Vortex structures around two colliding spheres at high Reynolds number

This study incorporates a hybrid Cartesian/immersed boundary (HCIB) method and the Navier-Stokes equations to simulate three-dimensional vortex flows around spheres swinging and colliding in viscous fluids. The motions of the spheres were prescribed in the model, and the simulated velocities around the spheres were validated by the results of laboratory experiments. The Reynolds number computed by the sphere diameter and the maximum swing velocity was Re = 13,500. The simulation results were examined in detail to elucidate the three-dimensional flows and pressure fields induced by the single swinging sphere and two colliding spheres. The evolution of the vortices can be divided into two parts: (i) Before the collision, the primary vortex ring induced by the swinging sphere grows in size, propagates obliquely downward, and eventually dissipates into turbulent flow. (ii) After the collision, the striking sphere transfers its momentum to the target sphere and another vortex ring is generated in front of the striking sphere owing to its impulsive deceleration. This vortex ring is separated from the sphere's boundary and the vorticity pattern is different from that of a single sphere case. After the collision, the target sphere up-swings with almost no vortical wake behind it, as observed in the experiments.