Interaction between a vortex ring and a rigid sphere

Abstract

The effect of vortex distortion on the flow arising from the interaction between a vortex ring and a rigid sphere is analyzed for three-dimensional, inviscid and incompressible how. Significant distortion of the vortex structure, owing to interaction with the sphere, can occur, especially during close interaction. The vorticity field is represented by a concentrated finite core along the vortex filament, The vortex filament curve is described by a parabolic blending curve function to minimize the numerical vortex instability resulting from discretization of the vortex filament. The discretized filaments and the image filaments inside the sphere are moved with the induced velocity. The interactions between a vortex ring and a sphere are calculated for several initial separation positions. The trajectories of the centroid of vorticity are obtained to investigate the motion of the vortex filament. The vortex filament is highly distorted and in the case of close interaction, it is even captured by the image vortex inside the rigid sphere. With small changes of the initial vertical separation between the vortex ring and the rigid sphere, three different interacting patterns can be observed; the vortex may either pass by the sphere, pass over the sphere, or be trapped (captured) by the sphere. The effect of a uniform flow is calculated for the capturing case. The induced variations of the force on the sphere can be a significant source of dipole sound, whereas the distortion of the vortex filament contributes to the quadrupole sound. The instantaneous forces acting on the sphere are obtained by using the unsteady Bernoulli equation. The unsteady pressure term, obtained by using the potential based panel method, contributes significantly to both the unsteady lift and the drag force during interactions.