A novel modified lattice Boltzmann method for simulation of gas flows in wide range of Knudsen number

To cover a wide range of the flow regimes, a new relaxation time formulation by considering the rarefaction effect and the effective dynamic viscosity has been obtained. By using the modified lattice Boltzmann method (LBM), pressure driven flow through micro and nano channels has been modeled for wide range of Knudsen number, Kn, covering the slip, transition and to some extent the free molecular regimes. The results agree very well with existing empirical and numerical data. The velocity profile was predicted as well as the volumetric flow rate and for the first time, the well known Knudsen minimum effect has been captured about Kn = 1.     

A Lattice Boltzmann Formulation for the Analysis of Radiative Heat Transfer Problems in a Participating Medium

Use of the lattice Boltzmann method (LBM) has been extended to analyze radiative transport problems in an absorbing, emitting, and scattering medium. In terms of collision and streaming, the present approach of the LBM for radiative heat transfer is similar to those being used in fluid dynamics and heat transfer for the analyses of conduction and convection problems. However, to mitigate the effect of the isotropy in the polar direction, in the present LBM approach, lattices with more number of directions than those being used for the 2-D system have been employed. The LBM formulation has been validated by solving benchmark radiative equilibrium problems in 1-D and 2-D Cartesian geometry. Temperature and heat flux distributions have been obtained for a wide range of extinction coefficients. The LBM results have been compared against the results obtained from the finite-volume method (FVM). Good comparison has been obtained. The numbers of iterations and CPU times for the LBM and the FVM have also been compared. The number of iterations in the LBM has been found to be much more than the FVM. However, computationally, the LBM has been found to be much faster than the FVM.     

Comparative Analysis of Thermal Models in the Lattice Boltzmann Method for the Simulation of Natural Convection in a Square Cavity

In this article, a comparative analysis of thermal models in the lattice Boltzmann method for the simulation of natural convection in a square cavity is presented. A hybrid method, in which the thermal equation is solved by the Navier-Stokes equation method while the mass and momentum equations are solved by the lattice Boltzmann method (LBM), is introduced and its merits are explained. All the governing equations are discretized on a cell-centered, nonuniform grid using the finite-volume method. The convection terms are treated by a second-order central-difference scheme with a deferred-correction method to ensure accuracy of solutions. The resulting algebraic equations are solved by a strongly implicit procedure. The hybrid method is applied to the simulation of natural convection in a square cavity and the predicted results are compared with the benchmark solutions given in the literatures. The predicted results are also compared with those by the double-population LBM and by the Navier-Stokes equation method. In general, the present hybrid method is as accurate as the Navier-Stokes equation method and the double-population LBM. The hybrid method shows better convergence and stability than the double-population LBM. These observations indicate that this hybrid method is an efficient and economic method for the simulation of incompressible fluid flow and heat transfer problems involving complex geometries.     

Computation of Turbulent Natural Convection in a Rectangular Cavity with the Lattice Boltzmann Method

A numerical study of a turbulent natural convection in a rectangular cavity with the lattice Boltzmann method (LBM) is presented. The primary emphasis of the present study is placed on investigation of accuracy and numerical stability of the LBM for the turbulent natural-convection flow. A HYBRID method in which the thermal equation is solved by the conventional Reynolds-averaged Navier-Stokes equation (RANS) method while the conservation of mass and momentum equations are resolved by the LBM is employed in the present study. The elliptic-relaxation model is employed for the turbulence model and the turbulent heat fluxes are treated by the algebraic flux model. All the governing equations are discretized on a cell-centered, nonuniform grid using the finite-volume method. The convection terms are treated by a second-order central-difference scheme with the deferred correction method to ensure accuracy and stability of solutions. The present LBM is applied to the prediction of a turbulent natural convection in a rectangular cavity and the computed results are compared with the experimental data commonly used for the validation of turbulence models and those by the conventional finite-volume method. It is shown that the LBM with the present HYBRID thermal model predicts mean velocity components and turbulent quantities which are as good as those by the conventional finite-volume method. It is also found that the accuracy and stability of the solution is significantly affected by the treatment of the convection term, especially near the wall.     

