High-order fully implicit SIMPLE-based model for fully implicit simulation of upward two-phase flow
|
摘要
The drift-flux model has a practical importance in two-phase flow analysis.In this study,a finite volume solution is developed for a transient four-equation drift-flux model through the staggered mesh,leading to the development of a fully implicit discretization method.The main advantage of the fully implicit method is its unconditional stability.Newton's scheme is a popular method of choice for the solution of a nonlinear system of equations arising from fully implicit discretization of field equations.However,the lack of convergence robustness and the construction of Jacobian matrix have created several difficulties for the researchers.In this paper,a fully implicit model is developed based on the SIMPLE algorithm for two-phase flow simulations.The drawbacks of Newton's method are avoided in the developed model.Different limiter functions are considered,and the stabilized method is developed under steady and transient conditions.The results obtained by the numerical modeling are in good agreement with the experimental data.As expected,the results prove that the developed model is not restricted by any stability limit.
The drift-flux model has a practical importance in two-phase flow analysis.In this study,a finite volume solution is developed for a transient four-equation drift-flux model through the staggered mesh,leading to the development of a fully implicit discretization method.The main advantage of the fully implicit method is its unconditional stability.Newton's scheme is a popular method of choice for the solution of a nonlinear system of equations arising from fully implicit discretization of field equations.However,the lack of convergence robustness and the construction of Jacobian matrix have created several difficulties for the researchers.In this paper,a fully implicit model is developed based on the SIMPLE algorithm for two-phase flow simulations.The drawbacks of Newton's method are avoided in the developed model.Different limiter functions are considered,and the stabilized method is developed under steady and transient conditions.The results obtained by the numerical modeling are in good agreement with the experimental data.As expected,the results prove that the developed model is not restricted by any stability limit.
The drift-flux model has a practical importance in two-phase flow analysis.In this study,a finite volume solution is developed for a transient four-equation drift-flux model through the staggered mesh,leading to the development of a fully implicit discretization method.The main advantage of the fully implicit method is its unconditional stability.Newton's scheme is a popular method of choice for the solution of a nonlinear system of equations arising from fully implicit discretization of field equations.However,the lack of convergence robustness and the construction of Jacobian matrix have created several difficulties for the researchers.In this paper,a fully implicit model is developed based on the SIMPLE algorithm for two-phase flow simulations.The drawbacks of Newton's method are avoided in the developed model.Different limiter functions are considered,and the stabilized method is developed under steady and transient conditions.The results obtained by the numerical modeling are in good agreement with the experimental data.As expected,the results prove that the developed model is not restricted by any stability limit.
引文
1.K.E.Carlson,R.A.Riemke,S.Z.Rouhani,R.W.Shumway,W.L.Weaver,Relap5/Mod3 code manual volume i:Code structure,system models,and solution methods.US NRC NUREG/CR-5535(Washington,DC,USA,1990)
2.S.Bajorek,TRACE V5.0 Theory manual,field equations,solution methods and physical models.United States Nuclear Regulatory Commission(2008)
