疏水表面滑移流动及减阻特性的格子Boltzmann方法模拟

采用格子Boltzmann方法研究了固体壁面对流体的作用强度与其润湿性的关系,在此基础上进一步模拟了疏水表面微通道内的流体流动,获得了润湿性对疏水表面滑移流动及减阻特性的影响规律,证实了疏水表面表观滑移的存在性并揭示了其产生机理.结果表明,疏水性作用在疏水表面的近壁区诱导了一个低密度层,而表观滑移则发生在低密度层上.表观滑移是疏水表面具有减阻作用的直接原因,减阻效果随滑移长度的增大而增大.对于特定的流体系统,滑移长度是疏水表面的固有属性,仅是壁面润湿性的单一函数,而与流动本身的性质无关.     

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.     

Lattice Boltzmann modeling and simulation of compressible flows

In this mini-review we summarize the progress of Lattice Boltzmann (LB) modeling and simulating compressible flows in our group in recent years. Main contents include (i) Single-Relaxation-Time (SRT) LB model supplemented by additional viscosity, (ii) Multiple-Relaxation-Time (MRT) LB model, and (iii) LB study on hydrodynamic instabilities. The former two belong to improvements of physical modeling and the third belongs to simulation or application. The SRT-LB model supplemented by additional viscosity keeps the original framework of Lattice Bhatnagar-Gross-Krook (LBGK). So, it is easier and more convenient for previous SRT-LB users. The MRT-LB is a completely new framework for physical modeling. It significantly extends the range of LB applications. The cost is longer computational time. The developed SRT-LB and MRT-LB are complementary from the sides of convenience and applicability.     

复杂微通道内气泡在浮力作用下上升行为的格子Boltzmann方法模拟

本文采用气-液两相流格子Boltzmann方法模拟了复杂微通道内气泡在浮力作用下的上升过程,主要研究障碍物表面润湿性、浮力大小、障碍物尺寸和气泡初始位置对气泡变形、分裂、合并的动力学行为以及对气泡上升速度、终端速度和气泡剩余质量的运动特性的影响.研究发现,障碍物表面接触角较小时气泡能够完整地通过障碍物通道,随着障碍物表面接触角增加,气泡通过障碍物通道时严重变形,并会发生分裂行为,使得部分气泡黏附在障碍物表面,从而导致气泡到达终端时质量减少.相应地,气泡上升速度以及终端速度也随着微通道表面接触角的增加而减小.另一方面,随着浮力的增加,气泡在上升过程中更容易发生分裂和合并现象,且气泡剩余质量和终端速度随着浮力的增加呈对数形式增加.此外,随着微通道障碍物半径增加,气泡剩余质量首先缓慢减小然后快速减小,而气泡终端速度近似呈线性减小.最后,数值结果还表明当气泡初始位置偏离管道中间时,其上升速度、气泡剩余质量以及气泡终端速度都与初始位置在管道中间时的变化趋势一致,然而对应的数值均减小,且气泡在上升过程中变形更严重.     

Simulation of microchannel flow using the lattice Boltzmann method

For microchannel flow simulation, the slip boundary model is very important to guarantee the accuracy of the solution. In this paper, a new slip model, the Langmuir slip model, instead of the popularly used Maxwell slip model, is incorporated into the lattice Boltzmann (LB) method through the non-equilibrium extrapolation scheme to simulate the rarefied gas flow. Its feasibility and accuracy are examined by simulations of microchannel flow. Although, for simplicity, in this paper our recently developed LB model is used to solve the flow field, this does not prevent the present boundary scheme from easily incorporating other LB models, for example the more advanced collision model with multiple relaxation times. In addition, the existing non-equilibrium extrapolation LB boundary scheme for macroscopic flows can be recovered naturally from the present scheme when the Knudsen number .     

微平行管道内Eyring流体的电渗滑移流动

研究了微平行管道内非牛顿流体––Eyring 流体在外加电场力和压力作用下的电渗流动. 在考虑微尺度效应, 电场作用, 非牛顿特性, 滑移边界等情况下, 建立Eyring流体在微平行管道内电渗流动的力学模型. 通过解线性Possion-Boltzmann方程和Cauchy动量方程, 给出Eyring 流体速度分布的精确解和近似解析解, 并探讨了上述因素对电渗流动的影响. 将电场力和压力对于Eyring流体电渗流动的速度分布的影响进行了比较分析, 得到有意义的结果.     

