Lattice Boltzmann simulations of turbulent shear flow between parallel porous walls

The effects of two parallel porous walls are investigated, consisting of the Darcy number and the porosity of a porous medium, on the behavior of turbulent shear flows as well as skin-friction drag. The turbulent channel flow with a porous surface is directly simulated by the lattice Boltzmann method （LBM）. The Darcy-Brinkman- Forcheimer （DBF） acting force term is added in the lattice Boltzmann equation to simu- late the turbulent flow bounded by porous walls. It is found that there are two opposite trends （enhancement or reduction） for the porous medium to modify the intensities of the velocity fluctuations and the Reynolds stresses in the near wall region. The parametric study shows that flow modification depends on the Darcy number and the porosity of the porous medium. The results show that, with respect to the conventional impermeable wall, the degree of turbulence modification does not depend on any simple set of param- eters obviously. Moreover, the drag in porous wall-bounded turbulent flow decreases if the Darcy number is smaller than the order of O（10-4） and the porosity of porous walls is up to 0.4.     

Intercomparison of boundary schemes in Lattice Boltzmann method for flow simulation in porous media

The Lattice Boltzmann method has been widely adopted to simulate flow in porous media. The choice of appropriate boundary schemes is essential to achieve simulation accuracy; however, the criteria for the most suitable boundary treatment in the simulation of flow in porous media flow remain unresolved. Here, three types of the most commonly used boundary conditions are tested: interpolation bounce back (IBB), partial saturated method (PSM), and immersed boundary method (IBM). The dimensionless drag of face-centered cubic (FCC) sphere array and the dimensionless permeability of a random closely packed (RCP) sphere array are calculated and compared at different viscosities and resolutions. In the FCC sphere array case where spheres are not contacted, the IBB and PSM exhibit the same accuracy and both are of the second-order convergence rate. The IBM is less accurate and is of the first-order convergence rate. In the RCP sphere array case where the spheres are contacted, the IBB shows finer results and a second-order convergence rate. PSM underestimates the dimensionless permeability and increases resolution only slightly improved the results of PSM. The IBM overestimates the dimensionless permeability. These results indicate that among the three methods, the IBB is the most accurate. The PSM has the same accuracy as the IBB when sediments are not contacted; however, it loses its accuracy in the simulation of flow in closely packed porous media. This work could serve as a benchmark for further research in choosing the most appropriate method in the simulation of flow in porous media.     

New studying of Lattice Boltzmann method for two-phase driven in porous media

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Lattice Boltzmann model for thermal free surface flows with liquid-solid phase transition

Purpose

The main objective of this work is to develop an algorithm to use the Lattice Boltzmann method for solving free surface thermal flow problems with solid/liquid phase changes.

Approach

A multi-distribution function model is applied to simulate hydrodynamic flow and the coupled thermal diffusion-convection problem.

Findings

The free surface problem, i.e. the reconstruction of the missing distribution functions at the interface, can be solved by applying a physical transparent momentum and heat flux based methodology. The developed method is subsequently applied to some test cases in order to assess its computational potentials.

Practical implications

Many industrial processes involve problems where non-isothermal motion and simultaneous solidification of fluids with free surface is important. Examples are all castings processes and especially foaming processes which are characterized by a huge and strongly changing surface.

Value

A reconstruction algorithm to treat a thermal hydrodynamic problem with free surfaces is presented which is physically transparent and easy to implement.     

Simulation of natural convection melting in a cavity with fin using lattice Boltzmann method

In this study, a numerical investigation of melting phenomenon with natural convection in a cavity with fin has been performed using enthalpy‐based lattice Boltzmann method. The lattice D2Q9 model was applied to determine the density and velocity fields, and the D2Q5 model for the temperature field. The effect of vertical position and length of the fin on the melting rate was studied. The simulations were carried out for Stefan number of 10, Rayleigh number of 10 ⁵ and relative thermal conductivity (k_fin∕k_fluid) ranging from 5 to 30. The obtained results show that the rate of melting increases when the relative thermal conductivity and the length of the fin become greater. We also found that the variation of vertical position of the fin from bottom to middle has an insignificant effect on melting while it causes the increase of full melting time when the fin is mounted on the top of the cavity. Copyright © 2011 John Wiley & Sons, Ltd.     

