Simulating high Reynolds number flow in two-dimensional lid-driven cavity by multi-relaxation-time lattice Boltzmann method

By coupling the non-equilibrium extrapolation scheme for boundary condition with the multi-relaxation-time lattice Boltzmann method, this paper finds that the stability of the multi-relaxation-time model can be improved greatly, especially on simulating high Reynolds number (Re) flow. As a discovery, the super-stability analysed by Lallemand and Luo is verified and the complex structure of the cavity flow is also exhibited in our numerical simulation when Re is high enough. To the best knowledge of the authors, the maximum of Re which has been investigated by direct numerical simulation is only around 50,000 in the literature; however, this paper can readily extend the maximum to 1000,000 with the above combination.     

一种新的模拟渗流运动的数值方法

根据格子Boltzmann方法及相关理论，建立了一个新的模拟渗流运动的数值模型，所得模型没有在边界上采取相应平均措施，同时还避免了一些非物理副产品的出现-实例计算数值结果与精确解符合较好，证明模型可靠- 关键词： 渗流 格子Boltzmann方法 数值模型     

Numerical analysis of fluid flow through a cylinder array using a lattice Boltzmann model

In this paper we present a detailed computational study of an incompressible Newtonian fluid flow across a periodic array of two-dimensional cylinders which is a simplest non-trivial representation of a porous media. A two-dimensional Lattice Boltzmann Method is used to solve the governing Navier－Stokes equation taking into account of viscous dissipation effects and influence of nonlinear fluid drag. Both the flow fields and the Darcy－Forchheimer drag coefficient as a function of the solid volume fraction are calculated for a wide range of flow Reynolds numbers. The predictions were compared with the results from conventional numerical and empirical models for verification. Apart from confirming that inertial effects can cause a significant deviation from Darcy's law for large velocities the results also show that the characteristics of the vorticity field vary considerably as the Reynolds number increases, which will have major implications to the transport of passive particulate substances within the pores and their removal rate.     

Lattice Boltzmann model for interface capturing of multiphase flows based on Allen–Cahn equation

A phase-field-based lattice Boltzmann model is proposed for the interface capturing of multi-phase flows based on the conservative Allen–Cahn equation(ACE).By adopting the improved form of a relaxation matrix and an equilibrium distribution function,the time derivative?t(φ)induced by recovering the diffusion term in ACE is eliminated.The conducted Chapman–Enskog analysis demonstrates that the correct conservative ACE is recovered.Four benchmark cases including Zalesak’s disk rotation,vortex droplet,droplet impact on thin film,and Rayleigh–Taylor instability are investigated to validate the proposed model.The numerical results indicate that the proposed model can accurately describe the complex interface deformation.     

Lattice Boltzmann Simulation of Convection in a Porous Medium with Temperature Jump and Velocity Slip Boundary Conditions

To investigate the convection in a porous medium, a horizontal quiescent layer of one fluid saturating a porous medium heated from bottom is numerically studied using single lattice-Boltzmann method (LBM) and the generalized Navier-Stokes equation proposed by Nithiarasu et al. [P. Nithiarasu, K.M. Seetharamu, and T Sundararajan, Int. J. Heat Mass Trans. 40 (1997) 3955]. Due to the rarefaction, the boundary conditions are considered as both temperature jump and velocity slip. The computational results are validated against the analytical results, and excellent agreement has been obtained. The results have shown that the Rayleigh number is increased with increasing temperature jump, the stabilization effect of temperature is much more significant than that of velocity slip, and the computation stability of present model is better than that of Darcy and Brinkman models.     

微尺度振荡Couette流的格子Boltzmann模拟

采用有效多松弛时间-格子Boltzmann方法(Effective MRT-LBM)数值模拟了微尺度条件下的振荡Couette和Poiseuille流动. 在微流动LBM中引入Knudsen边界层模型,对松弛时间进行修正. 模拟时平板或外力以正弦周期振动,Couette流中考虑了单平板振动、上下板同相振动这两类情况. 研究结果表明,修正后的MRT-LBM模型能有效用于这类非平衡的微尺度流动模拟;对于Couette流,随着Kn数的增大,壁面滑移效应变得越明显. St越大,板间速度剖面的非线性特性越剧烈;两板同相振荡时,若Kn,St均较小,板间流体受到平板拖动剪切的影响很小,板间速度几乎重叠在一起;在振荡Poiseuille流动中,St数增大到一定值时,相位滞后现象减弱;相对于Kn数,St数对振荡Couette 和Poiseuille流中不同位置处速度相位差的产生有较大影响. 关键词： 格子Boltzmann方法 有效MRT模型 Knudsen层 振荡流     

Lattice Boltzmann simulation of fluid flows in two-dimensional channel with complex geometries

