Simple Particle Model for Low-Density Granular Flow Interacting with Ambient Fluid

Abstract

To understand the time evolutions of frontal speed and shape in a low-density granular flow, we propose a simple particle model. This model solves the equation of motion for each particle and simulates the time evolution of low-density granular flow. Spherical particles constituting a low-density granular flow slide on a slope at a steeper angle than the angle of repose. The particle motion is determined based on three forces: gravity as the driving force, repulsive force due to particle collision, and drag force due to the particle interaction through the ambient fluid. Two-dimensional numerical simulations of this model are conducted on the slope: the x−y plane parallel to the slope and the x−z plane perpendicular to the slope. In the x−y plane, particles aggregate at the moving front of the granular flow, and subsequently, flow instability occurs as a wavy pattern. This flow pattern is caused by the interparticle interaction arising from the drag force. Additionally, a vortex convection of particles is formed inside the aggregations. Simultaneously, particle aggregation is also found at the moving front of the granular flow in the x−z plane. The aggregation resembles a head−tail structure, where the frontal angle against the slope approaches 60 ∘ from a larger angle as time progresses. Comparing the numerical result by varying the particle size reveals that the qualitative dynamics of the granular flow are independent of particle size. Although the model is not realistic, our study presents a new particle-based approach that elucidates the dynamics of low-density granular flow.

Keywords

• granular avalanches
• mathematical modeling
• particle model
• numerical simulation
• pattern formation