Structure and Liquid-Vapor Interface of a Simple Metal

This paper presents the results of a theoretical study of the structure of the liquidvapor interface of gallium, based on density functional pseudopotential representation of the electron-ion and the ion-ion interactions, and self-consistent quantum Monte Carlo simulation. These predictions of the bulk pair correlation function and the longitudinal density distribution are in very good agreement with the results of recent experimental studies.     

气泡成核过程的格子Boltzmann方法模拟

利用精确差分格子Boltzmann模型探讨水在特定温度下的亚稳态及不稳定平衡态, 获得等温相变过程中形成气泡和液滴的条件, 模型预测结果与理论解符合良好. 在该等温模型的基础上耦合能量方程, 通过调节流体-壁面相互作用力获得不同的气泡与固壁间接触角, 从而建立了一种新的描述气液相变的格子Boltzmann理论模型. 利用该新模型模拟不同流体-壁面相互作用力下凹坑气泡成核过程, 再现了气泡成核过程中的三阶段特性; 探讨了接触角、曲率半径及气泡体积随气泡成核过程的变化关系, 获得了与文献结果定性符合的曲率-气泡体积关系曲线. 关键词： 格子Boltzmann方法 气泡成核过程 气液相变 接触角     

A Discrete Effect of the Thermal Lattice BGK Model

In this article, a discrete effect in the thermal Lattice BGK two-speed model is studied. These effects are due to the non-equilibrium state in the particle distribution function, and the non-equilibrium occurs near walls. The mechanism of the LBM counterpart of the thermal creep flow, which appears due to the temperature gradient of the boundary in rarefied gases, is clarified analytically and numerical calculations are performed for some cases. A technique for eliminating this effect is also shown.     

枝晶生长和气泡形成的数值模拟

本文建立了二维的格子玻尔兹曼方法-元胞自动机(lattice Boltzmann method-cellular automaton, LBM-CA)耦合模型, 对凝固过程中枝晶生长和气泡形成进行模拟研究. 本模型采用CA方法模拟枝晶的生长, 根据界面溶质平衡法计算枝晶生长的驱动力. 采用基于Shan-Chen多相流的LBM模拟气泡在液相中的生长和运动. 在LBM-CA的耦合模型中包含了固-液-气三相之间的相互作用. 应用Laplace定理和模拟气-液-固三相之间的润湿现象对模型进行了验证. 应用所建立的LBM-CA耦合模型模拟研究了气-液相互作用系数对单气泡生长的影响. 发现单气泡的生长速度和平衡半径随气-液相互作用系数的增大而增大. 定向凝固过程中枝晶和气泡生长的模拟结果再现了枝晶的择优生长、 气泡的优先形核位置、气泡的长大、合并、在枝晶间受挤变形以及在液相通道中的运动等物理现象, 与实验结果符合良好. 此外, 初始气体含量越高, 凝固结束时气泡的体积分数也相对较高. 本模型的模拟结果可以揭示在凝固过程中气泡形核、 生长和运动演化以及与枝晶生长相互作用的物理机理.     

Thermal equation of state for lattice Boltzmann gases

The Galilean invariance and the induced thermo-hydrodynamics of the lattice Boltzmann Bhatnagar--Gross--Krook model are proposed together with their rigorous theoretical background. From the viewpoint of group invariance, recovering the Galilean invariance for the isothermal lattice Boltzmann Bhatnagar--Gross--Krook equation (LBGKE) induces a new natural thermal-dynamical system, which is compatible with the elementary statistical thermodynamics.     

用格子Boltzmann模型模拟可压缩完全气体流动

采用一种新的格子Boltzmann模型模拟超音速流动。在这种模型中,粒子的速度不受限制,可以取得很广。而平衡分布函数的支集却相对集中,使模型得以简化。粒子速度的这种自适应特性允许流体以较高的马赫数流动。通过引入粒子的势能使得该模型适用于具有任意比热比的完全气体。利用Chapman-Enskog方法,从BGK型Boltzmann方程推导出Navier-Stokes方程。在六边形网格上模拟了马赫数为3的前台阶绕流,得到了合理的结果。     

Polar Coordinate Lattice Boltzmann Kinetic Modeling of Detonation Phenomena

A novel polar coordinate lattice Boltzmann kinetic model for detonation phenomena is presented and applied to investigate typical implosion and explosion processes. In this model, the change of discrete distribution function due to local chemical reaction is dynamically coupled into the modified lattice Boltzmann equation which could recover the Navier-Stokes equations, including contribution of chemical reaction, via the Chapman-Enskog expansion. For the numerical investigations, the main focuses are the nonequilibrium behaviors in these processes. The system at the disc center is always in its thermodynamic equilibrium in the highly symmetric case. The internal kinetic energies in different degrees of freedom around the detonation front do not coincide. The dependence of the reaction rate on the pressure, influences of the shock strength and reaction rate on the departure amplitude of the system from its local thermodynamic equilibrium are probed.     

