过渡区微尺度流动的有效黏性多松弛系数格子Boltzmann模拟

为提高采用二维九速离散速度模型的格子Boltzmann方法 (LBM)模拟微尺度流动中非线性现象的精度和效率,引入Dongari等提出的有效平均分子自由程对黏性进行修正(Dongari N,Zhang Y H,Reese J M2011 J.Fluids Eng.133 071101);并针对以往研究微尺度流动时采用边界处理格式含有离散误差的问题,采用多松弛系数格子Boltzmann方法结合二阶滑移边界条件,对微尺度Couette流动和周期性Poiseuille流动进行模拟,并将速度分布以及质量流量等模拟结果与直接模拟蒙特卡罗方法模拟数据、线性Boltzmann方程的数值解以及现有的LBM模型模拟结果进行对比.结果表明,相对于现有的LBM模型,引入新的修正函数所建立的有效黏性多松弛系数LBM模型有效提高了LBM模拟过渡区的微尺度流动中的非线性现象的能力.     

微通道内气体流动的格子Boltzmann方法研究

采用格子Boltzmann方法模拟了微通道在滑移区内不同Knudsen数下的微气体Poiseuille流,分析了微气体流动的速度分布以及流量与压降的关系,并给出了相对滑移长度和Poiseuille数随Knudsen数的变化特性。研究结果表明,微气体Poiseuille流的速度轮廓呈抛物线分布,但是边界速度大于0,出现速...     

二维平板间驻波声流的MRT-LBM数值研究

采用多松弛时间格子玻尔兹曼方法（Multiple Relaxation Time Lattice Boltzmann Method,MRT-LBM）对二维平板间的驻波声流进行数值模拟,模拟结果与Rayleigh流近似解析解相符,研究黏度和板间宽度对驻波声流的影响,得到不同黏度下x=L/4截面无量纲水平速度分布和x=L/2截面无量纲竖直速度分布,板间宽度对边界层内声流区域厚度的影响及驻波声流的形成过程,结果表明MRT-LBM模型能有效模拟驻波声流效应.     

格子Boltzmann方法模拟微尺度流动和传热

本文采用格子Boltzmann方法(LBM)对微尺度Couette流的流动及传热进行了模拟.为了获得壁面边界的速度滑移和温度阶跃,在含有粘性热耗散的热格子模型的基础上,提出了一种新的直接基于宏观量的边界处理格式.模拟得到的速度场和温度分布与解析解吻合得相当好,充分说明了本文采用的模型和边界处理的合理性同时在模拟中还发现:对于不同的Kn数,均存在使得其上壁面的温度阶跃为零的临界Ec数,并且其临界值均在3.0附近.     

微尺度稀薄效应下颗粒沉降的格子Boltzmann方法模拟

基于多松弛格子Boltzmann模型,对竖直细长微通道内颗粒自由沉降过程进行模拟,分析气体稀薄效应、初始位置以及颗粒间相互作用对微颗粒沉降特性的影响.研究表明：随Knudsen数增大,微通道内气体稀薄效应增强,颗粒表面气体滑移速度增大,气相流体有效粘度减小,颗粒相同运动状态下受到气体阻力相应减小,颗粒沉降平衡速度明显增大;不同初始位置颗粒沉降过程存在明显差异,初始位置偏离中心线颗粒将发生水平方向位移且呈振荡趋势,最终稳定于中心线平衡位置;在微尺度双颗粒沉降DKT现象过程中,气体稀薄效应影响颗粒运动特性,后颗粒跟随过程明显增长.     

致密多孔介质中气体渗流的格子Boltzmann模拟

为了能用格子Boltzmann方法来正确地刻画致密多孔介质中微尺度流动问题,对单通道模型进行推广,并将其应用于孔隙群里气体渗流的数值模拟.通过对部分具有代表性的多孔介质中的实际流动问题进行模拟,研究渗透率与平均压力和Knudsen数之间的相互关系.基于理论分析及相关文献中的试验结果,验证模拟结果,为用格子Boltzmann方法深入研究气体渗流问题奠定基础.     

