Isotherm-evolution-based interface tracking algorithm for modelling temperature-driven solid-liquid phase-change in multiphase flows

Abstract

In this paper, an isotherm-evolution-based algorithm is proposed for effective tracking of the phase-change interface in temperature-driven solid-liquid phase-change process in multiphase flows (e.g., droplet freezing in the air). To fulfill the temperature condition on the interface, an interface indicator φ is defined, whose variation between specified maxima and minima marks the passing through the melting temperature. Previous approaches directly generate φ from the temperature field with explicit function and an artificial phase-change temperature interval, which could be affected by uneven temperature gradient and thus loses interfacial sharpness. The new algorithm devices an isotherm evolution equation to fulfill thermodynamic principles on the phase-change interface and maintain interface sharpness. Specifically, diffusive terms with explicit parameter are used to analytically ensure a finite interfacial width; and the migration term is introduced to cope with the phase-change temperature condition. The consistency of the proposed algorithm with the sharp interface limit is verified by comparing with analytical solutions of the Stefan problem. In numerical tests of the freezing droplet on substrate, the new algorithm presents better consistency of interfacial width throughout the computational domain and during the whole evolution process, as compared with the previous approach. The accuracy, convergence and robustness of the method as well as its capability in three-dimensional simulations are also validated through quantitative comparisons with reference results in the literature.