格子Boltzmann方法模拟泡沫金属内相变材料热传导融化传热过程

基于局部热非平衡条件下泡沫金属内热传导融化相变传热的非线性双温度方程,在表征单元尺度上构建双温度分布函数格子Boltzmann模型,其中相变非线性源项处理采用焓法迭代求解。数值模拟了金属骨架与相变材料的温度分布情况,重点分析了孔径、金属骨架与填充材料热传导比和Stefan数等对局部热非平衡效应的影响。模拟结果表明,孔径越大、金属骨架与填充材料热传导比越大,局部热非平衡效应越明显;相变过程的存在,加大了局部热非平衡效应,并且Stefan数越低局部热非平衡效应则越大。     

Lattice Boltzmann simulation of heat transfer with phase change in saturated soil during freezing process

A lattice Boltzmann model is presented for simulating heat transfer with phase change in saturated soil. The model includes a quartet structure generation set for creating soil structure, double distribution functions for simulating temperature field evolution of soil particles and water, respectively, and an enthalpy-based method for tracing phase interface. The model is validated by two cases with analytical solutions. Then, we investigate the influence of porosity on freezing process in saturated sandy loam soil. The results demonstrate that porosity is the predominant factor when the location is far from the cold source; otherwise, thermal gradient is more important.     

An implicit lattice Boltzmann model for heat conduction with phase change

In this work, a new variation of the lattice Boltzmann method (LBM) was developed to solve the heat conduction problem with phase change. In contrast to previous explicit algorithms, the latent heat source term was treated implicitly in the energy equation, avoiding iteration steps and improving the formulation stability and efficiency. The Bhatnagar–Gross–Krook (BGK) approximation with a D2Q9 lattice was applied and different boundary conditions including Dirichlet and Neumann boundary conditions were considered. The developed model was tested by solving a one-dimensional melting problem for a pure metal, and one and two-dimensional solidification problems for a binary alloy. The results of the LBM solution were compared with analytical and finite element solutions and a good consistency was observed. Considering the special capabilities that LBM offers, like local characteristic, and inherent parallel structure, the developed model is an interesting alternative to traditional continuum models.     

Lattice Boltzmann simulation of heat conduction problems in non‐isothermally heated enclosures

A numerical study following the lattice Boltzmann method (LBM) is performed to solve transient heat conduction problems with and without volumetric heat generation/absorption in 2D and 3D Cartesian geometries. Uniform lattices are considered for both geometries. To validate the correctness of LBM, a finite difference method (FDM) is also used to solve the 2D problem without heat generation/absorption and results are compared with that of LBM. For both 2D and 3D geometries one of the walls is heated and cooled with a sinusoidal function and the rest of the walls are cooled isothermally. Effects of amplitude of the sinusoidal function and volumetric heat generation/absorption on temperature profiles are analyzed. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20406     

Lattice Boltzmann simulation of tree-shaped fins enhanced melting heat transfer

Abstract

A thermal lattice Boltzmann model is developed to simulate the melting process with natural convection in a cavity filled with tree-shaped solid fins, in which the velocity field and temperature field distribution functions are considered. The present model incorporates the total enthalpy and a free parameter in the equilibrium distribution function to handle conjugate heat transfer. The results indicate that natural convection of liquid phase change material (PCM) plays a significant role in the melting heat transfer of PCM. Increasing the number of branching levels leads to a more rapid melting process, and selecting appropriate bifurcation angle has more efficient heat transfer performance.     

Lattice Boltzmann simulation of natural convection heat transfer in eccentric annulus

In this article, the natural convection flow in eccentric annulus is simulated numerically by Lattice Boltzmann Model (LBM) based on double-population approach. A numerical strategy presents for dealing with curved boundaries of second order accuracy for both velocity and temperature fields. The effect of vertical, horizontal, and diagonal eccentricity at various locations is examined at Ra = 10⁴ and σ = 2. Velocity and temperature distributions as well as Nusselt number are obtained. The results show that the average Nusselt number increases when the inner cylinder moves downward regardless of the radial position. The validation with previous studies shows that double-population approach can evaluate the velocity and temperature fields in curved boundaries with a good accuracy.     

