Theoretical and numerical modeling of multicomponent transcritical diffuses interfaces

In this study, we present a theoretical and numerical framework for simulating transcritical flows under a variety of conditions of interest for aerospace applications. A real multi-component and multi-phase thermodynamic model, based on a cubic equation of state and vapor-liquid equilibrium assumptions, is used to describe transcritical mixtures. The versatility of this model is reported since it can represent at the same time the supercritical states and subcritical stable two-phase states at equilibrium. We emphasize the difference in the mixing behaviors conducted with and without the VLE assumptions. The well-known numerical challenges that arise with the coupling between thermodynamics and governing equations under transcritical conditions are addressed by comparing a fully conservative to a quasi-conservative scheme in the context of density-based solvers while discussing the possibility of employing a pressure-based approach given the typically low-Mach number at play for the cases of interest