Migration-collision scheme of Lattice Boltzmann method for heat conduction problems involving solidification

The phase-change problem is solved by the migration-collision scheme of lattice Boltzmann method. After formula derivation, we find that this method can give a rigorous numerical value for the phase-change temperature, which is of crucial importance. One-dimensional solidification in half-space and two-dimensional solidification in a corner are simulated. The phase change temperature and the liquid-solid interface are both obtained, and the results conform to the analytical solution.     

LES-based filter-matrix lattice Boltzmann model for simulating turbulent natural convection in a square cavity

In this paper, a novel thermal filter-matrix lattice Boltzmann model based on large eddy simulation (LES) is proposed for simulating turbulent natural convection. In this study, the Vreman subgrid-scale eddy-viscosity model is introduced into the present framework of LES to accurately predict the flow in near-wall region. Two dimensional numerical simulations of natural convection in a square cavity were performed at high Rayleigh number varying from 10⁷ to 10¹⁰ with a fixed Prandtl number of Pr = 0.71. The influences of the higher-order terms upon the present results at high Rayleigh numbers are examined, taking Ra = 10⁷ and 10⁸ as the example, revealing that the proper minimization of the higher-order terms can improve numerical accuracy of present model for high Rayleigh convective flow. For the turbulent convective flow, the time-averaged quantities in the median lines are presented and compared against those available results from previous studies. The general structure of turbulent boundary layers is well predicted. All numerical results exhibit good agreement with the benchmark solutions available in the previous literatures.     

Permeability of microscale fibrous porous media using the lattice Boltzmann method

The permeabilities of microscale fibrous porous media were calculated using the multiple-relaxation-time (MRT) lattice Boltzmann method (LBM). Two models of the microscale fibrous porous media were constructed based on overlapping fibers (simple cubic, body-centered cubic). Arranging the fibers in skew positions yielded two additional models comprising non-overlapping fibers (skewed simple cubic, skewed body-centered cubic). As the fiber diameter increased, the fibers acted as granular inclusions. The effects of the overlapping fibers on the media permeability were investigated. The overlapping fibers yielded permeability values that were a factor of 2.5 larger than those obtained from non-overlapping fibers, but the effects of the fiber arrangement were negligible. Two correlations were obtained for the overlapping and non-overlapping fiber models, respectively. The effects of the rarefaction and slip flow are also discussed. As the Knudsen number increased, the dimensionless permeability increased; however, the increase differed depending on the fiber arrangement. In the slip flow regime, the fiber arrangement inside the porous media became an important factor.     

Three-dimensional flow driven pore-crack networks in porous composites: Boltzmann Lattice method and hybrid hypersingular integrals

This study introduces a hybrid hypersingular integral equation-Lattice Boltzmann method (HHIE-LBM) for analyzing extended 3D flow driven pore-crack networks problem in various porosity composites. First, the extended hybrid electronic-ionic, thermal, magnetic, electric and force coupled fields’ pressure and velocity boundary conditions for HHIE-LBM model are established, and the closed form solutions of extended distribution functions are given. Second, an extended 3D flow driven pore-crack networks problem in various porosity composites is translated into a coupled of HHIE-LBM equations, and the pore-crack networks propagation parameters are analyzed. Third, the extended dynamic stress intensity factors (EDSIFs) are calculated by using the parallel numerical technology and the visualization results are presented. Last, the relationship between the EDSIFs and the differential porosity is discussed, and several rules have been found, which can be utilized to understand the extended fluid flow mechanism in various porosity composites and analyze the extended fluid flow varying mechanism on coseismal slip.     

Lattice Boltzmann simulation of MHD natural convection in a cavity with porous media and sinusoidal temperature distribution

The lattice Boltzmann method (LBM) is used to simulate the effect of magnetic field on the natural convection in a porous cavity. The sidewalls of the cavity are heated sinusoidally with a phase derivation, whereas the top and bottom walls are thermally insulated. Numerical simulation is performed, and the effects of the pertinent parameters, e.g., the Hartmann number, the porosity, the Darcy number, and the phase deviation, on the fluid flow and heat transfer are investigated. The results show that the heat transfer is affected by the temperature distribution on the sidewalls clearly. When the Hartmann number is 0, the maximum average Nusselt number is obtained at the phase deviation 90°. Moreover, the heat transfer enhances when the Darcy number and porosity increase, while decreases when the Hartman number increases.     

