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.     

A lattice Boltzmann algorithm for fluid–solid conjugate heat transfer

A lattice Boltzmann algorithm for fluid–solid conjugate heat transfer is developed. A new generalized heat generation implement is presented and a “half lattice division” treatment for the fluid–solid interaction and energy transport is proposed, which insures the temperature and heat flux continuities at the interface. The new scheme agrees well with the classical CFD method for predictions of flow and heat transfer in a heated thick-wall microchannel with less mesh number and less computational costs.     

A lattice Boltzmann model for interphase conjugate heat transfer

A lattice Boltzmann model is proposed with a newly modified equilibrium distribution function for solving the conservation form of the energy equation to treat the interphase conjugate heat transfer problems under both steady state and unsteady state. The temperature and heat flux continuity conditions at the interface can be inherently satisfied without needing any additional treatments, such as iterative computation, correcting procedure for the incoming distribution function, and the complicated calculation procedure for the source term, to account for the interphase conjugate heat transfer. The implementation of the present LB model, therefore, is more straightforward and more efficient than those in most previous models, especially for problems with complex interfaces. The applicability and accuracy of the proposed LB model were evaluated by some benchmark problems including both simple flat interface and complex interface geometry. The results show excellent agreements with analytical solutions or finite volume results, demonstrating that the present model can serve as a promising numerical technique for dealing with fluid flow and heat transfer in complex heterogeneous systems.     

Coupled lattice Boltzmann finite volume method for conjugate heat transfer in porous media

This work presents a coupled lattice Boltzmann finite volume method for dealing with conjugate heat transfer problems. Lattice Boltzmann scheme is used for fluid-dynamics, while high-order finite volume method is implemented for temperature reconstruction. After a first validation with literature test cases, the method is applied to a heat exchanger with an insert made of porous medium, representative of an open-cell metal foam, innovative material largely used for its thermomechanical properties. This allows maximizing heat exchange processes with advantages in terms of efficiencies. Thus, the coupled method allows dealing with complex boundaries in multiphysics problems.     

基于格子Boltzmann方法的饱和土壤渗流与传热数值模拟

本文利用随机多孔介质生成算法重构了与真实土壤外貌相近的多孔介质几何结构。通过引入不可压耦合双分布格子Boltzmann模型（lattice Boltzmann model ,LBM）对孔隙尺度下单相饱和土壤渗流和传热进行了模拟。着重讨论了不同渗流压差、孔隙率、土壤固体颗粒尺寸分布对流动与传热的影响。结果表明：土壤渗流速度与渗流压差呈线性单调递增关系,平均温度随渗流压差增加而增大,但温升速率逐渐减缓;当孔隙率增大时,渗流速度增加,且当孔隙率大于0.58时,对流换热作用迅速增强,土壤温升速率显著加快;对于相同孔隙率,当土壤固相颗粒尺寸较大时,流动出现典型优先流效应;随着土壤固相颗粒尺寸减小,土壤温度变化逐渐趋于平缓,平均温度降低。     

A lattice Boltzmann simulation of enhanced heat transfer of nanofluids

Due to its distinctive characteristics nanofluid has drawn much attention from academic communities since the last decade. Compared with conventional fluids, nanofluid has higher thermal conductivity and surface to volume ratio, which enables it to be an effective working fluid in terms of heat transfer enhancement. Recent experimental works have shown that with low nanoparticle concentrations (1–5 vol.%), the effective thermal conductivity of the suspensions can increase by more than 20% for various mixtures. Although many outstanding experimental works have been carried out, the fundamental understanding of nanofluid characteristics and performance is still not sufficient. Much more theoretical and numerical studies are required. Over the past two decades, the lattice Boltzmann method (LBM) has experienced a rapid development and well accepted as a useful method to simulate various fluid behaviours. In the present study, the LBM is employed to investigate the characteristics of nanofluid flow and heat transfer. By coupling the density and temperature distribution functions, the hydrodynamics and thermal features of nanofluids are properly simulated. The effects of the parameters including Rayleigh number and volume fraction of nanoparticles on hydrodynamic and thermal performances are investigated. The results show that both Rayleigh number and solid volume fraction of nanoparticles have influences on heat transfer enhancement of nanofluids; and there is a critical value of Rayleigh number on the performance of heat transfer enhancement.     

