格子Boltzmann方法对于大粘度差两相流的模拟
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摘要
为了模拟具有大粘度差的两相流,对Boltzmann(LB)方法中的伪势多组分模型进行了改进.伪势模型将粒子作用力转化为速度形式,再将其引入离散的LB方程.改进模型把力的添加形式变为将力离散处理后,引入离散的LB方程中,以此提高数值计算的稳定性.该模型能够比原伪势模型得到更小的虚假速度和更大的粘度差.通过对沥青-水的大粘度差两相流体和粘性指进现象的模拟,验证了改进模型的正确性和有效性.该模型具有较好的适用性,它能模拟的两相流体最大粘度差可达到4 510倍.
The pseudo-potential multi-component model in Lattice Boltzmann(LB)Method is improved to simulate twophase flow with large viscosity difference.In the pseudopotential model,the interparticle forces are turned into velocity form and introduced into the discrete LB equation.In the improved model,the interparticle forces are discretized and added to the discrete LB equation,which leads to the better numerical stability.The improved model can get smaller spurious velocity and larger viscosity difference than the pseudo-potential model.Simulation of asphalt-water twophase flow,which is with large viscosity difference,and fingering in a channel are carried out to validate the improved model.It has a good applicability for simulation of fluids with viscosity difference,and the maximal viscosity difference of two-phase fluids is 4510 times.
The pseudo-potential multi-component model in Lattice Boltzmann(LB)Method is improved to simulate twophase flow with large viscosity difference.In the pseudopotential model,the interparticle forces are turned into velocity form and introduced into the discrete LB equation.In the improved model,the interparticle forces are discretized and added to the discrete LB equation,which leads to the better numerical stability.The improved model can get smaller spurious velocity and larger viscosity difference than the pseudo-potential model.Simulation of asphalt-water twophase flow,which is with large viscosity difference,and fingering in a channel are carried out to validate the improved model.It has a good applicability for simulation of fluids with viscosity difference,and the maximal viscosity difference of two-phase fluids is 4510 times.
引文
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[14]Kang Q,Zhang D,Chen S.Immiscible displacement in a channel:simulations of fingering in two dimensions[J].Advances in Water Resources,2004,27(1):13.
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[17]Guo Z L,Zheng C G,Shi B C,etal.Discrete lattice effects on the forcing term in the Lattice Boltzmann Method[J].Physical Review E,2002,65(4):046308.
[18]Rothman D H,Keller J M.Immiscible cellular-automaton fluids[J].Journal of Statistical Physics,1988,52(3):1119.
[2]He G P,Wong W G.Effects of moisture on strength and permanent deformation of foamed asphalt mix incorporating RAP materials[J].Construction and Bulding Materials,2008,21(1):30.
[3]李峰,黄颂昌,徐剑.泡沫沥青衰变方程与发泡特性评价[J].同济大学学报:自然科学版,2011,39(7):1031.LI Feng,HUANG Songchang,XU Jian.Foamed bitumen decay equation and bitumen foaming characteristics evaluation[J].Journal of Tongji University:Natural Science,2011,39(7):1031.
[4]徐金枝,赫培文.沥青发泡性能评价指标及优化设计研究[J].建筑材料学报,2011,14(6):776.XU Jinzhi,HAO Peiwen.Research on the evaluation index and optimization design of asphalt foaming characteristics[J].Journal of Building Materials,2011,14(6):776.
[5]Aidun C K,Clausen J R.Lattice-boltzmann method for complex flows[J].Annual Review of Fluid Mechanics,2010,42:439.
[6]Zhang J.Lattice Boltzmann method for microfluidics:models and applications[J].Microfluidics and Nanofluidics,2011,10(1):1.
[7]Gunstensen A K,Rothman D H,Zaleski S,et al.Lattice Boltzmann model of immiscible fluids[J].Physical Review A,1991,43(8):4320.
[8]Shan X W,Chen H D.Lattice Boltzmann model for simulating flows with multiple phases and components[J].Physical Review E,1993,47(3):1815.
[9]Swift M R,Orlandini S E,Osborn W R,et al.Lattice Boltzmann simulations of liquid-gas and binary fluid systems[J].Physical Review E,1996,54(5):5041.
[10]Luo L S,Girimaji S S.Lattice Boltzmann model for binary mixtures[J].Physical Review E,2002,66(3):035301.
[11]Shan X W,Doolen G.Multicomponent Lattice Boltzmann model with interparticle interaction[J].Journal of Statistical and Physics,1995,81(1):379.
[12]Shan X W.Multi-component Lattice Boltzmann model from continuum kinetic theory[J].Physical Review E,2010,81(4):045701.
[13]Shan X W.Analysis and reduction of the spurious current in a class of multiphase Lattice Boltzmann models[J].Physical Review E,2006,73(4):047701.
[14]Kang Q,Zhang D,Chen S.Immiscible displacement in a channel:simulations of fingering in two dimensions[J].Advances in Water Resources,2004,27(1):13.
[15]Kupershtokh A L.Criterion of numerical instability of liquid state in LBE simulations[J].Computers and Mathematics with Applications,2010,59(7):2236.
[16]Martys N S,Chen H D.Simulation of multicomponent fluids in complex three-dimensional geometries by the Lattice Boltzmann method[J].Physical Review E,1996,53(1):743.
[17]Guo Z L,Zheng C G,Shi B C,etal.Discrete lattice effects on the forcing term in the Lattice Boltzmann Method[J].Physical Review E,2002,65(4):046308.
[18]Rothman D H,Keller J M.Immiscible cellular-automaton fluids[J].Journal of Statistical Physics,1988,52(3):1119.