Simulation of Conjugate Heat Transfer Using the Lattice Boltzmann Method

The Lattice Boltzmann Method (LBM) is utilized to investigate conjugate heat transfer. Hot and cold streams enter the computational domain, and heat transfer takes place between the two streams through a finite thickness and finite thermal conductivity wall. The main objective of the work is to demonstrate that LBM can solve conjugate heat transfer by using one energy equation for solid and fluid phases. The flux continuity insures automatically. Furthermore, the effects of extended surfaces were investigated on the rate of heat transfer and pressure drop.     

Simulation of Mixed Convection in Eccentric Annulus: A Combined Lattice Boltzmann and Smoothed Profile Approach

ABSTRACT

Lattice Boltzmann Method is used to simulate mixed convection between two horizontal cylinders. This geometry is created using Smoothed Profile Method which produces proper fluid-solid interaction force as well as heat exchange. A two dimensional double distribution function lattice Boltzmann method is employed to simulate fluid flow and heat transfer simultaneously. In order to implement the velocity and temperature boundary conditions, the force term and heat source/sink are included in the evolution equations. While fixed Eulerian lattice nodes are employed, while different eccentricities are considered for inner cylinder. In order to simulate mixed convection, the radius ratio is set to be 2.5. Furthermore, the effect of Richardson number by choosing 0.01, 1, 100 and Prandtl number of 0.716 for air and 6.2 for water are investigated. Isotherms, streamlines and mean Nusselt numbers are given for each case. The results are in good agreement with previous related publications.     

高低热导率相间表面强化饱和池沸腾的格子玻尔兹曼模拟

采用格子玻尔兹曼方法模拟高低热导率相间表面的饱和池沸腾过程,研究不同表面高低热导率区域热导率比值、低热导率区域宽度和深度对沸腾换热性能的影响。对比均匀热导率表面与高低热导率相间表面的沸腾曲线发现：高低热导率相间表面的沸腾过程可被分为5个阶段,并且其临界热流密度最高可达均匀表面的12倍;高低热导率相间可促使表面维持一定的温度差异,从而保持明显的气液流动;随着低热导率区域宽度增大,气液分离更加明显,低热导率区域宽度存在一个最优值,其与毛细长度的量级接近;随着低热导率区域的深度增大,表面过热度的差异更加明显。     

Lattice Boltzmann Simulation of Two- and Three-Dimensional Incompressible Thermal Flows

This work is concerned with the application of the thermal lattice Boltzmann method (TLBM) to compute incompressible two- and three-dimensional flows in cavities. Two convection test cases, namely, the laminar flow in a differentially heated square cavity and a cubic cavity, are numerically analyzed through TLBM. The internal energy density distribution function approach with two three-dimensional particle velocity models, namely, the 15-velocity and the 19-velocity, and a two-dimensional model, namely, the nine-velocity, have been used in the present work. Computations are carried out for laminar flows in a differentially heated square cavity and a cubical cavity (Rayleigh numbers = 10³ to 10⁵). The boundary conditions used are stable and of good accuracy. To lend credibility to the thermal lattice Boltzmann model square cavity results, they are further compared with those obtained from a finite-difference-based code developed for this purpose.     

Lattice Boltzmann Simulation of Convective Heat Transfer from Heated Blocks in a Horizontal Channel

This article presents the application of the multiple-relaxation-time (MRT) lattice Boltzmann equation (LBE) method with nine-velocity model to the numerical prediction of a laminar and convective-heated transfer through a two-dimensional obstructed channel flow. The obstruction is carried out by three obstacles including two located on the upper wall and the other on the lower wall of the channel. The calculations are validated against results available in literature. Various physical arrangements are regarded as the size of the obstacles and the distance between the two upper obstacles to investigate their effects on thermal and flow characteristics. Results, presented for a Prandtl number equal to 0.71 and a Reynolds number ranging from 100 to 1200, showed that the heat transfer and the air flow depend both on the Reynolds number and geometric data of the configuration.     

