Numerical simulation of evolution of a vortex ring and its interaction with a rigid sphere

Evolution of an elliptic vortex ring and vortex ring interaction with a rigid sphere are simulated numerically for kinematic motion and sound propagation. The flow field is regarded as three dimensional inviscid and incompressible. The vorticity is assumed as concentrated inside the finite core of vortex filaments. The vortex filament, described by parabolic blending curve functions, is used to effectively solve the Biot-Savart equation. An elliptic vortex ring emits a strong sound signal due to significant distortion and stretching of the vortex filament. Interaction between a vortex ring and a rigid sphere using the integration scheme are calculated with several initial positions. The evolution mechanism for an circular vortex ring interaction with a rigid sphere is predicted. The circular vortex ring is distorted after interaction with a sphere, and it has a similar kinematic motion like the elliptic vortex ring. The force variations around the sphere during the interaction are also calculated by using the unsteady Bernoulli equation. The unsteady pressure term, obtained using the potential based panel method, contributes significantly both the unsteady lift and drag force during interaction.