3.L.Zou,H.Zhao,H.Zhang,Numerical implementation,verification and validation of two-phase flow four-equation drift flux model with Jacobian-free Newton-Krylov method.Ann.Nucl.Energy 87,707-719(2015).https://doi.org/10.1016/j.anucene.2015.07.033
4.J.A.Trapp,R.A.Riemke,A nearly-implicit hydrodynamics numerical scheme for two-phase flows.J.Comput.Phys.66,62-82(1986).https://doi.org/10.1016/0021-9991(86)90054-9
5.D.A.Knoll,D.E.Keyes,Jacobian-free Newton-Krylov methods:a survey of approaches and applications.J.Comput.Phys.193,357-397(2004).https://doi.org/10.1016/j.jcp.2003.08.010
6.M.A.Pope,V.A.Mousseau,Accuracy and efficiency of a coupled neutronics and thermal hydraulics model.Nucl.Eng.Technol.41,885-892(2008).https://doi.org/10.5516/net.2009.41.7.885
7.D.Bestion,The physical closure laws in the CATHARE code.Nucl.Eng.Des.124,229-245(1990).https://doi.org/10.1016/0029-5493(90)90294-8
8.F.Barre,M.Parent,B.Brun,Advanced numerical methods for thermal hydraulics.Nucl.Eng.Des.145,147-158(1993).https://doi.org/10.1016/0029-5493(93)90064-g
9.C.Frepoli,J.H.Mahaffy,K.Ohkawa,Notes on the implementation of a fully-implicit numerical scheme for a two-phase threefield flow model.Nucl.Eng.Des.225,191-217(2003).https://doi.org/10.1016/s0029-5493(03)00159-6
10.R.A.A.Saleem,T.Kozlowski,Development of accurate and stable two-phase two-fluid model solver.Proc.ICAPP 2014,6-9(2014).https://doi.org/10.1155/2015/575380
11.Y.Saad,Iterative Methods for Sparse Linear Systems,2nd edn,pp.535(2003).doi.:https://doi.org/10.2277/0898715342
12.V.A.Mousseau,Implicitly balanced solution of the two-phase flow equations coupled to nonlinear heat conduction.J.Comput.Phys.200,104-132(2004).https://doi.org/10.1016/j.jcp.2004.03.009
13.A.Ashrafizadeh,Investigation of a Jacobian-free Newton-Krylov solution to multiphase flows.(2014).https://doi.org/10.1002/fld.3999
14.T.F.Miller,D.J.Miller,Fourier analysis of the IPSA/PEAalgorithms applied to multiphase flows with mass transfer.Comput.Fluids 32,197-221(2003).https://doi.org/10.1016/s0045-7930(02)00005-1
15.S.Patankar,Numerical Heat Transfer and Fluid Flow(CRCPress,Boca Raton,1980)
16.N.Zuber,J.A.Findlay,Average volumetric concentration in twophase flow systems.J.Heat Transfer 87,453-468(1965).https://doi.org/10.1115/1.3689137
17.E.D.Hughes,M.P.Paulsen,L.J.Agee,A drift-flux model of twophase flow for RETRAN.Nucl.Technol.54,410-421(1981)
18.S.Talebi,H.Kazeminejad,H.Davilu,A numerical technique for analysis of transient two-phase flow in a vertical tube using the Drift Flux Model.Nucl.Eng.Des.242,316-322(2012).https://doi.org/10.1016/j.nucengdes.2011.10.038
19.Y.G.Lee,G.C.Park,TAPINS:a thermal-hydraulic system code for transient analysis of a fully-passive integral PWR.Nucl.Eng.Technol.45,439-458(2013).https://doi.org/10.5516/net.02.2013.025
20.H.J.Khan,H.C.Yi,Subchannel analysis in BWR fuel bundles.Ann.Nucl.Energy 12,559-572(1985).https://doi.org/10.1016/0306-4549(85)90029-5
21.T.Hibiki,M.Ishii,One-dimensional drift-flux model and constitutive equations for relative motion between phases in various two-phase flow regimes.Int.J.Heat Mass Transf.46,4935-4948(2003)
22.W.Wagner,The IAPWS formulation 1995 for the thermodynamic properties of ordinary water substance for general and scientific use.J.Phys.Chem.Ref.Data 31,387(1999).https://doi.org/10.1063/1.1461829
23.C.W.Hirt,T.A.Oliphant,W.C.Rivard et al.,SOLA-LOOP:a nonequilibrium,drift-flux code for two-phase flow in networks(Los Alamos Scientific Lab,New Mexico,1979)
24.L.Sun,K.Mishima,Evaluation analysis of prediction methods for two-phase flow pressure drop in mini-channels.Int.J.Multiph.Flow 35,47-54(2009).https://doi.org/10.1016/j.ijmultipha seflow.2008.08.003
25.R.T.Lahey,A mechanistic subcooled boiling model,in Proceedings of the 6th International Heat Transfer Conference,vol 1,pp.293-297(1978)
26.J.G.M.Andersen,R.Harrington,B.Hizoum,COBRAGSubchannel Code:Model Description Report NEDE-32199P,Revision 1(2007)
