三维方腔温盐双扩散的格子Boltzmann方法数值模拟

研究了温盐双扩散系统的多组分格子Boltzmann方法.通过对二维方腔的温盐双扩散系统的数值模拟，检验了方法的可行性及有效性，所得到的结果与差分法结果符合良好，继而将此方法推广到三维，建立了三维温盐双扩散系统的格子Boltzmann方法，对三维方腔双扩散问题进行了模拟和分析，并与差分法模拟的结果进行了比较，结果令人满意.最后，分析了格子Boltzmann方法在模拟双扩散对流问题时存在的局限性. 关键词： 格子Boltzmann方法 温盐双扩散 Boussinesq近似 数值模拟     

双扩散自然对流的格子Boltzmann模拟

建立了一个模拟双扩散自然对流系统的格子Boltzmann模型,用此模型对受温度和浓度梯度驱动的方腔流动进行了模拟,研究了浓度Rayleigh数对传热传质的影响,并与其它文献的结果进行了比较.     

利用格子Boltzmann方法模拟矩形腔内纳米流体Raleigh-Benard对流

利用格 子 Boltzmann方法模拟矩形腔内纳米流体Rayleigh-Benard对流, 得到温度场和流线分布, 比较分析不同Ra数、体积分数、粒径下纳米流体对流换热的变化情况. 结果表明: 在相同的Ra 数和体积分数下, 纳米流体的对流换热随着粒径的增大而减弱; 在相同的Ra数和粒径下, 纳米流体的对流换热随着体积分数增大而增强. 关键词： 纳米流体 Raleigh-Benard 多相流 格子Boltzmann方法     

格子Boltzmann方法模拟自然对流作用下融化传热过程

建立自然对流作用下融化的格子Boltzmann双分布函数模型,根据非线性对流扩散方程的格子Boltzmann模型理论提出一个新的表征融化温度场的分布函数演化方程,并通过变松弛时间方法处理固液两相变热物性传热问题.应用模型对热传导融化及自然对流融化特别固液变热物的融化过程进行模拟.模拟结果与分析解、经典的关联式结果吻合较好,模型的正确性得到了验证.模拟结果表明,自然对流对融化传热过程有着重要的影响,此外固相热传导也对融化传热、融化速率及固液两相温度分布都有一定影响.     

Simulation of Combustion Field with Lattice Boltzmann Method

Turbulent combustion is ubiquitously used in practical combustion devices. However, even chemically non-reacting turbulent flows are complex phenomena, and chemical reactions make the problem even more complicated. Due to the limitation of the computational costs, conventional numerical methods are impractical in carrying out direct 3D numerical simulations at high Reynolds numbers with detailed chemistry. Recently, the lattice Boltzmann method has emerged as an efficient alternative for numerical simulation of complex flows. Compared with conventional methods, the lattice Boltzmann scheme is simple and easy for parallel computing. In this study, we present a lattice Boltzmann model for simulation of combustion, which includes reaction, diffusion, and convection. We assume the chemical reaction does not affect the flow field. Flow, temperature, and concentration fields are decoupled and solved separately. As a preliminary simulation, we study the so-called counter-flow laminar flame. The particular flow geometry has two opposed uniform combustible jets which form a stagnation flow. The results are compared with those obtained from solving Navier–Stokes equations.     

用格子Boltzmann模型模拟垂直平板间的热对流

引入一个新的能量分布函数，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. 因而，这一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格子Boltzmann模型. 这一模型满足质量、动量和能量守恒的准则. 用该模型对垂直平板间的狭缝热对流进行了数值模拟，数值结果表明，在Prandtl数为1，Grashof数在1.3×10²—1×10⁶之间时，流场将出现多个旋涡结构的流型. 得出了与Lee相一致的结论. 关键词： 能量分布函数 Boltzmann方程 热对流     

An immersed boundary-thermal lattice Boltzmann method using an equilibrium internal energy density approach for the simulation of flows with heat transfer