Preliminary Results in the Use of Energy-Dependent Octagonal Lattices for Thermal Lattice Boltzmann Simulations

Thermal lattice Boltzmann simulations are prone to severe numerical instabilities. While octagonal velocity lattices increase the range of temperatures that can be successfully simulated, the ranges are insufficient for many applications. Second order interpolation is required to correlate diagonal streaming to the square spatial grid. Here, the role of energy-dependent octagonal lattices is examined, an idea spawned from Gauss–Hermite quadratures. A nontrivial allocation scheme is now required to ensure moment conservation in connecting to the spatial grid. For the energy-dependent lattices, it is shown that there are no lower bounds to the temperature, thus allowing for higher Reynolds number simulations. Simulations are presented and compared to theory (viscosity and sound speed dependence on temperature) showing excellent agreement.     

凝固前沿和气泡相互作用的大密度比格子玻尔兹曼方法模拟

建立了二维双组分两相流的大密度比格子玻尔兹曼方法 (lattice Boltzmann method, LBM)模型. 该模型基于改进的Shan-Chen伪势多相流LBM模型, 结合采用不同时间步长的方法, 实现密度比达800以上的气液两相流模拟. 为了对模型进行验证, 模拟了在不同气液相互作用系数和密度比条件下气泡内外压力差与其半径之间的关系, 其结果满足Laplace定律. 将所建立的大密度比LBM与介观尺度的元胞自动机(cellular automaton, CA)和有限差分法(FDM)相耦合, 用LBM模拟气液两相流, 用CA方法模拟固相生长, 用有限差分法模拟温度场, 采用LBM-CA-FDM耦合模型对定向凝固过程中凝固前沿的气泡与液-固界面之间的相互作用进行模拟研究. 结果表明, 绝热气泡的存在影响了温度场分布, 使得凝固前沿接近气泡时, 液-固界面凸起, 在不同的固相生长速度条件下, 出现凝固前沿淹没气泡或气泡脱离凝固前沿的不同情况, 模拟结果与实验结果符合良好. 关键词： 格子玻尔兹曼方法 元胞自动机 凝固 气泡     

多相非牛顿流体驱替过程的格子Boltzmann模拟

将非牛顿流体模型引入多相格子Boltzmann方法（LBM）,研究多相非牛顿流体的驱替过程.首先以牛顿流体驱替过程作对照,比较非牛顿流体的驱替特性.然后基于简单结构模型,分析不同界面张力下,非牛顿流体的驱替能力和驱替过程中被驱替相的形态变化规律,揭示界面张力的影响机理.结果表明：界面张力在驱替过程中起阻碍作用,其它参数相同情况下,界面张力越低,流体的驱替能力越强.最后,结合四参数随机生长（QSGS）结构生成方法,模拟不同压差、不同界面张力以及不同润湿性条件下多孔复杂结构内的非牛顿多相驱替过程,分析这些参数对过程的影响.     

The effect of surface roughness on rarefied gas flows by lattice Boltzmann method

This paper studies the roughness effect combining with effects of rarefaction and compressibility by a lattice Boltzmann model for rarefied gas flows at high Knudsen numbers. By discussing the effect of the tangential momentum accommodation coefficient on the rough boundary condition, the lattice Boltzmann simulations of nitrogen and helium flows are performed in a two-dimensional microchannel with rough boundaries. The surface roughness effects in the microchannel on the velocity field, the mass flow rate and the friction coefficient are studied and analysed. Numerical results for the two gases in micro scale show different characteristics from macroscopic flows and demonstrate the feasibility of the lattice Boltzmann model in rarefied gas dynamics.     

