A method to couple HEM and HRM two-phase flow models

Abstract

International audienceWe present a method for the unsteady coupling of two distinct two-phase flow models (namely the Homogeneous Relaxation Model, and the Homogeneous Equilibrium Model) through a thin interface. The basic approach relies on recent works devoted to the inter-facial coupling of CFD models, and thus requires to introduce an interface model. Many numerical test cases enable to investigate the stability of the coupling method

A new treatment of capillarity to improve the stability of IMPES two-phase flow formulation

“…An iterative scheme based on the sequential method is developed in [42,45,46], in which a pressure is solved implicitly and followed by an implicit saturation equation in each iteration. Iterative coupling is also popular in the simulation of single-phase and two-phase flow and reactive transport [3,22,25,50,[59][60][61]67].…”

Modelling the transition between fixed and mobile bed conditions in two-phase free-surface flows: The Composite Riemann Problem and its numerical solution

“…For i = m, the relevant set is given by the homogeneous part of system (14), while for i = f , the relevant system is the homogeneous part of system (3). The previous expression is valid for the case in which on the left of the discontinuity there is a mobile-bed condition and on the right a fixed-bed one.…”

The Coupling of Multi-phase Flow Models

“…The father model that is chosen in the coupling procedure is the three-field model (5). This choice means that the reconstruction procedure must only be applied on the side corresponding to the two-fluid model.…”

“…Furthermore, adding ninth and eleventh equations in (5), and inserting definitions of internal energies for the liquid continuous and liquid droplet phase (6) provides the governing equation for the liquid phase as follows:…”

“…2,5 The father model used in the second reference is an homogeneous relaxation model that includes a colour function (thus s = 5) which enables to select the relevant equation of state on each subdomain Ω l,r . References 29 and 27 focus on the coupling of problems (E2) and (E3), which are indeed quite similar.…”