Numerical study of MHD mixed convection under volumetric heat source in vertical square duct with wall effects
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摘要
Magnetohydrodynamic(MHD) mixed convection under strong magnetic field and volumetric heat source for buoyancy-assisted flows are studied numerically in this paper. Blanket is one of key components for energy conversion in Tokamak fusion reactor. The physical model employed for simulations is refined from dual-coolant lead-lithium(DCLL) blanket. A magnetic-convection code based on a consistent and conservative scheme is developed with the help of finite volume method, and validated by some Benchmark analytical solutions. The flows inside duct with thermal insulating and electric conducting walls under exponential neutron volumetric heat source are simulated. Based on Boussinesq assumption, the influences of wall electrical conductivity and buoyancy on velocity fields, temperature distributions and Nusselt numbers are investigated. Results illustrates that the wall conductance ratio dominates the flow at low Grashof numbers and high wall conductance ratio, while buoyancy effect dominates the jet flow near side wall at a high Grashof number. In addition, the velocity along flow direction substantially impacts features of the Nusselt number and temperature distribution. Besides, the jet flow results in a higher Nusselt number and lower temperature.
Magnetohydrodynamic(MHD) mixed convection under strong magnetic field and volumetric heat source for buoyancy-assisted flows are studied numerically in this paper. Blanket is one of key components for energy conversion in Tokamak fusion reactor. The physical model employed for simulations is refined from dual-coolant lead-lithium(DCLL) blanket. A magnetic-convection code based on a consistent and conservative scheme is developed with the help of finite volume method, and validated by some Benchmark analytical solutions. The flows inside duct with thermal insulating and electric conducting walls under exponential neutron volumetric heat source are simulated. Based on Boussinesq assumption, the influences of wall electrical conductivity and buoyancy on velocity fields, temperature distributions and Nusselt numbers are investigated. Results illustrates that the wall conductance ratio dominates the flow at low Grashof numbers and high wall conductance ratio, while buoyancy effect dominates the jet flow near side wall at a high Grashof number. In addition, the velocity along flow direction substantially impacts features of the Nusselt number and temperature distribution. Besides, the jet flow results in a higher Nusselt number and lower temperature.
Magnetohydrodynamic(MHD) mixed convection under strong magnetic field and volumetric heat source for buoyancy-assisted flows are studied numerically in this paper. Blanket is one of key components for energy conversion in Tokamak fusion reactor. The physical model employed for simulations is refined from dual-coolant lead-lithium(DCLL) blanket. A magnetic-convection code based on a consistent and conservative scheme is developed with the help of finite volume method, and validated by some Benchmark analytical solutions. The flows inside duct with thermal insulating and electric conducting walls under exponential neutron volumetric heat source are simulated. Based on Boussinesq assumption, the influences of wall electrical conductivity and buoyancy on velocity fields, temperature distributions and Nusselt numbers are investigated. Results illustrates that the wall conductance ratio dominates the flow at low Grashof numbers and high wall conductance ratio, while buoyancy effect dominates the jet flow near side wall at a high Grashof number. In addition, the velocity along flow direction substantially impacts features of the Nusselt number and temperature distribution. Besides, the jet flow results in a higher Nusselt number and lower temperature.
引文
[1]M. Abdou, D. Sze, C. Wong, et al., U.S. plans and strategy for iter blanket testing, Fusion Science and Technology 47(2005)475-487.
[2]S.Smolentsev,N.Morley,M.Abdou,Code development for analysis of mhd pressure drop reduction in a liquid metal blanket using insulation technique based on a fully developed flow model,Fusion Engineering and Design 73(2005)83-93.
[3]S.Smolentsev,R.Moreau,M.Abdou,Characterization of key magnetohydrodynamic phenomena in PbLi flows for the USDCLL blanket,Fusion Engineering and Design 83(2008)771-783.
[4]T.Tagawa,G.Authié,R.Moreau,Buoyant flow in long vertical enclosures in the presence of a strong horizontal magnetic field.Part 1.Fully-established flow,European Journal of Mechanics-B/Fluids 21(2002)383-398.
[5]G.Authié,T.Tagawa,R.Moreau,Buoyant flow in long vertical enclosures in the presence of a strong horizontal magnetic field.Part 2.Fnite enclosures,European Journal of MechanicsB/Fluids 22(2003)203-220.
[6]L.Chen,B.-Q.Liu,M.-J.Ni,Study of natural convection in a heated cavity with magnetic fields normal to the main circulation,International Journal of Heat and Mass Transfer 127(2018)267-277.
