Li Q, Luo K H, Li X J
Energy Technology Research Group, Faculty of Engineering and the Environment, University of Southampton, Southampton SO17 1BJ, United Kingdom.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 May;87(5):053301. doi: 10.1103/PhysRevE.87.053301. Epub 2013 May 3.
Owing to its conceptual simplicity and computational efficiency, the pseudopotential multiphase lattice Boltzmann (LB) model has attracted significant attention since its emergence. In this work, we aim to extend the pseudopotential LB model to simulate multiphase flows at large density ratio and relatively high Reynolds number. First, based on our recent work [Q. Li, K. H. Luo, and X. J. Li, Phys. Rev. E 86, 016709 (2012)], an improved forcing scheme is proposed for the multiple-relaxation-time pseudopotential LB model in order to achieve thermodynamic consistency and large density ratio in the model. Next, through investigating the effects of the parameter a in the Carnahan-Starling equation of state, we find that the interface thickness is approximately proportional to 1/√a. Using a smaller a will lead to a wider interface thickness, which can reduce the spurious currents and enhance the numerical stability of the pseudopotential model at large density ratio. Furthermore, it is found that a lower liquid viscosity can be gained in the pseudopotential model by increasing the kinematic viscosity ratio between the vapor and liquid phases. The improved pseudopotential LB model is numerically validated via the simulations of stationary droplet and droplet oscillation. Using the improved model as well as the above treatments, numerical simulations of droplet splashing on a thin liquid film are conducted at a density ratio in excess of 500 with Reynolds numbers ranging from 40 to 1000. The dynamics of droplet splashing is correctly reproduced and the predicted spread radius is found to obey the power law reported in the literature.
由于其概念简单且计算效率高，伪势多相格子玻尔兹曼（LB）模型自出现以来就引起了广泛关注。在这项工作中，我们旨在扩展伪势LB模型以模拟大密度比和相对高雷诺数下的多相流。首先，基于我们最近的工作[Q. Li, K. H. Luo, and X. J. Li, Phys. Rev. E 86, 016709 (2012)]，为多松弛时间伪势LB模型提出了一种改进的强迫方案，以实现模型中的热力学一致性和大密度比。接下来，通过研究卡纳汉 - 斯塔林状态方程中参数a的影响，我们发现界面厚度近似与1/√a成正比。使用较小的a会导致更宽的界面厚度，这可以减少虚假电流并增强伪势模型在大密度比下的数值稳定性。此外，发现通过增加气相和液相之间的运动粘度比，可以在伪势模型中获得较低的液体粘度。通过对静止液滴和液滴振荡的模拟对改进的伪势LB模型进行了数值验证。使用改进的模型以及上述处理方法，在密度比超过500且雷诺数范围为40至1000的情况下，对液滴在薄液膜上的飞溅进行了数值模拟。正确再现了液滴飞溅的动力学过程，并且发现预测的铺展半径符合文献中报道的幂律。
