The role of vortex–vortex interactions in thrust production for a plunging flat plate

Abstract

Oscillating plunging motion is one of the fundamental motions which comprise the kinematics used by many flying and swimming organism for locomotion. It is characterized by the frequency and amplitude of oscillation. Past studies have investigated this motion for relatively small amplitudes. In this paper we investigate reduced frequencies 0.25 ≤k≤ 16 and plunge amplitudes 0.03125 ≤h≤ 8 to give plunge velocities ranging from 0.25 ≤kh≤ 4 at Re = 100. It is found that unlike previous investigations for small plunge amplitudes, thrust does not increase monotonically with kh but reaches a maximum and then decreases reverting back to drag for high h values. It is shown that Leading Edge Vortices (LEVs) are responsible for the production of thrust whereas Trailing Edge Vortices (TEVs) induce drag on the plate. In the regime of increasing thrust with kh, the LEVs and TEVs are not strong enough to influence each other’s trajectory and vortex–vortex interactions are minimal. As kh increases to higher values, LEVs and TEVs gain in size and strength such that vortex induced velocities dominate the flow resulting in strong vortex–vortex interactions. Three main mechanisms of vortex–vortex interactions are identified, which either result in LEVs induced away from the plate or TEVs being induced near the plate. The net effect of these interactions result in reducing the residence time of the LEVs near the plate and decreasing thrust production. Finally, a detailed analysis of the wake is provided for the plunging plate. The inter-vortex distance in the wake is found to correlate directly with plunge amplitude and inversely with frequency. On the other hand, vortex strength is found to be a strong function of reduced frequency (k) where the functional relationship is near linear for different plunge velocities (kh).