In present paper, a novel immersed boundary-thermal lattice Boltzmann method by the name of “an equilibrium internal energy density approach” is proposed to simulate the flows around bluff bodies with the heat transfer. The main idea is to combine the immersed boundary method (IBM) with the thermal lattice Boltzmann method (TLBM) based on the double population approach. The equilibrium internal energy density approach based on the equilibrium velocity approach [X. Shan, H. Chen, Lattice Boltzmann model for simulating flows with multiple phases and components, Phys. Rev. E 47 (1993) 1815] is used to combine IBM with TLBM. The idea of the equilibrium internal energy density approach is that the satisfaction of the energy balance between heat source on the immersed boundary point and the amount of change of the internal energy density according to time ensures the temperature boundary condition on the immersed boundary. The advantages of this approach are the simple concept, easy implementation and the utilization of original governing equation without modification. The simulation of natural convection in a square cavity with various body shapes for different Rayleigh numbers has been conducted to validate the capability and the accuracy of present method on solving heat transfer problems. Consequently, the present results are found to be in good agreement with those of previous studies.     

Simulation of natural convection under high magnetic field by means of the thermal lattice Boltzmann method

The thermal lattice Boltzmann method (TLBM), which was proposed by J. G. M. Eggels and J. A. Somers previously, has been improved in this paper. The improved method has introduced a new equilibrium solution for the temperature distribution function on the assumption that flow is incompressible, and it can correct the effect of compressibility on the macroscopic temperature computed. Compared to the previous method, where the half-way bounce back boundary condition was used for non-slip velocity and temperature, a non-equilibrium extrapolation scheme has been adopted for both velocity and temperature boundary conditions in this paper. Its second-order accuracy coincides with the ensemble accuracy of lattice Boltzmann method. In order to validate the improved thermal scheme, the natural convection of air in a square cavity is simulated by using this method. The results obtained in the simulation agree very well with the data of other numerical methods and benchmark data. It is indicated that the improved TLBM is also successful for the simulations of non-isothermal flows. Moreover, this thermal scheme can be applied to simulate the natural convection in a non-uniform high magnetic field. The simulation has been completed in a square cavity filled with the aqueous solutions of KCl (11wt%), which is considered as a diamagnetic fluid with electrically low-conducting, with Grashof number Gr=4.64× 10^4 and Prandtl number Pr=7.0. And three cases, with different cavity locations in the magnetic field, have been studied. In the presence of a high magnetic field, the natural convection is quenched by the body forces exerted on the electrically low-conducting fluids, such as the magnetization force and the Lorentz force. From the results obtained, it can be seen that the quenching efficiencies decrease with the variation of location from left, symmetrical line, to the right. These phenomena originate from the different distributions of the magnetic field strengths in the zones of the symmetrical central line of the magnetic fields. The results are also compared with those without a magnetic field. Finally, we can conclude that the improved TLBM will enable effective simulation of the natural convection under a high magnetic field.     

基于总能形式的耦合的双分布函数热晶格玻尔兹曼数值方法

双分布函数热晶格玻尔兹曼数值方法在微尺度热流动系统中得到广泛的应用. 本文基于晶格玻尔兹曼平衡分布函数低阶Hermite展开式, 创新性地提出了包含黏性热耗散和压缩功的耦合的双分布函数热晶格玻尔兹曼数值方法, 将能量场内温度的变化以动量源的形式引入晶格波尔兹曼动量演化方程, 实现了能量场与动量场之间的耦合. 研究了考虑黏性热耗散和压缩功的和不考虑的两种热自然对流模型, 重点分析了不同瑞利数和普朗特数下流场内的流动情况以及温度、速度和平均努赛尔数的变化趋势. 本文实验结果与文献结果一致, 验证了本文数值方法的可行性和准确性. 研究结果表明: 随着瑞利数和普朗特数的增大, 方腔内对流传热作用逐渐增强, 边界处形成明显的边界层; 考虑黏性热耗散和压缩功的模型对流作用相对增强, 黏性热耗散和压缩功对自然对流的影响在微尺度流动过程中不能忽略.     