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.     

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.     

Analysis of hyperbolic heat conduction in 1-D planar,cylindrical, and spherical geometry using the lattice Boltzmann method

Analyses of hyperbolic heat conduction in an 1-D planar, cylindrical, and spherical geometry are analyzed using the lattice Boltzamnn method (LBM). Finite time lag between the imposition of temperature gradient and manifestation of heat flow causes the governing energy equation to be hyperbolic one. Temporal temperature distributions are analyzed for thermal perturbation of a boundary by suddenly raising its temperature and also by imposing a constant heat flux to it. Wave-like temperature distributions in the medium are obtained when constant temperature boundary condition is used. However, when constant heat flux boundary condition is used, temperature distribution fluctuates before it becomes stable. To check the accuracy of the LBM results, the problems are also solved using the finite difference method (FDM). LBM and FDM results compare exceedingly well. LBM has computational advantage over the FDM.     

Double dispersion,natural convection in an open end cavity simulation via Lattice Boltzmann Method

Double dispersion in an open end cavities are simulated using Lattice Boltzmann Method (LBM). The flow is driven by the buoyancy effect due to the heated vertical wall and species concentration at the heated wall of the cavity (closed end). The paper is intended to address the physics of flow, heat and mass transfers in open ended cavities and close end slots. Prandtl number (Pr) is fixed to 0.71 (air) for the thermal Rayleigh number (Ra_T) of 10⁴, 10⁵ and 10⁶. The results are presented for moderate Lewis number of 2, 4 and 8 and for a range of buoyancy ratio, N, (species to thermal). The species concentration induced buoyancy force either aids or opposes the thermally driven flow, which is determined by the value of buoyancy ratio (positive or negative, respectively). Interesting flow patterns were predicted for opposing buoyancy forces.     

Laminar flow in narrow ducts and circular tubes: Entrance effects

Series solutions are presented for laminar flow heat transfer in narrow rectangular ducts and circular tubes when the hydrodynamic and thermal boundary layers are developing simultaneously. In addition, simple engineering relationships are presented which agree well with literature values over a wide range of Peclet numbers.It is demonstrated how simplified local heat flux calculations may be performed using the results obtained.     

Thermal analysis of plate condensers in presence of flow maldistribution

Flow maldistribution in plate heat exchangers causes deterioration of both thermal and hydraulic performance. The situation becomes more complicated for two-phase flows during condensation where uneven distribution of the liquid to the channels reduces heat transfer due to high liquid flooding. The present study evaluates the thermal performance of falling film plate condensers with flow maldistribution from port to channel considering the heat transfer coefficient inside the channels as a function of channel flow rate. A generalized mathematical model has been developed to investigate the effect of maldistribution on the thermal performance as well as the exit quality of vapor. A wide range of parametric study is presented, which shows the effects of the mass flow rate ratio of cold fluid and two-phase fluid, flow configuration, number of channels and correlation for the heat transfer coefficient. The analysis presented here also suggests an improved method for heat transfer data analysis for plate condensers.     

Numerical prediction of effective thermal conductivity of ceramic fiber board using lattice Boltzmann method

Abstract

Application of the lattice Boltzmann method has been extended for the analysis of combined transient conduction and radiation heat transfer through highly porous fibrous insulation media. Firstly, LBM has been employed for the analysis of combined mode of transient conduction radiation heat transfer in a 2?D rectangular enclosure containing an absorbing, emitting and scattering medium and results are compared with already published ones. The results have been found in good accord for different values of radiation-conduction parameter, scattering albedo and south (hot) wall emissivity. Furthermore, the proposed LBM for the calculation of effective thermal conductivity of ceramic fiber board has been employed. A random-generation growth method for generating micro morphology of natural ceramic fiber board has been selected. The conductive, radiative and effective thermal conductivity has been numerically estimated using the present LBM. It is found that the predicted effective thermal conductivity for different values of fibrous bulk density is in good agreement with the experimental data.     

