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.     

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.     

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.     

Numerical analysis on supercritical natural convection by lattice Boltzmann method

Abstract

One of the main factors affecting the heat transfer efficiency of solar collector is that the ordinary fluid in it is in the state of natural convection. Supercritical fluid is expected to improve the heat transfer efficiency of solar collectors due to its dramatic changes in thermal properties, so it is necessary to carry out the research of natural convection of supercritical fluid. Although researchers have made lots of related experimental investigations, heat transfer mechanism of supercritical natural convection is still unclear. In order to clarify its heat transfer mechanism, this article conducts a numerical analysis for supercritical natural convection applying lattice Boltzmann method, which has been proved to be valid and convenient. Considering the influences of temperature difference and pressure on natural convective heat transfer of supercritical fluid are seldom studied, the relevant researches are carried out in the article. The results imply that pressure of supercritical fluid in solar collectors should be less than 11?MPa so that high heat transfer performance can be obtained. Finally, the correlations of average Nusselt number, Rayleigh number, and pressure are fitted for the convenience of heat transfer calculation.     

Numerical simulation of natural convection in an open-ended square cavity filled with porous medium by lattice Boltzmann method

In the present work, natural convection in an open-ended square cavity packed with porous medium is simulated. The double-population approach is used to simulate hydrodynamic and thermal fields, and the Taylor series expansion and the least-squares-based lattice Boltzmann method has been implemented to extend the thermal model. The effect of a porous medium is taken into account by introducing the porosity into the equilibrium distribution function and adding a force term to the evolution equation. The Brinkman–Forchheimer equation, which includes the viscous and inertial terms, is applied to predict the heat transfer and fluid dynamics in the non-Darcy regime. The present model is validated with the previous literature. A comprehensive parametric study of natural convective flows is performed for various values of Rayleigh number and porosity. It is found that these two parameters have considerable influence on heat transfer.     

Numerical simulation of compressible flows by lattice Boltzmann method

In this article, we propose a numerical framework based on multiple relaxation time lattice Boltzmann (LB) model and novel discretization techniques for simulating compressible flows. Highly efficient finite difference lattice Boltzmann methods are employed to simulate one- and two-dimensional compressible flows. These numerical techniques are applied on the single- and multiple-relaxation-time on the 16-discrete-velocity (Kataoka and Tsutahara, Phys. Rev. E, 69(5):056702, 2004) compressible lattice Boltzmann model. The Boltzmann equation is discretized via modified Lax-Wendroff and modified total variation diminishing schemes which have ability to damps oscillations at discontinuities, effectively. The results of compressible models are compared and validated with the well-known inviscid compressible flow benchmark test cases, so called Riemann problems. The proposed method shows its superiority over available techniques when compared to the analytical solutions. It is then used to solve two-dimensional inviscid compressible flow benchmarks, including regular shock reflection and Richtmyer–Meshkov instability problems to ensure its applicability for more complex problems. It is found that, the applied discretization techniques improve the stability of original LB models and enhance the robustness of compressible flow problems by preventing the formation of oscillation.     

Developing a ghost fluid lattice Boltzmann method for simulation of thermal Dirichlet and Neumann conditions at curved boundaries

ABSTRACT

In this paper, a ghost fluid thermal lattice Boltzmann method is developed to simulate Dirichlet and Neumann thermal boundary conditions at curved boundaries. As such, a new formulation for both thermal boundary conditions is developed using a bilinear interpolation method. The presented method is also formulated to address the special cases that arise when the values of the macroscopic variables are interpolated at the image points surrounded by many solid nodes as well as the fluid nodes. The results of the presented method are compared to those available in the literature from conventional numerical methods, and excellent agreement is observed.     

Pore-scale simulation of coupled multiple physicochemical thermal processes in micro reactor for hydrogen production using lattice Boltzmann method

A general numerical scheme based on the lattice Boltzmann method (LBM) is established to investigate coupled multiple physicochemical thermal processes at the pore-scale, in which several sets of distribution functions are introduced to simulate fluid flow, mass transport, heat transfer and chemical reaction. Interactions among these processes are also considered. The scheme is then employed to study the reactive transport in a posted micro reactor. Specially, ammonia (NH₃) decomposition, which can generate hydrogen (H₂) for fuel of proton exchange membrane fuel cells (PEMFCs), is considered where the endothermic decomposition reaction takes place at the surface of posts covered with catalysts. Simulation results show that pore-scale phenomena are well captured and the coupled processes are clearly predicted. Effects of several operating and geometrical conditions including NH₃ flow rate, operating temperature, post size, post insert position, post orientation, post arrangement and post orientation on the coupled physicochemical thermal processes are assessed in terms of NH₃ conversion, temperature uniformity, H₂ flow rate and subsequent current density generated in PEMFC.     

