Volume of Fluid method for low-Mach-number compressible supercritical liquid jet

Abstract

A two-phase, low-Mach-number compressible flow solver is proposed. Density variations are linked to changes in composition and temperature rather than pressure. The interface is tracked using a split Volume-of-Fluid method generalized for the case where the liquid velocity is not divergence-free and both phases exchange mass across the interface. A sharp interface is maintained by using a Piecewise Linear Interface Construction (PLIC). At supercritical pressures, the dissolution of lighter gas species into the liquid phase is enhanced and vaporization or condensation can happen simultaneously in different locations along the interface. Mass is conserved to machine-error precision in the limit of incompressible liquid. The numerical cost of solving two-phase supercritical flows increases substantially because: a) a thermodynamic model is used to determine fluid properties; b) local phase equilibrium and jump conditions are solved together at each interface cell; and c) phase-wise values for certain variables (e.g., velocity) are obtained via extrapolation techniques. To alleviate the increase in numerical cost, the pressure Poisson equation (PPE) is split into a constant coefficient part (implicit) and a variable coefficient part (explicit) and solved using a Fast Fourier Transform (FFT) method. Various tests at high pressures are performed to show the accuracy and viability of the present approach: one-dimensional unsteady flow, two-dimensional capillary wave and planar jet.