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.     

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.     

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.     

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.     

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.     

Coupling conjugate heat transfer with in-cylinder combustion modeling for engine simulation

A conjugate formulation to predict heat conduction in the solid domain and spray combustion in the fluid domain was developed for multidimensional engine simulation. Heat transfer through the wall affects the combustion process in the cylinder and the thermal loading on the combustion chamber surface. To account for the temporal and spatial variations of temperature on the chamber surface, a fully coupled numerical procedure was developed to simulate in-cylinder flow and solid heat conduction simultaneously. Temperature fields in both the fluid and the solid domains were coupled by imposing equal heat flux and equal temperature at the fluid–solid interface. The formulation was first validated against analytical solutions. The formulation was then applied to simulate the in-cylinder combustion process and the solid heat conduction in a diesel engine under different operating conditions. Results show that the present model is able to predict unsteady and non-uniform temperature distributions on the chamber surface, which can fluctuate by nearly 100 K during combustion. The highest temperature on the piston surface occurs at the bowl edge along the spray axis. Predicted global engine parameters agree well with the experimental data. The present approach can be used to improve engine design for optimal combustion and reduced thermal loading.     

Thermal analysis of a 2-D heat recovery system using porous media including lattice Boltzmann simulation of fluid flow

The present work deals with the fluid flow simulation and thermal analysis of a two-dimensional heat recovery system using porous media. A basic high-temperature flow system is considered in which a high-temperature non-radiating gas flows through a random porous matrix. The porous medium, in addition to its convective heat exchange with the gas, may absorb, emit and scatter thermal radiation. It is desirable to have large amount of radiative heat flux from the porous segment in the upstream direction (towards the thermal system). The lattice Boltzmann method (LBM) is used to simulate fluid flow in the porous medium. The gas and solid phases are considered in non-local thermal equilibrium, and separate energy equations are applied to these phases. Convection, conduction and radiation heat transfers take place simultaneously in solid phase, but in the gas flow, heat transfer occurs by conduction and convection. In order to analyze the thermal characteristics of the heat recovery system, volume-averaged velocities through the porous matrix obtained by LBM are used in the gas energy equation and then the coupled energy equations for gas and porous medium are numerically solved using finite difference method. For computing of radiative heat flux in the porous medium, discrete ordinates method is used to solve the radiative transfer equation. Finally the effect of various parameters on the performance of porous heat recovery system is studied.     

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.     

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.     

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.     

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.     

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。     

Three-dimensional numerical simulation of solid oxide fuel cell cathode based on lattice Boltzmann method with sub-grid scale models

In the present study, three-dimensional numerical simulations are carried out to predict the electrochemical characteristics of solid oxide fuel cell (SOFC) cathodes based on a coupled method using sub-grid scale (SGS) model in a lattice Boltzmann method (LBM). Lattice Boltzmann method is used to solve the governing equations. In each coarse computational grid, local gas diffusivities, ion and electron conductivities are obtained by directly solving diffusion equations using the original fine sub-grid scale information. Two types of SGS models are introduced in this study, i.e. isotropic and anisotropic local diffusivities and conductivities. Proposed SGS local diffusivities and conductivities can maintain detailed information of the original fine microstructure even when coarser grid is used in the calculation. In the anisotropic SGS model, weighted summation of particle distribution function is applied in the LBM to maintain the invariances of local concentrations and potentials. From the tortuosity factor and overpotential calculation results, it is concluded that the proposed SGS models can drastically improve the computational accuracy without costing additional calculation time. Moreover, SGS model considering geometric anisotropies inside the calculation grid presents more precise results than the isotropic SGS model.     

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.     

Numerical simulation of a 2D electrothermal pump by lattice Boltzmann method on GPU

ABSTRACT

Electrothermal flow in a microfluidic system is a fast-developing technology because of the advancement in micro-electro-mechanical systems. The motion is driven by the electrothermal force generated by the AC electric field and non-uniform temperature distribution inside the system. Electrothermal force can be explored for pumps in microfluidic systems. In this paper, the lattice Boltzmann method (LBM) is used to simulate a 2D electrothermal pump. As an alternative numerical method for fluid dynamics, LBM has many advantages compared with traditional CFD methods, such as its suitability for parallel computation. With its parallel characteristic, LBM is well fitted to the parallel hardware in graphic processor units (GPU). To save computational time in parametric studies, a CUDA code was developed for executing parallel computation. The comparison of computational time between CPU and GPU is presented to demonstrate the advantage of using GPU. The effects of the frequency, thermal boundary conditions, electrode size, and gap between electrodes on volumetric flow rate were investigated in this study. It was shown that LBM is an effective approach to studying 2D electrothermal pumps on a CUDA platform.