Integration of Hertz–Knudsen–Schrage phase change in phase-field lattice Boltzmann method: Validation and parametric studies

Abstract

The phase transition between liquid and vapor is of vital importance in daily life and industry. Given the importance of the lattice Boltzmann method (LBM), in particular the phase field method, in the simulation of two-phase flows, a robust LBM phase transition model is essential. This study introduces a novel approach by integrating the widely used, Hertz–Knudsen–Schrage (HKS) phase change rate into a conservative phase-field LBM. The phase-field and momentum equations are solved using the Boltzmann distribution function, whereas the energy equation is solved using the finite difference method. Once the necessary parameters for the calculation of the phase change rate are obtained, the corresponding source terms are incorporated into each equation. The model's validation is performed through a series of benchmark problems, including the one-dimensional Stefan problem, Nusselt's film condensation, bubble detachment, centered droplet evaporation, and sessile droplet evaporation. The results demonstrate favorable agreement between the LBM solution and analytical or empirical data. Furthermore, this study highlights the model's ability to approximate steady-state phenomena with minimal reliance on the phase change coefficient of the HKS theory. It also underscores the model's capacity to accurately capture transient phenomena by appropriately selecting values for this coefficient. In addition, parametric studies are conducted to investigate evaporation problems using the HKS theory for recognizing the effect of superheat, contact angle, and droplet size on evaporation. Finally, this model not only can detect trends and behaviors of phenomena but also can adapt empirical and analytical results with good agreement.