多孔介质中流固作用力的动量交换计算
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摘要
流经多孔介质的流动广泛存在于化工生产、多孔颗粒悬浮流等领域,如何准确计算流体与多孔介质之间的作用力是研究此类流动的一个关键因素.作为一种有效的流体计算方法,格子波尔兹曼方法(latticeBoltzmann method,LBM)常采用动量交换法计算流体与固体之间相互作用力.分析了流体流经多孔介质时两者的动量交换过程,提出了一种高效的动量交换法来计算流固作用力,并在孔隙尺度下对其进行了验证,结果表明该方法是可行的.进而将该方法推广到计算表征体元(表征体元)尺度下的流--固相互作用,并对不同雷诺数(Re)下的多孔方柱绕流问题进行了模拟和验证.
Flows over porous media are frequently encountered in industrial applications such as chemical engineering process and porous particles suspension. It's of great importance to evaluate the force between the fluid and the objects accurately. The momentum exchange method which is efficient and easy for implementation is widely used to determine the force in lattice Boltzmann method. In this work we propose an efficient momentum exchange method to calculate the force by analyzing the exchange process of the fluid and the object. The method is validated by simulating the flows over a porous object at the pore scale, and the method is also extended for fluid-object interaction at scale. Simulations of flows over a square cylinder at different Reynolds numbers are conducted, and the viability of the method is confirmed by the numerical results.
Flows over porous media are frequently encountered in industrial applications such as chemical engineering process and porous particles suspension. It's of great importance to evaluate the force between the fluid and the objects accurately. The momentum exchange method which is efficient and easy for implementation is widely used to determine the force in lattice Boltzmann method. In this work we propose an efficient momentum exchange method to calculate the force by analyzing the exchange process of the fluid and the object. The method is validated by simulating the flows over a porous object at the pore scale, and the method is also extended for fluid-object interaction at scale. Simulations of flows over a square cylinder at different Reynolds numbers are conducted, and the viability of the method is confirmed by the numerical results.
引文
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2 Machado R.Numerical simulations of surface reaction in porous media with lattice Boltzmann.Chemical Engineer Science,2012,69(1):628-643
3 Bohn CD,Scott SA,Dennis JS,et al.Validation of a lattice Boltzmann model for gas-solid reaction with experiments.Journal of Computational Physics,2012,231(16):5334-5350
4 Abade GC,Cichocki B,Ekiel-Jezewska ML,et al.Short-time dynamics of permeable particles in concentrated suspensions.The Journal of Chemical Physics,2010,132(1):014503
5 Abade GC,Cichocki B,Ekiel-Jezewska ML,et al.Diffusion,sedimen-tation,and rheology of concentrated suspensions of coreshell particles.The Journal of Chemical Physics,2012,136(10):104906
6 Davis RW,Moore EF.A numerical study of vortex shedding from rectangles.Journal of Fluid Mechanics,1986,116(3):475-506
7 Norberg C.Flow around rectangle cylinder:Pressure forces and frequencies.Journal of Wind Engineer and Industrial Aerodynamics,1993,49(1):187-196
8 Singh AP,De AK,Carpenter VK,et al.Flow past a transversely square cylinder in free stream at low Reynolds number.International Journal for Numerical Methods in Fluids,2009,61(6):658-682
9 毕继红,余化军,任洪鹏.静止方柱和圆柱绕流的数值分析.三峡大学学报(自然科学版),2012,34(1):41-45(Bi Jihong,Yu Huajun,Ren Hongpeng.Two dimensional numerical simulation of flow over a static square cylinder and a static circular cylinder.Journal of China Three Gorges University(Natural Sciences),2012,34(1):4-45(in Chinese))
10 Johnson TA,Patel VC.Flow past a sphere up to a Reynolds number of 300.Journal of Fluid Mechanics,1999,378:19-70
11 Yu DZ,Mei RW,Luo LS,et al.Viscous flow computations with the method of lattice Boltzmann equation.Progress in Aerospace Sciences,2003,39(5):329-367
12 Guo ZL,Liu HW,Luo LS,et al.A comparative study of the LBE and GKS methods for 2D near incompressible laminar flows.Journal of Computational Physics,2008,227(10):4955-4976
13 Zhou H,Mo GY,Cen KF.Numerical investigation of dispersed gassolid two-phase flow around a circular cylinder using lattice Boltzmann method.Computer&Fluids,2011,52:130-138
14 Wang L,Guo ZL,Shi BC,et al.Evaluation of three lattice Boltzmann models for particulate flows.Communications in Computational Physics,2013,13(4):1151-1172
15 Mei RW,Yu DZ,Wei S,et al.Force evaluation in the lattice Boltzmann method involving curved geometry.Physics Review E,2002,65(4):041203
16 Li HB,Lu XY,Fang HP,et al.Force evaluations in lattice Boltzmann simulations with moving boundaries in two dimensions.Physics Review E,2004,70(2):026701
17 Jue TC.Numerical analysis of vortex shedding behind a porous square cylinder.International Journal of Numerical Methods for Heat and Fluid Flow,2004,14(5):649-663
18 Chen XB,Yu P,Winoto SH,et al.Numerical analysis for the flow past a porous square cylinder based on the stress-jump interfacialconditions.International Journal of Numerical Methods for Heat and Fluid Flow,2008,18(5):635-655
