浸没边界–简化热格子Boltzmann方法研究及其应用

针对流固耦合传热问题,本文提出了一种基于浸没边界–简化热格子玻尔兹曼方法 (immersed boundary method–simplified thermal lattice Boltzmann method,IB-STLBM)的耦合模型.不同于传统的格子玻尔兹曼方法使用分布函数演化流场和温度场,简化热格子玻尔兹曼方法 (simplified thermal lattice Boltzmann method,STLBM)的演化过程不需要依赖分布函数,只涉及平衡态分布函数和非平衡态分布函数,能够直接演化宏观量,极大减小了计算过程中所占用的虚拟内存,简化了边界条件的实现方式,同时具有较高的稳定性.传统的浸没边界法对流场的计算采用欧拉网格,对固体边界采用拉格朗日网格,认为固体边界是对流场产生某种体积力.在应用浸没边界法时,汲取介观的思想,把固体的介入看作是对流场的干扰,打破了固体附近流体介观微团颗粒原始的平衡状态,这种干扰可以看作是在耦合边界上产生的一个非平衡项,可用非平衡态分布函数来表示.基于此,在模型中浸没边界法与简化热格子玻尔兹曼方法更紧密联系在一起,更大程度发挥二者的优点,整个计算过程更加简单直观,符合物理特性.通过对热圆柱绕流和内含热颗粒的封闭方腔自然对流问题的模拟以及对其结果的分析,验证了该算法在求解流固耦合传热问题的有效性和可行性.     

基于格子玻尔兹曼方法的局部网格加密算法——粗细网格间的数据转换

格子Boltzmann方法作为一种高效的介观计算流体力学方法在过去20多年里得到快速发展,其相对较高的计算效率和灵活性使其可以适用于各种复杂流动的模拟.然而标准的格子Boltzmann方法只能使用均匀的直角网格,这种网格排布方式并不利于复杂流动的计算.为此,基于格子Boltzmann方法的局部网格加密算法在文献中被提出.该算法需要在局部加密的界面处将粗细网格间的分布函数转换后交换.目前分布函数的转换方式大多是在没有源项的情况下推导的,而且现存考虑源项时转换公式的推导也都是基于Chapman-Enskog展开;其推导过程相对复杂,且需要对分布函数的非平衡态部分做一阶Chapman-Enskog近似,这有可能会限制局部网格加密算法在高阶格子Boltzmann方法中的应用.文章在忽略时空离散误差的前提下,以保证连续分布函数变量以及物理松弛系数一致为基础,构建了一套规范且简洁的粗细网格间在考虑任意源项时,分布函数转换关系的推导过程,该方法不依赖于Chapman-Enskog展开以及Chapman-Enskog近似,且该方法既可以适用于单松弛碰撞模型也可以适用于多松弛碰撞模型.此外,还从理论上证...     

基于热格子Boltzmann方法的自然对流数值模拟

对Eggels和Somers提出的热格子Boltzmann格式进行了改进. 在不可压缩流动的假设下,提出了一种新的温度平衡分布函数,可以克服压缩性对温度统计的影响,并且相应地修正了统计宏观温度的方法. Eggels和Somers的方法对速度和温度均采用半步长反弹格式边界条件,适合无滑移的速度边界条件.但是对温度采用该边界条件在物理本质上显得不够准确,所以在边界上对二者统一采取算法既简单又容易实现的非平衡态外推格式,同时可以与Boltzmann格式的整体二阶精度保持一致. 最后,利用改进的热格子Boltzmann方法(TLBM)模拟了Ra=10^6和Pr=0.71(空气)的方腔中的自然对流,模拟得到的流动参数与其它数值方法的结果吻合得很好,表明改进的热格子Boltzmann方法可以有效准确地模拟非等温流动.      

利用格子Boltzmann方法数值模拟Rayleigh-Benard对流

采用格子Boltzmann方法对较大Rayleigh数范围下的二维Rayleigh-Benard对流进行了模拟研究.引入能量分布函数,利用该能量分布函数与粒子速度分布函数耦合来求解一个热流场,能量分布函数与粒子速度分布函数和Boltzmann方程构成了一个新的双分布格子Boltzmann模型.在考虑密度随温度变化的情况下,进行数值模拟,得到了Rayleigh-Benard对流速度、温度随时间的变化规律、系统的流线和等温线分布及平均Nusselt数与Rayleigh数的之间的关系,与相关文献数据进行了对比,模拟结果非常吻合,证明了改进的双分布格子Boltzmann模型的有效性.     

