A Hybrid Lattice Boltzmann and Finite-Volume Method for Melting with Convection

A hybrid lattice Boltzmann and finite-volume model is proposed to solve the natural-convection-controlled melting problem. The lattice Boltzmann method (LBM) is applied to solve the velocity field, while the temperature field is obtained by the finite-volume method (FVM). The D2Q9 model and finite-difference velocity gradient boundary condition are used in the LBM and the SIMPLE algorithm with QUICK scheme is employed in the FVM. An interfacial tracking model based on energy balance at the interface is applied to obtain the location of the solid–liquid interface. The results from the present hybrid method are validated with experimental results, and good agreement is obtained.     

MHD Turbulent and Laminar Natural Convection in a Square Cavity utilizing Lattice Boltzmann Method

In this study, the lattice Boltzmann method was used to solve the turbulent and laminar natural convection in a square cavity. In this paper a fluid with Pr = 6.2 and different Rayleigh numbers (Ra = 10³, 10⁴,10⁵ for laminar flow and Ra = 10⁷, 10⁸,10⁹ for turbulent flow) in the presence of a magnetic field (Ha = 0, 25, 50, and 100) was investigated. (Results show that the magnetic field drops the heat transfer in the laminar flow as the heat transfer behaves erratically toward the presence of a magnetic field in a turbulent flow. Moreover, the effect of the magnetic field is marginal for a turbulent flow in contrast with a laminar flow.The greatest influence of the magnetic field is observed at Ra = 10⁵ from Ha = 0 to 100 as the heat transfer decreases significantly.     

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.     

A Parallel Unstructured Finite-Volume Method for All-Speed Flows

Parallel computational fluid dynamics is one of the key applications in the area of high-performance computations. The primary goals of this work are to develop a parallel unstructured finite-volume solver for all-speed flows based on a domain decomposition method, and to establish a comprehensive and intensive analysis method for the parallel performance. The numerical calculations of several typical flows using hundreds of CPU cores validate the accuracy and parallel performance of the parallel solver. The analysis of the decomposed efficiencies reveals the key factors that limit the parallel performance. This work is quite generic and can be extended to the large-scale parallel calculation and performance analysis of complex fluid flow and heat transfer problems.     

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．     

A Coupled Pressure-Based Co-Located Finite-Volume Solution Method for Natural-Convection Flows

A pressure-based coupled solution method based on a finite-volume discretization is presented. The method uses a cell-centered co-located variable arrangement on a nonorthogonal two-dimensional structured grid. The coupled algebraic analogs of the mass, momentum, and energy conservation equations for incompressible flow are solved. In addition to coupling the mass and momentum equations, the energy equation is coupled to the velocities via a Newton-Raphson linearization of the energy advection terms. The momentum equations are coupled to the energy equation via an implicit temperature in the Boussinesq approximation. The convergence behavior of the new method is demonstrated on the solution of steady, laminar natural convection in an annulus for Prandtl numbers of 0.707 and 13,050 at a Rayleigh number of 1 × 10⁶. A significant reduction in the number of iterations to convergence is obtained with the new method compared to a method with only velocity-to-temperature coupling and a method with energy and momentum decoupled. An improvement to the new method was obtained by using an approach that uses a delayed time-step increase and a modified face temperature value estimation.     

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.     

Computation of Turbulent Natural Convection in a Rectangular Cavity with the Lattice Boltzmann Method

