Stress balance for a viscous flow with a single rolling particle

Abstract

One of the most important aspects in hydraulic engineering is to describe flows over mobile porous media in a continuum sense to derive models for sediment transport. This remains a challenging task due to the complex coupling of the particle and the fluid phase. Computational Fluid Dynamics can provide the data needed to understand the coupling of the two phases. To this end, we carry out grain-resolving Direct Numerical Simulations of multiphase flow. The particle phase is introduced by the Immersed Boundary Method and the particle-particle interaction is described by a sophisticated Discrete Element Method. We derive the stress budgets of the fluid and the particle phases separately through a rigorous analysis of the governing equations using the Double Averaging Methodology and the Coarse-Graining Method. As a next step, we perform a simple simulation of a heavy particle exposed to a Poiseuille flow rolling along a wall to understand the physical implications of the fluid-particle coupling. All terms of the stress balances can be computed in a straightforward manner allowing to close the budgets for the two phases separately. However, we encounter problems when attempting to combine the fluid-resolved local stresses with the coarse-grained particle stresses into a single balance for the fluid-particle mixture.

Consolidation of freshly deposited cohesive and noncohesive sediment: Particle-resolved simulations

“…To understand the settling and the consolidation of the fluid-particle mixture, we analyze the balance of the wallnormal stress components for the two phases separately. According to Biegert et al [46] and Biegert [47], we can write the momentum balance of the fluid (2) in an integral sense to obtain fluid stresses for a control volume Ω CV that extends from the top-wall (y = L y ) to an arbitrary height y in the vertical direction and encompasses the entire domain in the x-and z-directions (figure 3). We can write the integral form of (2) as…”

“…The present study addresses these issues from a computational perspective. Following our earlier particleresolved simulations [45][46][47], we present simulation data of settling cohesive and noncohesive sediment where we compute the motion of every particle in a fully resolved three-dimensional flow field without side walls. We present a detailed stress balance for the fluid-particle mixture that allows for a direct transfer of the governing equations to the classical 'effective stress concept'.…”