In the framework of its research programme on severe nuclear reactor accidents, IRSN investigates the water flooding of an overheated porous bed, where complex two-phase flows are likely to exist. A better understanding of the flow at the pore level appears to be necessary in order to justify and improve closure laws of macroscopic models. To investigate the local features of a two-phase flow in complex geometries, two alternative ways are available : experiments with high accuracy local measurements or direct numerical simulation (DNS) of the flows in small scale volumes. Within the framework of the second gradient theory, diffuse interface models can be derived for both single-component and binary fluids. The latter model is often referred to as the Cahn-Hilliard model.
In this paper, the Cahn-Hilliard model is used to simulate immiscible two-phase flows in a representative geometry of a particle bed. The results are used to characterize the configuration of the phases and possible flow regimes as a function of the saturation. Correlations for the relative permeabilities of each phase as a function of saturation are also presented. The results are discussed and compared with classical correlations.