27.B.Chexal,The Chexal-Lellouche void fraction correlation for generalized applications.Electr.Power Res.Inst.Rep.EPRINSAC/139(1991)
28.S.Levy,Forced convection subcooled boiling-prediction of vapor volumetric fraction.Int.J.Heat Mass Transf.10,951-965(1967).https://doi.org/10.1016/0017-9310(67)90071-3
29.J.M.Delhaye,F.Maugin,J.M.Ochterbeck,Void fraction predictions in forced convective subcooled boiling of water between10 and 18 Mpa.Int.J.Heat Mass Transf.47,4415-4425(2004).https://doi.org/10.1016/j.ijheatmasstransfer.2004.05.018
30.W.Frost,G.S.Dzakowic,An extension of the method of predictive incipient boiling on commercially finished surfaces.ASME-AICh E Heat Transfer Conference,Seattle(1967)
31.H.K.Versteegand,W.Malalasekera,An Introduction to Computational Fluid Dynamics(Longman Scientific&Technical,New York,1995)
32.G.Bartolomei,V.Chanturiya,Experimental study of true void fraction when boiling subcooled water in vertical tubes.Therm.Eng.14,123-128(1967)
33.G.G.Bartolomei,V.G.Brantov,Y.S.Molochnikov et al.,An experimental investigation of true volumetric vapor content with subcooled boiling in tubes.Therm.Eng.29(3),132-135(1982)
34.A.S.Devkin,A.S.Podosenov,International Agreement Report RELAP5/MOD3 Subcooled Boiling Model Assessment.NUREG/IA-0,(1998)
35.S.Hari,Y.A.Hassan,Refinement of the RELAP5/MOD3.2subcooled boiling model for low-pressure conditions,in Proceedings of 8th International Conference in Nuclear Engineering,Baltimore,USA(2000)
36.A.Ashrafizadeh,C.B.Devaud,N.U.Aydemir,A Jacobian-free Newton-Krylov method for thermal hydraulics simulations.Int.J.Numer.Methods Fluids 77(10),590-615(2015).https://doi.org/10.1002/fld.3999
37.V.A.Mousseau,A fully implicit hybrid solution method for a two-phase thermal-hydraulic model.J.Heat Transfer 127,531-539(2005).https://doi.org/10.1115/1.1865223
2.S.Bajorek,TRACE V5.0 Theory manual,field equations,solution methods and physical models.United States Nuclear Regulatory Commission(2008)
3.L.Zou,H.Zhao,H.Zhang,Numerical implementation,verification and validation of two-phase flow four-equation drift flux model with Jacobian-free Newton-Krylov method.Ann.Nucl.Energy 87,707-719(2015).https://doi.org/10.1016/j.anucene.2015.07.033
4.J.A.Trapp,R.A.Riemke,A nearly-implicit hydrodynamics numerical scheme for two-phase flows.J.Comput.Phys.66,62-82(1986).https://doi.org/10.1016/0021-9991(86)90054-9
5.D.A.Knoll,D.E.Keyes,Jacobian-free Newton-Krylov methods:a survey of approaches and applications.J.Comput.Phys.193,357-397(2004).https://doi.org/10.1016/j.jcp.2003.08.010
6.M.A.Pope,V.A.Mousseau,Accuracy and efficiency of a coupled neutronics and thermal hydraulics model.Nucl.Eng.Technol.41,885-892(2008).https://doi.org/10.5516/net.2009.41.7.885
7.D.Bestion,The physical closure laws in the CATHARE code.Nucl.Eng.Des.124,229-245(1990).https://doi.org/10.1016/0029-5493(90)90294-8
8.F.Barre,M.Parent,B.Brun,Advanced numerical methods for thermal hydraulics.Nucl.Eng.Des.145,147-158(1993).https://doi.org/10.1016/0029-5493(93)90064-g
9.C.Frepoli,J.H.Mahaffy,K.Ohkawa,Notes on the implementation of a fully-implicit numerical scheme for a two-phase threefield flow model.Nucl.Eng.Des.225,191-217(2003).https://doi.org/10.1016/s0029-5493(03)00159-6
10.R.A.A.Saleem,T.Kozlowski,Development of accurate and stable two-phase two-fluid model solver.Proc.ICAPP 2014,6-9(2014).https://doi.org/10.1155/2015/575380
11.Y.Saad,Iterative Methods for Sparse Linear Systems,2nd edn,pp.535(2003).doi.:https://doi.org/10.2277/0898715342
12.V.A.Mousseau,Implicitly balanced solution of the two-phase flow equations coupled to nonlinear heat conduction.J.Comput.Phys.200,104-132(2004).https://doi.org/10.1016/j.jcp.2004.03.009
13.A.Ashrafizadeh,Investigation of a Jacobian-free Newton-Krylov solution to multiphase flows.(2014).https://doi.org/10.1002/fld.3999
