Numerical investigation of the interaction of a finite-size particle with a tangentially moving boundary

Abstract

The motion of a finite-size particle in steady two-dimensional lid- and shear-driven square-cavity flows is investigated. The coupled equations are solved numerically using a discontinuous Galerkin-finite-element method (DG-FEM) combined with the so-called smoothed-profile method (SPM). The spectral convergence enables an accurate and efficient computation of particle trajectories without moving grids. Particle trajectories are obtained by solving the Navier–Stokes and Newtons’s equations for the particle motion using simulations without additional model assumptions fully resolving all scales down to the flow in the lubrication gap. Particle trajectories are compared with streamlines and trajectories from one-way coupling. In the shear-driven square cavity with convex streamlines finite-size particles suffer a significant displacement effect when passing the moving boundary closely. While inertia displaces the particle towards outer streamlines, the finite-size effect alone displaces the particle towards inner streamlines. For weakly inertial particles the latter displacement effect is shown to be qualitatively similar to the displacement modelled by inelastic collision in a one-way-coupling approach.