School of Energy Science and Engineering, Central South University, Changsha 410083, China.
Phys Rev E. 2017 Dec;96(6-1):063303. doi: 10.1103/PhysRevE.96.063303. Epub 2017 Dec 4.
In this paper, an improved thermal lattice Boltzmann (LB) model is proposed for simulating liquid-vapor phase change, which is aimed at improving an existing thermal LB model for liquid-vapor phase change [S. Gong and P. Cheng, Int. J. Heat Mass Transfer 55, 4923 (2012)10.1016/j.ijheatmasstransfer.2012.04.037]. First, we emphasize that the replacement of ∇·(λ∇T)/∇·(λ∇T)ρc_{V}ρc_{V} with ∇·(χ∇T) is an inappropriate treatment for diffuse interface modeling of liquid-vapor phase change. Furthermore, the error terms ∂{t{0}}(Tv)+∇·(Tvv), which exist in the macroscopic temperature equation recovered from the previous model, are eliminated in the present model through a way that is consistent with the philosophy of the LB method. Moreover, the discrete effect of the source term is also eliminated in the present model. Numerical simulations are performed for droplet evaporation and bubble nucleation to validate the capability of the model for simulating liquid-vapor phase change. It is shown that the numerical results of the improved model agree well with those of a finite-difference scheme. Meanwhile, it is found that the replacement of ∇·(λ∇T)/∇·(λ∇T)ρc_{V}ρc_{V} with ∇·(χ∇T) leads to significant numerical errors and the error terms in the recovered macroscopic temperature equation also result in considerable errors.
本文提出了一种改进的热格子玻尔兹曼（LB）模型，用于模拟液-气相变，旨在改进现有的用于液-气相变的热 LB 模型 [S. Gong 和 P. Cheng, Int. J. Heat Mass Transfer 55, 4923 (2012)10.1016/j.ijheatmasstransfer.2012.04.037]。首先，我们强调用∇·(χ∇T)替代∇·(λ∇T)/∇·(λ∇T)ρc_{V}ρc_{V}是对液-气相变的弥散界面建模的不恰当处理。此外，在从先前模型恢复的宏观温度方程中存在的误差项∂{t{0}}(Tv)+∇·(Tvv)在本模型中通过与 LB 方法的原理一致的方式被消除。此外，本模型还消除了源项的离散效应。通过蒸发液滴和气泡成核的数值模拟验证了该模型模拟液-气相变的能力。结果表明，改进模型的数值结果与有限差分方案的结果吻合较好。同时，发现用∇·(χ∇T)替代∇·(λ∇T)/∇·(λ∇T)ρc_{V}ρc_{V}会导致显著的数值误差，而且在恢复的宏观温度方程中的误差项也会导致相当大的误差。