[7]Z.Jing,M.-J.Ni,Z.-H.Wang,Numerical study of MHD natural convection of liquid metal with wall effects,Numerical Heat Transfer Part A:Applications 64(2013)676-693.
[8]M.Abdou,N.B.Morley,S.Smolentsev,et al.,Blanket/first wall challenges and required R&D on the pathway to demo,Fusion Engineering and Design 100(2015)2-43.
[9]J.Umavathi,M.Malashetty,Magnetohydrodynamic mixed convection in a vertical channel,International Journal of Non-Linear Mechanics 40(2005)91-101.
[10]S.Mahmud,S.H.Tasnim,M.A.H.Mamun,Thermodynamic analysis of mixed convection in a channel with transverse hydromagnetic effect,International Journal of Thermal Sciences42(2003)731-740.
[11]L.T.Benos,S.Kakarantzas,I.Sarris,et al.,Analytical and numerical study of mhd natural convection in a horizontal shallow cavity with heat generation,International Journal of Heat and Mass Transfer 75(2014)19-30.
[12]T.Alboussiere,J.Garandet,Buoyancy-driven convection with a uniform magnetic field.Part 1.Asymptotic analysis,Journal of Fluid Mechanics 253(1993)545-563.
[13]L.Davoust,M.Cowley,R.Moreau,et al.,Buoyancy-driven convection with a uniform magnetic field.Part 2.Experimental investigation,Journal of Fluid Mechanics 400(1999)59-90.
[14]S.Smolentsev,S.Badia,R.Bhattacharyay,et al.,An approach to verifcation and validation of MHD codes for fusion applications,Fusion Engineering and Design 100(2015)65-72.
[15]N.Vetcha,S.Smolentsev,M.Abdou,et al.,Study of instabilities and quasi-two-dimensional turbulence in volumetrically heated magnetohydrodynamic flows in a vertical rectangular duct,Physics of Fluids 25(2013)024102.
[16]A.Hudoba,S.Molokov,Linear stability of buoyant convective flow in a vertical channel with internal heat sources and a transverse magnetic field,Physics of Fluids 28(2016)114103.
[17]E.M.de Les Valls,L.Batet,V.De Medina,et al.,Modelling of integrated effect of volumetric heating and magnetic field on tritium transport in a U-bend flow as applied to HCLL blanket concept,Fusion Engineering and Design 86(2011)341-356.
[18]X.Zhang,O.Zikanov,Two-dimensional turbulent convection in a toroidal duct of a liquid metal blanket of a fusion reactor,Journal of Fluid Mechanics 779(2015)36-52.
[19]O.Zikanov,Y.Listratov,Numerical investigation of mhd heat transfer in a vertical round tube affected by transverse magnetic field,Fusion Engineering and Design 113(2016)151-161.
[20]I.Melnikov,E.Sviridov,V.Sviridov,et al.,Experimental investigation of mhd heat transfer in a vertical round tube affected by transverse magnetic field,Fusion Engineering and Design 112(2016)505-512.
[21]I.Kirillov,D.Obukhov,L.Genin,et al.,Buoyancy effects in vertical rectangular duct with coplanar magnetic field and single sided heat load,Fusion Engineering and Design 104(2016)1-8.
[22]S.Smolentsev,N.Morley,M.Abdou,Magnetohydrodynamic and thermal issues of the SiCf/SiC flow channel insert,Fusion Science and Technology 50(2006)107-119.
[23]D.D.Gray,A.Giorgini,The validity of the boussinesq approx-imation for liquids and gases,International Journal of Heat and Mass Transfer 19(1976)545-551.
[24]M.-J.Ni,R.Munipalli,N.B.Morley,et al.,A current density conservative scheme for incompressible mhd flows at a low magnetic reynolds number.Part I:On a rectangular collocated grid system,Journal of Computational Physics 227(2007)174-204.
[25]M.-J.Ni,R.Munipalli,P.Huang,et al.,A current density conservative scheme for incompressible mhd flows at a low magnetic reynolds number.Part II:On an arbitrary collocated mesh,Journal of Computational Physics 227(2007)205-228.
[2]S.Smolentsev,N.Morley,M.Abdou,Code development for analysis of mhd pressure drop reduction in a liquid metal blanket using insulation technique based on a fully developed flow model,Fusion Engineering and Design 73(2005)83-93.
[3]S.Smolentsev,R.Moreau,M.Abdou,Characterization of key magnetohydrodynamic phenomena in PbLi flows for the USDCLL blanket,Fusion Engineering and Design 83(2008)771-783.
[4]T.Tagawa,G.Authié,R.Moreau,Buoyant flow in long vertical enclosures in the presence of a strong horizontal magnetic field.Part 1.Fully-established flow,European Journal of Mechanics-B/Fluids 21(2002)383-398.
