A consistent, volume preserving, and adaptive mesh refinement-based framework for modeling non-isothermal gas–liquid–solid flows with phase change

Abstract

This work expands on our recently introduced low Mach enthalpy method (Thirumalaisamy and Bhalla 2023) for simulating the melting and solidification of a phase change material (PCM) alongside (or without) an ambient gas phase. The method captures PCM’s volume change (shrinkage or expansion) by accounting for density change-induced flows. We present several improvements to the original work. First, we introduce consistent time integration schemes for the mass, momentum, and enthalpy equations, which enhance the method stability. Demonstrating the effectiveness of this scheme, we show that a system free of external forces and heat sources can conserve its initial mass, momentum, enthalpy, and phase composition. This allows the system to transition from a non-isothermal, non-equilibrium, phase-changing state to an isothermal, equilibrium state without exhibiting unrealistic behavior. Furthermore, we show that the low Mach enthalpy method accurately simulates thermocapillary flows without introducing spurious phase changes. To reduce computational costs, we solve the governing equations on adaptively refined grids. We investigate two cell tagging/untagging criteria and find that a gradient-based approach is more effective. This approach ensures that the moving thin mushy region is always captured at fine grid levels, even when it temporarily falls within a subgrid level. We propose an analytical model to validate advanced computational fluid dynamics (CFD) codes used to simulate metal manufacturing processes (welding, 3D printing). These processes involve a heat source (like a laser) melting metal or its alloy in the presence of an ambient (inert) gas. Traditionally, studies relied on artificially manipulating material properties to match complex experiments for validation purposes. Leveraging the analytical solution to the Stefan problem with a density jump, this model offers a straightforward approach to validating multiphysics simulations involving heat sources and phase change phenomena in three-phase flows. Lastly, we demonstrate the practical utility of the method in modeling porosity defects (gas bubble trapping) during metal solidification. A field extension technique is used to accurately apply surface tension forces in a three-phase flow situation. This is where part of the bubble surface is trapped within the (moving) solidification front.