基于格子Boltzmann方法的挤出胀大的数值模拟

将单相格子Boltzmann方法(lattice Boltzmann method, LBM)引入到粘弹流体的瞬态挤出胀大的数值模拟中,建立了基于双分布函数的自由面粘弹性流动格子Boltzmann模型．分析得到的流道中流动速度分布和构型张量结果与理论解十分吻合．对粘弹流体瞬态挤出胀大过程进行了模拟,并分析了运动粘度比和剪切速率对挤出胀大率的影响,得到的胀大率结果与理论分析和其它模拟结果基本一致．表明给出的LBM可以捕捉挤出胀大的瞬态效应．     

格子Boltzmann方法中基于内插值的曲线边界处理新方法

对格子Boltzmann方法提出了一种新的曲面边界条件处理方法。在笛卡尔坐标系中,这种处理方法是现有的格子Boltzmann方法有关边界条件处理与浸入式边界条件的混合,它采用内插值方法计算靠近物理边界的网格点速度,使其保证最低精度为二阶,然后利用格子Boltzmann方法中的边界条件技术得到相应的分布函数。由理论推导和数值计算表明,本文提出的方法比其他方法更稳定且具有二阶精度。     

格子Boltzmann方法处理复杂边界新进展

格子玻尔兹曼方法是相对较新的计算流体力学方法,具有其独特的优点,如自然并行计算以及复杂边界的处理．在日益重要的高性能计算上,将发挥越来越大的作用．在已经较为成熟的计算模型基础上,为计算复杂几何边界对流场的作用,大量学者提出了各类针对格子玻尔兹曼方法的边界处理格式．边界处理方式对计算的影响主要有三个方面：计算精度,算法稳定性以及并行性．本文简单介绍格子玻尔兹曼方法在边界处理上的一些最新进展．并通过对实际算例的计算比较各类边界处理方式的优劣．     

基于反馈力浸入边界法模拟复杂动边界流动

浸入边界法是模拟流固耦合的重要数值方法之一。本文采用反馈力浸入边界方法,对旋转圆柱和水轮机活动导叶旋转摆动绕流后的动边界流场进行数值模拟。其中,固体边界采用一系列离散的点近似代替,流体为不可压缩牛顿流体,使用笛卡尔自适应加密网格,利用有限差分法进行求解。固体对流场的作用通过构造适宜的反馈力函数实现。本文首先通过旋转圆柱绕流的计算结果同实验结果进行对比,吻合较好,验证了该计算方法的可靠性。然后针对水电站水力过渡过程中水轮机活动导叶旋转摆动绕流后的动边界流场进行数值模拟,得到导叶动态绕流后的流场分布特性和涡结构的演化特性。     

基于隐式扩散的直接力格式浸没边界格子Boltzmann方法

采用浸没边界格子Boltzmann(immersed boundary-lattice Boltzmann,IB-LB)模型执行动边界绕流数值模拟时,信息交互界面和边界力计算格式直接影响流动求解器的数值精度和计算效率.基于隐式扩散界面,一种改进的直接力格式IB-LB模型被提出.边界力表达式基于欧拉/拉格朗日变量同一性准...     

FVM与LBM分区耦合模拟圆柱绕流

构造了用于模拟远场边界下圆柱绕流的有限容积法(FVM)与格子Boltzmann方法(LBM)的分区耦合模型.模型中,靠近圆柱处采用多块网格的LBM,远离圆柱处采用FVM,并将计算结果同适体网格LBM以及多块网格LBM进行了比较.结果表明,耦合模型能在保证计算精度的前提下,显著提高计算效率.     

