Lattice Boltzmann simulations of impedance tube flows

An original time-domain surface acoustic impedance condition for Lattice Boltzmann methods has been developed. The basis for this method is the extension proposed by Delattre et al. [Delattre G, Manoha E, Redonnet S, Sagaut P. Time-domain simulation of sound absorption on curved wall. 13th AIAA/CEAS Aeroacoustics conference, Rome, Italy, AIAA-2007-3493; 2007] of the z-transform approach suggested by Özyörük et al. [Özyörük Y, Long LN, Jones M. Time-domain numerical simulation of a flow impedance tube. J Comput Phys 1998;146:29-57]. Using this boundary condition that links the normal velocity and the pressure, the basic idea consists in calculating the Lattice Boltzmann populations at a boundary node thanks to the gradients of the fluid velocity. This paper describes the proposed LBM boundary conditions and its assessment on the NASA Langley flow-impedance tube with a constant depth ceramic tubular liner. We performed both single and broadband-frequency simulations, without mean flow and with sheared mean flows. Excellent agreement is shown with both experimental data and other simulation results at various frequencies up to a Mach number equal to 0.5.     

Lattice Boltzmann equation for axisymmetric thermal flows

A simple lattice Boltzmann equation (LBE) model for axisymmetric thermal flow is proposed in this paper. The flow field is solved by a quasi-two-dimensional nine-speed (D2Q9) LBE, while the temperature field is solved by another four-speed (D2Q4) LBE. The model is validated by a thermal flow in a pipe and some nontrivial thermal buoyancy-driven flows in vertical cylinders, including Rayleigh-Bénard convection, natural convection, and heat transfer of swirling flows. It is found that the numerical results agree excellently with analytical solution or other numerical results.     

Lattice Boltzmann simulations of drop dynamics

We present a free energy lattice Boltzmann approach to modelling the dynamics of liquid drops on chemically patterned substrates. We start by describing a choice of free energy that reproduces the bulk behaviour of a liquid–gas system together with the varying contact angles on surfaces with chemical patterning. After showing how the formulation of the free energy fits in to the framework of lattice Boltzmann simulations, numerical results are presented to highlight the applicability of the approach.     

Optimizing lattice Boltzmann simulations for unsteady flows

We present detailed analysis of a lattice Boltzmann approach to model time-dependent Newtonian flows. The aim of this study is to find optimized simulation parameters for a desired accuracy with minimal computational time. Simulation parameters for fixed Reynolds and Womersley numbers are studied. We investigate influences from the Mach number and different boundary conditions on the accuracy and performance of the method and suggest ways to enhance the convergence behavior.     

Extension of a hybrid thermal LBE scheme for large-eddy simulations of turbulent convective flows

Following the work of Lallemand and Luo [Lallemand P, Luo L-S. Theory of the lattice Boltzmann method: acoustic and thermal properties in two and three dimensions. Phys Rev E 2003;68:036706] we validate, apply and extend the hybrid thermal lattice Boltzmann scheme (HTLBE) by a large-eddy approach to simulate turbulent convective flows. For the mass and momentum equations, a multiple-relaxation-time LBE scheme is used while the heat equation is solved numerically by a finite difference scheme. We extend the hybrid model by a Smagorinsky subgrid scale model for both the fluid flow and the heat flux. Validation studies are presented for laminar and turbulent natural convection in a cavity at various Rayleigh numbers up to 5 × 10¹⁰ for Pr = 0.71 using a serial code in 2D and a parallel code in 3D, respectively. Correlations of the Nusselt number are discussed and compared to benchmark data. As an application we simulated forced convection in a building with inner courtyard at Re = 50 000.     

MRT Lattice Boltzmann schemes for confined suspension flows

We introduce a novel multiple-relaxation time (modified MRT) Lattice Boltzmann scheme for simulation of confined suspension flow. Via careful tuning of the free eigenvalues of the collision operator we can substantially reduce the error in the so-called hydrodynamic radius. Its performance has been compared to that of the TRT scheme for several benchmark problems. We have found that the optimal value of the free eigenvalue depends on the curvature of the solid-fluid interfaces. Hence, we have investigated suspension flow problems, with confining boundaries of different curvatures. We have found that the modified MRT scheme is better suited for suspension flow in curved confining walls, while the TRT scheme is better for suspension flow confined between planar walls.With both schemes we have investigated problems for confined suspension flows, namely 1) drag forces experienced by spheres flowing in confining flow channels of different cross sections, and 2) the lubrication force between a sedimenting sphere and the end cap of a confining cylindrical capillary.     

