Volume-of-Fluid computational foundation for variable-density, two-phase, supercritical-fluid flows

Abstract

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.Comment: 52 pages, 19 figure