  A two-phase, low-Mach-number flow solver is proposed for compressible liquid
and gas with phase change. The interface is tracked using a split
Volume-of-Fluid method, which solves the advection of the liquid phase. This
split advection method is generalized for the case where the liquid velocity is
not divergence-free and both phases exchange mass across the interface, as
happens at near-critical and supercritical pressure conditions. In this
thermodynamic environment, the dissolution of lighter gas species into the
liquid phase is enhanced and vaporization or condensation can occur
simultaneously at different locations along the interface. A sharp interface is
identified with a Piecewise Linear Interface Construction (PLIC). Mass
conservation to machine-error precision is achieved in the limit of
incompressible liquid, but not with the liquid compressibility and mass
exchange. The numerical cost of solving two-phase, supercritical flows is very
high because: a) local phase equilibrium is imposed at each interface cell to
determine the interface solution (e.g., temperature); b) a complete
thermodynamic model is used to obtain fluid properties; and c) phase-wise
values for certain variables (i.e., velocity) are obtained via extrapolation
techniques. Furthermore, the Volume-of-Fluid method and the PLIC add extra
computational costs. To alleviate this numerical cost, the pressure Poisson
equation (PPE) is split into a constant-coefficient implicit part and a
variable-coefficient explicit part. Thus, a Fast Fourier Transform (FFT) method
can be used to solve the PPE. Various validation tests are performed to show
the accuracy and viability of the present approach. Then, the growth of surface
instabilities in a binary system composed of liquid n-decane and gaseous oxygen
at supercritical pressures for n-decane are analyzed. Other features of
supercritical liquid injection are also shown.