A numerical study of a turbulent natural convection in a rectangular cavity with the lattice Boltzmann method (LBM) is presented. The primary emphasis of the present study is placed on investigation of accuracy and numerical stability of the LBM for the turbulent natural-convection flow. A HYBRID method in which the thermal equation is solved by the conventional Reynolds-averaged Navier-Stokes equation (RANS) method while the conservation of mass and momentum equations are resolved by the LBM is employed in the present study. The elliptic-relaxation model is employed for the turbulence model and the turbulent heat fluxes are treated by the algebraic flux model. All the governing equations are discretized on a cell-centered, nonuniform grid using the finite-volume method. The convection terms are treated by a second-order central-difference scheme with the deferred correction method to ensure accuracy and stability of solutions. The present LBM is applied to the prediction of a turbulent natural convection in a rectangular cavity and the computed results are compared with the experimental data commonly used for the validation of turbulence models and those by the conventional finite-volume method. It is shown that the LBM with the present HYBRID thermal model predicts mean velocity components and turbulent quantities which are as good as those by the conventional finite-volume method. It is also found that the accuracy and stability of the solution is significantly affected by the treatment of the convection term, especially near the wall.     

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.     

An Unstructured Finite-Volume Method for Incompressible Flows with Complex Immersed Boundaries

A numerical method is developed for solving three-dimensional, unsteady, incompressible flows with immersed moving solids of arbitrary geometric complexity. A co-located (nonstaggered) pressure-based finite-volume method is employed to solve the Navier-Stokes equations for the flow region, and the solid region is represented by material points with known position and velocity. The influence of the body on the flow is accounted for by reconstructing implicitly the velocity on the immersed boundary faces b-tween fluid and solid. Canonical test cases and mesh convergence tests are carried out. A validation test for the vibration of microcantilevers shows good agreement between computed and measured damping factor values.     

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.     

Experiments on the Laminar/Turbulent Transition of Liquid Flows in Rectangular Microchannels

The advances of micro-fabrication techniques allow for the manufacturing of micro-heat exchangers or micro-reactors. These micro-devices are characterized by a large surface-to-volume ratio and, hence, allow for the transfer of large heat fluxes or offer large catalytic surfaces for reactions. The design and optimization of such micro-devices heavily relies on correlations for pressure drop and heat transfer, as well as on information on the laminar/turbulent transition. As these questions are still discussed controversially in literature, a careful investigation appears highly desirable. This paper concentrates on rectangular stainless steel micro-channels with a hydraulic diameter of about 133 μm. Three aspect ratios of 1:1, 1:2, 1:5 are studied, whereas the hydraulic diameter is kept constant. The average roughness depth of the channel walls is about 1–2 μm in general, and specific channels are of roughness depth of about 25 μm. Filtered and degassed de-ionized water is driven at pressure differences up to 20 bar through the channels, allowing for Reynolds numbers up to 4000. The measuring techniques allow for a highly accurate determination of the mass flow rate (precision weighting), the temperatures at inlet and outlet, the pressure drop, and the time-resolved velocity field (μPIV). The measured quantities consistently show that the laminar/turbulent transition for smooth channels is in the Reynolds number range of 1900–2200, which is in agreement with findings for macroscopic channels. The influence of rough channel walls appears particularly strong for the micro channels of aspect ratio 1:5 (Reynolds number of about 1000). This raises the question of whether the relative roughness remains the relevant parameter at extreme aspect ratios. In this article, we focus on the μPIV results.     

A Comparative Study of Submicron Phonon Transport Using the Boltzmann Transport Equation and the Lattice Boltzmann Method

The subcontinuum energy transport mechanism in solids can be explained by the Lattice Boltzmann Method (LBM), a discrete representation of the Boltzmann Transport Equation (BTE). The present study focuses on a detailed comparison of the LBM and BTE. Results reveal that at continuum scale, the LBM follows the BTE almost precisely. However, as the device dimensions are reduced, approaching the ballistic limit, the LBM deviates from the BTE results in terms of thermal property estimation. The inherent nonisotropic lattice configuration has a dominant contribution to the performance of the LBM. A threshold length scale is also proposed for successful implementation of the LBM solver.     

