A two-phase, low-Mach-number flow solver is proposed for variable-density liquid and gas with phase change. The interface is captured using a split Volume-of-Fluid method, which solves the advection of the reference phase, generalized for the case where the liquid velocity is not divergence-free and both phases exchange mass. A sharp interface is identified by using PLIC. Mass conservation is achieved in the limit of incompressible liquid, but not with the liquid compressibility and mass exchange. This is a relevant modeling choice for two-phase mixtures at near-critical and supercritical pressure conditions for the liquid but away from the mixture critical temperature. Under this thermodynamic environment, the dissolution of lighter gas species into the liquid phase is enhanced and vaporization or condensation can occur simultaneously at different interface locations. The numerical challenge of solving two-phase, supercritical-pressure flows is greater than simpler two-phase solvers because: a) local phase equilibrium is imposed at each interface cell to determine temperature, composition, or surface tension coefficient; b) a real-fluid thermodynamic model is used to obtain fluid properties; and c) necessary phase-wise values for certain variables are obtained via extrapolation techniques. To alleviate the increased numerical cost, the pressure Poisson equation (PPE) used to solve the low-Mach-number flow is split into a constant-coefficient implicit part and a variable-coefficient explicit part. Thus, a Fast Fourier Transform method can be used for the PPE. Various verification tests are performed to show the accuracy and viability of the present approach. The growth of surface instabilities in a binary system composed of liquid n-decane and gaseous oxygen at supercritical pressures for n-decane is analyzed. Other features of supercritical liquid injection are also shown.
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