Fluid Flow Analysis in Anisotropic Porous Media by Lattice Boltzmann Method

The lattice Boltzmann method (LBM) is applied to simulation of natural convection in anisotropic porous media using Brinkman equation. The Brinkman equation is recovered from a kinetic equation for the density distribution function with a forcing term. The temperature equation is calculated by a kinetic equation for thermal energy distribution function. The velocity profiles of the LBM shows good agreement with those of the analytical solutions for the Poiseuille flow and for the Couette flow filled with anisotropic porous media. For various values of Darcy and Rayleigh numbers, the solutions of the LBM are compared with those of earlier studies in natural convection. This paper leads to the conclusion that the LBM can simulate natural convection in anisotropic porous media for the non-Darcy model

A modified lattice Bhatnagar-Gross-Krook model for convection heat transfer in porous media

The lattice Bhatnagar-Gross-Krook (LBGK) model has become the most popular one in the lattice Boltzmann method for simulating the convection heat transfer in porous media. However, the LBGK model generally suffers from numerical instability at low fluid viscosities and effective thermal diffusivities. In this paper, a modified LBGK model is developed for incompressible thermal flows in porous media at the representative elementary volume scale, in which the shear rate and temperature gradient are incorporated into the equilibrium distribution functions. With two additional parameters, the relaxation times in the collision process can be fixed at a proper value invariable to the viscosity and the effective thermal diffusivity. In addition, by constructing a modified equilibrium distribution function and a source term in the evolution equation of temperature field, the present model can recover the macroscopic equations correctly through the Chapman-Enskog analysis, which is another key point different from previous LBGK models. Several benchmark problems are simulated to validate the present model with the proposed local computing scheme for the shear rate and temperature gradient, and the numerical results agree well with analytical solutions and/or those well-documented data in previous studies. It is also shown that the present model and the computational schemes for the gradient operators have a second-order accuracy in space, and better numerical stability of the present modified LBGK model than previous LBGK models is demonstrated.Comment: 38pages,50figure

Challenges and progress on the modelling of entropy generation in porous media: a review

Depending upon the ultimate design, the use of porous media in thermal and chemical systems can provide significant operational advantages, including helping to maintain a uniform temperature distribution, increasing the heat transfer rate, controlling reaction rates, and improving heat flux absorption. For this reason, numerous experimental and numerical investigations have been performed on thermal and chemical systems that utilize various types of porous materials. Recently, previous thermal analyses of porous materials embedded in channels or cavities have been re-evaluated using a local thermal non-equilibrium (LTNE) modelling technique. Consequently, the second law analyses of these systems using the LTNE method have been a point of focus in a number of more recent investigations. This has resulted in a series of investigations in various porous systems, and comparisons of the results obtained from traditional local thermal equilibrium (LTE) and the more recent LTNE modelling approach. Moreover, the rapid development and deployment of micro-manufacturing techniques have resulted in an increase in manufacturing flexibility that has made the use of these materials much easier for many micro-thermal and chemical system applications, including emerging energy-related fields such as micro-reactors, micro-combustors, solar thermal collectors and many others. The result is a renewed interest in the thermal performance and the exergetic analysis of these porous thermochemical systems. This current investigation reviews the recent developments of the second law investigations and analyses in thermal and chemical problems in porous media. The effects of various parameters on the entropy generation in these systems are discussed, with particular attention given to the influence of local thermodynamic equilibrium and non-equilibrium upon the second law performance of these systems. This discussion is then followed by a review of the mathematical methods that have been used for simulations. Finally, conclusions and recommendations regarding the unexplored systems and the areas in the greatest need of further investigations are summarized

The development of thermal lattice Boltzmann models in incompressible limit

In this paper, an incompressible two-dimensional (2-D) and three-dimensional (3-D) thermohydrodynamics for the lattice Boltzmann scheme are developed. The basic idea is to solve the velocity field and the temperature field using two different distribution functions. A derivation of the lattice Boltzmann scheme from the continuous Boltzmann equation for 2-D is discussed in detail. By using the same procedure as in the derivation of the discretised density distribution function, we found that new lattice of four-velocity (2-D) and eight-velocity(3-D) models for internal energy density distribution function can be developed where the viscous and compressive heating effects are negligible. These models are validated by the numerical simulation of the 2-D porous plate Couette flow problem where the analytical solution exists and the natural convection flows in a cubic cavity

Towards modeling heat transfer using a lattice boltzmann method for porous media

I present in this thesis a fluid flow and heat transfer model for porous media using the lattice Boltzmann method (LBM). A computer simulation of this process has been developed and it is written using MATLAB software. The simulation code is based on a two dimensional model, D2Q9. Three physical experiments were designed to prove the simulation model through comparision with numerical results. In the experiments, physical properties of the air flow and the porous media were used as input for the computer model. The study results are not conclusive but show that the LBM model may become a reliable tool for the simulation of natural convection heat transfer in porous media. Simulations leading to improved understanding of the processes of air flow and heat transfer in porous media may be important into improving the efficiency of methods of air heating or cooling by passing air through fragmented rock.Master's Thesi