A flexible high‐performance Lattice Boltzmann GPU code for the simulations of fluid flows in complex geometries

We describe the porting of the Lattice Boltzmann component of MUPHY, a multi‐physics/scale simulation software, to multiple graphics processing units using the Compute Unified Device Architecture. The novelty of this work is the development of ad hoc techniques for optimizing the indirect addressing that MUPHY uses for efficient simulations of irregular domains. Copyright © 2009 John Wiley & Sons, Ltd.     

Lattice Boltzmann modeling of microchannel flows in the transition flow regime

Owing to its kinetic nature and distinctive computational features, the lattice Boltzmann method for simulating rarefied gas flows has attracted significant research interest in recent years. In this article, a lattice Boltzmann (LB) model is presented to study microchannel flows in the transition flow regime, which have gained much attention because of fundamental scientific issues and technological applications in various micro-electro-mechanical system (MEMS) devices. In the model, a Bosanquet-type effective viscosity is used to account for the rarefaction effect on gas viscosity. To match the introduced effective viscosity and to gain an accurate simulation, a modified second-order slip boundary condition with a new set of slip coefficients is proposed. Numerical investigations demonstrate that the results, including the velocity profile, the non-linear pressure distribution along the channel, and the mass flow rate, are in good agreement with the solution of the linearized Boltzmann equation, the direct simulation Monte Carlo (DSMC) results, and the experimental results over a broad range of Knudsen numbers. It is shown that taking the rarefaction effect on gas viscosity into consideration and employing an appropriate slip boundary condition can lead to a significant improvement in the modeling of rarefied gas flows with moderate Knudsen numbers in the transition flow regime.     

Lattice Boltzmann simulations of the motion induced by variable surface tension

Methods for implementing variable surface tension in the multiphase Lattice Boltzmann model with the color model and Shan-Chen scheme are tested by analyzing the models’ abilities to reproduce a theoretical result by Levich and Kuznetzov. If the surface tension around a droplet is asymmetrical, the droplet moves towards the side where the surface tension is lower. The droplet’s velocity is proportional to the surface tension gradient, the droplet’s radius, and the inverse of the viscosity. The model is tested to determine whether the simulated droplets move in the manner predicted by theory. Although the discreteness of the underlying lattice causes a spurious oscillation to the velocity, the numerical results concerning the average velocity show a good correspondence between theory and the model in regards to the surface tension gradient and droplet size. The color model also produces good simulations in the scenarios with different viscosities, while the diffusive properties and unknown relationships between the parameters and surface tension in the Shan-Chen model make the numerical results of that model more dubious, even though several of the results are qualitatively in agreement.     

Thermal boundary conditions for thermal lattice Boltzmann simulations

Consistent 2D and 3D thermal boundary conditions for thermal lattice Boltzmann simulations are proposed. The boundary unknown energy distribution functions are made functions of known energy distribution functions and correctors, where the correctors at the boundary nodes are obtained directly from the definition of internal energy density. This boundary condition can be easily implemented on the wall and corner boundary using the same formulation. The discrete macroscopic energy equation is also derived for a steady and fully developed channel flow to assess the effect of the boundary condition on the solutions, where the resulting second order accurate central difference equation predicts continuous energy distribution across the boundary, provided the boundary unknown energy distribution functions satisfy the macroscopic energy level. Four different local known energy distribution functions are experimented with to assess both this observation and the applicability of the present formulation, and are scrutinized by calculating the 2D thermal Poiseuille flow, thermal Couette flow, thermal Couette flow with wall injection, natural convection in a square cavity, and 3D thermal Poiseuille flow in a square duct. Numerical simulations indicate that the present formulation is second order accurate and the difference of adopting different local known energy distribution functions is, as expected, negligible, which are consistent with the results from the derived discrete macroscopic energy equation.     