An enthalpy-based lattice Boltzmann formulation for unsteady convection-diffusion heat transfer problems in heterogeneous media

In this paper, we propose a direct extension of a previous work presented by Hamila et al. [1 R. Hamila, M. Nouri, S. Ben Nasrallah, and P. Perré, Int. J. Heat Mass Transfer, vol. 100, pp. 728–736, 2016.[Crossref], [Web of Science ®] , [Google Scholar]] dealing with the simulation of conjugate heat transfer by conduction in heterogeneous media. In [1 R. Hamila, M. Nouri, S. Ben Nasrallah, and P. Perré, Int. J. Heat Mass Transfer, vol. 100, pp. 728–736, 2016.[Crossref], [Web of Science ®] , [Google Scholar]] a novel enthalpy-based lattice Boltzmann (LB) formulation was successfully simulated in several conjugate heat transfer problems by conduction. We propose testing this enthalpic LB formulation in solving convection-diffusion heat transfer problems in heterogeneous media. The main idea of this formulation is to introduce an extra source term, avoiding any additional treatment of the distribution functions at the interface. Continuity of temperature and normal heat flux at the interface is satisfied automatically. The performance of the present method is successfully validated by comparison to the control volume methods (CVMs) solutions of several heat convection-diffusion problems in heterogeneous media.     

Research on heat transfer law of cement clinker accumulation body in grate cooler based on lattice Boltzmann method

In view of the porous media characteristics of the clinker accumulation body in the cement cooler, this paper combined the seepage heat transfer theory with the lattice Boltzmann method (LBM) to analyze the heat transfer of the particle accumulation body. According to the principle of nonmutation of permeability, the minimum feature unit model of cement particles was established, and its heat transfer law was analyzed by LBM. The heat transfer law of the boundary of the feature unit was obtained, and it was used to analyze the heat transfer law of the whole accumulation body by using the double‐loop nesting algorithm. The correctness of this study result was verified by particle heat transfer experiments.     

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.     

基于LBM多孔介质复合腔体交界面热滑移效应的研究

本文采用格子Boltzmann方法对真实多孔介质复合腔体内的对流换热进行研究,分析了不同Ra数、多孔介质高度Y和厚度δ条件下交界面处的热滑移效应,并确定热滑移系数。利用X-CT技术对真实多孔介质材料进行断层扫描,获得实际材料内部结构图片,并进行图片处理,再导入格子Boltzmann模型中进行求解。计算结果表明：等效热滑移系数随高度Y的影响较大,靠近壁面或固体表面的系数偏大,而间隙处的系数偏小,但两处各自的值基本相同;Ra数和厚度δ的变化对等效热滑移系数的作用较小。     

Analysis of combined mode heat transfer in a porous medium using the lattice Boltzmann method

ABSTRACT

Application of the lattice Boltzmann method (LBM) in solving a combined mode conduction, convection, and radiation heat transfer problem in a porous medium is extended. Consideration is given to a 1-D planar porous medium with a localized volumetric heat generation zone. Three particle distribution functions, one each for the solid temperature, the gas temperature, and the intensity of radiation, are simultaneously used to solve the gas- and the solid-phase energy equations. The volumetric radiation source term appears in the solid-phase energy equation, and it is also computed using the LBM. To check the accuracy of the LBM results, the same problem is also solved using the finite volume method (FVM). Effects of convective coupling, flow enthalpy, solid-phase conductivity, scattering albedo porosity, and emissivity on axial temperature distribution are studied and compared with the FVM results. Effects of flow enthalpy, solid-phase conductivity, and emissivity are also studied on radiative output. LBM results are in excellent agreement with those of the FVM.     

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.     

Convection heat transfer with internal heat generation in porous media: Implementation of thermal lattice Boltzmann method

Evaluation of lattice parameters for convection heat transfer in porous media with internal heat generation from physical and macroscale properties was described. A hierarchical process was defined to implement thermal Lattice Boltzmann Method (LBM) to investigate convection heat transfer with internal heat generation in different geometries; from a simple geometry (flow channel) to complex ones (porous media). In this regard, seven different without any obstacle cases with different geometries were designed and the detailed information about how thermal LBM should be implemented for these cases are addressed. Going from one case to the next, the cases with more complex physics and/or geometries were examined. The results showed that LBM is an appropriate method to predict heat transfer with internal heat generation in porous media.     

