Flow regimes and dynamic similarity of immersed granular collapse: a CFD-DEM investigation

Abstract

Immersed granular collapses may encounter different flow regimes, such as free-fall (dry), fluid-inertial, and viscous regimes, depending on column geometry, particle size, particle density, fluid viscosity, and many other parameters. Understanding the controlling parameters of these regimes is important for both industrial and geological applications where grains and fluids coexist. It is also important to combine these parameters into dimensionless groups to guide down-scaled experiments and numerical simulations. In this work, we derive a set of dimensionless numbers (i.e., Stokes number, density ratio, and Reynolds number) based on typical time scales in the sedimentation of a sphere, and successfully verify the relevance of these numbers in determining flow regimes and maintaining dynamic similitude across length scales. The numerical method we use couples the computational fluid dynamics and discrete element method (CFD-DEM), which allows a wide variety of particle size and fluid viscosity to be chosen, keeping constant the Stokes number and density ratio. Quantitative data of front propagation and energy evolution are presented to characterize flow dynamics in different flow regimes. The collapse exhibits a transition from sliding-dominant to suspension-dominant behaviors as the Stokes number decreases, which gives rise to distinct deposit morphology in different regimes. Our findings enhance the understanding of inertial and viscous behaviors of immersed granular flows. The verified scaling rules and dimensionless parameters are of potential use in small-scale experiments and simulations where appropriate scaling is essential.