A Molecular Dynamics and Lattice Boltzmann Multiscale Simulation for Dense Fluid Flows

A molecular dynamics (MD)-lattice Boltzmann (LB) hybrid scheme has been adopted to simulate dense fluid flows. Based on the domain decomposition method and the Schwarz alternating scheme, the “Maxwell Demon” approach is used to impose boundary conditions from the continuum to the atomistic region, while the “reconstruction operator” is implemented to construct the single-particle distribution function of the LB method from the results of the MD simulation. Couette flows and the flow of a dense fluid argon around a carbon nanotube (CNT) are solved to validate the hybrid method. When the mesh of the LB domain is refined and the size of corresponding sampling cells of the MD domain is reduced, the fluctuations of the results between two successive iterations of the hybrid method become more severe, although the results get closer to the MD reference solutions. To decrease the fluctuation due to the mesh refinement, a new weighting function is proposed for the sampling of MD simulation results. Numerical practice demonstrates its feasibility.     

Analysis of Conduction-Radiation Heat Transfer in a 2D Enclosure Using the Lattice Boltzmann Method

Application of the lattice Boltzmann method (LBM) recently extended by Pietro et al. [P. Asinari, S. C. Mishra, and R. Borchiellini, A Lattice Boltzmann Formulation to the Analysis of Radiative Heat Transfer Problems in a Participating Medium, Numer. Heat Transfer B, 57(2), 126–146, 2010] for calculation of volumetric radiative information is extended for the analysis of a combined mode transient conduction and radiation heat transfer in a 2D rectangular enclosure containing an absorbing, emitting and scattering medium. Unlike all previous studies, with volumetric radiative information computed using the proposed LBM, the energy equation is formulated and solved using the LBM. In the combined mode conduction–radiation problem, to assess the computational advantage of computing the radiative information too using the LBM, the same problem is also solved using the LBM–finite volume method (FVM) formulation. In this LBM–FVM formulation, the FVM is used to calculate the volumetric radiative information needed for the energy equation, and the energy equation is solved using the LBM. Comparisons are made for the effects of the extinction coefficient, the scattering albedo and the conduction–radiation parameter on the temperature distributions in the medium. Although the number of iterations for the converged solution in LBM–LBM is much more than that of the LBM–FVM, computationally, the LBM–LBM is faster than the LBM–FVM.     

格子Boltzmann方法模拟土体渗流场研究

格子Boltzmann方法模拟土体渗流场,较传统的数值计算方法具有并行计算能力好、能得到流场细节信息、擅长处理复杂边界的独特优势。通过构建入口边界为非平衡外推格式、出口边界为充分发展格式、左右边界为反弹格式的基于通用渗流模型的LBM模型,编程实现格子Boltzmann方法模拟水在同一级配三种颗粒随机分布的土壤中的渗流情况。通过经典算例验证了所编程序的正确性和有效性,并由得到的渗流场图分析发现,土体颗粒的均匀性和通透性较好时渗流场流线的形状和畅通性也较好。     

并列双柱绕流的格子Boltzmann模拟

采用格子Boltzmann方法模拟研究了并列双圆柱的绕流现象,利用非平衡外推法进行边界条件处理,基于C++编制程序,获得了不同雷诺数Re和柱间距比H/D下的流速及回流区分布,并分析了并列双柱绕流的流动特性。结果表明,随Re的增大,流场由层流向卡门涡街转变,回流区长度先增大后减小,临界值为Re=50;随H/D的增大,可将流动模式分为单体模式、交替翻转模式、同相模式及反相模式四种,回流区长度在这四种模式下随H/D的增大而增大。     

A Simple Finite-Volume Formulation of the Lattice Boltzmann Method for Laminar and Turbulent Flows

A finite-volume formulation commonly employed in the well-known SIMPLE family algorithms is used to discretize the lattice Boltzmann equations on a cell-centered, non-uniform grid. The convection terms are treated by a higher-order bounded scheme to ensure accuracy and stability of solutions, especially in the simulation of turbulent flows. The source terms are linearized by a conventional method, and the resulting algebraic equations are solved by a strongly implicit procedure. A method is also presented to link the lattice Boltzmann equations and the macroscopic turbulence modeling equations in the frame of the finite-volume formulation. The method is applied to two different laminar flows and a turbulent flow. The predicted solutions are compared with the experimental data, benchmark solutions, and solutions by the conventional finite-volume method. The results of these numerical experiments for laminar flows show that the present formulation of the lattice Boltzmann method is slightly more diffusive than the finite-volume method when the same numerical grid and convection scheme are used. For a turbulent flow, the finite-volume lattice Boltzmann method slightly underpredicts the reattachment length in a separated flow. In general, the finite-volume lattice Boltzmann method is as accurate as the conventional finite-volume method in predicting the mean velocity and the pressure at the wall. These observations show that the present method is stable and accurate enough to be used in practical simulations of laminar and turbulent flows.     

