A unified hyperbolic interface capturing scheme for gas-liquid flows

摘要

We present a novel numerical framework for computing multiphase systems with a dense dispersed phase. ^The formulation described solves for a unified, consistent set of conservation equations for the entire flow domain. ^The interface between phases is captured as part of the solution permitting solution of the complex 3D transient evolution of the interface. ^An upwind flux-differenced procedure is developed for generalized thermodynamic state equations which reproduces the correct physical acoustic speed. ^This upwind numerical formulation is also extended to simulate a dense dispersed phase which is in nonequilibrium with the continuum. ^The wave propagation process for these nonequilibrium flows is shown to be physically consistent, and the numerical instability associated with multiphase flows is interpreted as arising from source terms involving gradients of porosity. ^A range of studies, from fundamental shock tubes studies to 3D transient problems are presented. ^In particular, considerable success has been achieved in modeling various combustion instability phenomena in interior ballistic problems where acoustic waves have coupled with liquid propellant combustion to generate high frequency waves. ^(Author)