基于伪焓法的多孔介质固液相变格子Boltzmann方法

The Lattice Boltzmann Model for Solid-liquid Phase Change in Porous Medium Based on Quasi-enthalpy

格子Boltzmann方法是求解相变材料(PCM,phase change material)固液相变界面上复杂质量、能量和动量传递的有效方法。本文将伪焓LB模型推广至多孔介质固液相变中,构建相应的LB模型,并通过焓和温度的关系,获得下一时间步的焓、温度和对应液相率。为验证多孔介质固液相变LB模型的正确性,本文分别对一维Stefan问题和二维方腔多孔介质内固液相变问题进行求解。结果表明,在无自然对流作用下(一维Stefan问题),本文所构建模型能精确还原温度分布,与解析解相对误差控制在2%以内。除此之外,本文模型能反映自然对流对固液相变过程的影响,与已有工作差别较小,能准确追踪固液相变界面位置。

The lattice Boltzmann（LB） method is effective powerful tool to obtain the complicated mass, momentum and energy transfer through the solid-liquid interface of phase change material（PCM）. In this paper, the quasi-enthalpy based LB model is extended to the problem of solid-liquid phase change in porous medium and the corresponding model is developed. The enthalpy, temperature and liquid fraction are at new time step are obtained by the relation between enthalpy and temperature. The one-region phase change problem and two-dimensional phase change in porous cavity are solved to verify the present model. The results show that without natural convection（one-region problem）, the temperature distribution can be obtained accurately by the present model and the error is less than 2% compared with analytical solution. Furthermore, the present model is able to reveal the effects of natural convection on phase change and track the solid-liquid interface accurately, compared with other model.