Lattice Boltzmann simulation of mixed convection heat transfer in eccentric annulus

Mixed convection heat transfer in eccentric annulus was simulated numerically by lattice Boltzmann model (LBM) based on multi-distribution function double-population approach. The effect of eccentricity on heat transfer at various locations was examined at Ra = 10⁴ and σ = 2. Velocity and temperature distributions as well as Nusselt number are obtained. The results are validated with published results and shown that multi-distribution function approach can evaluate the velocity and temperature fields in curved moving boundaries with a good accuracy in comparison with the previous studies. The results show that the average Nusselt number increases when the inner cylinder moves downward regardless of the radial position.     

Treatment of the interfacial temperature jump condition with non-Fourier heat conduction effects

Transient energy transport with non-Fourier heat conduction effects in a two-layer structure of dissimilar materials subject to ultra-fast laser heating is studied using the proper interfacial temperature jump condition. The solution obtained is compared with solutions available in literature that use diffusion-type interfacial conditions in conjunction with non-Fourier heat conduction effects. The dual-phase lag heat conduction model is used in this work as it includes both the temporal and spatial non-Fourier effects. It is found that the diffusion-type interfacial temperature jump condition with non-Fourier heat conduction models can lead to discrepancies and erroneous trends in theoretical predictions. Moreover, a comparison between the functional forms of the two solutions obtained utilizing both interfacial conditions shows that implementing the proper interfacial temperature jump condition does not add any complexity to the solution obtained. This study – implementing the proper interfacial temperature jump condition – is further extended to show the strong effects of the thermal contact conductance and the surface layer thickness on the transient thermal response of a two-layer material in a semi-infinite domain subject to ultra-fast laser heating processes in terms of the reflectivity change of the surface layer, the temperature distribution in the two-layer structure as well as the temporal variation of the interfacial temperature difference.     

Lattice Boltzmann simulation of natural convection heat transfer in an elliptical-triangular annulus

A numerical study for steady-state, laminar natural convection in a horizontal annulus between a heated triangular inner cylinder and cold elliptical outer cylinder was investigated using lattice Boltzmann method. Both inner and outer surfaces are maintained at the constant temperature and air is the working fluid. Study is carried out for Rayleigh numbers ranging from 1.0 × 10³ to 5.0 × 10⁵. The effects of different aspect ratios and elliptical cylinder orientation were studied at different Rayleigh numbers. The local and average Nusselt numbers and percentage of increment heat transfer rate were presented. The average Nusselt number was correlated. The results show that by decreasing the value of aspect ratio and/or increasing the Rayleigh number, the Nusselt number increases. Also the heat transfer rate increases when the ellipse positioned vertically.     

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.     

Fast transient thermal analysis of Fourier and non-Fourier heat conduction

In this paper, asymptotic waveform evaluation (AWE) has been successfully used for fast transient characterization of Fourier and non-Fourier heat conduction. The Fourier and non-Fourier equations are reduced to a system of linear differential equations, respectively, using finite element method and then solved with AWE. Besides providing equivalent accuracy in its solution, it is also shown that AWE is at least three orders faster in term of computational time as compared to conventional iterative solvers. Its accuracy is also independent of the time step used and it has the capability of providing local transient solution. However, the moment matching process in AWE is inherently ill-conditioned and thus may yield unstable response even for stable system. This numerical instability is addressed and two stability schemes are also successfully implemented to yield stable and accurate solutions from AWE. The limitation of AWE is also discussed.     

Lattice Boltzmann simulation of natural convection and heat transfer from multiple heated blocks

This study is aimed to investigate the natural convection heat transfer from discrete heat sources (similar to heated microchips) using Bhatnagar‐Gross‐Krook lattice Boltzmann method via graphics process unit computing. The simulation is carried out separately for three and six heated blocks model for different Rayleigh numbers and fixed Prandtl number, $Pr=0.71$ (air). The uniformly heated blocks are placed at the bottom wall inside a rectangular enclosure. The enclosure is maintained by the cold temperature at its left and right walls. The top and bottom surface is maintained by adiabatic conditions apart from the regions where blocks are attached to the bottom wall. The numerical code is validated with the benchmark heat transfer problem of side‐heated square cavity as well as with an experimental study for one discrete heat source. The rate of heat transfer is presented in terms of the local Nusselt and average Nusselt number for each block. It is found that the heat transfer rate becomes maximized in the leftmost and rightmost blocks due to the adjacent cold walls. It is found that the number of blocks and their positions play a substantial role in determining their collective performance on the heat transfer rate.     