多孔介质内黏弹性流体的热对流稳定性研究

基于修正的Darcy模型, 介绍了多孔介质内黏弹性流体热对流稳定性研究的现状和主要进展. 通过线性稳定性理论, 分析计算多孔介质几何形状(水平多孔介质层、多孔圆柱以及多孔方腔)、热边界条件(底部等温加热、底部等热流加热、底部对流换热以及顶部自由开口边界)、黏弹性流体的流动模型(Darcy-Jeffrey, Darcy-Brinkman-Oldroyd以及Darcy-Brinkman -Maxwell模型)、局部热非平衡效应以及旋转效应对黏弹性流体热对流失稳的临界Rayleigh数的影响. 利用弱非线性分析方法, 揭示失稳临界点附近热对流流动的分叉情况, 以及失稳临界点附近黏弹性流体换热Nusselt数的解析表达式. 采用数值模拟方法, 研究高Rayleigh数下黏弹性流体换热Nusselt数和流场的演化规律,分析各参数对黏弹性流体热对流失稳和对流换热速率的影响.主要结果:(1)流体的黏弹性能够促进振荡对流的发生;(2)旋转效应、流体与多孔介质间的传热能够抑制黏弹性流体的热对流失稳;(3)在临界Rayleigh数附近,静态对流分叉解是超临界稳定的, 而振荡对流分叉可能是超临界或者亚临界的,主要取决于流体的黏弹性参数、Prandtl数以及Darcy数;(4)随着Rayleigh数的增加,热对流的流场从单个涡胞逐渐演化为多个不规则单元涡胞, 最后发展为混沌状态.      

正弦波温度边界下多孔介质方腔内非热平衡对流传热数值模拟

采用局部非热平衡模型,在方腔左侧壁面温度正弦波变化、右侧壁面温度均一的边界条件下,通过SIM-PLER算法数值研究了固体骨架发热多孔介质方腔内的稳态非达西自然对流,主要探讨了不同正弦波波动参数N及方腔的高宽比M/L对方腔内自然对流与传热的影响规律。计算结果表明:正弦波温度边界使得方腔内的流场出现了复杂的变化,流体及固体区域左侧壁面附近出现了周期性的正负变化的温度场分布,左侧壁面局部Nusselt数出现了周期性的震荡现象;存在一个最佳温度波动参数N=1,此时多孔介质方腔内的整体散热量达到最大值;增加方腔高宽比会显著地削弱方腔内的自然对流传热过程,小高宽比也会在一定的程度上削弱多孔介质方腔内的对流传热。     

Unsteady numerical simulation of double diffusive convection heat transfer in a pulsating horizontal heating annulus

A numerical study is conducted on time-dependent double-diffusive natural convection heat transfer in a horizontal annulus. The inner cylinder is heated with sinusoidally-varying temperature while the outer cylinder is maintained at a cold constant temperature. The numerical procedure used in the present work is based on the Galerkin weighted residual method of finite-element formulation by incorporating a non-uniform mesh size. Comparisons with previous studies are performed and the results show excellent agreement. In addition, the effects of pertinent dimensionless parameters such as the thermal Rayleigh number, Buoyancy ratio, Lewis number, and the amplitude of the thermal forcing on the flow and heat transfer characteristics are considered in the present study. Furthermore, the amplitude and frequency of the heated inner cylinder is found to cause significant augmentation in heat transfer rate. The predictions of the temporal variation of Nusselt and Sherwood numbers are obtained and discussed.     

Lattice Boltzmann Pore Scale Simulation of Natural Convection in a Differentially Heated Enclosure Filled with a Detached or Attached Bidisperse Porous Medium

In this research, pore scale simulation of natural convection in a differentially heated enclosure filled with a conducting bidisperse porous medium is investigated using the thermal lattice Boltzmann method. For the first time, the effect of connection of the bidisperse porous medium to the enclosure walls is studied by considering the attached geometry in addition to the detached one. Effect of most relevant parameters on the streamlines and isotherms as well as hot wall average Nusselt number is studied for two of the bidisperse porous medium configurations. It is observed that effect of geometrical and thermo-physical parameters of the bidisperse porous medium on the heat transfer characteristics is more complicated for the attached configuration. To assess the validity of the local thermal equilibrium condition in the micro-porous media, the pore scale results are used to compute the percentage of the local thermal non-equilibrium for two of the bidisperse porous medium configurations. It is concluded that for the detached configuration, the local thermal equilibrium condition is confirmed in the entire micro-porous media for the ranges of the parameters studied here. However, for the attached geometry, it is shown that departure from the local thermal equilibrium condition is observed for the higher values of the Rayleigh number, micro-porous porosity, solid–fluid thermal conductivity ratio, and the smaller values of the macro-pores volume fraction.     

