格子Boltzmann方法模拟湍流流动

概述了国内外利用分子动力学研究流动的方法，主要介绍一种新的数值计算方法——格子Boltzmann方法。对此法的原理、模拟的模型及其在湍流流动中的应用进行了综述。分析这种方法在模拟湍流时存在的问题。为湍流流动研究指出了一条新的途径——用分子动力学理论研究湍流流动。     

Numerical simulations of gas resonant oscillations in a closed tube using lattice Boltzmann method

Numerical studies are presented for gas resonant oscillations in a two-dimensional closed tube using the lattice Boltzmann method. A multi-distribution function model of thermal lattice Boltzmann method is adopted in this work. The oscillating flow of the gas is generated by a plane piston at one end, and reflected by the other closed end. Both isothermal and adiabatic walls of the closed tube are considered. Boundary treatments such as moving adiabatic boundary are given in detail. The time dependent velocity, density and temperature at various locations of the tube for various frequencies and wall boundary conditions are presented. Shock waves with resonant frequency or slightly off-resonant frequencies are numerically captured. From the simulation results, the gas flow and heat transfer characteristics obtained are consistent qualitatively with those from previous simulations using conventional numerical methods.     

Simulating magnetohydrodynamic natural convection flow in a horizontal cylindrical annulus using the lattice Boltzmann method

A numerical study is presented about the effect of a uniform magnetic field on free convection in a horizontal cylindrical annulus using the lattice Boltzmann method. The inner and outer cylinders are maintained at uniform temperatures and it is assumed the walls are insulating with a magnetic field. Detailed numerical results of heat transfer rate, temperature, and velocity fields have been presented for Pr=0.7, Ra=10³ to 5 × 10⁴, and Ha=0 to 100. The computational results show that in a horizontal cylindrical annulus the flow and heat transfer are suppressed more effectively by a radial magnetic field. It is also found that the flow oscillations can be suppressed effectively by imposing an external radial magnetic field. The average Nusselt number increases by increasing the radius ratio while it decreases by increasing the Hartmann number. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21008     

Simulation of droplets impact on curved surfaces with lattice Boltzmann method

Several dimensionless parameters are studied to describe their effects on the deformation of a droplet after impact on a 2D round surface by using lattice Boltzmann implementation of pseudo-potential model. Four typical deformation process can be found: moving, spreading, nucleating and falling. In addition, in some special cases, part splashing is involved. It is observed that impact velocity of droplet has a significant influence on the droplet impacting dynamics. With the increasing of the impact velocity, different states have been found during the process. Moreover, when the surface is hydrophobic, splash occurs.     

Simulation of high Rayleigh number natural convection in a square cavity using the lattice Boltzmann method

A thermal lattice Boltzmann method based on the BGK model has been used to simulate high Rayleigh number natural convection in a square cavity. The model uses the double populations approach to simulate hydrodynamic and thermal fields. The traditional lattice Boltzmann method on a uniform grid has unreasonably high grid requirements at higher Rayleigh numbers which renders the method impractical. In this work, the interpolation supplemented lattice Boltzmann method has been utilized. This is shown to be effective even at high Rayleigh numbers. Numerical results are presented for natural convection in a square cavity with insulated horizontal walls and isothermal vertical walls maintained at different temperatures. Very fine grids (wall y⁺ < 0.3) have been used for the higher Rayleigh number simulations. A universal structure is shown to exist in the mean velocity turbulent boundary layer profile for y⁺ < 10. This agrees extremely well with previously reported experimental data. The numerical results (for Rayleigh numbers up to 10¹⁰) are in very good agreement with the benchmark results available in the literature. The highlight of the calculations is that no turbulence model has been employed.     