Multiplicity of steady solutions in two-dimensional lid-driven cavity flows by Lattice Boltzmann Method

This work is concerned with the computation of two- and four-sided lid-driven square cavity flows and also two-sided rectangular cavity flows with parallel wall motion by the Lattice Boltzmann Method (LBM) to obtain multiple stable solutions. In the two-sided square cavity two of the adjacent walls move with equal velocity and in the four-sided square cavity all the four walls move in such a way that parallel walls move in opposite directions with the same velocity; in the two-sided rectangular lid-driven cavity flow the longer facing walls move in the same direction with equal velocity. Conventional numerical solutions show that the symmetric solutions exist for all Reynolds numbers for all the geometries, whereas multiplicity of stable states exist only above certain critical Reynolds numbers. Here we demonstrate that Lattice Boltzmann method can be effectively used to capture multiple steady solutions for all the aforesaid geometries. The strategy employed to obtain these solutions is also described.     

Lattice Boltzmann simulation of the dispersion of aggregated particles under shear flows

The lattice Boltzmann method (LBM) for multicomponent immiscible fluids is applied to simulations of the deformation and breakup of a particle-cluster aggregate in shear flows. In the simulations, the solid particle is modeled by a droplet with strong interfacial tension and large viscosity. The van der Waals attraction force is taken into account for the interaction between the particles. The ratio of the hydrodynamic drag force to cohesive force, I, is introduced, and the effect of I on the aggregate deformation and breakup in shear flows is investigated. It is found that the aggregate is easier to deform and to be dispersed when I is over 100.     

求解二维对流扩散方程的格子Boltzmann方法

针对二维对流扩散方程,基于D2Q4格子速度,用Chapman-Enskog多尺度分析技术,将时间尺度取为二阶,空间尺度取为一阶,推导了各个速度方向上的平衡态分布函数所满足的条件,给出了简单且对称的平衡态分布函数表达式,所得到的平衡态分布函数能正确地恢复出二维对流扩散方程,从而构建了一种新的求解二维对流扩散方程的D2Q4格子Boltzmann（LB）模型。用所给LB模型对扩散方程和两个不同初边界条件的对流扩散方程进行了数值求解,数值实验结果表明数值解与精确解吻合较好,与相关文献结果比较边界误差要小得多,验证了模型的有效性。     

Combined Lattice Boltzmann and phase-field simulations for incompressible fluid flow in porous media

A Lattice-Boltzmann method for incompressible fluid flow is coupled with the dynamic equations of a phase-field model for multiple order parameters. The combined model approach is applied to computationally evaluate the permeability in porous media. At the boundaries between the solid and fluid phases of the porous microstructure, we employ a smooth formulation of a bounce-back condition related to the diffuse profile of the interfaces. We present simulations of fluid flow in both, static porous media with stationary non-moving interfaces and microstructures performing a dynamic evolution of the phase and grain boundaries. For the latter case, we demonstrate applications to dissolving grain structures with partial melt inclusions and computationally analyse the temporal evolution of the microporosity under wetting conditions at the melt-grain boundaries. In any development state of the material, the Darcy number and the hydraulic conductivity of the porous medium are evaluated for various types of fluid.     

Three-dimensional lattice Boltzmann simulations of high density ratio two-phase flows in porous media

A three-dimensional multiphase lattice Boltzmann model is implemented to study the spontaneous phase transport in complex porous media. The model is validated against the analytical solution of Young’s and Laplace’s laws. Afterward, three-dimensional porous layers are randomly generated to investigate droplet penetration into a substrate, liquid transport in a porous channel as well as extraction of a droplet from a porous medium. Effects of several geometrical and flow parameters such as porosity, density ratio, Reynolds number, Weber number, Froude number and contact angle are considered. A parametric study of the influence of main non-dimensional parameters upon the impact of liquid drops on permeable surface is performed. Results show that while increasing Froude number causes spreading of the droplet on the surface, increasing Reynolds number, Weber number, porosity and liquid-air density ratio will enhance the penetration rate into the surface. Furthermore, increasing the contact angle decreases both the spreading and the penetration rate at the same time. In the same way, for the liquid transport in a porous channel, it is found that increasing the porosity and Reynolds number will result in increasing penetration rate in the channel. For the extraction of a droplet from a porous medium, it is shown that by increasing the gravitational force and/or porosity the droplet extracts faster from the substrate.     