一种滑移区气体流动的格子Boltzmann曲边界处理新格式

针对滑移区复杂气-固边界存在速度滑移现象,提出了一种基于格子Boltzmann方法的非平衡态外推与有限差分相结合的曲边界处理新格式.该格式具有可考虑实际物理边界与网格线偏移量的优势,较传统half-way DBB(diffusive bounce-back)格式更能准确反映实际边界情况,同时还可获取壁面处气体宏观量及其法向梯度等信息.采用本文所提曲边界处理格式模拟分析了滑移区气体平直/倾斜微通道Poiseuille流、微圆柱绕流和同心微圆柱面旋转Couette流问题.研究结果表明,采用曲边界处理新格式所得结果与理论值以及文献结果符合良好,适用于滑移区气体流动的复杂边界处理,且比half-way DBB格式具有更高的精度,较修正DBB格式具有更好的适应性.     

考虑转动能的一维/二维Boltzmann-Rykov模型方程数值算法

研究考虑转动能的Boltzmann-Rykov模型方程,基于转动自由度对气体分子速度分布函数矩积分,引入约化速度分布函数,应用离散速度坐标法与数值积分技术,将气体运动论模型方程化为在离散速度坐标点处关于三个约化速度分布函数的联立方程组.应用拓展计算流体力学有限差分方法,数值计算考虑转动自由度的双原子气体一维、二维Boltzmann模型方程,得到高、低Knudsen数一维激波管内流动和二维竖直平板绕流问题的流场,分析验证考虑转动能的Boltzmann-Rykov模型方程全流域统一算法求解一维/二维气体流动问题的可靠性.结果表明,气体稀薄程度与分子内自由度对流场具有较大影响,且Knudsen数较高的稀薄气体流动呈现严重的非平衡流动特点.     

微通道中压力驱动Poiseuille流数值分析

采用26阶矩方程方法对稀薄气体在平板微通道与微圆通道中压力驱动的Poiseuille流动进行数值分析,获得稀薄气体在微通道内的速度分布、压力分布规律。数值分析结果表明:气体压力在微通道中沿主流方向呈非线性分布,且非线性程度随Kn数的增大而减小,分布趋势随Kn数的改变产生微小的变化;随Kn数的增大,微圆通道中气体沿径向速度分布出现双峰现象。研究结果与DSMC方法及格子-Boltzmann方法对比符合较好。     

棒状分子聚合物溶液的微宏观数值模拟

利用微宏观耦合方法模拟了棒状分子聚合物溶液在平板Couette流动中的复杂流变行为,其中微宏观模型通过非均匀Doi理论来描述.数值模拟中,应用有限体积方法耦合求解了介观尺度上的Smoluchowski方程和宏观尺度上的流场守恒方程.数值结果不仅得到了若干种典型的流动类型,而且还预测了另外两种新的复合瑕疵结构.数值试验表明：棒状分子聚合物的流变结构主要依赖于De数、分子相对尺度以及溶液浓度常数的取值;并且De数对分子指向矢的翻滚周期、随流取向角等微观特性也均有明显影响. 关键词： 棒状分子 聚合物溶液 微宏观模拟     

Simulation of micro- and nano-scale flows via the lattice Boltzmann method

We use the lattice Boltzmann method (LBM) for analysis of high and moderate Knudsen number phenomena. Simulation results are presented for microscale Couette and Poiseuille flows. The slip velocity, nonlinear pressure drop, and mass flow rate are compared with previous numerical results and/or experimental data. The Knudsen minimum is successfully predicted for the first time within the LBM framework. These results validate the usage of the LBM based commercial, arbitrary geometry code PowerFLOW for simulating nanoscale problems.     

Discrete Boltzmann Method with Maxwell-Type Boundary Condition for Slip Flow

The rarefied effect of gas flow in microchannel is significant and cannot be well described by traditional hydrodynamic models. It has been known that discrete Boltzmann model(DBM) has the potential to investigate flows in a relatively wider range of Knudsen number because of its intrinsic kinetic nature inherited from Boltzmann equation.It is crucial to have a proper kinetic boundary condition for DBM to capture the velocity slip and the flow characteristics in the Knudsen layer. In this paper, we present a DBM combined with Maxwell-type boundary condition model for slip flow. The tangential momentum accommodation coefficient is introduced to implement a gas-surface interaction model.Both the velocity slip and the Knudsen layer under various Knudsen numbers and accommodation coefficients can be well described. Two kinds of slip flows, including Couette flow and Poiseuille flow, are simulated to verify the model.To dynamically compare results from different models, the relation between the definition of Knudsen number in hard sphere model and that in BGK model is clarified.     