Test of the Possible Application of the Half—Way Bounce—Back Boundary Condition for Lattice Boltzmann Methods in Complex Geometry

The way of handling boundary conditions with simple bounce-back rule in the lattice gas and lattice Boltzmann method had been considered as one of the advantage compared with other numerical schemes,The half-way bounce-back rule inherits the advantage of the bounce-back rule and improves the accuracy to the second-order on flat boundaries,In this paper,we test the possible application of the half-way bounce-back rule to the system with complex geometry,Our simulation results show that the half-way bounce-back rule is a good boundary condition in the problems without emphasis on accuracy.     

三维十五点格子Boltzmann模型仿真

格子气和格子Ｂｏｌｔｚｍａｎｎ方法的迅速发展提供了一类求解流体力学问题的新方法。格子Ｂｏｌｔｚｍａｎｎ方法在保留了格子气模型优点的同时,克服了它的不足之处。本文讨论了一种三维十五点格子Ｂｏｌｔｚｍａｎｎ模型,通过选择适当的平衡分布及参数,并用Ｃｈａｐｍａｎ－Ｅｎｓｋｏｇ展开和多尺度技术导出了Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程．在微机上模拟了工程中比较常见的管排绕流问题,并与实验观察到的结果进行了比较,结果表明该模型能较好的模拟复杂流动现象,并具有较好的工程应用背景。     

CORRECTIONS TO THE COLLISION TERM IN THE BGK BOLTZMANN EQUATION

With the discrete method of the hexagonal cell and three different velocities of particle population in each cell, a two-dimensional lattice Boltzmann model is developed in this paper.^[1,2] The collision operator in the Boltzmann equation is expanded to fourth order using the Taylor expansion.^[3,4] With this model, good results have been obtained from the numerical simulation of the reflection phenomenon of the shock wave on the surface of an obstacle, and the numerical stability is also good. Thus the applicability of the D2Q 19 model is verified.     

Droplet dynamics on patterned substrates

We present a lattice Boltzmann algorithm which can be used to explore the spreading of droplets on chemically and topologically patterned substrates. As an example we use the method to show that the final configuration of a drop on a substrate comprising hydrophobic and hydrophilic stripes can depend sensitively on the dynamical pathway by which the state is reached. We also consider a substrate covered with micron-scale posts and investigate how this can lead to superhydrophobic behaviour. Finally we model how a Namibian desert beetle collects water from the wind.     

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.     

Lattice Boltzmann Study of Mixed Convection in aCubic Cavity

The problem of the mixed convection in a cubic cavity is studied with lattice Boltzmann method. A multiple-relaxation-time lattice Boltzmann model for incompressible flow in the cubic cavity and another thermal lattice Boltzmann model for solving energy/temperature equation are proposed. The present models are first validated through a comparison with some available results, and then, we present a detailed parameter study on the mixed
convection in the cubic cavity. The numerical results show that the flow and temperature patterns change greatly with variations of the Reynolds and Richardson numbers.     

Thermal Lattice Boltzmann Flux Solver for Natural Convection of Nanofluid in a Square Enclosure

In the present study, mathematical modeling was performed to simulate natural convection of a nanofluid in a square enclosure using the thermal lattice Boltzmann flux solver (TLBFS). Firstly, natural convection in a square enclosure, filled with pure fluid (air and water), was investigated to validate the accuracy and performance of the method. Then, influences of the Rayleigh number, of nanoparticle volume fraction on streamlines, isotherms and average Nusselt number were studied. The numerical results illustrated that heat transfer was enhanced with the augmentation of Rayleigh number and nanoparticle volume fraction. There was a linear relationship between the average Nusselt number and solid volume fraction. and there was an exponential relationship between the average Nusselt number and Ra. In view of the Cartesian grid used by the immersed boundary method and lattice model, the immersed boundary method was chosen to treat the no-slip boundary condition of the flow field, and the Dirichlet boundary condition of the temperature field, to facilitate natural convection around a bluff body in a square enclosure. The presented numerical algorithm and code implementation were validated by means of numerical examples of natural convection between a concentric circular cylinder and a square enclosure at different aspect ratios. Numerical simulations were conducted for natural convection around a cylinder and square in an enclosure. The results illustrated that nanoparticles enhance heat transfer in higher Rayleigh number, and the heat transfer of the inner cylinder is stronger than that of the square at the same perimeter.     

Energy-Conserving Lattice Boltzmann Thermal Model in Two Dimensions

A discrete velocity model is presented for lattice Boltzmann thermal fluid dynamics. This model is implemented and tested in two dimensions with a finite difference scheme. Comparison with analytical solutions shows an excellent agreement even for wide temperature differences. An alternative approximate approach is then presented for traditional lattice transport schemes