Numerical prediction of heat transfer by natural convection and radiation in an enclosure filled with an isotropic scattering medium

This paper deals with the numerical solution for natural convection and volumetric radiation in an isotropic scattering medium within a heated square cavity using a hybrid thermal lattice Boltzmann method (HTLBM). The multiple relaxation time lattice Boltzmann method (MRT-LBM) has been coupled to the finite difference method (FDM) to solve momentum and energy equations, while the discrete ordinates method (DOM) has been adopted to solve the radiative transfer equation (RTE) using the S8 quadrature. Based on these approaches, the effects of various influencing parameters such as the Rayleigh number (Ra), the wall emissivity (ε_ι), the Planck number (Pl), and the scattering albedo (ω), have been considered. The results presented in terms of isotherms, streamlines and averaged Nusselt number, show that in absence of radiation, the temperature and the flow fields are centro-symmetrics and the cavity core is thermally stratified. However, radiation causes an overall increase in the temperature and velocity gradients along both thermally active walls. The maximum heat transfer rate is obtained when the surfaces of the enclosure walls are regarded as blackbodies. It is also seen that the scattering medium can generate a multicellular flow.     

Simulations of complex fluids by mixed lattice Boltzmann—finite difference methods

We present the numerical results of simulations of complex fluids under shear flow. We employ a mixed approach which combines the lattice Boltzmann method for solving the Navier–Stokes equation and a finite difference scheme for the convection–diffusion equation. The evolution in time of shear banding phenomenon is studied. This is allowed by the presented numerical model which takes into account the evolution of local structures and their effect on fluid flow.     

方腔内Cu/Al2O3水混合纳米流体自然对流的格子Boltzmann模拟

纳米流体作为一种较高的导热介质, 广泛应用于各个传热领域. 鉴于纳米颗粒导热系数和成本之间的矛盾, 本文提出了一种混合纳米流体. 为了研究混合纳米流体颗粒间相互作用机理和自然对流换热特性, 在考虑颗粒间相互作用力的基础上, 利用多尺度技术推导了纳米流体流场和温度场的格子Boltzmann方程, 通过耦合流动和温度场的演化方程, 建立了Cu/Al₂O₃水混合纳米流体的格子Boltzmann模型, 研究了混合纳米流体颗粒间的相互作用机理和纳米颗粒在腔体内的分布. 发现在颗粒间相互作用力中, 布朗力远远大于其他作用力, 温差驱动力和布朗力对纳米颗粒的分布影响最大. 分析了纳米颗粒组分、瑞利数对自然对流换热的影响, 对比了混合纳米流体(Cu/Al₂O₃-水)与单一金属颗粒纳米流体(Al₂O₃-水)的自然对流换热特性, 发现混合纳米流体具有更强的换热特性.     

Lattice Boltzmann Simulation of Free-Surface Temperature Dispersion in Shallow Water Flows

We develop a lattice Boltzmann method for modeling free-surface temperature dispersion in the shallow water flows. The governing equations are derived from the incompressible Navier-Stokes equations with assumptions of shallow water flows including bed frictions, eddy viscosity, wind shear stresses and Coriolis forces. The thermal effects are incorporated in the momentum equation by using a Boussinesq approximation. The dispersion of free-surface temperature is modelled by an advection-diffusion equation. Two distribution functions are used in the lattice Boltzmann method to recover the flow and temperature variables using the same lattice structure. Neither upwind discretization procedures nor Riemann problem solvers are needed in discretizing the shallow water equations. In addition, the source terms are straightforwardly included in the model without relying on well-balanced techniques to treat flux gradients and source terms. We validate the model for a class of problems with known analytical solutions and we also present numerical results for sea-surface temperature distribution in the Strait of Gibraltar.     

基于LBM的部分热活跃边界下多孔腔体内自然对流换热

采用Boltzmann方法模拟部分热活跃边界下的多孔腔体内自然对流,探讨不同热边界布置方案、孔隙度、Da数及Ra数对其流动传热的影响.数值计算表明：Da=10^-4时,腔体内中央出现一个循环流模式,只在Ra数很大时孔隙度才对传热有影响; Da=10^-2时,腔体内出现两个循环流,在Ra数很小时孔隙度对传热产生强烈的的影响.热活跃边界位置影响腔体内流体对流传热的强度,加热边界布置在底部、而冷却边界布置在顶部（Bottom-Top布置方式）,对多孔腔体内对流传热最有利,优于全热边界布置方式的传热效果.     