Improving the Stability of the Multiple-Relaxation-Time Lattice Boltzmann Method by a Viscosity Counteracting Approach

Numerical instability may occur when simulating high Reynolds number flows by the lattice Boltzmann method (LBM). The multiple-relaxation-time (MRT) model of the LBM can improve the accuracy and stability, but is still subject to numerical instability when simulating flows with large single-grid Reynolds number (Reynolds number/grid number). The viscosity counteracting approach proposed recently is a method of enhancing the stability of the LBM. However, its effectiveness was only verified in the single-relaxation-time model of the LBM (SRT-LBM). This paper aims to propose the viscosity counteracting approach for the multiple-relaxation-time model (MRT-LBM) and analyze its numerical characteristics. The verification is conducted by simulating some benchmark cases: the two-dimensional (2D) lid-driven cavity flow, Poiseuille flow, Taylor-Green vortex flow and Couette flow, and three-dimensional (3D) rectangular jet. Qualitative and Quantitative comparisons show that the viscosity counteracting approach for the MRT-LBM has better accuracy and stability than that for the SRT-LBM.     

A Lattice Boltzmann Kinetic Model for Microflow and Heat Transfer

In this paper, we propose a lattice Boltzmann BGK model for simulation of micro flows with heat transfer based on kinetic theory and the thermal lattice Boltzmann method (He et al., J. Comp. Phys. 146:282, 1998). The relaxation times are redefined in terms of the Knudsen number and a diffuse scattering boundary condition (DSBC) is adopted to consider the velocity slip and temperature jump at wall boundaries. To check validity and potential of the present model in modelling the micro flows, two two-dimensional micro flows including thermal Couette flow and thermal developing channel flow are simulated and numerical results obtained compare well with previous studies of the direct simulation Monte Carlo (DSMC), molecular dynamics (MD) approaches and the Maxwell theoretical analysis     

Implementation of diffuse reflection boundary conditions in a thermal lattice Boltzmann model with flux limiters

We discuss three new implementation versions of diffuse reflection boundary conditions in a thermal lattice Boltzmann model. Their accuracy is investigated in the case of Couette flow by considering the slip regime. The best results are recovered with versions 2 and 3, which rely on outgoing fluxes to express the particle distribution functions in the ghost nodes outside the flow domain. Version 2 is found to be more economical since it involves no interpolation procedure. This version was thereafter used to investigate the temperature profile in Couette flow for various values of Prandtl number, as well as the capability of the thermal LB model to capture the Knudsen minimum in Poiseuille flow.     

Local second-order boundary methods for lattice Boltzmann models

A new way to implement solid obstacles in lattice Boltzmann models is presented. The unknown populations at the boundary nodes are derived from the locally known populations with the help of a second-order Chapman-Enskog expansion and Dirichlet boundary conditions with a given momentum. Steady flows near a flat wall, arbitrarily inclined with respect to the lattice links, are then obtained with a third-order error. In particular, Couette and Poiseuille flows are exactly recovered without the Knudsen layers produced for inclined walls by the bounce back condition.     

Analytical solutions of the lattice Boltzmann BGK model

Analytical solutions of the two-dimensional triangular and square lattice Boltzmann BGK models have been obtained for the plane Poiseuille flow and the plane Couette flow. The analytical solutions are written in terms of the characteristic velocity of the flow, the single relaxation time , and the lattice spacing. The analytic solutions are the exact representation of these two flows without any approximation. Using the analytical solution, it is shown that in Poiseuille flow the bounce-back boundary condition introduces an error of first order in the lattice spacing. The boundary condition used by Kadanoffet al. in lattice gas automata to simulate Poiseuille flow is also considered for the triangular lattice Boltzmann BGK model. An analytical solution is obtained and used to show that the boundary condition introduces an error of second order in the lattice spacing.     

Modified relaxation time Monte Carlo method for continuum-transition gas flows

Gas flows in the continuum-transition regime often occur in micro-electro-mechanical systems. The relaxation time Monte Carlo (RTMC) method was modified by using an ellipsoid statistical model and a multiple translational temperature model in the BGK model equation to simulate continuum-transition gas flows. The modified RTMC method uses a simplified form of the generalized relaxation time, which is related to the macro velocity and the local Knudsen number. The results for Couette flow and Poiseuille flow in microchannels predicted using the modified RTMC and the DSMC are in good agreement with the modified RTMC being much faster than the DSMC for continuum-transition gas flow simulations.