微尺度稀薄效应下颗粒沉降的格子Boltzmann方法模拟
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摘要
基于多松弛格子Boltzmann模型,对竖直细长微通道内颗粒自由沉降过程进行模拟,分析气体稀薄效应、初始位置以及颗粒间相互作用对微颗粒沉降特性的影响.研究表明:随Knudsen数增大,微通道内气体稀薄效应增强,颗粒表面气体滑移速度增大,气相流体有效粘度减小,颗粒相同运动状态下受到气体阻力相应减小,颗粒沉降平衡速度明显增大;不同初始位置颗粒沉降过程存在明显差异,初始位置偏离中心线颗粒将发生水平方向位移且呈振荡趋势,最终稳定于中心线平衡位置;在微尺度双颗粒沉降DKT现象过程中,气体稀薄效应影响颗粒运动特性,后颗粒跟随过程明显增长.
Sedimentation of micro particles in a narrow microchannel was simulated with multiple-relaxation-time lattice Boltzmann model. Influence of gas rarefaction, initial position of particle and interaction between particles on sedimentation process is analyzed. It is found that gas rarefaction effect becomes obvious with increase of Knudsen number. And the effective viscosity of gas is decreased. At the same time, slip velocity on the surface of particle increases and viscosity resistance of particle decreases, which results in an increase of particle equilibrium velocity. For different initial positions of particle, there exists a significant difference in sedimentation process. It reveals that horizontal motion of micro particle exists besides moving in the vertical direction. And the particle has oscillating tendency before stabilizing on the central position in horizontal direction. For DKT phenomenon in microscale, rarefaction effect is obvious on trajectory of particles and the drafting process is prolonged.
Sedimentation of micro particles in a narrow microchannel was simulated with multiple-relaxation-time lattice Boltzmann model. Influence of gas rarefaction, initial position of particle and interaction between particles on sedimentation process is analyzed. It is found that gas rarefaction effect becomes obvious with increase of Knudsen number. And the effective viscosity of gas is decreased. At the same time, slip velocity on the surface of particle increases and viscosity resistance of particle decreases, which results in an increase of particle equilibrium velocity. For different initial positions of particle, there exists a significant difference in sedimentation process. It reveals that horizontal motion of micro particle exists besides moving in the vertical direction. And the particle has oscillating tendency before stabilizing on the central position in horizontal direction. For DKT phenomenon in microscale, rarefaction effect is obvious on trajectory of particles and the drafting process is prolonged.
引文
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[2] HEINE D,GREST G,PETERSEN M.Effect of particle shape and charge on bulk rheology of nanoparticle suspensions[J].Journal of Chemical Physics,2010,132(18):9234.
[3] WU J,SHU C.Particulate flow simulation via a boundary condition-enforced immersed boundary-lattice Boltzmann scheme[J].Communications in Computational Physics,2010,7(4):793-812.
[4] FENG J,HU H H,JOSEPH D D.Direct simulation of initial value problems for the motion of solid bodies in a Newtonian fluid Part 1:Sedimentation[J].Journal of Fluid Mechanics,1994,261(1):95-134.
[5] NIE D,LIN J Z.A LB-DF/FD method for particle suspensions[J].Communications in Computational Physics,2010,7(3):544-563.
[6] YAN R Q,CHEN L P,ZHOU B.Lattice Boltzmann simulation on motion characteristics of indoor respirable particles[J].Chinese Journal of Computational Physics,2016,33(6):698-706.
[7] NIE D M,LIN J Z.Brownian motion of non-spherical particles:Fluctuating lattice Boltzmann investigation[J].Chinese Journal of Computational Physics,2012,29(1):101-107.
[8] LIN J Z,SHAO X M,SHI X,et al.Study on the interaction of sedimenting cylindrical particles in still fluid[J].Acta Mechanica Sinica,2004,20(1):32-45.
[9] LEE M P,GIBSON G M,PHILLIPS D,et al.Dynamic stereo microscopy for studying particle sedimentation[J].Optics Express,2014,22(4):4671.
[10] ZOUAOUI S,DJEBOURI H,BILEK A,et al.Modelling and simulation of solid particle sedimentation in an incompressible Newtonian fluid[J].Mathematics in Computer Science,2017,11(2):527-539.
[11] ARDEKANI M N,COSTA P,BREUGEM W P,et al.Numerical study of the sedimentation of spheroidal particles[J].International Journal of Multiphase Flow,2016,87:16-34.
[12] LUO H,POZRIKIDIS C.Interception of two spheres with slip surfaces in linear Stokes flow[J].Journal of Fluid Mechanics,2007,581(581):129-156.
[13] SUN Q,KLASEBOER E,KHOO B C,et al.Stokesian dynamics of pill-shaped janus particles with stick and slip boundary conditions[J].Physical Review E,2013,87(4):43009.
[14] TROFA M,D AVINO G,HULSEN M A,et al.Numerical simulations of the dynamics of a slippery particle in Newtonian and viscoelastic fluids subjected to shear and Poiseuille flows[J].Journal of Non-Newtonian Fluid Mechanics,2016,228:46-54.
[15] VERHAEGHE F,LUO L S,BLANPAIN B.Lattice Boltzmann modeling of microchannel flow in slip flow regime[J].Journal of Computational Physics,2009,228(1):147-157.
[16] GUO Z,ZHENG C.Analysis of lattice Boltzmann equation for microscale gas flows:Relaxation times,boundary conditions and the Knudsen layer[J].International Journal of Computational Fluid Dynamics,2008,22(7):465-473.
[17] TANG G H,TAO W Q,HE Y L.Lattice Boltzmann method for simulating gas flow in microchannels[J].International Journal of Modern Physics C,2004,15(2):335-347.
[18] LALLEMAND P,LUO L S.Theory of the lattice Boltzmann method:Dispersion,dissipation,isotropy,Galilean invariance,and stability[J].Physical Review E,2000,61(6):6546-6562.
[19] SUN Y,BARBER R W,EMERSON D R.Inverted velocity profiles in rarefied cylindrical Couette gas flow and the impact of the accommodation coefficient[J].Physics of Fluids,2005,17(4):047102.
[20] 顾娟,黄荣宗,刘振宇,等.一种滑移区气体流动的格子Boltzmann曲边界处理新格式[J].物理学报,2017,66(11):220-228.
[21] GUO Z,ZHENG C,SHI B.An extrapolation method for boundary conditions in lattice Boltzmann method[J].Physics of Fluids,2002,14(6):2007-2010.
[22] GUO Z,SHI B,ZHENG C.Velocity inversion of micro cylindrical Couette flow:A lattice Boltzmann study[J].Computers & Mathematics with Applications,2011,61(12):3519-3527.
[23] TAO S,GUO Z.Boundary condition for lattice Boltzmann modeling of microscale gas flows with curved walls in the slip regime[J].Physical Review E,2015,91:043305.
[24] HUANG R Z,WANG L,GUO Z L.Three boundary particulate flows in treatment schemes for lattice Boltzmann method[J].Chinese Journal of Computational Physics,2012,29(06):799-806.