14.T.F.Miller,D.J.Miller,Fourier analysis of the IPSA/PEAalgorithms applied to multiphase flows with mass transfer.Comput.Fluids 32,197-221(2003).https://doi.org/10.1016/s0045-7930(02)00005-1
15.S.Patankar,Numerical Heat Transfer and Fluid Flow(CRCPress,Boca Raton,1980)
16.N.Zuber,J.A.Findlay,Average volumetric concentration in twophase flow systems.J.Heat Transfer 87,453-468(1965).https://doi.org/10.1115/1.3689137
17.E.D.Hughes,M.P.Paulsen,L.J.Agee,A drift-flux model of twophase flow for RETRAN.Nucl.Technol.54,410-421(1981)
18.S.Talebi,H.Kazeminejad,H.Davilu,A numerical technique for analysis of transient two-phase flow in a vertical tube using the Drift Flux Model.Nucl.Eng.Des.242,316-322(2012).https://doi.org/10.1016/j.nucengdes.2011.10.038
19.Y.G.Lee,G.C.Park,TAPINS:a thermal-hydraulic system code for transient analysis of a fully-passive integral PWR.Nucl.Eng.Technol.45,439-458(2013).https://doi.org/10.5516/net.02.2013.025
20.H.J.Khan,H.C.Yi,Subchannel analysis in BWR fuel bundles.Ann.Nucl.Energy 12,559-572(1985).https://doi.org/10.1016/0306-4549(85)90029-5
21.T.Hibiki,M.Ishii,One-dimensional drift-flux model and constitutive equations for relative motion between phases in various two-phase flow regimes.Int.J.Heat Mass Transf.46,4935-4948(2003)
22.W.Wagner,The IAPWS formulation 1995 for the thermodynamic properties of ordinary water substance for general and scientific use.J.Phys.Chem.Ref.Data 31,387(1999).https://doi.org/10.1063/1.1461829
23.C.W.Hirt,T.A.Oliphant,W.C.Rivard et al.,SOLA-LOOP:a nonequilibrium,drift-flux code for two-phase flow in networks(Los Alamos Scientific Lab,New Mexico,1979)
24.L.Sun,K.Mishima,Evaluation analysis of prediction methods for two-phase flow pressure drop in mini-channels.Int.J.Multiph.Flow 35,47-54(2009).https://doi.org/10.1016/j.ijmultipha seflow.2008.08.003
25.R.T.Lahey,A mechanistic subcooled boiling model,in Proceedings of the 6th International Heat Transfer Conference,vol 1,pp.293-297(1978)
26.J.G.M.Andersen,R.Harrington,B.Hizoum,COBRAGSubchannel Code:Model Description Report NEDE-32199P,Revision 1(2007)
27.B.Chexal,The Chexal-Lellouche void fraction correlation for generalized applications.Electr.Power Res.Inst.Rep.EPRINSAC/139(1991)
28.S.Levy,Forced convection subcooled boiling-prediction of vapor volumetric fraction.Int.J.Heat Mass Transf.10,951-965(1967).https://doi.org/10.1016/0017-9310(67)90071-3
29.J.M.Delhaye,F.Maugin,J.M.Ochterbeck,Void fraction predictions in forced convective subcooled boiling of water between10 and 18 Mpa.Int.J.Heat Mass Transf.47,4415-4425(2004).https://doi.org/10.1016/j.ijheatmasstransfer.2004.05.018
30.W.Frost,G.S.Dzakowic,An extension of the method of predictive incipient boiling on commercially finished surfaces.ASME-AICh E Heat Transfer Conference,Seattle(1967)
31.H.K.Versteegand,W.Malalasekera,An Introduction to Computational Fluid Dynamics(Longman Scientific&Technical,New York,1995)
32.G.Bartolomei,V.Chanturiya,Experimental study of true void fraction when boiling subcooled water in vertical tubes.Therm.Eng.14,123-128(1967)
33.G.G.Bartolomei,V.G.Brantov,Y.S.Molochnikov et al.,An experimental investigation of true volumetric vapor content with subcooled boiling in tubes.Therm.Eng.29(3),132-135(1982)
34.A.S.Devkin,A.S.Podosenov,International Agreement Report RELAP5/MOD3 Subcooled Boiling Model Assessment.NUREG/IA-0,(1998)
35.S.Hari,Y.A.Hassan,Refinement of the RELAP5/MOD3.2subcooled boiling model for low-pressure conditions,in Proceedings of 8th International Conference in Nuclear Engineering,Baltimore,USA(2000)
36.A.Ashrafizadeh,C.B.Devaud,N.U.Aydemir,A Jacobian-free Newton-Krylov method for thermal hydraulics simulations.Int.J.Numer.Methods Fluids 77(10),590-615(2015).https://doi.org/10.1002/fld.3999
37.V.A.Mousseau,A fully implicit hybrid solution method for a two-phase thermal-hydraulic model.J.Heat Transfer 127,531-539(2005).https://doi.org/10.1115/1.1865223