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。     

Experimental Analysis of Pressure Drop and Laminar to Turbulent Transition for Gas Flows in Smooth Microtubes

The results of numerical and experimental works dealing with the behavior of gas flow through microchannels are by no means univocal, sometimes agreeing with the classical correlations and other times contradicting them. It is now agreed upon that the effects due to both rarefaction and compressibility must be accounted for. In addition, the experimental works have demonstrated that sometimes compressibility and rarefaction effects can be coupled in microchannels: because these two actions contrast each other, the scatter of the friction factor data for gaseous flows is remarkably large. This paper is aimed at determining the friction factor for commercial short and long Peek microtubes with nominal internal diameters between 300 and 100 μ m and values of the length-to-diameter ratio, L/D, ranging between 167 and 5000. Nitrogen flows inside the microtubes, with a maximum value of the supply pressure equal to 10 bar. Very low Knudsen numbers (Kn < 0.001) are considered in order to uncouple the rarefaction effects from the compressibility effects. The role of the minor losses related to the inlet and outlet of the test section and of the gas compressibility on the friction factor are analyzed and discussed in order to draw their limit of significance in microchannels. In addition, the effects of the gas compressibility and of the L/D ratio on the critical Reynolds number for which the laminar to turbulent transition takes place will be analyzed and discussed by comparing the experimental results with the other data published in the literature.     

A Least-Squares-Based Immersed Boundary Approach for Complex Boundaries in the Lattice Boltzmann Method

A least-squares algorithm for handling complex boundaries with the lattice Boltzmann method is proposed. The method is an extension to an immersed boundary implementation of the solver. We impose additional rules that are designed to conserve the mass flux through cut-cell control volumes and also to satisfy the continuity condition on the numerical boundary points. Then, we use the least-squares method to find the best achievable solution of the overdetermined system. Further, computational cost assessments are considered. The qualitative and quantitative results show that the velocity values obtained from simulation of a flow with curved and moving boundaries, i.e., the Taylor-Couette flow, are closer to the exact solution than the values found from the traditional approach. Finally, we present some statistical analysis to show that the velocities are obtained confidently.     

Effect of Laminar and Turbulent Buoyancy-Driven Flows on Thermal Energy Storage using Supercritical Fluids

Efficient heat transfer to storage fluid is required for the desirable operation of thermal energy storage systems. Most of the fluid candidates for supercritical thermal storage have poor thermal conductivity; therefore, conduction does not provide sufficient heat transfer. The current study concerns a supercritical thermal energy storage system consisting of horizontal tubes filled with a storage fluid in its supercritical state. The results of this study show that the heat transfer to the supercritical fluid is dominated by laminar and turbulent natural convection. The buoyancy-driven flow inside the storage tubes enhances the heat transfer and dramatically reduces the charge time.     

Analysis of a Localized Fire in a 3-D Tunnel Using a Hybrid Solver: Lattice Boltzmann Method,Finite-Volume Method,and Fully Explicit Upwind Scheme

A localized fire in a 3-D tunnel is analyzed by solving a combined-mode natural-convection and radiation problem. Nonlocal thermal equilibrium between air and smoke is considered. Separate energy equations are used for the two species. The density and temperature fields required for the solution of the energy equation are computed using the lattice Boltzmann method. The finite-volume method is used to compute radiative information. The energy equations are solved using the fully explicit upwind scheme. The Boussinesq approximation is used to account for the buoyancy effect. Effects of the scattering albedo, the convection-radiation parameter, and the wall emissivities on temperature profiles in the tunnel have been studied.     

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.     

High Knudsen Number Thermal Flows with the D2Q13 Lattice Boltzmann Model

Lattice Boltzmann models have been successfully utilized to simulate conditions in rarefied flows. To further improve the characterization of transition flow expected in nano-scale channels, we explore implementing two wall-distance functions based on the integral of probability distribution functions to a D2Q13 model. A series of tests are performed to determine model performance in capturing the flow characteristics of highly rarefied conditions. The resulting model is validated using numerical data. The results show that the modified model is capable of simulating rarefied flow conditions, extending to the high end of the transition regime, up to Kn ～ 5, representing a significant improvement over existing models.