Boundary conditions (BCs) play an essential role in lattice Boltzmann (LB) simulations. This paper investigates several most commonly applied BCs by evaluating the relative L₂-norm errors of the LB simulations for two-dimensional (2-D) Poiseuille flow. It is found that the relative L₂-norm error resulting from FHML's BC is smaller than that from other BCs as a whole. Then, based on the FHML's BC, it formulates an LB model for simulating fluid flows in 2-D channel with complex geometries. Afterwards, the flows between two inclined plates, in a pulmonary blood vessel and in a blood vessel with local expansion region, are simulated. The numerical results are in good agreement with the analytical predictions and clearly show that the model is effective. It is expected that the model can be extended to simulate some real biologic flows, such as blood flows in arteries, vessels with stenosises, aneurysms and bifurcations, etc.     

具有多孔介质覆面层的柱体绕流流场分析

建立多孔结构覆面柱体绕流模型, 采用含Darcy-Brinkman-Forchheimer作用力项的格子Boltzmann方程对覆盖多孔介质层的方柱绕流进行数值模拟, 研究多孔介质对钝体绕流流场特性的影响。结果表明: 相比于不可渗透壁的柱体, 引入合适参数的多孔介质覆面层后可以有效降低其升力脉动幅值, 但阻力有所增加。同时, 较高雷诺数下多孔方柱的数值模拟表明: 多孔介质壁面使得尾迹区域的剪切层相距更远, 降低了尾流处湍动能, 并将雷诺应力的峰值移动到尾迹区域, 抑制了方柱两侧的动量交换, 使动量交换的位置发生在尾迹区域, 继而使得尾迹的涡街更加规则化。     

多孔介质内交变流动与换热的格子Boltzmann研究

针对制约脉冲管制冷机效率提高的蓄冷器内交变流动与换热问题,本文使用格子Boltzmann方法计算并分析了多孔介质内交变流动与换热特性。结果表明,交变流动压力波振幅对速度与压力和温度间的相位差的影响很小;通道界面处速度与压力的相位差在某一孔隙率下有一极小值;多孔介质内最大阻力系数与雷诺数的关系可以为设计蓄冷器时填料结构的...     

多孔介质中流体流动及扩散的耦合格子Boltzmann模型

多孔介质中高Péclet数和大黏性比下混溶流体的流动和扩散广泛存在于二氧化碳驱油、化工生产等工业过程中.用数值方法对该问题进行研究时,关键在于如何正确描述高Péclet数和大黏性比下多孔介质内流体的行为.为此,提出了一种基于多松弛模型和格子动理模型的耦合格子Boltzmann模型.通过Chapman-Enskog分析,证明该模型能有效求解不可压Navier-Stokes方程和对流扩散方程.数值结果表明,该模型不仅具有二阶精度和良好的稳健性,而且对于高Péclet数和大黏性比的问题具有良好的数值稳定性,为模拟此类问题提供了有效工具.     

用晶格玻尔兹曼方法研究颗粒在涡流中的运动

用晶格玻尔兹曼方法研究小颗粒在涡流中的运动.涡流由流经空腔的流体产生.用动量交换法和压力张量积分法计算颗粒在涡流中的运动轨迹、速度和角速度.最后用张量积分法计算两个不同半径的颗粒在涡流中的运动. 关键词： 晶格玻尔兹曼方法 涡流 颗粒     

Simulations of Bingham plastic flows with the multiple-relaxation-time lattice Boltzmann model

Fresh cement mortar is a type of workable paste,which can be well approximated as a Bingham plastic and whose flow behavior is of major concern in engineering.In this paper,Papanastasiou’s model for Bingham fluids is solved by using the multiplerelaxation-time lattice Boltzmann model(MRT-LB).Analysis of the stress growth exponent m in Bingham fluid flow simulations shows that Papanastasiou’s model provides a good approximation of realistic Bingham plastics for values of m108.For lower values of m,Papanastasiou’s model is valid for fluids between Bingham and Newtonian fluids.The MRT-LB model is validated by two benchmark problems:2D steady Poiseuille flows and lid-driven cavity flows.Comparing the numerical results of the velocity distributions with corresponding analytical solutions shows that the MRT-LB model is appropriate for studying Bingham fluids while also providing better numerical stability.We further apply the MRT-LB model to simulate flow through a sudden expansion channel and the flow surrounding a round particle.Besides the rich flow structures obtained in this work,the dynamics fluid force on the round particle is calculated.Results show that both the Reynolds number Re and the Bingham number Bn afect the drag coefcients CD,and a drag coefcient with Re and Bn being taken into account is proposed.The relationship of Bn and the ratio of unyielded zone thickness to particle diameter is also analyzed.Finally,the Bingham fluid flowing around a set of randomly dispersed particles is simulated to obtain the apparent viscosity and velocity fields.These results help simulation of fresh concrete flowing in porous media.     