Convection-dominated melting of phase change material in partially heated cavity: lattice Boltzmann study

Heat transfer and fluid flow processes of natural convection melting of a phase change material are simulated numerically inside a partially heated square cavity. The momentum and energy equations are solved by using enthalpy-based lattice Boltzmann method combined with multi distribution function model. In this communication, the dependence of liquid fraction, temperatures of vertical nodes and average Nusselt number on the positions of heated plates is investigated quantitatively.     

Stability of buoyancy-driven convection in an Oldroyd-B fluid-saturated anisotropic porous layer

The nonlinear stability of thermal convection in a layer of an Oldroyd-B fluid-saturated Darcy porous medium with anisotropic permeability and thermal diffusivity is investigated with the perturbation method. A modified Darcy-Oldroyd model is used to describe the flow in a layer of an anisotropic porous medium. The results of the linear instability theory are delineated. The thresholds for the stationary and oscillatory convection boundaries are established, and the crossover boundary between them is demarcated by identifying a codimension-two point in the viscoelastic parameter plane. The stability of the stationary and oscillatory bifurcating solutions is analyzed by deriving the cubic Landau equations. It shows that these solutions always bifurcate supercritically. The heat transfer is estimated in terms of the Nusselt number for the stationary and oscillatory modes. The result shows that, when the ratio of the thermal to mechanical anisotropy parameters increases, the heat transfer decreases.     

Natural convection heat transfer from a long heated vertical cylinder to an adjacent air gap of concentric and eccentric conditions

In this work, the natural convection heat transfer from a long vertical electrically heated cylinder to an adjacent air gap is experimentally studied. The aspect and diameter ratios of the cylinder are 55.56 and 6.33, respectively. The experimental measurements were obtained for a concentric condition and six eccentricities from 0.1 to 0.92 at five different heat fluxes. The surface temperature of the heated rod is measured at different heights, and the Nusselt number is calculated at the temperature measurement locations. A correlation is suggested to determine the Nusselt number based on the variation of the eccentric ratio values. The experimental results show a good agreement with other studies.     

A numerical simulation of combined radiation and natural convection heat transfer in a square enclosure heated by a centric circular cylinder

A numerical simulation of combined natural convection and radiation in a square enclosure heated by a centric circular cylinder and filled with absorbing-emitting medium is presented. The ideal gas law and the discrete ordinates method are used to model the density changes due to temperature differences and the radiation heat transfer correspondingly. The influence of Rayleigh number, optical thickness and temperature difference on flow and temperature fields along with the natural convection, radiation and total Nusselt number at the source surfaces is studied. The results reveal that the radiation heat transfer as well as the optical thickness of the fluid has a distinct effect on the fluid flow phenomena, especially at high Rayleigh number. The heat transfer and so the Nusselt number decreases with increase in optical thickness, while increases greatly with increase in temperature difference. The variation in radiation heat transfer with optical thickness and temperature difference is much more obvious as comparison with convection heat transfer.     

Lattice Boltzmann simulation of MHD natural convection in a cavity with porous media and sinusoidal temperature distribution

The lattice Boltzmann method (LBM) is used to simulate the effect of magnetic field on the natural convection in a porous cavity. The sidewalls of the cavity are heated sinusoidally with a phase derivation, whereas the top and bottom walls are thermally insulated. Numerical simulation is performed, and the effects of the pertinent parameters, e.g., the Hartmann number, the porosity, the Darcy number, and the phase deviation, on the fluid flow and heat transfer are investigated. The results show that the heat transfer is affected by the temperature distribution on the sidewalls clearly. When the Hartmann number is 0, the maximum average Nusselt number is obtained at the phase deviation 90°. Moreover, the heat transfer enhances when the Darcy number and porosity increase, while decreases when the Hartman number increases.     

Effect of local thermal non-equilibrium on unsteady heat transfer by natural convection of a nanofluid over a vertical wavy surface

This paper uses thermal non-equilibrium model to study transient heat transfer by natural convection of a nanofluid over a vertical wavy surface. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. Three-temperature model is applied to represent the local thermal non-equilibrium among the particle, fluid, and solid-matrix phases. Finite difference method is used to solve the dimensionless governing equations of the problem. The obtained results are displayed in 2D graphs to illustrate the influences of the different physical parameters on local skin-friction coefficient, local Nusselt numbers for fluid, particle and solid phases and local Sherwood number. The results for velocity component, nanoparticle volume fraction, fluid temperature, particle temperature and solid-matrix temperature are presented in 3D graphs as a function of the axial and transverse coordinates. All the obtained results are discussed.