19 d’Humieres D.Generalized lattice Boltzmann equation.Progress Aercant Astronant,1992,159:450-458
20 Lallemand P,Luo LS.Theory of lattice Boltzmann method:Dispersion,dissipation,isotropy,Galilean invariance,and stability.Physics Review E,2000,61(6):6546-6562
21 d’Humieres D,Ginzberg I,Krafczyk M,et al.Multiple-relaxationtime lattice Boltzmann models in three dimensions.Philosophical Transactions of the Royal Society of London.Series A:Mathematical,Physical and Engineering Sciences,2002,360(1792):437-451
22 Chai ZH,Shi BC,Zheng L.Simulating high Reynolds number flow in two-dimensional lid-drive cavity by multi-relaxation-time lattice Boltzmann method.Chinese Physics,2006,15(8):1855-1863
23 Pan CX,Luo LS,Miller CT.An evaluation of lattice Boltzmann schemes for porous medium flow simulation.Computers&Fluids,2006,35(8):898-909
24 He XY,Luo LS.Lattice Boltzmann model for the incompressible Navier-Stokes equation.Journal Statistical Physics,1997,88(3-4):927-944
25 Guo ZL,Zhao TS.Lattice Boltzmann method for incompressible flows through porous media.Physics Review E,2002,66(3):036304
2 Machado R.Numerical simulations of surface reaction in porous media with lattice Boltzmann.Chemical Engineer Science,2012,69(1):628-643
3 Bohn CD,Scott SA,Dennis JS,et al.Validation of a lattice Boltzmann model for gas-solid reaction with experiments.Journal of Computational Physics,2012,231(16):5334-5350
4 Abade GC,Cichocki B,Ekiel-Jezewska ML,et al.Short-time dynamics of permeable particles in concentrated suspensions.The Journal of Chemical Physics,2010,132(1):014503
5 Abade GC,Cichocki B,Ekiel-Jezewska ML,et al.Diffusion,sedimen-tation,and rheology of concentrated suspensions of coreshell particles.The Journal of Chemical Physics,2012,136(10):104906
6 Davis RW,Moore EF.A numerical study of vortex shedding from rectangles.Journal of Fluid Mechanics,1986,116(3):475-506
7 Norberg C.Flow around rectangle cylinder:Pressure forces and frequencies.Journal of Wind Engineer and Industrial Aerodynamics,1993,49(1):187-196
8 Singh AP,De AK,Carpenter VK,et al.Flow past a transversely square cylinder in free stream at low Reynolds number.International Journal for Numerical Methods in Fluids,2009,61(6):658-682
9 毕继红,余化军,任洪鹏.静止方柱和圆柱绕流的数值分析.三峡大学学报(自然科学版),2012,34(1):41-45(Bi Jihong,Yu Huajun,Ren Hongpeng.Two dimensional numerical simulation of flow over a static square cylinder and a static circular cylinder.Journal of China Three Gorges University(Natural Sciences),2012,34(1):4-45(in Chinese))
10 Johnson TA,Patel VC.Flow past a sphere up to a Reynolds number of 300.Journal of Fluid Mechanics,1999,378:19-70
11 Yu DZ,Mei RW,Luo LS,et al.Viscous flow computations with the method of lattice Boltzmann equation.Progress in Aerospace Sciences,2003,39(5):329-367
12 Guo ZL,Liu HW,Luo LS,et al.A comparative study of the LBE and GKS methods for 2D near incompressible laminar flows.Journal of Computational Physics,2008,227(10):4955-4976
13 Zhou H,Mo GY,Cen KF.Numerical investigation of dispersed gassolid two-phase flow around a circular cylinder using lattice Boltzmann method.Computer&Fluids,2011,52:130-138
14 Wang L,Guo ZL,Shi BC,et al.Evaluation of three lattice Boltzmann models for particulate flows.Communications in Computational Physics,2013,13(4):1151-1172
15 Mei RW,Yu DZ,Wei S,et al.Force evaluation in the lattice Boltzmann method involving curved geometry.Physics Review E,2002,65(4):041203
16 Li HB,Lu XY,Fang HP,et al.Force evaluations in lattice Boltzmann simulations with moving boundaries in two dimensions.Physics Review E,2004,70(2):026701
17 Jue TC.Numerical analysis of vortex shedding behind a porous square cylinder.International Journal of Numerical Methods for Heat and Fluid Flow,2004,14(5):649-663
18 Chen XB,Yu P,Winoto SH,et al.Numerical analysis for the flow past a porous square cylinder based on the stress-jump interfacialconditions.International Journal of Numerical Methods for Heat and Fluid Flow,2008,18(5):635-655
19 d’Humieres D.Generalized lattice Boltzmann equation.Progress Aercant Astronant,1992,159:450-458
20 Lallemand P,Luo LS.Theory of lattice Boltzmann method:Dispersion,dissipation,isotropy,Galilean invariance,and stability.Physics Review E,2000,61(6):6546-6562
21 d’Humieres D,Ginzberg I,Krafczyk M,et al.Multiple-relaxationtime lattice Boltzmann models in three dimensions.Philosophical Transactions of the Royal Society of London.Series A:Mathematical,Physical and Engineering Sciences,2002,360(1792):437-451
22 Chai ZH,Shi BC,Zheng L.Simulating high Reynolds number flow in two-dimensional lid-drive cavity by multi-relaxation-time lattice Boltzmann method.Chinese Physics,2006,15(8):1855-1863
23 Pan CX,Luo LS,Miller CT.An evaluation of lattice Boltzmann schemes for porous medium flow simulation.Computers&Fluids,2006,35(8):898-909
24 He XY,Luo LS.Lattice Boltzmann model for the incompressible Navier-Stokes equation.Journal Statistical Physics,1997,88(3-4):927-944
25 Guo ZL,Zhao TS.Lattice Boltzmann method for incompressible flows through porous media.Physics Review E,2002,66(3):036304