[5]G.Authié,T.Tagawa,R.Moreau,Buoyant flow in long vertical enclosures in the presence of a strong horizontal magnetic field.Part 2.Fnite enclosures,European Journal of MechanicsB/Fluids 22(2003)203-220.
[6]L.Chen,B.-Q.Liu,M.-J.Ni,Study of natural convection in a heated cavity with magnetic fields normal to the main circulation,International Journal of Heat and Mass Transfer 127(2018)267-277.
[7]Z.Jing,M.-J.Ni,Z.-H.Wang,Numerical study of MHD natural convection of liquid metal with wall effects,Numerical Heat Transfer Part A:Applications 64(2013)676-693.
[8]M.Abdou,N.B.Morley,S.Smolentsev,et al.,Blanket/first wall challenges and required R&D on the pathway to demo,Fusion Engineering and Design 100(2015)2-43.
[9]J.Umavathi,M.Malashetty,Magnetohydrodynamic mixed convection in a vertical channel,International Journal of Non-Linear Mechanics 40(2005)91-101.
[10]S.Mahmud,S.H.Tasnim,M.A.H.Mamun,Thermodynamic analysis of mixed convection in a channel with transverse hydromagnetic effect,International Journal of Thermal Sciences42(2003)731-740.
[11]L.T.Benos,S.Kakarantzas,I.Sarris,et al.,Analytical and numerical study of mhd natural convection in a horizontal shallow cavity with heat generation,International Journal of Heat and Mass Transfer 75(2014)19-30.
[12]T.Alboussiere,J.Garandet,Buoyancy-driven convection with a uniform magnetic field.Part 1.Asymptotic analysis,Journal of Fluid Mechanics 253(1993)545-563.
[13]L.Davoust,M.Cowley,R.Moreau,et al.,Buoyancy-driven convection with a uniform magnetic field.Part 2.Experimental investigation,Journal of Fluid Mechanics 400(1999)59-90.
[14]S.Smolentsev,S.Badia,R.Bhattacharyay,et al.,An approach to verifcation and validation of MHD codes for fusion applications,Fusion Engineering and Design 100(2015)65-72.
[15]N.Vetcha,S.Smolentsev,M.Abdou,et al.,Study of instabilities and quasi-two-dimensional turbulence in volumetrically heated magnetohydrodynamic flows in a vertical rectangular duct,Physics of Fluids 25(2013)024102.
[16]A.Hudoba,S.Molokov,Linear stability of buoyant convective flow in a vertical channel with internal heat sources and a transverse magnetic field,Physics of Fluids 28(2016)114103.
[17]E.M.de Les Valls,L.Batet,V.De Medina,et al.,Modelling of integrated effect of volumetric heating and magnetic field on tritium transport in a U-bend flow as applied to HCLL blanket concept,Fusion Engineering and Design 86(2011)341-356.
[18]X.Zhang,O.Zikanov,Two-dimensional turbulent convection in a toroidal duct of a liquid metal blanket of a fusion reactor,Journal of Fluid Mechanics 779(2015)36-52.
[19]O.Zikanov,Y.Listratov,Numerical investigation of mhd heat transfer in a vertical round tube affected by transverse magnetic field,Fusion Engineering and Design 113(2016)151-161.
[20]I.Melnikov,E.Sviridov,V.Sviridov,et al.,Experimental investigation of mhd heat transfer in a vertical round tube affected by transverse magnetic field,Fusion Engineering and Design 112(2016)505-512.
[21]I.Kirillov,D.Obukhov,L.Genin,et al.,Buoyancy effects in vertical rectangular duct with coplanar magnetic field and single sided heat load,Fusion Engineering and Design 104(2016)1-8.
[22]S.Smolentsev,N.Morley,M.Abdou,Magnetohydrodynamic and thermal issues of the SiCf/SiC flow channel insert,Fusion Science and Technology 50(2006)107-119.
[23]D.D.Gray,A.Giorgini,The validity of the boussinesq approx-imation for liquids and gases,International Journal of Heat and Mass Transfer 19(1976)545-551.
[24]M.-J.Ni,R.Munipalli,N.B.Morley,et al.,A current density conservative scheme for incompressible mhd flows at a low magnetic reynolds number.Part I:On a rectangular collocated grid system,Journal of Computational Physics 227(2007)174-204.
[25]M.-J.Ni,R.Munipalli,P.Huang,et al.,A current density conservative scheme for incompressible mhd flows at a low magnetic reynolds number.Part II:On an arbitrary collocated mesh,Journal of Computational Physics 227(2007)205-228.