格子Boltzmann方法模拟层流对冲预混火焰

运用格子Boltzmann方法对气体燃烧进行了模拟,其中包括了对流、扩散和反应等过程．在模拟中假设化学反应对流场没有影响,因而流场、温度场和组分场没有相互耦合,可以分别用LB方程进行求解．选择层流对冲火焰作为对燃烧的基础计算模拟．该模型的几何特征是有两个相对的相同燃烧喷口喷出燃料与空气的混合气体,而形成稳定的流场．计算结果与传统的Navier—Stokes方法计算得到的结果进行了对比,结果能够较好地吻合,说明格子Boltzmann方法可以对燃烧进行模拟．     

Numerical Simulation of Melting Problems Using the Lattice Boltzmann Method with the Interfacial Tracking Method

A lattice Boltzmann method with an interfacial tracking method is used to solve melting problem in an enclosure. Both conduction- and convection-controlled melting problems are solved to validate the proposed method. For the conduction-controlled melting problem, the results agreed very well with those from the analytical solution. The results for the convection-controlled melting problem also agreed with those in the literature. The proposed approach is valid for numerical simulation of the melting problem.     

Radiation Element Method Coupled with the Lattice Boltzmann Method Applied to the Analysis of Transient Conduction and Radiation Heat Transfer Problem with Heat Generation in a Participating Medium

This article deals with the implementation of the radiation element method (REM) with the lattice Boltzmann method (LBM) to solve a combined mode transient conduction-radiation problem. Radiative information computed using the REM is provided to the LBM solver. The planar conducting-radiating participating medium is contained between diffuse gray boundaries, and the system may contain a volumetric heat generation source. Temperature and heat flux distributions in the medium are studied for different values of parameters such as the extinction coefficient, the scattering albedo, the conduction-radiation parameter, the emissivity of the boundaries, and the heat generation rate. To check the accuracy of the results, the problem is also solved using the finite-volume method (FVM) in conjunction with the LBM. In this case, the data for radiation field are calculated using the FVM. The REM has been found to be compatible with the LBM, and in all the cases, results of the LBM-REM and the LBM-FVM have been found to provide an excellent comparison.     

A Lattice Boltzmann Formulation for the Analysis of Radiative Heat Transfer Problems in a Participating Medium

Use of the lattice Boltzmann method (LBM) has been extended to analyze radiative transport problems in an absorbing, emitting, and scattering medium. In terms of collision and streaming, the present approach of the LBM for radiative heat transfer is similar to those being used in fluid dynamics and heat transfer for the analyses of conduction and convection problems. However, to mitigate the effect of the isotropy in the polar direction, in the present LBM approach, lattices with more number of directions than those being used for the 2-D system have been employed. The LBM formulation has been validated by solving benchmark radiative equilibrium problems in 1-D and 2-D Cartesian geometry. Temperature and heat flux distributions have been obtained for a wide range of extinction coefficients. The LBM results have been compared against the results obtained from the finite-volume method (FVM). Good comparison has been obtained. The numbers of iterations and CPU times for the LBM and the FVM have also been compared. The number of iterations in the LBM has been found to be much more than the FVM. However, computationally, the LBM has been found to be much faster than the FVM.     

Lattice Boltzmann Simulation of Conjugate Heat Transfer from Multiple Heated Obstacles Mounted in a Walled Parallel Plate Channel

In the present study, lattice Boltzmann simulation of conjugate heat transfer from multiple heated obstacles mounted in a walled parallel-plate channel is carried out. The aim is to investigate the effects of the pertinent thermophysical and geometrical parameters on the local Nusselt number around the obstacle's periphery. The result showed that increasing the obstacle to fluid thermal conductivity ratio and decreasing wall-to-obstacle thermal conductivity ratio results in increasing the local Nusselt number around the obstacle's periphery. The results of the present study are compared with those available from the conventional numerical methods, and good agreement is observed.     