两相方腔流的格子Boltzmann模拟

利用基于Shan-Chen多相模型的格子Boltzmann方法对方腔内上板拖动的两相流动问题开展较为系统的数值模拟,详细研究雷诺数(Re),毛细数(Ca)和壁面润湿性对流动以及混合特性的影响.结果表明:Re数、Ca数越大,方腔内两相流体的混合界面长度越大,混合效果越好.另外,壁面憎水程度越高,混合界面长度增加越快,然而对于强亲水壁面,混合界面长度最终趋于一常数.     

方腔内微细颗粒物运动特性的格子Boltzmann方法模拟

对Masselot and Chopard提出的模拟气固两相流动的格子Boltzmann-格子气(LBE-LGA)方法进行推广,能够反映两相间拖曳作用.利用该方法研究封闭方腔内的气固两相流运动特性,分析斯托克斯数St和模拟颗粒数目对颗粒群运动的影响,并与文献结果进行比较,表明LBE-LGA方法模拟颗粒运动是可行的.     

有限雷诺数情况下微槽道可压缩流动滑移流模型稳定性的数值模似

通过对微槽道一阶滑移流模型稳定性的理论研究，发现在不可压缩流和雷诺数趋于零的情况下，当Knudsen数Kn大于1／9时，会出现不稳定现象．这一理论结论在可压缩流和有限雷诺数情况下是否成立，尚不清楚，采用成熟的计算方法，用数值计算来研究可压缩流和有限雷诺数情况下一阶滑移流模型的稳定性，发现随着雷诺数的减小，不稳定的临界Knudsen数也不断减小，逐渐趋近于在不可压缩流和雷诺数趋于零的情况下得到的理论分析结果。     

底部局部加热多孔介质自然对流传热的格子Boltzmann模拟

运用格子Boltzmann方法研究了底部局部加热多孔介质方腔的自然对流传热.方腔的上壁面为低温热源,下壁面为局部高温热源,左右壁面为绝热条件.重点分析了高温热源位置a及尺寸b对多孔介质方腔自然对流传热性能的影响,提出了平均Nusselt数Nu和位置a及尺寸b的拟合关系式.研究结果表明:高温热源位置及尺寸对多孔介质方腔内自然对流传热性质的影响很大,且存在最佳高温热源位置(a=4/16)和尺寸(b=0.75),以达到最强的对流换热强度(Nu_(max)≈10.35)和最大的对流换热量(Q_(max)≈5.69).     

相变过程的格子Boltzmann方法模拟

应用Shan提出的伪势多相模型替代R-K着色模型,建立一种新的描述气液相变过程的格子Boltzmann理论模型,模拟蒸发(高密度转化为低密度)过程.改进了计算效率,且得到较好的计算结果.同时应用该模型从孔隙尺度模拟了多孔介质中的相变现象,验证了该模型模拟复杂相变问题的可行性.     

Variability of permeability with diameter of conduit

An entry length is always observed before laminar flow is achieved in fluid flowing in a conduit. This depends on the Reynolds number of the flow and the degree of smoothness of the conduit. This work examined this region and the point where laminar flow commences in the context of flow through conduit packed with porous material like beads, of known porosity. Using some theoretical assumptions, it is demonstrated that permeability varies from zero at wall-fluid boundary to maximum at mid-stream, creating a permeability profile similar to the velocity profile. An equation was obtained to establish this. We also found that peak values of permeability increase with increasing porosity, and therefore entry length increases with increasing porosity with all other parameters kept constant. A plot of peak permeability versus porosity revealed that they are linearly related.      

基于格子Boltzmann大密度比模型的多孔介质内气泡动力学行为数值模拟

基于格子Boltzmann两相流大密度模型,研究气泡穿过多孔介质的动力学行为.研究发现:当孔隙率较大时,气泡只变形不破裂,能完整地通过多孔介质;而孔隙率较小时,气泡变形更加剧烈且发生破裂,穿过多孔介质所需的时间更长.另外,当障碍物表面接触角(θ)较小时,气泡均能完整地通过多孔介质,随着接触角的增大,气泡开始发生破裂,且...     

Thermodynamic Foundations of Kinetic Theory and Lattice Boltzmann Models for Multiphase Flows

This paper demonstrates that thermodynamically consistent lattice Boltzmann models for single-component multiphase flows can be derived from a kinetic equation using both Enskog's theory for dense fluids and mean-field theory for long-range molecular interaction. The lattice Boltzmann models derived this way satisfy the correct mass, momentum, and energy conservation equations. All the thermodynamic variables in these LBM models are consistent. The strengths and weaknesses of previous lattice Boltzmann multiphase models are analyzed.