A four-field three-phase flow model with both miscible and immiscible components

Jean-Marc Hérard (1, 2) , Olivier Hurisse (1) , Lucie Quibel (1, 3)

1 EDF - EDF
2 I2M - Institut de Mathématiques de Marseille
3 IRMA - Institut de Recherche Mathématique Avancée

A three-phase flow model with hybrid miscibility constraints is proposed: three immiscible phases are considered (liquid water, liquid metal and gas) but the gaseous phase is composed with two miscible components (steam water and non-condensable gas). The modelling approach is based on the building of an entropy inequality for the system of partial differential equations: once an interfacial velocity is given by the user, the model is uniquely defined, up to some relaxation time scales, and source terms complying with the second principle of thermodynamics can then be provided. The convec-tive part of the system is hyperbolic when fulfilling a non-resonance condition and classical properties are studied (Riemann invariants, symmetrization). A key property is that the system possesses uniquely defined jump conditions. Last, preservation of thermodynamically admissible states and pressure relaxation are investigated.

Mots clés: Three-phase flow; entropy; jump conditions; miscible components

Domaines: Equations aux dérivées partielles [math.AP]; Mécanique des fluides [physics.class-ph]

Jean-Marc Hérard, Olivier Hurisse, Lucie Quibel. A four-field three-phase flow model with both miscible and immiscible components. ESAIM: Mathematical Modelling and Numerical Analysis, 2021, 55, pp.S251-S278. ⟨10.1051/m2an/2020037⟩. ⟨hal-02432793⟩