER HEAT TR B-FUND, V37, P103; Patankar S. V., 1981, NUMERICAL HEAT TRANS; Pereira JCF, 1996, J HAZARD MATER, V46, P253, DOI 10.1016-0304-3894(95)00077-1; RAJASEKARAN A, 2006, 42 AIAA ASME SAE ASE; Sazhin SS, 2006, PROG ENERG COMBUST, V32, P162, DOI 10.1016-j.pecs.2005.11.001; Sazhin SS, 2005, INT J HEAT MASS TRAN, V48, P4215, DOI 10.1016-j.ijheatmasstransfer.2005.04.007; SHI JM, 2004, 2004 ANN REPORT I SA, P21; Sommerfeld M, 1998, INT J HEAT FLUID FL, V19, P10, DOI 10.1016-S0142-727X(97)10002-9; Spalding D.B., 1953, P 4 S INT COMB, P847; TALLEY DG, 1986, P 21 S INT COMB COMB, P609; TSOURIS C, 1994, AICHE J, V40, P395, DOI 10.1002-aic.690400303; Yeoh GH, 2004, CHEM ENG SCI, V59, P3125, DOI 10.1016-j.ces.2004.04.02322
Heat and Mass Transfer in Moist Soil, Part I. Formulation and Testing
No full textAn unsteady two-dimensional model of heat and mass transfer through soil is implemented within a finite-volume-based numerical method. The model follows a phenomenological formulation for the transfer processes with temperature and matric potential (?) as the dependent variables. The finite-volume method being inherently conservative, the mass imbalance problem reported in the literature when employing the ?-based formulation with other numerical methods is prevented. A partial elimination algorithm is applied within the iterative solution procedure to increase its implicitness and improve its robustness. The accuracy of the model is established by solving the following three test problems: temperature distribution in dry soil; moisture distribution in isothermal soil; and coupled heat and water vapor diffusion in soil. Results are presented in the form of temporal profiles of temperature and moisture content and compared against analytical values. Excellent agreement is obtained, with numerical profiles falling on top of theoretical values.ASHRAE, 2001, 2001 ASHRAE HDB FUND; CAMPBELL GS, 1994, SOIL SCI, V158, P307, DOI 10.1097-00010694-199411000-00001; CELIA M, 1990, WATER RESOUR RES, V23, P1483; CHRISTOPHER P, 1982, WATER RESOUR RES, V18, P489; Crank J., 1956, MATH DIFFUSION; De VRIES D. A., 1958, TRANS AMER GEOPHYS UNION, V39, P909; de Vries DA, 1963, PHYS PLANT ENV, P210; Deru M., 2003, NRELTP55033954; HAVERKAMP R, 1977, SOIL SCI SOC AM J, V41, P285; Hillel D., 1998, ENV SOIL PHYS; Incropera F. P., 2002, FUNDAMENTALS HEAT MA; JANSSEN H, 2002, THESIS KATHOLIEKE U; KIRKLAND MR, 1992, WATER RESOUR RES, V28, P2049, DOI 10.1029-92WR00802; MILLY PCD, 1985, ADV WATER RESOUR, V8, P32, DOI 10.1016-0309-1708(85)90078-8; Moukalled F, 2000, NUMER HEAT TR B-FUND, V37, P103; Moukalled F, 2006, NUMER HEAT TR B-FUND, V49, P487, DOI 10.1080-10407790500510965; Patankar S. V., 1980, NUMERICAL HEAT TRANS; PHILIP J. R., 1957, TRANS AMER GEOPHYS UNION, V38, P222; PHILIP J. R., 1957, SOIL SCI, V83, P435; SOPHOCLEOUS M, 1979, WATER RESOUR RES, V15, P1195, DOI 10.1029-WR015i005p01195; SPALDING DB, 1983, CDF834 MECH ENG IMP; TAYLOR STERLING A., 1964, SOIL SCI SOC AMER PROC, V28, P167; VANGENUCHTEN MT, 1980, SOIL SCI SOC AM J, V44, P892; Zwart PJ, 1998, NUMER HEAT TR B-FUND, V34, P257, DOI 10.1080-1040779980891505711101
The performance of geometric conservation-based algorithms for incompressible multifluid flow
