Abstract
The motion of a heavy finite-size tracer is numerically calculated in a two-dimensional shear-driven cavity. The particle motion is computed using a discontinuous Galerkin-finite-element method combined with a smoothed profile method resolving all scales, including the flow in the lubrication gap between the particle and the boundary. The centrifugation of heavy particles in the recirculating flow is counteracted by a repulsion from the shear-stress surface. The resulting limit cycle for the particle motion represents an attractor for particles in dilute suspensions. The limit cycles obtained by fully resolved simulations as a function of the particle size and density are compared with those obtained by one-way coupling using the Maxey–Riley equation and an inelastic collision model for the particle–boundary interaction, solely characterized by an interaction-length parameter. It is shown that the one-way coupling approach can faithfully approximate the true limit cycle if the interaction length is selected depending on the particle size and its relative density.
Highlights
Dispersed multiphase flows arise in a wide range of natural phenomena [1]
The flow is calculated in the absence of a particle and the particle motion is calculated by one-way coupling supplemented by a suitable particle–surface interaction (PSI) model when the particle moves close to any of the boundaries
To solve the full problem, we use an Eulerian approach in which the flow-field equations are solved by a discontinuous Galerkin-finite-element method (DG-FEM) coupled to a smoothed profile method (SPM)
Summary
Dispersed multiphase flows arise in a wide range of natural phenomena [1]. Particle-laden flows are dealing with a continuously connected fluid phase and an immiscible dispersed phase made of particles. Examples for such flows are sand storms, debris flows, and transport of volcanic ash [2]. Particle-laden flows are important in many technical processes like combustion [3], steel making [4], drug delivery and other biological applications [5]. Owing to the abundance of particle-laden flows their understanding, prediction and control has become an active research field for theoretical, experimental and computational fluid dynamics
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