Lattice Boltzmann method featuring nonmaterial enthalpy for solid-liquid phase change in noncondensable gas

This paper presents a lattice Boltzmann (LB) method based on nonmaterial enthalpy (NME) to simulate the solidification process of the liquid phase in the presence of noncondensable gas. The method employs a nonmaterial enthalpy distribution function format, which fundamentally avoids the issue of cross-distribution of thermal physical property parameters between different components that we previously addressed in our work [Dai et al., Phys. Rev. E 110, 025301 (2024)10.1103/PhysRevE.110.025301], using an enthalpy distribution function. Additionally, it overcomes the problem of low precision in latent heat treatment in the temperature distribution function's source term. Benefiting from the advantage that nonmaterial enthalpy distribution function (NMEDF) has the same dimension as temperature, the error associated with high-density gradients can be addressed by referring to the mature LB method already applied to boiling models [Li et al., Phys. Rev. E 105, 025308 (2022)10.1103/PhysRevE.105.025308]. Considering that the actual solidification process involves changes in density and volume, we introduced the modified linear state equation density-volume variation model, which enables simultaneous changes in both density and volume. Numerical results indicate that the LB method based on NME accurately captures the impact and subsequent solidification process of a water droplet on a cold surface in air, in agreement with experimental results, and effectively represents the significant differences in the thermal physical properties of air and water.