Modeling of inertial multi-phase flows through high permeability porous media: Friction closure laws

Abstract

During a severe accident in a nuclear reactor, the core may be fragmented in a debris bed made of millimetric particles. The main safety procedure consists in injecting water into the core leading to a steamwater flow through a hot porous medium. To assess the coolability of debris bed, there is a need for an accurate two-phase flow model including closure laws for the pressure drop. In this article, a new model for calculating pressure losses in two-phase, incompressible, Newtonian fluid flows through homogeneous porous media is proposed. It has been obtained following recent developments in theoretical averaging of momentum equations in porous media. The pressure drops in the momentum equations are determined by eight terms corresponding to the viscous and inertial friction in liquid and gas phases, and interfacial friction between the phases. Analytical correlations with the void fraction have been formulated for each term using an original experimental database containing measurements of pressure drops, average velocities and void fractions from the IRSN CALIDE experiment. The new model has then been validated against the experimental data for various liquid and gas Reynolds numbers up to several hundreds. Finally, it has been compared to the models, usually used in the "severe accident" codes, which are based on a generalization of the Ergun law for multi-phase flows. The results show that the new model gives a better prediction both for the pressure drop and for the void fraction.

Modeling two-phase flow of immiscible fluids in porous media: Buckley-Leverett theory with explicit coupling terms

“…III to the one obtained by Rothman in [25], Zarcone and Lenormand in [20], and Kalaydjian in [18]. The first closure relations used in this paper have been recently obtained [17] from the experimental database presented in [3] (CALIDE experiment). The experiments, which focus on water-air flow in a column filled with coarse particles, were part of a large work studying water-steam flows in a debris bed in the context of a severe accident in a nuclear reactor.…”

“…The first configuration corresponds to the experiments of Chikhi et al in [3], which consists of an air-water system in a particle bed, a configuration known to emphasize the impact of the coupling terms as discussed in [17]. It corresponds to a drainage process, since the nonwetting phase (air) is displacing the wetting phase (water) out of the column.…”

“…We consider two classes of closures for the effective parameters: one obtained from Clavier et al [17] (constructed from experimental data [3]) and one based on the analytical solution of an annular two-phase viscous flow within a capillary tube. These closures are also compared in Sec.…”

“…Among these models, there has been recently a renewed interest in those that include an explicit coupling for the description of mass and momentum exchanges between the phases [3,17]. Cross terms that couple the equations for momentum transport of each phase can be obtained theoretically, either by considering the case of the annular viscous two-phase flow in tubes, for which a simple analytical solution analogous to that of Poiseuille can be derived [18,19], or from upscaling techniques such as the method of volume averaging [16] (more details are in Sec.…”

“…This is also the case for boiling-water-steam flows in nuclear debris beds, for which various heuristic models have been developed [27][28][29][30]. Experiments for such systems show that many observations cannot be reproduced by the classical models without cross terms [3,17,29].…”