Lattice Boltzmann simulation of droplet collision dynamics

A lattice Boltzmann method for two-phase fluid flows with large density ratios is presented. The method is applied to the simulations of binary droplet collisions for various Weber numbers of 20<We<80 and for impact parameters of 0?B<0.82 at the Reynolds number of Re=2000. Two droplets with the same diameter are considered. The density ratio of the liquid to the gas is fixed at 50. Coalescence collision and two different types of separating collisions, namely reflexive and stretching separations, are simulated. The boundaries between the coalescence collision and both of the separating collisions are found and compared with an available theoretical prediction in good agreement. The mixing processes during separating collisions are also simulated for various impact parameters at We≈80, and the relation between the mixing rate and the impact parameter is obtained.     

Lattice Boltzmann simulation of nanofluid in lid-driven cavity

Lattice Boltzmann Method is applied to investigate the mixed convection flows utilizing nanofluids in a lid-driven cavity. The fluid in the cavity is a water-based nanofluid containing Cu, Cuo or Al₂O₃ nanoparticles. The effects of Reynolds number and solid volume fraction for different nanofluids on hydrodynamic and thermal characteristics are investigated. The effective thermal conductivity and viscosity of nanofluid are calculated by Chon and Brinkman models, respectively. The results indicate that the effects of solid volume fraction grow stronger sequentially for Al₂O₃, Cuo and Cu. In addition the increases of Reynolds number leads to decrease the solid concentration effect.     

A crack in a finite medium under transient non-Fourier heat conduction

This paper investigates the problem of a finite crack in a material layer under the theory of non-Fourier heat conduction. The concept of thermal flow intensity factor is introduced to show the singularity of the thermal flow at the crack tip. Dependence of the crack tip thermal flow field on the thermal flow intensity factor is established in closed-form. Time-varying crack tip thermal flow intensity factors are obtained with sufficient accuracy. In addition to the single crack problem, solution technique and numerical results for the problem of two collinear cracks are given. Effects of crack length and layer thickness on the thermal flow intensity factors are discussed in detail.     

Combined mode conduction and radiation heat transfer in a spherical geometry with non-Fourier effect

This article deals with the analysis of combined mode non-Fourier conduction and radiation heat transfer in a concentric spherical enclosure containing a conducting–radiating medium. The finite volume method (FVM) has been employed to calculate the volumetric radiative information and also to solve the governing energy equation, which is of hyperbolic nature. The non-Fourier effect which manifests in the form of a sharp discontinuity in the temporal temperature distribution and propagates with a finite speed has been investigated. As time progress, the discontinuity in the temperature distribution decays and in the steady-state, results with and without non-Fourier effect are the same. Detailed study of the effect of various parameters such as the extinction coefficient, the scattering albedo, the conduction radiation parameter, the emissivity and the anisotropy factor has been carried out. Results of the present work have been compared with the steady-state response of the combined mode Fourier conduction–radiation problems available in literature. Results have been found to agree well.     

DPL Model Analysis of Non—Fourier Heat Conduction Restricted by Continuous Boundary Interface

IntroductionAs widely known, the hahonal Fourier law isbased on a large quantity of regular heat transfer (i.e. thethermal bine scale is comparatively lOng and the heatflux density is comparatively small) experiments and it'sjust a phenomenological descriphon of regular thermalProcesses. The Fourier law itself mpes an infinitespeed of Propagation of thermal distUrbance, indicatingthat a local change in tempera~ causes aninstantaneous per'tUrbation in the temperatore at eachPOint in the medi…     

Notable physical anomalies manifested in non-Fourier heat conduction under the dual-phase-lag model

In this study, a number of notable physical anomalies concerning non-Fourier heat conduction under the dual-phase-lag (DPL) model are observed and investigated. It is found that, during the transient heat transfer process, the over-diffusion mode predicts a “hyper-active” to “under-active” transition in thermal behavior. The main cause behind it lies in the time-varying effect of τ_T (the phase lag of the temperature gradient) on the thermal response. Also, change of polarity in reflected thermal waves can be observed when a constant-temperature boundary is involved, which hints that a heating process may be followed by a spontaneous cooling effect. A fairly strong connection is present between the τ_T-induced dispersive effect and an unusual thermal accumulation phenomenon in an on–off periodic heating process. Furthermore, a paradox involving a moving medium is detected in the DPL model, which can be solved by replacing the temporal partial derivatives in the DPL equation with the material derivatives. During the process of analysis, a high-order characteristics-based TVD scheme is relied on to provide accurate and reliable numerical simulations to the DPL heat conduction equation under various initial-boundary conditions.