Application of a high-order MP scheme to computation of multi-phase flows with heat and mass transfer

Abstract

Reliable prediction of unsteady multiphase flows with mass changes, large density ratios, and complex flow features is very challenging due to the need to accurately resolve both complex interface deformations and steep gradients associated with material interfaces. This paper describes an application of our recently developed high-order monotonicity preserving (MP) scheme – a reliable and robust scheme for long-term computations of flows contain complex smooth structures interspersed with discontinuities (Ha and Lee, 2020) − to the solution of unsteady incompressible two-phase flows in the presence of heat and mass changes. The flow is governed by the multiphase Navier–Stokes equations, which comprises of the mixture continuity equation, the mixture momentum equations, the mixture energy equation, and the continuity equation for the individual phase. The numerical discretization is implemented on generalized curvilinear grids for facilitating flow simulations of the complex geometries. Our high-order MP scheme is applied to the calculations of the convective and surface tension terms. To obtain an effectively simultaneous solution of all equations, a novel dual-time stepping approach in conjunction with an implicit Runge–Kutta three-stage scheme is proposed. The reliability of the proposed numerical algorithm is then examined for a 1D Stefan condensation problem and two condensing flows including single bubble and steam-jet condensation problems. Particularly, for the single bubble condensation test, the bubble characteristics at different time instants are evaluated both qualitatively and quantitatively. For the steam-jet condensation test, the capability for capturing the evolution of interface deformations under different thermal and hydrodynamic flow conditions is highlighted. Finally, the effects of subcooling degree and steam mass flow rate on heat and mass transfer characteristics are investigated and discussed.