No full textThis article deals with the implementation and testing of seven segregated pressure-based algorithms for the prediction of incompressible multifluid flow. These algorithms belong to the geometric conservation-based algorithm (GCBA) group, in which the pressure-correction equation is derived from the constraint on volume fractions (i.e., the sum of volume fractions equals 1). The pressure-correction schemes in these algorithms are based on SIMPLE, SIMPLEC, SIMPLEX, SIMPLEM, SIMPLEST, PISO, and PRIME. The performance and accuracy of these algorithms are assessed by solving eight one-dimensional two-phase flow problems and comparing results with published data. The effects of grid size on convergence characteristics are analyzed by solving each problem over different grid sizes. Results clearly demonstrate the capability of all GCBA algorithms to predict a wide range of multifluid flow situations. Based on the convergence history plots and CPU times obtained for the problems solved, the GCBA can be divided into two groups, with the one composed of SIMPLEST and PRIME being generally less efficient than the second group, to which the remaining algorithms belong.ACHARYA S, 1989, NUMER HEAT TR B-FUND, V15, P131, DOI 10.1080-10407798908944897; AlTaweel AM, 1996, CHEM ENG RES DES, V74, P445; AMSDEN AA, 1975, LANUREG5680 LANL; AMSDEN AA, 1977, LANUREG6994 LANL; BAGHDADI AHA, 1979, THESIS U LONDON IMPE; Beckermann C., 1993, APPL MECH REV, V46, P1; BEHROUZI P, 1993, P 6 WORLD FILTR C NA, P474; Boisson N, 1996, INT J NUMER METH FL, V23, P1289, DOI 10.1002-(SICI)1097-0363(19961230)23:121289::AID-FLD4733.0.CO;2-Q; BOUILLARD JX, 1989, AICHE J, V35, P908, DOI 10.1002-aic.690350604; CARVER MB, 1986, NUMER HEAT TRANSFER, V10, P229, DOI 10.1080-10407788608913518; CARVER MB, 1984, J FLUID ENG-T ASME, V106, P147; CELIK I, 1990, FED ASME, V91, P19; Darwish M, 2001, NUMER HEAT TR B-FUND, V40, P99; DARWISH MS, 1994, NUMER HEAT TR B-FUND, V26, P79, DOI 10.1080-10407799408914918; Darwish MS, 1998, NUMER HEAT TR B-FUND, V34, P191, DOI 10.1080-10407799808915054; DEMIRDZIC I, 1993, INT J NUMER METH FL, V16, P1029, DOI 10.1002-fld.1650161202; Dohi N, 1999, CHEM ENG COMMUN, V171, P211, DOI 10.1080-00986449908912758; DREW DA, 1983, ANNU REV FLUID MECH, V15, P261, DOI 10.1146-annurev.fl.15.010183.001401; ERDAL FM, 1998, P SPE ANN TECHN C EX; Ferziger J, 1996, COMPUTATIONAL METHOD; Forrester SE, 1998, CHEM ENG SCI, V53, P603, DOI 10.1016-S0009-2509(97)00352-7; GASKELL PH, 1988, INT J NUMER METH FL, V8, P617, DOI 10.1002-fld.1650080602; GHANI AG, 1999, 10 WORLD C FOOD SCI; Gidaspow D., 1994, MULTIPHASE FLOW FLUI; GOMEZ LE, 1998, SPE ANN TECHN C EXH; GOSMAN AD, 1992, AICHE J, V38, P1853; GRAY WG, 1989, INT J MULTIPHAS FLOW, V15, P81, DOI 10.1016-0301-9322(89)90087-6; HUANG B, 1989, THESIS U C BERNARD L; Ishii M., 1975, THERMOFLUID DYNAMIC; ISSA RI, 1982, FS8215 IMP COLL; KELLY JM, 1993, PNLSA18878 BAT PAC N; LEONARD BP, 1987, NUMERICAL METHODS LA, V15, P35; Lines PC, 2000, CHEM ENG RES DES, V78, P342, DOI 10.1205-026387600527455; LO SM, 1990, 13432 ARER HARW LAB; MALISKA CR, 1983, P 3 INT C NUM METH L, P656; Mitchell CR, 1994, 940642 AIAA; MORSI SA, 1972, J FLUID MECH, V55, P193, DOI 10.1017-S0022112072001806; Moukalled F, 2002, NUMER HEAT TR B-FUND, V42, P259, DOI 10.1080-10407790190053941; Moukalled F, 2001, J COMPUT PHYS, V168, P101, DOI 10.1006-jcph.2000.6683; Mundo C, 1998, ATOMIZATION SPRAY, V8, P625; PATANKAR SV, 1972, INT J HEAT MASS TRAN, V15, P1787, DOI 10.1016-0017-9310(72)90054-3; Rhie C.M., 1986, 860207 AIAA; RIVARD WW, 1978, LANUREG6623; Ruger M, 2000, ATOMIZATION SPRAY, V10, P47; Soo S. L., 1990, MULTIPHASE FLUID DYN; Spalding DB, 1980, RECENT ADV NUMERICAL, V1, P139; SPALDING DB, 1976, HTS7611 IMP COLL MEC; SPALDING DB, 1981, HTS811 IMP COLL MECH; VANDOORMAAL JP, 1984, NUMER HEAT TRANSFER, V7, P147, DOI 10.1080-10407798408546946; VANDOORMAAL JP, 1985, NAT HEAT TRANSF C DE; WITT PJ, 1995, STUDY MULTIPHASE MOD; Zwart PJ, 1998, NUMER HEAT TR B-FUND, V34, P257, DOI 10.1080-1040779980891505767
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