Unsteady flow interactions between an advected cylindrical vortex tube and a spherical particle

Abstract

The unsteady, three-dimensional, incompressible, viscous flow interactions between a vortical (initially cylindrical) structure advected by a uniform free stream and a spherical particle held fixed in space is investigated numerically for a range of particle Reynolds numbers 20 ≤ Re ≤ 100. The counter-clockwise rotating vortex tube is initially located ten sphere radii upstream from the sphere centre. The finite-difference computations yield the flow properties and the temporal distributions of lift, drag, and moment coefficients of the sphere. Initially, the lift force is positive owing to the upwash on the sphere, then becomes negative owing to the downwash as the vortex tube passes the sphere. Varying the size of the vortex core (σ) shows that the r.m.s. lift coefficient is linearly proportional to the circulation of the vortex tube at small values of σ. At large values of σ, the r.m.s. lift coefficient is linearly proportional to the maximum fluctuation velocity (vmax) induced by the vortex tube but independent of σ. For intermediate values of σ, the r.m.s. lift coefficient depends on both σ and vmax (or equivalently both σ and the circulation). We observe some interesting flow phenomena in the near wake as a function of time owing to the passage of the vortex tube.