A thermal immiscible multiphase flow simulation by lattice Boltzmann method

The lattice Boltzmann (LB) method, as a mesoscopic approach based on the kinetic theory, has been significantly developed and applied in a variety of fields in the recent decades. Among all the LB community members, the pseudopotential LB plays an increasingly important role in multiphase flow and phase change problems simulation. The thermal immiscible multiphase flow simulation using pseudopotential LB method is studied in this work. The results show that it is difficult to achieve multi-bubble/droplet coexistence due to the unphysical mass transfer phenomenon of “the big eat the small” – the small bubbles/droplets disappear and the big ones getting bigger before a physical coalescence when using an internal energy based temperature equation for single-component multiphase (SCMP) pseudopotential models. In addition, this unphysical effect can be effectively impeded by coupling an entropy-based temperature field, and the influence on density fields with different energy equations are discussed. The findings are identified and reported in this paper for the first time. This work gives a significant inspiration for solving the unphysical mass transfer problem, which determines whether the SCMP LB model can be used for multi-bubble/droplet systems.     

Solution of inverse heat conduction problem using the lattice Boltzmann method

In this paper the D2Q9 lattice Boltzmann method (LBM) was utilized for the solution of a two-dimensional inverse heat conduction (IHCP) problem. The accuracy of the LBM results was validated against those obtained from prevalent numerical methods using a common benchmark problem. The conjugate gradient method was used in order to estimate the heat flux test case. A complete error analysis was performed. As the LBM is attuned to parallel computations, its use is recommended in conjugation with IHCP solution methods.     

低雷诺数下翼型绕流的格子Boltzmann方法数值模拟

文章采用混合格子Boltzmann方法模拟NACA0012翼型流场分离,该方法是将标准格子Boltzmann方法与非结构化有限体积方程相结合的一种方法。首先,分析不同网格分辨率下的计算精度;然后,分析了在雷诺数等于103的情况下不同攻角下翼型的气动特性;最后,计算了不同雷诺数下攻角为0°时的翼型流场。结果证明,混合格子Boltzmann方法在固体壁面有较高的计算精度,可以准确地评估翼型绕流流场。     

Numerical study of flow and heat transfer characteristics of alumina-water nanofluids in a microchannel using the lattice Boltzmann method

In the present study, mathematical modeling is performed to simulate force d convection flow of Al₂O₃/water nanofluids in a microchannel using the lattice Boltzmann method (LBM). Simulations are conducted at low Reynolds numbers (Re ≦ 16). Results indicate that the average Nusselt number increases with the increase of Reynolds number and particle volume concentration. The fluid temperature distribution is more uniform with the use of nanofluid than that of pure water. Furthermore, great deviations of computed Nusselt numbers using different models associated with the physical properties of a nanofluid are revealed. The results of LBM agree well with the classical CFD method for predictions of flow and heat transfer in a single channel and a microchannel heat sink concerning the conjugate heat transfer problem, and consequently LBM is robust and promising for practical applications.     

An investigation into fixed-bed microreactors using lattice Boltzmann method simulations

The fixed-bed microreactor is an important component in many biochip, microsensor, and microfluidic devices. The lattice Boltzmann method (LBM) provides a powerful technique for investigating such microfluidic systems. Accordingly, this study performs LBM-based simulations to examine fluid flows through a fixed-bed microreactor comprising a microarray of porous solids. During operation, the fluid and porous solid species are heated to prompt the chemical reaction necessary to generate the required products. Using the LB model, the flow fields and temperature fields in the microreactor are simulated for different Reynolds numbers, heat source locations, the reacting block aspect ratios, and porosity. A simple model is proposed to evaluate the chemical reactive efficiency of the microreactor based on the steady-state temperature field. The results of this model enable the optimal configuration and operating parameters to be established for the microreactor.     

Numerical simulation of direct methanol fuel cells using lattice Boltzmann method

In this study Lattice Boltzmann Method (LBM) as an alternative of conventional computational fluid dynamics method is used to simulate Direct Methanol Fuel Cell (DMFC). A two dimensional lattice Boltzmann model with 9 velocities, D2Q9, is used to solve the problem. The computational domain includes all seven parts of DMFC: anode channel, catalyst and diffusion layers, membrane and cathode channel, catalyst and diffusion layers. The model has been used to predict the flow pattern and concentration fields of different species in both clear and porous channels to investigate cell performance. The results have been compared well with results in literature for flow in porous and clear channels and cell polarization curves of the DMFC at different flow speeds and feed methanol concentrations.     