Lattice Boltzmann simulations for flow and heat/mass transfer problems in a three‐dimensional porous structure

The lattice Boltzmann method (LBM) for a binary miscible fluid mixture is applied to problems of transport phenomena in a three‐dimensional porous structure. Boundary conditions for the particle distribution function of a diffusing component are described in detail. Flow characteristics and concentration profiles of diffusing species at a pore scale in the structure are obtained at various Reynolds numbers. At high Reynolds numbers, the concentration profiles are highly affected by the flow convection and become completely different from those at low Reynolds numbers. The Sherwood numbers are calculated and compared in good agreement with available experimental data. The results indicate that the present method is useful for the investigation of transport phenomena in porous structures. Copyright © 2003 John Wiley & Sons, Ltd.     

用格子Boltzmann方法模拟液滴撞击固壁动力学行为

首次用格子Boltzmann方法中的伪势模型对液滴撞击固壁的动力学行为进行了数值模拟.详细研究了液滴在壁面上的流动状态以及各种因素对撞击过程的影响.通过数值模拟得到:壁面的可润湿性越小,液滴越容易发生反弹,液滴的回缩速度越快;液滴的撞击速度越大,所得到的相对直径越大,回缩速度越快;液滴的粘性越小,所得到的相对直径越大;液滴的表面张力越大,液滴越容易发生反弹现象.另外,液滴的最大相对直径与We数满足一定的线性关系,这些结果与前人的理论预测和实验结果完全吻合.     

Shear‐improved Smagorinsky modeling of turbulent channel flow using generalized Lattice Boltzmann equation

Generalized Lattice Boltzmann equation (GLBE) was used for computation of turbulent channel flow for which large eddy simulation (LES) was employed as a turbulence model. The subgrid‐scale turbulence effects were simulated through a shear‐improved Smagorinsky model (SISM), which is capable of predicting turbulent near wall region accurately without any wall function. Computations were done for a relatively coarse grid with shear Reynolds number of 180 in a parallelized code. Good numerical stability was observed for this computational framework. The results of mean velocity distribution across the channel showed good correspondence with direct numerical simulation (DNS) data. Negligible discrepancies were observed between the present computations and those reported from DNS for the computed turbulent statistics. Three‐dimensional instantaneous vorticity contours showed complex vortical structures that appeared in such flow geometries. It was concluded that such a framework is capable of predicting accurate results for turbulent channel flow without adding significant complications and the computational cost to the standard Smagorinsky model. As this modeling was entirely local in space it was therefore adapted for parallelization. Copyright © 2010 John Wiley & Sons, Ltd.     

Lattice Boltzmann model for predicting the deposition of inertial particles transported by a turbulent flow

Deposition of inertial solid particles transported by turbulent flows is modelled in a framework of a statistical approach based on the particle velocity Probability Density Function (PDF). The particle-turbulence interaction term is closed in the kinetic equation by a model widely inspired from the famous BGK model of the kinetic theory of rarefied gases. A Gauss-Hermite Lattice Boltzmann model is used to solve the closed kinetic equation involving the turbulence effect. The Lattice Boltzmann model is used for the case of the deposition of inertial particles transported by a homogeneous isotropic turbulent flows. Even if the carrier phase is homogeneous and isotropic, the presence of the wall coupled with particle-turbulence interactions leads to inhomogeneous particle distribution and non-equilibrium particle fluctuating motion. Despite these complexities the predictions of the Lattice Boltzmann model are in very good accordance with random-walk simulations. More specifically the mean particle velocity, the r.m.s. particle velocity and the deposition rate are all well predicted by the proposed Lattice Boltzmann model.     