Mixed convection heat transfer in two-dimensional open-ended enclosures

Mixed convection heat transfer in open-ended enclosures has been studied numerically for three different flow angles of attack. Discretization of the governing equations is achieved using a finite element scheme based on the Galerkin method of weighted residuals. Comparisons with previously published work on special cases of the problem are performed and the results show excellent agreement. A wide range of pertinent parameters such as Grashof number, Reynolds number, and the aspect ratio are considered in the present study. The obtained results show that thermal insulation of the cavity can be achieved through the use of high horizontal velocity flow. Various results for the streamlines, isotherms and the heat transfer rates in terms of the average Nusselt number are presented and discussed for different parametric values.     

Study on fluid–solid coupling heat transfer in fractal porous medium by lattice Boltzmann method

A lattice Boltzmann model is applied to simulate fluid–solid coupling heat transfer in fractal porous medium. The numerical simulation is conducted to investigate the influences of pressure drop and porosity on fluid flows and the effect of thermal conductivity ratio of solid matrix to fluid on heat transfer. The simulation results indicate that fluid flows still obey Darcy’s Law in the range of flow and pressure level in this paper, and that both velocity field and temperature evolution conform to the local structural characteristics of porous medium. The comparison of temperature results from lattice Boltzmann model against those from the finite-volume method (FVM, one of the conventional CFD methods) is also presented to demonstrate the reliability of LBM. The present results agree well with those from FVM, All these indicate the feasibility and the reliability for the lattice Boltzmann model to be used to reveal the phenomenon and rules of fluid–solid coupling heat transfer in complex porous structures.     

Numerical analysis of combined-mode dual-phase-lag heat conduction and radiation in an absorbing,emitting, and scattering cylindrical medium

Combined-mode dual-phase-lag (DPL) heat conduction and radiation heat transfer is analyzed in a concentric cylindrical enclosure filled with a radiatively absorbing, emitting, and scattering medium. The governing energy equation is incorporated with volumetric radiation as a source term, essentially to take the effect of radiative heat flux into account. While the energy equation is solved using the lattice Boltzmann method (LBM), the finite volume method (FVM) is used to calculate the radiative information. To establish the accuracy of the proposed LBM formulation, the governing energy equation is also solved with the finite difference method (FDM). Thermal perturbation is caused by suddenly changing the temperature at the boundaries. Radial temperature distributions during transience as well as steady state (SS) are presented for a wide range of parameters such as lag ratio, extinction coefficient, scattering albedo, conduction–radiation (C-R) parameter, boundary emissivity, and radius ratio. Sample results are benchmarked with those available in the literature, and a good agreement between the present and reported results is found.     

A Review on the Application of the Lattice Boltzmann Method for Turbulent Flow Simulation

The Lattice Boltzmann Method (LBM) is a potent numerical technique based on kinetic theory, which has been effectively employed in various complicated physical, chemical, and fluid mechanics problems. In recent years, turbulent flow simulation by using this new class of computational fluid dynamics technique has attracted more attention. In this article, a review of previous studies on turbulence in the frame of LBM is presented. Recent extensions of this method are categorized based on three main groups of turbulence simulation: DNS, LES and RANS methods.     

Advances in mathematical modeling of hydrogen adsorption and desorption in metal hydride beds with lattice Boltzmann method

This study presents numerical modeling and simulations of thermal fluid flows in high-volumetric-density metal hydride beds during hydrogen (H₂) adsorption and desorption within the lattice Boltzmann method (LBM) framework. A novel LBM is developed for predicting the flow and conjugate heat transfer in a practical lab apparatus involving a combination of solid chamber, free expansion zone, and porous media metal hydride that have not been addressed to date. With a correction term in the collision operator and a new equilibrium distribution function, the present model has a consistent expression of the heat capacity ratio for different fluid regions and derives the correct form of macroscopic energy and generalized momentum equations (including Darcy, Brinkman, and Forchheimer terms). The model is then validated through comparisons of the simulated results with previous experimental data under different initial pressure and temperature conditions for LaNi₅–H₂ storage systems as well Mg–H₂ reactors, achieving excellent agreement. In addition, accounting for conjugate heat transfer and other porous forces in the present LBM yields improved predictions over prior numerical approaches.     