Estimation of the thermal dispersion in a porous medium of complex structures using a lattice Boltzmann method

The thermal dispersion in a porous medium of complex structure is investigated by using the lattice Boltzmann method. The media under consideration include two-dimensional arrays of uniformly distributed circular and square cylinders, and uniformly distributed spherical and cubical inclusions. Upon validating the procedure, calculations have been performed for flows of various Prandtl and Reynolds number combinations. The porosity and the fluid–solid diffusivity ratio have been varied to investigate their effects on the dispersivity. For both 2D and 3D cases, the dispersivity is found to increase with the Peclet number raised to the same constant exponent regardless of the medium structures. The in-line arrangement yields higher dispersivity than the staggered arrangement, however, the dispersivity is independent of the inclusion shape except for the 3D staggered cases. New correlations for dispersivity for 2D and 3D cases are then proposed in terms of Peclet number, porosity, and the fluid–solid diffusivity ratio.     

Three dimensional lattice Boltzmann simulation for mixed convection of nanofluids in the presence of magnetic field

In the present study, a three dimensional thermal lattice Boltzmann model was developed to investigate the flow dynamics and mixed convection heat transfer of Al₂O₃/water nanofluid in a cubic cavity in the presence of magnetic field. The model was first validated with previous numerical and experimental results. Satisfactory agreement was obtained. Then the effects of Rayleigh number, nanoparticle volume fraction, Hartmann number and Richardson number on nanofluid flow dynamics and heat transfer were examined. Numerical results indicate that adding nanoparticles to pure water leads to heat transfer enhancement for low Rayleigh numbers. However, this enhancement might be weakened and even reversed for high Rayleigh numbers. In addition, the results show the external applied magnetic field has an effect of suppressing the convective heat transfer in the cavity. Moreover, the results demonstrate that the Richardson number in mixed convection has significant influences on both streamlines and temperature field.     

Numerical study of mixed convection in a ventilated square enclosure with the lattice Boltzmann method

In this article, numerical study of heat transfer by convection in a square cavity was investigated. The vertical walls of the cavity are differentially heated and the horizontal walls are considered adiabatic. A ventilation jet is created by a fan placed in the cavity. A lattice Boltzmann model for incompressible flow equation is used to simulate the problem. A parametric study was performed presenting the influence of Reynolds number (20 ≤ Re?≤?500), Rayleigh number (10≤Ra?≤?10⁺⁶), and fan position (0.2?≤?L_F≤0.8). It has been observed that heat transfer rate increases with the Reynolds number increasing and it is maximal for the L_F=0.2.     

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.     

Numerical implementation of thermal boundary conditions in the lattice Boltzmann method

This work proposed a non-equilibrium mirror-reflection scheme to implement thermal boundary conditions for the two-distribution lattice Boltzmann method (TLBM). The study showed that the most popular non-equilibrium bounce-back scheme would become inadequate when the predictions of temperature gradient were examined in TLBM. This work used the native method in TLBM to verify temperature gradient instead of the conventional finite difference approximation. The simulation results demonstrated that the mirror-reflection scheme is a scheme of second-order accuracy and can predict the temperature and temperature gradient correctly. With help of calculating the heat flux on the boundary, this work also suggested a more efficient and realistic way to determine the Nusselt number in Rayleigh–Bénard convection problems.     

Estimation of thermal and mass diffusivity in a porous medium of complex structure using a lattice Boltzmann method

The thermal and mass diffusivity in a porous medium of complex structure is studied by using the lattice Boltzmann method. The media under consideration include two-dimensional medium with an array of periodically distributed circular and square cylinders, three-dimensional granular medium of overlapping or non-overlapping spherical and cubical inclusions of different size, and randomly generated fibrous medium. The calculated effective diffusivities are in good agreement with existing analytical and numerical results when the inclusions, regardless of their shapes, are not overlapped. For the medium of overlapping inclusions, the effective diffusivity deviates from existing correlations as the inclusion fraction increases. In particular, the deviation increases dramatically if the thermal diffusivity of the inclusion is greater than that of the fluid in the medium for enhanced thermal conduction. A new empirical correlation between the effective diffusivity and the volume fraction for the medium of overlapping inclusions is proposed.     

Modelling of thermal contact resistance within the framework of the thermal lattice Boltzmann method

A novel numerical approach, termed the partial bounce back scheme, is introduced within the framework of the thermal lattice Boltzmann method to account for thermal contact resistance between contacting surfaces. The correlation between thermal contact resistance and the partial bounce back parameter is established. A special case of the scheme leads to a new approach that can be directly applied for the treatment of adiabatic thermal boundary conditions in the thermal lattice Boltzmann method. Numerical examples are provided to validate and demonstrate the accuracy and effectiveness of the proposed methodology.     

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.     

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。     

基于混合热格子玻尔兹曼模型的液滴蒸发数值模拟

采用格子玻尔兹曼方法(LBM)的单组分伪势模型与有限差分耦合的混合热格子玻尔兹曼模型(TLBM)对液滴蒸发过程进行了研究。首先,通过对液滴在方腔内蒸发过程进行模拟,验证了所采用计算方法及程序的有效性。随后,模拟了液滴撞击高温壁面后的蒸发过程,研究了壁面温度、液滴邦德数和液滴雷诺数对蒸发过程的影响。结果表明,壁面温度、液滴邦德数和液滴雷诺数的增加均会造成液滴撞击高温壁面后蒸发速率的增大。