Study on forcing schemes in the thermal lattice Boltzmann method for simulation of natural convection flow problems

The present study addresses the effect of various schemes for applying an external force term on the accuracy and performance of the thermal lattice Boltzmann method (LBM) for simulation of free convection problems. Herein, the forcing schemes of Luo, shifted velocity method, Guo, and exact difference method are applied by considering three velocity discrete models of D2Q4, D2Q5, and D2Q9. The accuracy and performance of these schemes are evaluated with the simulation of three natural convection problems, namely, free convection in a closed cavity, in a square enclosure with a hot obstacle inside, and the Rayleigh-Benard problem. The obtained results based on the present thermal LBM with different forcing schemes and velocity discrete models are compared with the existing experimental and numerical data in the literature. This comparison study indicates that imposing all employed forcing schemes leads to similar performance for the simulation of free convection problems studied at the middle range of Rayleigh numbers. It is found that the Luo forcing scheme is simple for implementation in comparison with the other three forcing schemes and provides the results with acceptable accuracy at moderate Rayleigh numbers. At higher Rayleigh numbers, however, the Guo scheme is not only numerically stable but a more precise forcing scheme in comparison with the other three methods. It is illustrated that employing the discrete velocity model of D2Q4 has more appropriate numerical stability along with less computational cost in comparison with two other discrete velocity models for simulation of natural convection heat transfer.     

Numerical study of natural convection and acoustic waves using the lattice Boltzmann method

In this paper, the lattice Boltzmann method is used to study the acoustic waves propagation inside a differentially heated square enclosure filled with air. The waves are generated by a point sound source located at the center of this cavity. The main aim of this simulation is to simulate the interaction between the thermal convection and the propagation of these acoustic waves. The results have been validated with those obtained in the literature and show that the effect of natural convection on the acoustic waves propagation is almost negligible for low Rayleigh numbers (Ra ≤ 10⁴), which begins to appear when the Rayleigh number begins to become important (Ra ≥ 10⁵) and it becomes considerable for large Rayleigh numbers (Ra ≥ 10⁶) where the thermal convection is important.     

Simulation of gas exothermic chemical reaction in porous media reactor with lattice Boltzmann method

Exothermic reactor is the main part in a chemical heat pump. It involves complex multi-component exothermal chemical reaction in catalyst-filled porous media. The lattice Boltzmann method (LBM) is developed to simulate the characteristics of fluid flow, heat and mass transfer coupling chemical reaction in the exothermic reactor of the isopropanol/acetone/hydrogen chemical heat pump system. Fractal theory is used to structure a porous medium model in the reactor. The simulation results show that LBM is suitable for the simulation and the conversion has an optimal value with different inlet velocities.     

Comparing through-plane diffusibility correlations in PEFC gas diffusion layers using the lattice Boltzmann method

One of the key elements in a polymer electrolyte fuel cell (PEFC) is the gas diffusion layer (GDL). The GDL offers mechanical support to the cell and provides the medium for diffusing the reactant gases from the flow plates to the electrolyte enabling the electrochemical reactions, and therefore the energy conversion. At the same time, it has the task of transporting the electrons from the active sites, near to the electrolyte, towards the flow plates.Describing the fluid flow and mass transport phenomena through the GDLs is not an easy task not only because of their complex geometries, but also because of these phenomena occur at microscale levels. Most of the PEFC models at cell scale make assumptions about certain microscale transport parameters, assumptions that can make a model less close to the reality. The purpose of this study is to analyze five different proposed correlations to estimate the through-plane (TP) diffusibility of digitally created GDLs and using lattice Boltzmann (LB) models. The correlations are ranked depending on their precision, accuracy and symmetry. The results show that the best estimation is given when the porosity and gas-phase tortuosity are taken into account in the correlation.     

