In situ adaptive tabulation of vapor-liquid equilibrium solutions for multi-component high-pressure transcritical flows with phase change

Vapor-liquid equilibrium (VLE) is a family of first-principled thermodynamic models for transcritical multiphase flows, which can accurately capture the phase transitions at high-pressure conditions that are difficult to deal with using other models. However, VLE-based computational fluid dynamics (CFD) simulation is computationally very expensive for multi-component systems, which severely limits its applications to real-world systems. In this work, we developed a new ISAT-VLE method based on the in situ adaptive tabulation (ISAT) method to improve the computational efficiency of VLE-based CFD simulation with reduced memory usage. We developed several ISAT-VLE solvers for both fully conservative (FC) and double flux (DF) schemes. New methods are proposed to delete redundant records in the ISAT-VLE table and the ISAT-VLE method performance is further improved. To improve the convergence of the VLE solvers, a modified initial guess for equilibrium constant is also introduced. Simulations of high-pressure transcritical two-phase temporal mixing layers and shock-droplet interaction were conducted using the ISAT-VLE CFD solvers. The simulation results show that the new method obtains a speed-up factor approximately from 10 to 60 and the ISAT errors can be controlled within 1%. The shock-droplet interaction results show that the DF scheme can achieve a higher speed-up factor than the FC scheme. The two sets of simulations exhibit the phase separation at high-pressure conditions. It was found that even at supercritical pressures with respect to each component, the droplet surface could still be in a subcritical two-phase state, because the mixture critical pressure is often significantly higher than each component and hence triggers phase separation. In addition, a shock wave could partially or completely convert the droplet surface from a subcritical two-phase state to a single-phase state by raising temperature and pressure.