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.     

Direct-forcing immersed boundary lattice Boltzmann simulation of particle/fluid interactions for spherical and non-spherical particles

The lattice Boltzmann method (LBM) is a useful technique for simulating multiphase flows and modeling complex physics. Specifically, we use LBM combined with a direct-forcing (DF) immersed boundary (IB) method to simulate fluid–particle interactions in two-phase particulate flows. Two grids are used in the simulation: a fixed uniform Eulerian grid for the fluid phase and a Lagrangian grid that is attached to and moves with the immersed particles. Forces are calculated at each Lagrangian point. To exchange numerical information between the two grids, discrete delta functions are used. The resulting DF IB-LBM approach is then successfully applied to a variety of reference flows, namely the sedimentation of one and two circular particles in a vertical channel, the sedimentation of one or two spheres in an enclosure, and a neutrally buoyant prolate spheroid in a Couette flow. This last application proves that the developed approach can be used also for non-spherical particles. The three forcing schemes and the different factors affecting the simulation (added mass effect, corrected radius) are also discussed.     

Lattice Boltzmann simulation of multiple droplets impingement and coalescence in an inkjet-printed line patterning process

Three-dimensional computations on the basis of the index-function lattice Boltzmann method are performed to simulate the process of multiple droplets impinging and coalescing into a line pattern on a solid substrate. The employed calculation model is validated by theoretical calculated values and experimental data from the literature. The influences of the equilibrium contact angle, droplet spacing and impinging velocity on the droplets impingement and coalescence behaviours are investigated. Numerical results demonstrate the width of the formed line depends significantly on the equilibrium contact angle and droplet spacing. The droplet spacing plays a significant role in controlling the coalescence moment of multiple droplets. The resolution of the printed pattern can be slightly increased with increase in impinging velocity.     

Lattice Boltzmann modeling of transport phenomena in fuel cells and flow batteries

Fuel cells and flow batteries are promising technologies to address climate change and air pollution problems. An understanding of the complex multiscale and multiphysics transport phenomena occurring in these electrochemical systems requires powerful numerical tools. Over the past decades, the lattice Boltzmann(LB) method has attracted broad interest in the computational fluid dynamics and the numerical heat transfer communities, primarily due to its kinetic nature making it appropriate for modeling complex multiphase transport phenomena. More importantly, the LB method fits well with parallel computing due to its locality feature, which is required for large-scale engineering applications. In this article, we review the LB method for gas–liquid two-phase flows, coupled fluid flow and mass transport in porous media, and particulate flows. Examples of applications are provided in fuel cells and flow batteries. Further developments of the LB method are also outlined.     

脉冲流在Y型和倒Y型微反应器中强化传质的格子Boltzmann模拟

连续流微反应器的迅速发展为化学合成技术提供了一条可精准控制的路径。微反应器中流体的流动、混合和传质是反应的物理基础,因此强化传递就能够合理改善混和效果,增加相接触面积,减小微通道尺寸,以缩短分子扩散距离。由于微反应器中对流传递数量级非常低,不容易控制。通过改进微混合器构型和引入脉冲流动等主被动强化措施,可以有效改善对流和传质,影响化合反应。如何量化分析这些影响,是微反应器强化传质和优化控制反应过程的基础。本文基于有效的虚拟串行竞争反应格子Boltzmann模型,通过对Y型和倒Y型的微反应器的流场结构、混合传质和化合反应进行数值研究,定量分析了脉冲流动在不同流场构型下传质和化学反应的影响,所得结论可为连续流微反应器设计以及微反应精准控制提供有意义的参考。     

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.     

Analysis of reflective and non-reflective boundary conditions in LBM simulations of flow past an obstacle in a channel

This paper analyses the effects of considering non-reflective (characteristic boundary conditions) versus reflective boundary conditions (BCs) on the flow past a square object. We observe a clear dependence of the force exerted over the obstacle on the choice of BCs. Recirculation lengths, lift and drag coefficients, phase diagrams and streamlines for several angles of incidence are compared for a range of low Reynolds numbers (50–150) and two different values of the ratio of the object cross section to the channel width, 1/8 and 1/16. We remark distinct effects depending on the combination of BCs used at the inlet and at the outlet.     

Stress-strain analysis of conical shells with different boundary conditions and thickness varying in two directions at constant mass

A method developed for solving two-dimensional problems in the theory of conical shells is used to analyze the stress-strain state of shells with different boundary conditions and thickness varying in two directions at constant mass. Numerical results are given in the form of plots and tables __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 3, pp. 70–79, March 2006.