Visual experiment research of the inhaled particle thermophoresis deposition rule in the rectangle turbulent flow tube

In order to solve the problem of removing inhaled particle caused by the combustion source, the dynamics characteristics of the inhaled particle in additional temperature field have to be studied. The dynamics characteristics of the inhaled particle in temperature field are measured in designed and processed a rectangle experiment channel by the PDA instrument. This method is visual. The dynamic characteristic of the particle at 0.15 mm near by water wall surface in boundary layer can be measured through the direction change of beam of PDA light. The movement rules of the inhaled particle in the additional temperature field are obtained through the experiment. The experiment results show that the thermophoresis force has strong influence on the particle which diameter is about 6 μm and the experience formulas are put forward to calculate the thermophoresis deposition efficiency. The thermophoresis deposition efficiency formulas obtained from this experiment is consistent with Batchelor and Shen formulas. The research shows that the PM_2.5 thermophoresis deposition efficiency is direct proportion to the temperature ratio between the inlet temperature and the water wall surface but is not the temperature difference in the rectangle channel.     

Effects of slip boundaries on thermal convection in 2D box using lattice Boltzmann method

This work studied the thermal convection under various slip boundary conditions in a 2D box with aspect ratio equal to two. The slip parameter is the normalized tangential momentum accommodation coefficient (TMAC, 0 ? σ ? 1). The results show that the slip boundary conditions of vertical side walls (σ_v) and horizontal plates (σ_h) will affect the pattern selections of the flow and temperature fields. When σ_h < 0.02, the pattern is the one-roll mode for all σ_v. When σ_h ? 0.02 and σ_v ? 0.1, the fluids prefer the two-roll mode where two rolls make the fluids to move upwards in the middle of the box. While σ_h ? 0.02 and σ_v ? 0.2, the fluids prefer the other two-roll mode which makes the fluid to move downwards in the middle of the box.     

Multi-phase micro-scale flow simulation in the electrodes of a PEM fuel cell by lattice Boltzmann method

The gas diffusion layer of a polymer electrolyte membrane (PEM) fuel cell is a porous medium generally made of carbon cloth or paper. The gas diffusion layer has been modeled conventionally as a homogeneous porous medium with a constant permeability in the literature of PEM fuel cell. However, in fact, the permeability of such fibrous porous medium is strongly affected by the fiber orientation having non-isotropic permeability. In this work, the lattice Boltzmann (LB) method is applied to the multi-phase flow phenomenon in the inhomogeneous gas diffusion layer of a PEM fuel cell. The inhomogeneous porous structure of the carbon cloth and carbon paper has been modeled as void space and porous area using Stokes/Brinkman formulation and void space and impermeable fiber distributions obtained from various microscopic images. The permeability of the porous medium is calculated and compared to the experimental measurements in literature showing a good agreement. Simulation results for various fiber distributions indicate that the permeability of the medium is strongly influenced by the effect of fiber orientation. Present lattice Boltzmann flow models are applied to the multi-phase flow simulations by incorporating multi-component LB model with inter-particle interaction forces. The model successfully simulates the complicated unsteady behaviors of liquid droplet motion in the porous medium providing a useful tool to investigate the mechanism of liquid water accumulation/removal in a gas diffusion layer of a PEM fuel cell.     

Nanofluid multi-phase convective heat transfer in closed domain: Simulation with lattice Boltzmann method

The lattice Boltzmann method is applied to simulate the thermal field and flow field of nanofluid natural convection in a square cavity. The heat transfer characteristics of nanofluid are compared with that of water to explore nanofluid heat transfer mechanism. The flow field shows different characters at different Rayleigh number and the average Nusselt number is obtained changing with Rayleigh number.     

Solving transient heat conduction problems on uniform and non-uniform lattices using the lattice Boltzmann method

The lattice Boltzmann method (LBM) has been used to solve transient heat conduction problems in 1-D, 2-D and 3-D Cartesian geometries with uniform and non-uniform lattices. To study the suitability of the LBM, the problems have also been solved using the finite difference method (FDM). To check the performance of LBM for the non-uniform lattices, the results have been compared with uniform lattices. Cases with volumetric heat generation have also been considered. In 1-D problems, the FDM with implicit scheme was found to take more number of iterations and also the CPU time was more. However, with explicit scheme, with increase in the number of control volumes, the LBM was found faster than the FDM. In 2-D and 3-D problems, with increase in the number of control volumes, the LBM was found faster than the FDM. In 2-D problems, number of iterations in the two methods was comparable, while in 3-D problems, the LBM was found to take less number of iterations. The accurate results were found in all the cases.