A Comparative Study of Submicron Phonon Transport Using the Boltzmann Transport Equation and the Lattice Boltzmann Method

The subcontinuum energy transport mechanism in solids can be explained by the Lattice Boltzmann Method (LBM), a discrete representation of the Boltzmann Transport Equation (BTE). The present study focuses on a detailed comparison of the LBM and BTE. Results reveal that at continuum scale, the LBM follows the BTE almost precisely. However, as the device dimensions are reduced, approaching the ballistic limit, the LBM deviates from the BTE results in terms of thermal property estimation. The inherent nonisotropic lattice configuration has a dominant contribution to the performance of the LBM. A threshold length scale is also proposed for successful implementation of the LBM solver.     

The effects of thermal non-equilibrium and inlet temperature on two-phase flow pressure drop type instabilities in an upflow boiling system

In this paper a theoretical model for the two-phase flow pressure drop type instabilities in an upflow boiling system is presented. The thermal non-equilibrium effect between the two phases is included assuming the enthalpy profile in the subcooled boiling region. The system of differential equations describing the single-phase and boiling regions of the system (drift-flux model) is solved using finite difference method for the steady state characteristics of the system over a wide range of operating conditions. Upon obtaining the steady state characteristics, the dynamic formulation of the pressure drop type oscillation is solved numerically. The modeling results are verified by the experimental findings. The effect of the thermal non-equilibrium on the steady state characteristics, stability boundaries and oscillation periods at different heat inputs and inlet temperatures are presented as being compared with the experimental measurements as well as the results obtained from the thermal equilibrium model.     

Optimum wall-to-wall spacing in solar chimney shaped channels in natural convection by numerical investigation

A numerical study on the laminar and turbulent flows induced by natural convection in channels, with solar chimney configuration, for a wide range of Rayleigh number, several values of the relative wall-to-wall spacing and different heating conditions has been performed. The low-Reynolds k–ω turbulence model has been employed to simulate the turbulent cases. Numerical results for the average Nusselt number and the non-dimensional induced mass-flow rate have been obtained for values of Rayleigh number varying from 10⁵ to 10¹² for symmetrically, isothermal heating. For this heating condition, a correlation for the thermal optimum aspect ratio has been presented. The sudden change reached in the flow pattern for given conditions drives to obtain a different behavior of the optimum aspect ratio that maximizes the mass-flow rate with respect to the thermal optimum aspect ratio.     

Effect of volumetric radiation on natural convection in a square cavity using lattice Boltzmann method with non-uniform lattices

This study deals with the effect of volumetric radiation on the natural convection in a square cavity containing an absorbing, emitting and scattering medium. Numerical simulation has been carried out using lattice Boltzmann method (LBM) with non-uniform lattices. Non-uniform lattices/control volumes have been implemented to deal with the sharp gradients and achieve reasonably accurate solutions. Separate equations dealing with different particle distribution functions in the LBM are used to calculate the density and velocity fields and the thermal fields. The finite volume method (FVM) is used to compute the radiative term of the energy equation. The results obtained in the present study is compared and validated against available results in literature. The centerline temperature across the cavity, the isotherms, the vertical velocity in the horizontal mid-plane, the horizontal velocity in the vertical mid-plane and the streamlines are studied for different parameters such as Rayleigh number, conduction–radiation parameter, extinction coefficient and scattering albedo. The results obtained by using the non-uniform lattices-based LBM are compared with the results for uniform lattice based-LBM. It is found that the non-uniform lattice-based LBM provides accurate results and it is computationally more efficient.