Assessment of numerical schemes for complex two-phase flows with real equations of state

Abstract

Some accidental scenarii studied in the framework of the nuclear safety analysis involve liquids undergoing strong pressure drops at high temperature. In order to perform realistic simulations of such situations, a code based on a model that can handle both the thermodynamical disequilibrium between liquid and vapor and complex equations of state is required. We propose herein to test a homogeneous model built on the basis of the Euler system of equations and complemented by a mixture pressure law. The latter is defined in accordance with the Gibbs relation on the basis of the phasic pressures which are defined through a look-up table based on the IAPWS-97 formulation. A wide range of verification problems (Riemann problems) is then studied to assess the behavior of the numerical schemes for this complex equation of state. The tested relaxation scheme is the best compromise between accuracy and stability. At last, a simple test case of vaporization near a wall is investigated in order to test some return to thermodynamical-equilibrium timescale based on the nucleation theory.

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

“…Source terms complying with the second principle of thermodynamics can now be explicitely introduced, like for instance in [31]. They involve relaxation time scales, that need to be defined by the user; some propositions can be found for instance see [40] for τ u and also [41,28] for τ Γ and τ T , and more recently [42,43,44] for τ p relaxation time scales (considering different averaging processes).…”

“…Fewer references are available about three-phase flow models, see [9,10,11,12,13,3,14,15,16]. Among all these models, two classes can be distinguished: models based on the multifluid approach [17,18,19,20,9,10,11,3,14,15,16], where each component has its own velocity field, and models based on the homogeneous approach [21,22,23,24,25,26,27,12,13,28], where the kinematic equilibrium is assumed between all constituents.…”

“…Nevertheless, a mixture equation of state should be carefully built in the homogeneous models (see [12,13]), whereas the thermodynamical behavior is decoupled phase by phase in the multifluid models. Numerically, building the mixture equation of state in a homogeneous model can be somehow tricky when considering realistic equations of state, so that very robust numerical schemes are required as highlighted in [28]. Moreover, for some applications like for the vapor explosion (see [2,7]), evaluating each phasic velocity is sometimes unavoidable, because the velocity gaps are required to estimate interfacial transfers through the interfacial area.…”

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

“…They seem appropriate to simulate complex scenarii involving strong shock waves traveling in large domain, as those described above. Many diffuse-interface two-phase flow models have been proposed in order to perform numerical simulations, see among many others [7,8,9,10,11,12,13,14,15]. LOCA scenarii have in particular been studied for instance in [11,12,13,14].…”

“…Many diffuse-interface two-phase flow models have been proposed in order to perform numerical simulations, see among many others [7,8,9,10,11,12,13,14,15]. LOCA scenarii have in particular been studied for instance in [11,12,13,14]. In all these references, the models do not account for the incondensable gases and the air has thus been replaced by hot vapor.…”