Development of a mathematical model for submarine granular flows

Abstract

An Eulerian-Eulerian two-phase model based on a collisional-frictional law for the granular stress is proposed for the description of underwater granular flows and is applied to the collapses of immersed granular columns, which can be viewed as an idealized physical model of submarine landslides. In the mathematical model, the kinetic theory for dry granular flows is extended to take into account the particle-fluid interaction when formulating the collisional stress in the granular material, while the frictional stress is modeled based on an existing relation obtained by statistically averaging the individual contact forces among cohesionless particles. The drag force and the virtual-mass force are considered to represent the inter-phase interaction. The two-phase model is then employed to simulate the laboratory experiments of the collapses of granular columns immersed in an ambient liquid with an emphasis on the effect of the initial packing condition of the granular particles. It has been shown that the computed collapsing process of granular columns is in very good agreement with the experimental observations, and the proposed model can well capture the dynamic features of underwater granular flows. The effects of fluid pressure, drag force, and particle and fluid properties on the granular collapse are also discussed. It is demonstrated that the interstitial fluid flow plays a significant role in the collapsing process.