A study of the upper limit of solid scatters density for gray Lattice Boltzmann Method

The upper limit of the solid scatters density ns （x）, a key parameter for the simulation of flows in porous media with a gray Lattice Boltzmann Method, is studied by an analytical way for the infiltration Poiseuille flow between two infinite parallel plates. Analyses of three different gray Lattice Boltzmann schemes, separately proposed by Gao and Sharma et al., Dardis and McCloskey, and Thorne and Sukop, indicate that the effective domain of Gao and Sharma＇s scheme is restricted to ns 〈 1/2√3≈0.289, Dardis and McCloskey＇s scheme is restricted to ns 〈 （√57-1）/28≈0.234, and that there is no extra restriction on ns（x） with Thorne and Sukop＇s scheme. These results are obtained for the dimensionless relaxation time τ= 1. The above analytical results are verified by our numerical simulations. The use of a gray LBM is further illustrated by simulating the flow at the interface of a porous medium. Simulation results yield velocity profiles which agree very well with Brinkman＇s prediction.     

A reference solution for phase change with convection

A reference solutions for phase change involving convection in the melt is currently missing. In the present study, we focus on the problem of melting of pure tin in a square cavity heated from the side, which is used as a benchmark test problem. The mathematical model used for the simulations is based on the enthalpy formulation. Extensive numerical computations are performed with grids as fine as 800 × 800. The convergence of the numerical solution is demonstrated and its level assessed. Data values and plots are provided for use as a reference solution. Copyright © 2005 John Wiley & Sons, Ltd.     

Determination of permeability in fibrous porous media using the lattice Boltzmann method with application to PEM fuel cells

The lattice Boltzmann method (LBM) is used to simulate the flow through an idealized proton exchange membrane fuel cell (PEMFC) porous transport layer (PTL) geometry generated using a Monte Carlo method. Using the calculated flow field, Darcy's law is applied and the permeability is calculated. This process is applied in both through‐ and in‐plane directions of the paper as both of these permeability values are important in computational fluid dynamics models of PEMFCs. It is shown that the LBM can be used to determine permeability in a random porous media by solving the flow in the microstructure of the material. The permeability in the through‐ and in‐plane directions is shown to be different and the anisotropic nature of the geometry creates anisotropic permeability. It is also found that fiber arrangement plays a large role in the permeability of the PTL. New correlations are presented for in‐ and though‐plane permeabilities of fibrous porous media with (0.6<ε<0.8). Copyright © 2008 John Wiley & Sons, Ltd.     

Lattice Boltzmann modeling of pore‐scale fluid flow through idealized porous media

In order to capture the hydro‐mechanical impacts on the solid skeleton imposed by the fluid flowing through porous media at the pore‐scale, the flow in the pore space has to be modeled at a resolution finer than the pores, and the no‐slip condition needs to be enforced at the grain–fluid interface. In this paper, the lattice Boltzmann method (LBM), a mesoscopic Navier–Stokes solver, is shown to be an appropriate pore‐scale fluid flow model. The accuracy and lattice sensitivity of LBM as a fluid dynamics solver is demonstrated in the Poiseuille channel flow problem (2‐D) and duct flow problem (3‐D). Well‐studied problems of fluid creeping through idealized 2‐D and 3‐D porous media (J. Fluid Mech. 1959; 5 (2):317–328, J. Fluid Mech. 1982; 115 :13–26, Int. J. Multiphase Flow 1982; 8 (4):343–360, Phys. Fluids A 1989; 1 (1):38–46, Int. J. Numer. Anal. Meth. Geomech. 1999; 23 :881–904, Int. J. Numer. Anal. Meth. Geomech. 2010; DOI: 10.1002/nag.898, Int. J. Multiphase Flow 1982; 8 (3):193–206) are then simulated using LBM to measure the friction coefficient for various pore throats. The simulation results agree well with the data reported in the literature. The lattice sensitivity of the frictional coefficient is also investigated. Copyright © 2010 John Wiley & Sons, Ltd.     

Multiphase flow in the vascular system of wood: From microscopic exploration to 3-D Lattice Boltzmann experiments

This paper provides insights into liquid free water dynamics in wood vessels based on Lattice Boltzmann experiments. The anatomy of real wood samples was reconstructed from systematic 3-D analyses of the vessel contours derived from successive microscopic images. This virtual vascular system was then used to supply fluid–solid boundary conditions to a two-phase Lattice Boltzmann scheme and investigate capillary invasion of this hydrophilic porous medium. Behavior of the liquid phase was strongly dependent on anatomical features, especially vessel bifurcations and reconnections. Various parameters were examined in numerical experiments with ideal vessel bifurcations, to clarify our interpretation of these features.