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
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摘要
为了研究土体的细观渗流特性,假设土体是完全饱和且在渗流过程中水分的流动始终处于层流状态。考虑宏观统计参数(孔隙率、渗透率及有效黏滞系数等)的影响,基于表征体元(REV)尺度的格子博尔兹曼(Boltzmann)方法,建立了压力作用下土体细观渗流的数值模型。采用D2Q9模型考虑水分流动的离散速度分布,宏观边界条件为左右侧面为不透水边界(0)x yu=u=,上下边界设置不同的密度来控制压力边界,在微观边界条件上采用非平衡态外推格式。编制相应的计算程序,将计算区域内的多孔介质材料设置成流体(孔隙率φ=1.0,渗透率K=∞),验证了经典的Poiseuille流。此外,结合算例分别讨论了土体在压力作用下孔隙率、渗透率及渗透压力等影响因素与渗流速度的相互关系,研究表明该数值方法与Darcy定律得到的计算结果较为吻合。因此,基于REV尺度的格子Boltzmann方法可以有效地模拟土体的渗流机制,为进一步研究土体渗流特性提供了一种新的研究手段。
In order to study seepage mechanism of soil, there are some basic assumptions, the soil is saturated, and flow is laminar in the process of seepage. Based on lattice Boltzmann method at the representative elementary volume(REV) scale, the mesoscopic seepage numerical model of soil under pressure is established, considering the effects of macroscopic statistical parameters, i.e. porosity, permeability and effective viscosity coefficient. The D2Q9 model is applied for the discrete velocity direction. In the macroscopic boundary condition, it is impermeable in the left and right sides; and it is controlled by pressure in the upper and lower boundaries, which is decided by setting different density. And the non- equilibrium extrapolation scheme is used in the microscopic boundary. The porous media is set to be fluid in the study region by letting φ = 1.0 and K = ∞, the corresponding program is compiled to verify the Poiseuille flow. Combined with an example, the influence of porosity, permeability and seepage pressure on the seepage velocity driven by pressure is discussed for soil, and the results of this paper are in good agreement with that calculated by Darcy's law. Therefore, lattice Boltzmann method at the REV scale could effectively simulate the seepage characteristics of soil, and it provides a new research approach for further study of seepage mechanism.
In order to study seepage mechanism of soil, there are some basic assumptions, the soil is saturated, and flow is laminar in the process of seepage. Based on lattice Boltzmann method at the representative elementary volume(REV) scale, the mesoscopic seepage numerical model of soil under pressure is established, considering the effects of macroscopic statistical parameters, i.e. porosity, permeability and effective viscosity coefficient. The D2Q9 model is applied for the discrete velocity direction. In the macroscopic boundary condition, it is impermeable in the left and right sides; and it is controlled by pressure in the upper and lower boundaries, which is decided by setting different density. And the non- equilibrium extrapolation scheme is used in the microscopic boundary. The porous media is set to be fluid in the study region by letting φ = 1.0 and K = ∞, the corresponding program is compiled to verify the Poiseuille flow. Combined with an example, the influence of porosity, permeability and seepage pressure on the seepage velocity driven by pressure is discussed for soil, and the results of this paper are in good agreement with that calculated by Darcy's law. Therefore, lattice Boltzmann method at the REV scale could effectively simulate the seepage characteristics of soil, and it provides a new research approach for further study of seepage mechanism.
引文
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[11]SUKOP M C,THORNE D T.Lattice Boltzmann modeling:An introduction for geoscientists and engineers[M].Berlin:Springer Verlag,2006.
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[16]邓英尔,刘慈群,黄润秋,等.高等渗流理论与方法[M].北京:科学出版社,2004.
[2]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.
[3]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.
[4]鲁建华.基于格子Boltzmann方法的多孔介质内流动与传热的微观模拟[D].武汉:华中科技大学,2009.
[5]荣伏梅.基于格子Boltzmann方法的多孔介质REV尺度的流动与强化传热研究[D].武汉:华中科技大学,2011.
[6]张霞,李凤滨,盛金昌,等.格子Boltzmann方法模拟土体渗流场研究[J].水电能源科学,2012,30(10):61-64.ZHANG Xia,LI Feng-bin,SHENG Jin-chang,et al.Lattice Boltzmann method for simulation seepage field of\ssoil[J].Water Resources and Power,2012,30(10):61-64.
[7]YAN Wei-wei,LIU Yang,XU You-sheng,et al.Numerical simulation of air flow through a biofilter with\sheterogeneous porous media[J].Bioresource Technology,2008,99(7):2156-2161.
[8]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.
[9]朱益华,陶果,方伟,等.3D多孔介质渗流率的格子Boltzmann模拟[J].测井技术,2008,32(1):25-28.ZHU Yi-hua,TAO Guo,FANG Wei.Lattice Boltzmann\ssimulation of permeability in 3D porous medium[J].Well\sLogging Technology,2008,32(1):25-28.
[10]杨佳庆.格子Boltzmann方法的细观渗流数值模拟[D].合肥:中国科学技术大学,2010.
[11]SUKOP M C,THORNE D T.Lattice Boltzmann modeling:An introduction for geoscientists and engineers[M].Berlin:Springer Verlag,2006.
[12]NITHIARASU P,SEETHARAMU K N,SUND-ARARAGJAN T.Natural convective heat transfer in a\sfluid saturated variable porosity medium[J].International Journal of Heat and Mass Transfer,1997,40(16):3955-3967.
[13]ERGUN S.Fluid flow through packed columns[J].Chemical Engineering Progress,1952,48(2):89-94.
[14]QIAN Y H,D’HUMIèRES D,LALLEMAND P.Lattice\sBGK model for Navier-Stokes equation[J].Europhysics\sLetters,1992,17(6):479-484.
[15]GUO Zhao-li,ZHENG Chu-guang,SHI Bao-chang.Non-equilibrium extrapolation method for velocity and\spressure boundary conditions in the lattice Boltzmann\smethod[J].Chinese Physics,2002,11(4):366-374.
[16]邓英尔,刘慈群,黄润秋,等.高等渗流理论与方法[M].北京:科学出版社,2004.