Simulations of liquid-vapor water flows with non-condensable gases on the basis of a two-fluid model

Abstract

Two phase flows including liquid water, vapor and non-condensable gases are often encountered in industrial applications. In this paper, an extension of the classical Baer-Nunziato two-fluid model is presented in order to account for the non-condensable gases. In this model, the vapor and non-condensable gases form a miscible mixture of gases at temperature equilibrium and kinematic equilibrium. The complete model then allows to account for the full kinematic and thermodynamic disequilibrium between the liquid phase and the gas phase. Moreover, a new form for the masstransfer source-term has been retained. It leads to a more straightforward numerical integration. When focusing on the numerical scheme, a new algorithm is proposed here for the pressure relaxation effect. At last, some numerical experiments are performed in order to assess the behavior of the model with respect to the relaxation time-scales.

Simulation of a homogeneous relaxation model for a three-phase mixture with miscible phases

“…The first one, referred in [20] as BGK source term, corresponds to a linearization around the equilibrium vector Y eq . Introduced in [9,15,3], it is used in multiphase configurations with complex phasic equations of state [23,22]. The alternative source terms, proposed in [27], corresponds to the gradient of the mixture entropy which directly satisfies (27).…”

“…The Date: June 1, 2022. literature about immiscible multiphase configurations is huge; the reader may refer to recent publications [16,13] for the modelling and analysis and to [28,31] for numerical approximations of such immiscible models. Recently models of compressible flows with miscible phases have been proposed [27,22,23,18,17], see also [1]. They depict the dynamical and thermodynamical behaviour of a mixture composed of a liquid, its vapor and an inert gas ( [17] considers in addition another liquid phase).…”

“…In [18,17] the phases evolve with their own velocities, leading to a system of nonconservative evolution equations with so-called interfacial quantities (velocity and pressure terms) with relaxation source terms towards equilibrium. In [27,22,23] all the phases evolve with a common velocity, leading to a so-called Homogeneous Relaxation Model (HRM) similar to an Euler system. It is endowed with additional evolution equations on fractions of volume, mass and energy of the phases which contain relaxation source terms towards the thermodynamical equilibrium.…”

“…Among all possible choices, two sets of source terms have been proposed in [27], namely BGK-like source terms, corresponding to a linearization around the equilibrium state, and source term corresponding to the gradient of the entropy. When considering realistic equations of state for each phase, Quibel and Hurisse propose in [22,23] numerical simulations of the HRM model with BGK-like source term. The aim of the present paper is, among other things, to compare with the gradient of entropy source term.…”