基于格子Boltzmann方法土体CT扫描切片细观渗流场的数值模拟
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摘要
基于格子Boltzmann方法,采用D2Q9基本模型,上、下边界采用非平衡外推格式,左、右不透水边界及土颗粒采用反弹格式设置边界条件,对土体细观渗流场进行数值模拟。首先将试验测得物理单位的数据转化为格子单位,然后用Matlab编制程序,对CT扫描切片进行处理,生成土体细观的数据结构,最后把格子单位表示的结果再转为物理单位,分析了渗流流速的变化规律,得到了整体和局部渗流场的分布情况。分析结果表明:(1)孔道处的流速U随着入渗时间的延长而逐渐达到一个相对稳定值,进而得到流体从开始入渗至稳定状态经历的准确时间T;(2)平均渗流速度由入口处沿y轴负方向逐渐递减,且小于入口处的平均渗流流速;(3)渗流量主要受控于通道的连通性、孔隙大小,最大渗流速度集中在通道的窄孔道处,封闭的孔道和孔隙渗流速度为0。格子Boltzmann方法能有效地对CT扫描得到的2D切片进行数值模拟,可以定量、准确地研究真实土体渗流场的变化机制。
Mesoscopic seepage field of real soil is simulated based on lattice Boltzmann method. In this simulation, the basic model D2Q9 is used; and the inlet and outlet boundaries are constructed by setting the non-equilibrium extrapolation format. The soil particles boundary as well as left and right waterproof boundaries are set by the bounce-back format. At first, the data denoted by physical units from experiments are transformed into lattice units. According to data structure generated by CT scanned slices, the corresponding calculation program is applied to simulate mesoscopic seepage field of real soil. Finally, the results of lattice units are transform into physical units once again. The variation of seepage velocity is analyzed; and the whole and partial distributions of seepage field are obtained. The results show that: 1) Seepage velocity U finally reaches a relatively stable figure in pore channels over time. Accurate time T is obtained from the beginning of seepage to the steady-state of seepage. 2) The average seepage velocity gradually decreases along with the negative direction of y axis from the inlet boundary; and it is less than the average seepage velocity in inlet boundary. 3) The quantity of seepage is dominated by the connectivity and pore size of channels. The maximum seepage velocity is concentrated in a narrow channel. The velocity in closed pore channel and pore is zero. Lattice Boltzmann method is effective in simulating two dimensional CT scanned slice and can be used to research the mechanism of real seepage field quantitatively and accurately.
Mesoscopic seepage field of real soil is simulated based on lattice Boltzmann method. In this simulation, the basic model D2Q9 is used; and the inlet and outlet boundaries are constructed by setting the non-equilibrium extrapolation format. The soil particles boundary as well as left and right waterproof boundaries are set by the bounce-back format. At first, the data denoted by physical units from experiments are transformed into lattice units. According to data structure generated by CT scanned slices, the corresponding calculation program is applied to simulate mesoscopic seepage field of real soil. Finally, the results of lattice units are transform into physical units once again. The variation of seepage velocity is analyzed; and the whole and partial distributions of seepage field are obtained. The results show that: 1) Seepage velocity U finally reaches a relatively stable figure in pore channels over time. Accurate time T is obtained from the beginning of seepage to the steady-state of seepage. 2) The average seepage velocity gradually decreases along with the negative direction of y axis from the inlet boundary; and it is less than the average seepage velocity in inlet boundary. 3) The quantity of seepage is dominated by the connectivity and pore size of channels. The maximum seepage velocity is concentrated in a narrow channel. The velocity in closed pore channel and pore is zero. Lattice Boltzmann method is effective in simulating two dimensional CT scanned slice and can be used to research the mechanism of real seepage field quantitatively and accurately.
引文
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[3]钱吉裕,李强,宣益民,等.确定多孔介质流动参数的格子Boltzmann方法[J].工程热物理学报,2004,25(4):655-657.QIAN Ji-yu,LI Qing,XUAN Yi-min,et al.Application of lattice Boltzmann scheme on determining flow parameters of porous media[J].Journal of Engineering Thermophysics,2004,25(4):655-657.
[4]李广信.岩土工程50讲——岩坛漫话(第二版)[M].北京:人民交通出版社,2010.LI Guang-xin.Geotechniacal engineering 50 speaks—rock alters talk at random(second edition)[M].Beijing:China Communication Press,2010.
[5]申林方,王志良,李邵军.基于格子博尔兹曼方法表征体元尺度土体细观渗流场的数值模拟[J].岩土力学,2015,36(增刊2):689-694.SHEN Lin-fang,WANG Zhi-ling,LI Shao-Jun.Numerical simulation for mesoscopic seepage field of soil based on lattice Boltzmann method at REV scale[J].Rock and Soil Mechanics,2015,36(Supp.2):689-694.
[6]PAN C,LUO L S,MILLER C T.An evaluation of lattice Boltzmann schemes for porous medium flow simulation[J].Computers&Fluids,2006,35(8):898-909.
[7]GUO Z L,ZHENG C G,SHI B C.Non-equilibrium extrapolation method for velocity and pressure boundary conditions in the lattice Boltzmann method[J].Chinese Physics,2002,11(4):366.
[8]HILL R J,KOCH D L,LADD A J C.The first effects of fluid inertia on flows in ordered and random arrays of spheres[J].Journal of Fluid Mechanics,2001,448:213-241.
[9]SHU C,NIU X D,CHEW Y T,et al.A fractional step lattice Boltzmann method for simulating high Reynolds number flows[J].Mathematics and Computers in Simulation,2006,72(2):201-205.
[10]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.
[11]HE X,LUO L S.Theory of the lattice Boltzmann method:From the Boltzmann equation to the lattice Boltzmann equation[J].Physical Review E,1997,56(6):6811-6817.
[12]CHEN S,DOOLEN G D.Lattice Boltzmann method for fluid flows[J].Annual Review of Fluid Mechanics,1998,30(1):329-364.
[13]郭照立,郑楚光.格子Boltzmann方法的原理及应用[M].北京:科学出版社,2008:17-21.GUO Zhao-li,ZHENG Chu-guang.Principle and application of lattice Boltzmann method[M].Beijing:Science Press,2008:17-21.
[14]QIAN Yue-hong,D’HUMIères D,LALLEMAND P.Lattice BGK model for Navier-Stokes equation[J].Europhysics Letters,1992,17(6):479-484.
[15]何雅玲,王勇,李庆.格子Boltzmann方法的理论及应用[M].北京:科学出版社,2008.HE Ya-ling,WANG Yong,LI Ying.Lattice boltzmann method:Theory and applications[M].Beijing:Science Press,2008.