Depth-averaged Lattice Boltzmann and Finite Element methods for single-phase flows in fractures with obstacles

We use Lattice Boltzmann Method (LBM) MRT and Cumulant schemes to study the performance and accuracy of single-phase flow modeling for propped fractures. The simulations are run using both the two- and three-dimensional Stokes equations, and a 2.5D Stokes–Brinkman approximate model. The LBM results are validated against Finite Element Method (FEM) simulations and an analytical solution to the Stokes–Brinkman flow around an isolated circular obstacle. Both LBM and FEM 2.5D Stokes–Brinkman models are able to reproduce the analytical solution for an isolated circular obstacle. In the case of 2D Stokes and 2.5D Stokes–Brinkman models, the differences between the extrapolated fracture permeabilities obtained with LBM and FEM simulations for fractures with multiple obstacles are below 1%. The differences between the fracture permeabilities computed using 3D Stokes LBM and FEM simulations are below 8% . The differences between the 3D Stokes and 2.5 Stokes–Brinkman results are less than 7% for FEM study, and 8% for the LBM case. The velocity perturbations that are introduced around the obstacles are not fully captured by the parabolic velocity profile inherent to the 2.5D Stokes–Brinkman model.     

Lattice Boltzmann large eddy simulation of subcritical flows around a sphere on non-uniform grids

In this work, the suitability of the lattice Boltzmann method is evaluated for the simulation of subcritical turbulent flows around a sphere. Special measures are taken to reduce the computational cost without sacrificing the accuracy of the method. A large eddy simulation turbulence model is employed to allow efficient simulation of resolved flow structures on non-uniform computational meshes. In the vicinity of solid walls, where the flow is governed by the presence of a thin boundary layer, local grid-refinement is employed in order to capture the fine structures of the flow. In the test case considered, reference values for the drag force in the Reynolds number range from 2000 to 10 000 and for the surface pressure distribution and the angle of separation at a Reynolds number of 10 000 could be quantitatively reproduced. A parallel efficiency of 80% was obtained on an Opteron cluster.     

A thermal lattice Boltzmann model with diffuse scattering boundary condition for micro thermal flows

A lattice Boltzmann model for simulating isothermal micro flows has been proposed by us recently [Niu XD, Chew YT, Shu C. A lattice Boltzmann BGK model for simulation of micro flows. Europhys Lett 2004;67(4):600]. In this paper, we extend the model to simulate the micro thermal flows. In particular, the thermal lattice Boltzmann equation (TLBE) [He X, Chen S, Doolen GD. A novel thermal model for the lattice Boltzmann method in incompressible limit. J Comput Phys 1998;146:282] is used with modification of the relaxation times linking to the Knudsen number. The diffuse scattering boundary condition (DSBC) derived in our early model is extended to consider temperature jump at wall boundaries. Simple theoretical analyses of the DSBC are presented and the results are found to be consistent with the conventional velocity slip and temperature jump boundary conditions. Numerical validations are carried out by simulating two-dimensional thermal Couette flows and developing thermal flows in a microchannel, and the obtained results are found to be in good agreement with those given from the direct simulation Monte Carlo (DSMC), the molecular dynamics (MD) approaches and the Maxwell theoretical prediction.     

Lattice Boltzmann simulations to determine drag, lift and torque acting on non-spherical particles

The drag, lift and moment coefficients of differently shaped single particles have been determined as a function of the angle of incidence at particle Reynolds numbers between Re = 0.3 and 240 under different conditions. For this purpose simulations of the flow around these particles have been performed using the three-dimensional Lattice Boltzmann method. In the first case studied a particle is fixed in a uniform flow, in the second case the particle is rotating in a uniform flow to determine, among others, the Magnus lift force and in the third case the particle is fixed in a linear shear flow. In the first case six particle shapes are considered, i.e. a sphere, a spheroid, a cube, a cuboid and two cylinders with an axis ratio of 1 and 1.5, respectively. In the second and third case the sphere and the spheroid are considered. At the higher Re considered, the drag depends strongly on particle shape, the angle of incidence and particle rotation. The lift and the torque of both the sphere and the spheroid are strongly affected by particle rotation and fluid shear. For approximately Re ? 1, the shear induced lift for unbounded flow could not be simulated as the top and bottom wall have a significant influence in the current flow configuration. The shear induced lift of the sphere changes direction at approximately Re = 50 and the mean (over the orientation) shear induced lift of the spheroid changes direction at approximately Re = 90.