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     

基于格子Boltzmann方法的液液不混溶两相流动数值模拟

具有介观特性的格子Boltzmann方法能够准确方便地捕捉相界面细节,在两相流动领域具有广泛的应用前景.本文在简要介绍格子Boltzmann方法的基础上,利用格子Boltzmann方法的颜色模型对四类经典两相流动问题进行了模拟,界面张力的Laplace定律验证、单液滴松弛过程、两个液滴融合过程、水平通道内不混溶液液两相流动.结果表明,液滴界面张力符合Laplace定律;黏性越大,液滴松弛过程越稳定;界面张力越大,液滴融合速度越快;格子Boltzmann方法能够有效描述液液两相流动的界而信息。研究工作为应用格子Boltzmann方法分析两相流动问题奠定了理论基础.     

相同尺度下气泡与复杂壁面的耦合特性研究

采用格子Boltzmann方法(LBM)建立了气液固三相耦合的动力学模型,研究了相同尺度下上浮气泡与复杂壁面的相互耦合作用.首先,基于黏性流体理论,通过构建一组格子Boltzmann(LB)方程来描述气液两相的运动,并以LB离散体积力的形式计入了黏性力、表面张力和重力.同时,采用LBM中的Half-way反弹模型与有限差分格式相结合的方式进行固壁边界的处理.然后,利用本文建立的模型,对不同特征尺寸比条件下,气泡与考虑边缘效应的平面固壁和曲面固壁的耦合特性进行了研究.研究发现固壁边界条件以及特征尺寸比对气泡的运动和拓扑结构的变化都具有明显的非线性影响.最后,研究了流体属性对气泡与复杂壁面耦合规律的影响.     

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.     

应用格子Boltzmann模型模拟一类二维偏微分方程

针对一类含源的二维非线性偏微分方程, 通过Chapman-Enskog展开技术和多尺度分析提出了带修正项的简单格子Boltzmann模型. 用模型模拟了几类二维偏微分方程, 数值模拟结果与精确解相符合. 成功将格子Boltzmann方法应用到二维偏微分方程的数值求解中. 关键词： 二维非线性偏微分方程 格子Boltzmann模型 Chapman-Enskog多尺度展开     

非正交多松弛系数轴对称热格子Boltzmann方法

提出了一种模拟轴对称热流动的非正交多松弛系数格子Boltzmann(MRT-LB)模型.通过采用非正交转换矩阵,建立了基于D2Q9离散速度的求解流场的MRT-LB模型和基于D2Q5离散速度的求解温度场的MRT-LB模型.Chapman-Enskog分析表明,该模型可以恢复对应的柱坐标下的宏观连续方程、动量方程和能量方程.与现有的轴对称MRT-LB模型相比,本文采用的非正交转换矩阵中含有更多的零元素,因而具有更高的计算效率.采用本文模型对几种典型的轴对称热流动问题,包括热Womersley流动、竖直圆柱体内的Rayleigh-Bénard对流和环形柱体内的自然对流进行了数值模拟,通过等温线图和流线图以及定量数据的对比,验证了本文模型的可行性和可靠性.并且数值模拟结果表明,相对现有模型,本文模型具有更好的数值稳定性和计算效率.     

格子Boltzmann亚格子模型的研究

为了将格子Boltzmann法应用于大雷诺数流动的模拟,本文将Smagorinsky亚格子模型和LBGK模型相结合,并对该亚格子LBM模型进行了研究。利用该亚格子LBM模型,对二维顶盖驱动流进行了模拟,得到了若干大雷诺数下流线图和方腔中心线上无量纲速度分布。计算结果与基准解进行比较,两者相互吻合。     

大学物理中流体力学问题的计算机模拟研究

格子玻尔兹曼模拟方法(Lattice Boltzmann Method,LBM)被广泛应用于流体力学问题的研究中,本文采用LBM方法对牛顿流体和非牛顿流体的泊肃叶流动进行了模拟,还通过模拟圆柱绕流问题演示了层流和湍流现象并阐明了雷诺数的概念.将LBM模拟结果与大学物理的相关流体力学知识相联系,不仅可以直观地解释抽象的流体力学概念,而且能够培养学生采用计算物理学手段解决实际问题的思维方式.     

