A Robust Seven-Equation Formulation for Compressible Two-Phase Flows for High-Speed Applications

Classical diffuse-interface methods for non-equilibrium formulations of two-phase flows are not capable of preserving interface thickness. Furthermore, when coupled with shock-capturing schemes, the interface may diffuse in its entirety. Thus, it is of utmost importance for accurate simulation of two-phase flows to develop interface-preserving formulations. However, standard phase field models are observed to remove any initial boundedness of small amounts of other phase added for robustness of diffuse interface methods. Therefore, the previously proposed conservative interface-regularization formulation based on the phase-field method is modified to guarantee that the initial volume fraction bound is retained throughout the simulations. The formulation is shown to retain the interface thickness and the small amount of the other phase added even when discretized with low-cost and low-dissipation kinetic energy–and entropy preserving schemes. Surface tension is coupled with the compressible two-phase formulation and validated against a standard test case. Lastly, robustness of the formulation is also assessed for highly compressible cases, which uses a flux blending strategy with a Lax-Friedrichs flux to achieve a positivity-preserving and entropy stable formulation. In highly compressible scenarios, such as shock-water column interaction, the framework is demonstrated to be robust and qualitative agreement is observed.