Modeling Phase Separation in Grain‐Fluid Mixture Flows by a Depth‐Averaged Approach With Dilatancy Effects

In this work, we propose a comprehensive two‐layer depth‐averaged model to study the dynamic behavior of grain‐fluid mixtures, which considers the granular dilatancy effects and the different frictional rheologies of grains in different states. Unlike single‐phase flows, not only the interaction between granular and fluid phases significantly influence the dynamics of mixtures, but also the phase separation, so that different flow regimes can occur. These include five different possible regimes: two‐layer regimes of (a) under‐saturated mixture and (b) over‐saturated mixture as well as single‐layer regimes of (c) saturated mixture, (d) pure grains and (e) pure fluid. Most depth‐averaged models in previous studies have considered only one of these flow regimes. The present model is an improved and integrated version of these depth‐averaged models. Taking into account that the pure grains and pure fluid in the upper layer, which occur in the regimes of the under‐saturated and over‐saturated grain‐fluid mixtures, respectively, exhibit different flow features than in the lower layer of the saturated mixture, we use a two‐phase two‐layer depth‐averaged model to describe these regimes. This proposed model is possibly the first to employ a two‐layer structure to describe all possible different flow regimes simultaneously. The proposed model is then solved numerically using a high‐resolution central‐upwind scheme and shows its ability to handle different flow regimes. To demonstrate the robustness of the numerical implementation and to evaluate the performance of the model, the numerical results are compared with several experiments reported in the literature, showing a certain qualitative agreement.