Lattice Boltzmann Solid Particles in a Lattice Boltzmann Fluid

We define a lattice Boltzmann model of solid, deformable suspensions immersed in a fluid itself described in terms of the lattice Boltzmann method. We discuss the rules governing the internal dynamics of the solid object as well as the rules specifying the interaction between solid and fluid particle. We perform a numerical drag experiment to validate the model. Finally we consider the case of a population of flexible chains in suspension in a shear stress flow and study the influence on the velocity profile.     

Lattice Boltzmann representation of neutral turbulence in the cold gas blanket divertor regime

In the divertor plasma detachment regime one expects to encounter turbulent collisional neutral gas dynamics. These conditions are ideally simulated by lattice Boltzmann methods — methods ideal for application on multi-parallel processors. As illustrative of this method, we specifically show the effect of conductivity in the Rayleigh-Benard convection cells, using an octagonal velocity lattice. This work was supported by DoE and a joint U.S-Czech grant. These results were presented at the 6th International Workshop on Plasma Edge Theory in Fusion Devices, 15–17 September 1997.     

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     

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     

格子玻尔兹曼方法模拟弯流道中粒子的惯性迁移行为

本文发展了一个能够模拟微流场环境下粒子惯性迁移行为的三维耦合模型.该模型采用基于动理论的格子玻尔兹曼方法(LBM)描述流体流动,采用牛顿动力学模型描述粒子的平动和转动,采用基于LBM反弹格式的运动边界法实现流体与粒子模型的耦合.模拟了重力作用下粒子的沉降过程和Couette流条件下粒子的转动过程,通过将模拟结果与文献中的基准解进行对比定量验证了模型的可靠性.模拟了不同大小的球形粒子在环形流道中的迁移,成功复现了经典的流道截面二次流形成过程,分析了粒径大小对粒子在流道中平衡位置的影响机理.结果表明,粒子在弯流道中的平衡位置与粒径大小密切相关,小半径粒子的平衡位置靠近流道外侧而大半径粒子则靠近流道内侧.通过实验对模拟结果进行了定性验证.本模型为深入研究微流场环境下粒子的运动特性以及开发微流控粒子分选器件提供了参考依据.     

Lattice Boltzmann simulations of flow past a cylindrical obstacle

We present lattice Boltzmann simulations of flow past a cylindrical obstacle. Our study is based on the Lévy walk model of turbulence in a lattice Boltzmann model. We discuss pressure around the cylinder with laminar and turbulent incident flows, as well as the dependence of the von Karman street on the analog of integral scale in our model.     

Lattice Boltzmann simulations of a dumbbell moving in a Poiseuille flow

In this paper, the lattice Boltzmann method is applied to simulate a dumbbell moving in a pressure-driven flow in a planar channel with the stress-integration method for the evaluation of hydrodynamic force acting on the cylinders. The simulation results show that the dumbbell also has the important feature of the Segr\'e--Silberberg effect like a particle in a Poiseuille flow. The dumbbell trajectories, orientations, the cylinders vertical velocities and angular velocities all reach their equilibrium values separately independent of their initial positions. It is also found that the dumbbell equilibrium positions depend on the flow Reynolds number, blockage ratio and elastic coefficient. This study is expected to be helpful to understand the dynamics of polymer solutions, polymer synthesis and reaction, etc.     

Multi-relaxation time lattice Boltzmann simulation of inertial secondary flow in a curved microchannel

The inertial secondary flow is particularly important for hydrodynamic focusing and particle manipulation in biomedical research.In this paper,the development of the inertial secondary flow structure in a curved microchannel was investigated by the multi relaxation time lattice Boltzmann equation model with a force term.The numerical results indicate that the viscous and inertial competition dominates the development of secondary flow structure development.The Reynolds number,Dean number,and the cross section aspect ratio influence significantly on the development of the secondary vortexes.Both the intensity of secondary flow and the distance between the normalized vortex centers are functions of Dean numbers but independent of channel curvature radius.In addition,the competition mechanism between the viscous and inertial effects were discussed by performing the particle focusing experiments.The present investigation provides an improved understanding of the development of inertial secondary flows in curved microchannels.     