格子玻尔兹曼方法对不同张角聚焦声束的建模

高强度聚焦超声(HIFU)是一种新型的无创治疗肿瘤新技术,其中换能器声场数值计算能够为HIFU治疗提供重要的依据。传统非线性KZK和SBE模型广泛应用于换能器声场数值计算,但依然存在某些不足。我们采用一种介观尺度的新型流体力学方法,即格子Boltzmann方法(LBM),基于2维9离散速度(D2Q9)格子构建了轴对称多弛豫参数LBM模型,并通过调节弛豫参数分析其对模型的影响;利用该模型对两个具有不同张角的球面聚焦换能器的声场进行数值模拟,并与KZK和SBE模型的计算结果进行比较。结果表明LBM模型能够很好地描述超声波的激发和传播机制,从流体力学的角度描述聚焦声场的分布,具有清晰的物理意义,且计算过程不受换能器张角的限制,在换能器声场的理论分析和模拟计算及其在HIFU治疗中的应用有着积极的意义。      

基于几何重建的气液两相流孔隙尺度模拟

本文基于二维micro CT扫描图像进行数值重构得到三维多孔介质几何模型,采用Shan-Chen多相格子Boltzmann方法(LBM)建立适用不规则几何边界区域内气液两相流动数值模型,在此基础上对复杂多孔介质内的两相流动过程进行孔隙尺度模拟。结果表明,气-液两相流动受限于多孔介质的复杂孔隙结构,气液表面张力、壁面润湿特性以及进出口压差对两相流动特性将产生明显影响。     

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.     

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.     

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.     

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.     

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...     

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.     

Development of a new correlation to calculate permeability for flows with high Knudsen number

Flows with high Knudsen number play a prominent role in many engineering applications. The present study is an effort toward the simulation of flow with high Knudsen number using modified lattice Boltzmann method(LBM) through a porous medium in a channel. The effect of collision between molecules and solid walls, which is required to accurately simulate transition flow regime, is taken into account using a modified relaxation time. Slip velocity on the wall, which is another significant difficulty in simulating transition flow regime, is captured using the slip reflection boundary condition(SRBC). The geometry of porous medium is considered as in-line and staggered. The results are in good agreement with previous works. A new correlation is obtained between permeability, Knudsen number and porosity for flows in transition flow regimes.     

Gas kinetic algorithm for flows in Poiseuille-like microchannels using Boltzmann model equation

~~Gas kinetic algorithm for flows in Poiseuille-like microchannels using Boltzmann model equation1. Feynman, R., There's plenty of room at the bottom, Journal of Microelectromechanical Systems, 1992, 1: 60 -66. 2. Piekos, E. S., Breuer, K. S., Numerical modeling of micromechanical devices using the direct simulation Monte Carlo method, Transactions of the ASME, Journal of Fluids Engineering, 1996, 118: 464-469. 3. Beskok, A., Karniadakis, G. E., Trimmer, W., Rarefaction and …     

Lattice Boltzmann modeling of microchannel flow in slip flow regime

We present the lattice Boltzmann equation (LBE) with multiple relaxation times (MRT) to simulate pressure-driven gaseous flow in a long microchannel. We obtain analytic solutions of the MRT-LBE with various boundary conditions for the incompressible Poiseuille flow with its walls aligned with a lattice axis. The analytical solutions are used to realize the Dirichlet boundary conditions in the LBE. We use the first-order slip boundary conditions at the walls and consistent pressure boundary conditions at both ends of the long microchannel. We validate the LBE results using the compressible Navier–Stokes (NS) equations with a first-order slip velocity, the information-preservation direct simulation Monte Carlo (IP-DSMC) and DSMC methods. As expected, the LBE results agree very well with IP-DSMC and DSMC results in the slip velocity regime, but deviate significantly from IP-DSMC and DSMC results in the transition-flow regime in part due to the inadequacy of the slip velocity model, while still agreeing very well with the slip NS results. Possible extensions of the LBE for transition flows are discussed.