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

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 steam-water 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.