用格子玻尔兹曼方法研究流动-反应耦合的非线性渗流问题

根据格子玻尔兹曼计算技术以及相应渗流理论，对多孔介质内流动-反应(矿物介质的溶解等)耦合这一非线性渗流问题进行了数值研究，计算结果与解析解基本符合.数字图像重构技术反映的结果表明流体流动和反应之间可以发生强烈的耦合和反耦合作用，同时可以形成条带结构这一自组织现象，与实验和其他理论分析结果符合也很好. 关键词： 非线性渗流 耦合反应 数值模型     

Roughness induced boundary slip in microchannel flows

Surface roughness becomes relevant if typical length scales of the system are comparable to the variations as it is the case in microfluidic setups. Here, an apparent slip is often detected which can have its origin in the misleading assumption of perfectly smooth boundaries. We investigate the problem by means of lattice Boltzmann simulations and introduce an "effective no-slip plane" at an intermediate position between peaks and valleys of the surface. Our simulations agree with analytical results for sinusoidal boundaries, but can be extended to arbitrary geometries and experimentally obtained data. We find that the apparent slip is independent of the detailed boundary shape, but only given by the distribution of surface heights. Further, we show that slip diverges as the amplitude of the roughness increases which highlights the importance of a proper treatment of surface variations in very confined geometries.     

Extended Lattice Boltzmann Model

Conventional lattice Boltzmann models for the simulation of fluid dynamics are restricted by an error in the stress tensor that is negligible only for small flow velocity and at a singular value of the temperature. To that end, we propose a unified formulation that restores Galilean invariance and the isotropy of the stress tensor by introducing an extended equilibrium. This modification extends lattice Boltzmann models to simulations with higher values of the flow velocity and can be used at temperatures that are higher than the lattice reference temperature, which enhances computational efficiency by decreasing the number of required time steps. Furthermore, the extended model also remains valid for stretched lattices, which are useful when flow gradients are predominant in one direction. The model is validated by simulations of two- and three-dimensional benchmark problems, including the double shear layer flow, the decay of homogeneous isotropic turbulence, the laminar boundary layer over a flat plate and the turbulent channel flow.     

Lattice Boltzmann modeling with discontinuous collision components: Hydrodynamic and Advection-Diffusion Equations

Irrespective of the nature of the modeled conservation laws, we establish first the microscopic interface continuity conditions for Lattice Boltzmann (LB) multiple-relaxation time, link-wise collision operators with discontinuous components (equilibrium functions and/or relaxation parameters). Effective macroscopic continuity conditions are derived for a planar implicit interface between two immiscible fluids, described by the simple two phase hydrodynamic model, and for an implicit interface boundary between two heterogeneous and anisotropic, variably saturated soils, described by Richard’s equation. Comparing the effective macroscopic conditions to the physical ones, we show that the range of the accessible parameters is restricted, e.g. a variation of fluid densities or a heterogeneity of the anisotropic soil properties. When the interface is explicitly tracked, the interface collision components are derived from the leading order continuity conditions. Among particular interface solutions, a harmonic mean value is found to be an exact LB solution, both for the interface kinematic viscosity and for the interface vertical hydraulic conductivity function. We construct simple problems with the explicit and implicit interfaces, matched exactly by the LB hydrodynamic and/or advection-diffusion schemes with the aid of special solutions for free collision parameters.     

Lattice Boltzmann simulation of electrowetting

A numerical scheme based on the lattice Boltzmann method, which can simulate the electrowetting of an electrolyte droplet and flow is proposed. The accuracy and robustness of this model are demonstrated by numerically simulating a droplet on a flat surface, on which the cosine of contact angle shows parabolic increase consistent with the Lippmann-Young equation. This scheme is expected to the application in the study of the mechanism of electrowetting on dielectric and electrowetting fluid in complex geometry.