A Review on the Application of the Lattice Boltzmann Method for Turbulent Flow Simulation

The Lattice Boltzmann Method (LBM) is a potent numerical technique based on kinetic theory, which has been effectively employed in various complicated physical, chemical, and fluid mechanics problems. In recent years, turbulent flow simulation by using this new class of computational fluid dynamics technique has attracted more attention. In this article, a review of previous studies on turbulence in the frame of LBM is presented. Recent extensions of this method are categorized based on three main groups of turbulence simulation: DNS, LES and RANS methods.     

格子Boltzmann方法的竖壁汽液降膜数值研究

对原有的格子Boltzmann伪势模型进行了改进,提出表面张力可调的伪势模型,并基于改进后的伪势两相模型在二维条件下模拟了雷诺数为5、10和20时竖壁降膜的流动,进一步研究了液膜在入口处存在正弦扰动时的流动特性,分析了入口扰动和表面张力作用对液膜稳态波动的影响,总结了液膜稳态波动的规律.结果表明:数值计算得到的流形拓扑及波动特征与实验结论能较好地吻合,表明伪势模型能够较为真实地反映降膜流动的物理过程.     

基于格子Boltzmann方法的柴油机SCR脱硝模拟

基于格子Boltzmann方法,对应用于柴油机的选择性催化还原(SCR)进行了介观尺度数值模拟.采用D2Q9模型描述速度场,D2Q5模型描述浓度场,通过耦合化学反应分析了空速比、催化剂孔隙率及颗粒半径对柴油机SCR脱硝效率的影响,并描述了介观尺度上SCR反应过程中的流动、扩散与反应现象.其中,空速比选取范围为10000...     

Analysis of Conduction and Radiation Heat Transfer in a 2-D Cylindrical Medium Using the Modified Discrete Ordinate Method and the Lattice Boltzmann Method

This article deals with the analysis of radiative transport with and without conduction in a finite concentric cylindrical enclosure containing absorbing, emitting, and scattering medium. Isothermal medium as the radiation source confined between the cold cylinders and a nonisothermal medium with the inner cylinder as the radiation source are the two nonradiative and radiative equilibrium problems. They involve only calculation of radiative information. In the third problem, a conducting-radiating medium is thermally perturbed by raising the temperature of the inner cylinder. In all problems, radiative information is computed using the modified discrete ordinate method (MDOM), and in the third problem, the lattice Boltzmann method (LBM) is used to formulate and solve the energy equation. Depending on the problems, effects of various parameters such as the extinction coefficient, the scattering albedo, the boundary emissivity, the conduction-radiation parameter, and the radius ratio are studied on temperature and heat flux distributions. The MDOM and the LBM-MDOM results are compared with those available in the literature. To further establish the accuracy of the MDOM and the LBM-MDOM results, in all problems, comparisons are made with the results obtained from the finite volume method (FVM) and the finite difference method-FVM approach, in which FVM provides the radiative information. The selection of the FDM-FVM for the third problem is also with the objective that for this problem, not much work is reported in which the FVM is used to calculate the radiative information. MDOM and LBM-MDOM results are found to compare well with those available in the literature, and in all cases they are in excellent agreement with FVM and FDM-FVM approaches.     

Mixed Convection Heat Transfer Analysis in an Enclosure with Two Hot Cylinders: A Lattice Boltzmann Approach

The aim of this work is to study laminar mixed convection heat transfer characteristics within an obstructed enclosure by using the Lattice Boltzmann method. Flow is driven by a top cold lid while other walls are stationary and adiabatic. Hot cylinders are located at different places inside the cavity to explore the best arrangement. Comparison of streamlines, isotherms, average Nusselt number are presented to evaluate the influence of Richardson number and location of cylinders on flow field and heat transfer. Results indicate that heat transfer decreases with a rise of Richardson number for all considered arrays of cylinders. Among them, horizontally‐located cylinders at the top of the cavity have the greatest heat transfer at all Richardson numbers. Horizontally located cylinders at the bottom of the cavity have the lowest heat transfer at Richardson numbers of 0.1 and 1 while the lowest heat transfer rate belongs to cross diagonal located cylinders at a Richardson number of 10.