Study of heat transfer in multilayered structure within the framework of dual-phase-lag heat conduction model using lattice Boltzmann method

The effect of the phase lag of temperature gradient, τ_T, on the transmission-reflection phenomenon, induced by a pulsed thermal energy passing the interface of a two-layered structure, within the framework of dual-phase-lag based heat conduction equation is studied numerically by the lattice Boltzmann (LB) method. An extended LB equation, with truncation error of order two, and a numerical solution procedure are developed for the solution of the governing equation and the derived interfacial boundary condition. Results show that the interface reflects a negative followed by a positive waveform when the pulsed thermal wave propagates from the media with lower τ_T into the media with higher τ_T and vice versa if the wave propagates from higher into lower τ_T media. These special phenomena which have not been presented in the available literatures are unable to be predicted in the framework of hyperbolic heat conduction equation.     

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.     

A new method for heat transfer and fluid flow performance simulation of plate heat exchangers

Successful numerical simulation on heat transfer and fluid flow performances of plate heat exchangers is vital. Their complex structures often make the numerical calculation quite difficult and time-consuming. Conclusions drawn by the present work are promising for greatly simplifying the simulation. Different types of plates consisting of different numbers of periods are analyzed and it is concluded that the Nusselt number remains constant for different periods of different plates under different inlet velocities. The central friction coefficients behave the same as Nusselt number. For the first and last periods, the respective friction coefficient also remains for different plates. A small plate fraction with four periods is enough for performance prediction of any-sized plates.     

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.     

Lattice Boltzmann method simulation of backward-facing step on convective heat transfer with field synergy principle

The lattice Boltzmann method (LBM) is applied to simulate the two-dimensional incompressible steady low Reynolds number backward-facing step flows. In order to restrict the approach to the two-dimensional flow, the largest Reynolds number chosen was Re = 200. To increase the uniformity of the radial temperature profile for fluid flow in channel and consequently to enhance the heat transfer, the inserted square blockage is used and investigated numerically. In addition, the field synergy principle is also applied to demonstrate that an interruption within fluid results in decreased intersection angle between the velocity and temperature gradient. The numerical results of velocity and temperature field agree well with the available experimental and numerical results.     

Simplified model and lattice Boltzmann algorithm for microscale electro-osmotic flows and heat transfer

The extremely small length scale of the electric double layer (EDL) of electro-osmotic flows (EOF) in a microchannel makes it difficult to simulate such flows and associated thermal behaviors. A feasible solution to this problem is to neglect the details in the thin EDL and replace its effects on the bulk flow and heat transfer with effective velocity-slip and temperature-jump boundary conditions outside the EDL. In this paper, by carrying out a scale analysis on the fluid flow and heat transfer in the thin EDL, we analytically obtain the velocity and the temperature at the interface between the EDL and the bulk flow region. The Navier–Stokes equations and the conservation equation of energy, along with the interfacial velocity and temperature as the velocity-slip and temperature-jump boundary conditions, form a simple model for the electro-osmotic flows with thermal effects in a microchannel with a thin EDL. We use the double distribution function lattice Boltzmann algorithm to solve this model and found that numerical results are in good agreement with those by the conventional complete model with inclusion of the EDL, particularly for the cases when channel size is about 400 times larger than the Debye length. Moreover, we found that the present model can substantially reduce the computational time by four to five times of that using the conventional complete model. Therefore, the simplified model proposed in this work is an efficient tool for simulating electro-osmosis-based microfluidic systems.     

Estimation of computational grid for thermal convection simulation with lattice Boltzmann method

Accurate, quantitative but not empirical estimation of computational grids helps quickly formulate appropriate computational schemes and shorten the preprocessing of simulations. In this paper, some formulas are proposed to limit a certain range of computational grid N_L for the thermal convection simulations with double distribution function lattice Boltzmann method (DDF-LBM). These formulas are induced from the analysis of relationships among DDF-LBM mathematical limits, mesoscopic physic limits, and flow boundary layer limits, with certain nondimensional parameters Pr, Ra, and Ma. After discussing the essence of the common way in which Ma value is increased to enhance the simulating stability of DDF-LBM, it is confirmed that above formulas also benefit the equivalence between the grid number and increased Ma value. To verify the above formulas, the simulations of Rayleigh–Bénard convection in a square enclosure filled with air at Ra?=?10⁴–10⁸ have been performed. The results coincide well with those in other published references, which suggests the validity of the present study.