CFD-DEM耦合计算中的体积分数算法
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摘要
CFD-DEM耦合方法已越来越广泛地应用于多相流研究,流体体积分数模型是其连接宏观尺度(连续介质)与微观尺度(离散介质)的桥梁。该文提出了一种基于特征点剖分的SKM(statistical kernel method)改进型体积分数算法,通过在颗粒空间影响范围的三维方向上布置特征点,实现对所影响CFD网格的标记和对颗粒体积的分解,将CFD网格的迭代搜索转化为空间特征点的识别;结合算法参数优化,有效解决传统算法在并行计算中内部边界处的截断误差,显著提升计算效率。数值实验表明:改进的算法可以有效处理颗粒粒径D与CFD网格尺寸L相当时的情形,覆盖传统的颗粒不解析(unresolved particle,L>>D)耦合方法与颗粒解析(resolved particle,D>>L)耦合方法间的过渡区域。该算法有助于拓展CFD-DEM耦合计算中颗粒粒径的适用范围,在大规模固液耦合模拟计算中具有广泛应用前景。
The coupled CFD-DEM method has been widely used for multiphase flows where the fluid volume fraction links the continuous medium(fluid)and the discrete medium(particles).This paper presents an improved volume fraction allocation algorithm based on the traditional SKM(statistical kernel method)model with subdividing of the characteristic points. Spatially distributed characteristic points within the region influenced by aparticle mark all the CFD cells influenced by the particle so that the particle volume is correctly decomposed into each CFD cell.A traditional grid search algorithm then recognizes the characteristic points.After calibration of the model parameters,the algorithm reduces the truncation error at inner boundaries in parallel computing models.Numerical tests show that the algorithm is effective and efficient when the particle diameter size Dand the CFD cell size Lare of the same order of magnitude.The model reverts to the traditional unresolved particle model for L>>D and to the resolved particle model for D>>L.The algorithm improves coupled CFD-DEM calculations having a wide range of particle diameters to improve solid-liquid two-phase flow simulations.
The coupled CFD-DEM method has been widely used for multiphase flows where the fluid volume fraction links the continuous medium(fluid)and the discrete medium(particles).This paper presents an improved volume fraction allocation algorithm based on the traditional SKM(statistical kernel method)model with subdividing of the characteristic points. Spatially distributed characteristic points within the region influenced by aparticle mark all the CFD cells influenced by the particle so that the particle volume is correctly decomposed into each CFD cell.A traditional grid search algorithm then recognizes the characteristic points.After calibration of the model parameters,the algorithm reduces the truncation error at inner boundaries in parallel computing models.Numerical tests show that the algorithm is effective and efficient when the particle diameter size Dand the CFD cell size Lare of the same order of magnitude.The model reverts to the traditional unresolved particle model for L>>D and to the resolved particle model for D>>L.The algorithm improves coupled CFD-DEM calculations having a wide range of particle diameters to improve solid-liquid two-phase flow simulations.
引文
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[2]XIAO Shaoping,Belytschko T.A bridging domain method for coupling continua with molecular dynamics[J].Computer Methods in Applied Mechanics&Engineering,2004,193(17-20):1645-1669.
[3]PENG Zhengbiao,Doroodchi E,LUO Caimao,et al.Influence of void fraction calculation on fidelity of CFD-DEM simulation of gas-solid bubbling fluidized beds[J].AIChE Journal,2014,60(6):2000-2018.
[4]ZHU Haiping,YU Aibing.The effects of wall and rolling resistance on the couple stress of granular materials in vertical flow[J].Physica A:Statistical Mechanics and Its Applications,2003,325(3):347-360.
[5]WU Chunliang,Berrouk A S,Nandakumar K.Three-dimensional discrete particle model for gas-solid fluidized beds on unstructured mesh[J].Chemical Engineering Journal,2009,152(2-3):514-529.
[6]XIAO Heng,SUN Rui.Algorithms in a robust hybrid CFD-DEM solver for particle-laden flows[J].Communications in Computational Physics,2011,9(2):297-323.
[7]ZHU Haiping,YU Aibing.Averaging method of granular materials[J].Physical Review E Statistical Nonlinear&Soft Matter Physics,2002,66(2):404-409.
[8]Babic M.Average balance equations for granular materials[J].International Journal of Engineering Science,1997,35(5):523-548.
[9]Duggleby A,Camp J L,Doron Y,et al.Massively parallel computational fluid dynamics with large eddy simulation in complex geometries[C]//ASME 2011 International Mechanical Engineering Congress and Exposition.New York,USA:American Society of Mechanical Engineers,2011:817-824.
[10]Walker D W,Dongarra J J.MPI:A standard message passing interface[J].Supercomputer,1996,12:56-68.
[11]Ries A,Brendel L,Wolf D E.Coarse graining strategies at walls[J].Computational Particle Mechanics,2014,1(2):177-190.
[12]Steinhaus H.Mathematical Snapshots[M].New York:USA Dover,1999.
[13]Wells D G.The Penguin Dictionary of Curious and Interesting Numbers[M].London:Penguin Books,1986.
[14]SUN Rui,XIAO Heng.Diffusion-based coarse graining in hybrid continuum-discrete solvers:Theoretical formulation and a priori tests[J].International Journal of Multiphase Flow,2015,77:142-157.
[15]SUN Jin,XIAO Heng,GAO Donghong.Numerical study of segregation using multiscale models[J].International Journal of Computational Fluid Dynamics,2009,23(2):81-92.
[16]Concha A F.Settling velocities of particulate systems[J].Kona Powder and Particle Journal,2009,27:18-37.
[17]Cate A T,Nieuwstad C H,Derksen J J,et al.Particle imaging velocimetry experiments and lattice—Boltzmann simulations on a single sphere settling under gravity[J].Physics of Fluids,2002,14(11):4012-4025.
[18]Peskin C S.Flow patterns around heart valves:A numerical method[J].Journal of Computational Physics,1972,10(2):252-271.