Improved thermal lattice Boltzmann model for simulation of liquid-vapor phase change

TL;DR

This paper introduces an improved thermal lattice Boltzmann model for simulating liquid-vapor phase change, addressing inaccuracies in previous models by refining the temperature equation and eliminating error terms, validated through droplet evaporation and bubble nucleation simulations.

Contribution

The paper presents a novel thermal LB model that corrects previous inaccuracies by properly handling temperature equations and eliminating error terms, enhancing simulation accuracy for phase change.

Findings

Significant reduction in numerical errors compared to previous models

Accurate simulation of droplet evaporation and bubble nucleation

Validated improvements through numerical experiments

Abstract

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)]. First, we emphasize that the replacement of \[{\left( {\rho {c_V}} \right)^{ - 1}}\nabla \cdot \left( {\lambda \nabla T} \right)\] with \[\nabla \cdot \left( {\chi \nabla T} \right)\] is an inappropriate treatment for diffuse interface modeling of liquid-vapor phase change. Furthermore, the error terms ${\partial_{t0}}\left( {Tv} \right) + \nabla \cdot \left( {Tvv} \right)$, which exist in the macroscopic temperature equation recovered from the standard thermal LB equation, are eliminated in the present model through a way that is consistent with the philosophy of the LB method. In addition, 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 improved model for simulating liquid-vapor phase change. Numerical comparisons show that the aforementioned replacement leads to significant numerical errors and the error terms in the recovered macroscopic temperature equation also result in considerable errors.