A lattice Boltzmann–cellular automaton study on dendrite growth with melt convection in solidification of ternary alloys

A lattice Boltzmann(LB)–cellular automaton(CA) model is employed to study the dendrite growth of Al-4.0 wt%Cu–1.0 wt%Mg alloy. The effects of melt convection, solute diffusion, interface curvature, and preferred growth orientation are incorporated into the coupled model by coupling the LB–CA model and the CALPHAD-based phase equilibrium solver,Pan Engine. The dendrite growth with single and multiple initial seeds was numerically studied under the conditions of pure diffusion and melt convection. Effects of initial seed number and melt convection strength were characterized by newdefined solidification and concentration entropies. The numerical result shows that the growth behavior of dendrites, the final microstructure, and the micro-segregation are significantly influenced by melt convection during solidification of the ternary alloys. The proposed solidification and concentration entropies are useful characteristics bridging the solidification behavior and the microstructure evolution of alloys.     

Simulating high Reynolds number flow in two-dimensional lid-driven cavity by multi-relaxation-time lattice Boltzmann method

By coupling the non-equilibrium extrapolation scheme for boundary condition with the multi-relaxation-time lattice Boltzmann method, this paper finds that the stability of the multi-relaxation-time model can be improved greatly, especially on simulating high Reynolds number (Re) flow. As a discovery, the super-stability analysed by Lallemand and Luo is verified and the complex structure of the cavity flow is also exhibited in our numerical simulation when Re is high enough. To the best knowledge of the authors, the maximum of Re which has been investigated by direct numerical simulation is only around 50,000 in the literature; however, this paper can readily extend the maximum to 1000,000 with the above combination.     

多孔介质内溶解与沉淀过程的格子Boltzmann方法模拟

本文采用格子Boltzmann方法模拟了多孔介质内的溶解和沉淀现象, 并分析了雷诺数、施密特数、达姆科勒数对多孔介质孔隙结构及浓度分布的影响. 结果表明: 对于多孔介质内的溶解(沉淀)过程, 当雷诺数越大时, 孔隙率越大(小), 平均浓度值越小(大); 当达姆科勒数或施密特数较小时, 溶解和沉淀过程均受反应控制, 此时反应在多孔介质的固体表面较为均匀的发生; 当达姆科勒数或施密特数较大时, 溶解和沉淀过程均受扩散控制, 此时反应主要发生在上游及大孔隙区域.     

致密多孔介质中气体渗流的格子Boltzmann模拟

为了能用格子Boltzmann方法来正确地刻画致密多孔介质中微尺度流动问题,对单通道模型进行推广,并将其应用于孔隙群里气体渗流的数值模拟.通过对部分具有代表性的多孔介质中的实际流动问题进行模拟,研究渗透率与平均压力和Knudsen数之间的相互关系.基于理论分析及相关文献中的试验结果,验证模拟结果,为用格子Boltzmann方法深入研究气体渗流问题奠定基础.     

液滴撞击液膜过程的格子Boltzmann方法模拟

本文采用格子Boltzmann方法对液滴撞击液膜过程进行了研究, 主要考察了雷诺数(Re)、韦伯数(We)、相对液膜厚度 (h) 以及表面张力 (σ) 等物理参数对界面运动过程的影响. 首先, 随着Re数和We数的增加, 可以明显观察到液滴撞击液膜过程中形成的皇冠状水花以及卷吸现象; 当Re数较大时, 液体会发生飞溅, 由液体飞溅形成的小液滴则会继续下落, 并与液膜再次发生碰撞. 其次, 当相对液膜厚度较小时, 液滴撞击液膜并最终导致液膜断裂; 然而随着相对液膜厚度的增大, 尽管撞击过程溅起的液体会越来越多, 但是液膜并不会发生断裂. 再次, 随着表面张力的增大, 界面变形阻力增大, 撞击过程中产生的界面形变也逐渐减弱. 最后还发现皇冠(由液滴溅起形成)半径r 随时间满足r/(2R) ≈ α√Ut/(2R), 这一结果与已有结论是一致的.     

利用多松弛格子Boltzmann方法预测多孔介质的渗透率

多孔介质内的流动问题在工程热物理领域有着重要的研究价值和应用背景。本文利用多松弛格子Boltzmann方法详细预测了两种二维多孔介质中的渗透率。研究结果表明:一方面,多松弛模型可以用来克服由单松弛模型带来的一些不足;另一方面,借助于达西定律,多松弛模型可以准确预测多孔介质的渗透率,并将计算结果与已有文献做了对比。     

Cole-Hopf Transformation Based Lattice Boltzmann Model for One-dimensional Burgers' Equation

In this paper,we present a Cole-Hopf transformation based lattice Boltzmann(LB) model for solving one-dimensional Burgers' equation,and compared to available LB models,the effect of nonlinear convection term can be eliminated.Through Chapman-Enskog analysis,it can be found that the converted diffusion equation based on the Cole-Hopf transformation can be recovered correctly from present LB model.Some numerical tests are also performed to validate the present LB model,and the numerical results show that,similar to previous LB models,the present model also has a second-order convergence rate in space,but it is more accurate than the previous ones.