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。     

Provide a suitable range to include the thermal creeping effect on slip velocity and temperature jump of an air flow in a nanochannel by lattice Boltzmann method

The thermal creeping effect on slip velocity of air forced convection through a nanochannel is studied for the first time by using a lattice Boltzmann method. The nanochannel side walls are kept hot while the cold inlet air streams along them. The computations are presented for the wide range of Reynolds number, Knudsen number and Eckert number while slip velocity and temperature jump effects are involved. Moreover appropriate validations are performed versus previous works concerned the micro–nanoflows.The achieved results are shown as the velocity and temperature profiles at different cross sections, streamlines and isotherms and also the values of slip velocity and temperature jump along the nanochannel walls. The ability of the lattice Boltzmann method to simulate the thermal creeping effects on hydrodynamic and thermal domains of flow is shown at this study; so that its effects should be involved at lower values of Eckert number and higher values of Reynolds number especially at entrance region where the most temperature gradient exists.     

Kinetic theory based lattice Boltzmann equation with viscous dissipation and pressure work for axisymmetric thermal flows

A lattice Boltzmann equation (LBE) for axisymmetric thermal flows is proposed. The model is derived from the kinetic theory which exhibits several features that distinguish it from other previous LBE models. First, the present thermal LBE model is derived from the continuous Boltzmann equation, which has a solid foundation and clear physical significance; Second, the model can recover the energy equation with the viscous dissipation term and work of pressure which are usually ignored by traditional methods and the existing thermal LBE models; Finally, unlike the existing thermal LBE models, no velocity and temperature gradients appear in the force terms which are easy to realize in the present model. The model is validated by thermal flow in a pipe, thermal buoyancy-driven flow, and swirling flow in vertical cylinder by rotating the top and bottom walls. It is found that the numerical results agreed excellently with analytical solution or other numerical results.     

强制对流和自然对流作用下枝晶生长的数值模拟

建立了一个基于格子玻尔兹曼方法 （LBM） 的二维模型,对强制对流和自然对流作用下合金凝固过程中的枝晶生长行为进行了模拟研究. 与传统的基于求解Navier-Stokes方程计算流场的方法不同,本模型采用基于分子动理论的LBM对凝固过程中的传输现象进行数值计算. 用三组粒子分布函数分别建立了计算流场、由对流和扩散所控制的浓度场和温度场的LBM演化方程. 通过求解LBM演化方程获得固/液界面前沿的浓度和温度分布. 然后,基于溶质平衡方法计算了枝晶生长的驱动力. 为了对模型进行验证,将模拟在强制和自然对流作用下枝晶上游尖端的稳态生长特征分别与Oseen-Ivantsov 解析解和修正的Lipton-Glicksman-Kurz 模型预测结果进行了比较, 模拟结果和理论预测结果符合良好. 模拟结果还表明,对流使热量和溶质从上游传输到下游,从而加速了枝晶在上游方向的生长,而抑制了下游方向的生长,形成了非对称的枝晶形貌. 关键词： 微观组织模拟 枝晶生长 对流 格子玻尔兹曼方法     

热动力学格子Boltzmann模型

提出了一类热动力学格子Boltzmann模型,其分布函数中含有内能项与高阶速度项。以三个HPP模型为基础,建立了一个三迭加HPP格子Boltzmann模型,并给出其局部平衡分布函数。设计了热动力学现象模拟中的外力处理方法和温度边界条件处理方法,用该模型成功地模拟了Benard热对流现象。     

Lattice Boltzmann Simulation of Mixed Convection Heat Transfer in a Driven Cavity with Non-uniform Heating of the Bottom Wall

The goal of this article is to study numerically the mixed convection in a differentially heated lid-driven cavity with non-uniform heating of the bottom wall. The velocity field is solved by a hybrid scheme with multiple relaxation time Lattice Boltzmann(MRT-LBM) model, while the temperature field is obtained by resolution of the energy balance equation using the finite difference method(FDM). First, the model is checked and validated using data from the literature. Validation of the present results with those available in the literature shows a good agreement.A good efficiency in time simulation is confirmed. Thereafter, the model has been applied to mixed convection in a driven cavity with non-uniform heating wall at the fixed Grashof number Gr = 106. It is found that, the heat transfer is weakened as the Richardson number is augmented. For Gr = 106, we note the appearance of secondary vortices at different positions of the cavity corners.