Clapping propulsion and thin vortex rings: a computational study of vortex dynamics, energy equivalence, and core potential energy

Abstract: We present a numerical study on clapping propulsion using a body consisting of two rigid plates hinged at one end, with a 60-degree interplate cavity. The closing of the cavity generates a thrust-producing jet. Our previous experimental study (Mahulkar and Arakeri, PRF, 2024) compared the flow fields of the clapping body in two cases: free-moving (dynamic) and forward-constrained (stationary). The experiments revealed significant differences in body motion and flow structures. This numerical study further investigates these differences using plate motion data from the experiments. Our computations show that, in dynamic cases, interplate cavity pressure is lower than in stationary cases. A basic unsteady Bernoulli analysis explains that forward acceleration reduces interplate pressure. Furthermore, stationary cases exhibit distinct vortex dynamics, with starting vortex tubes forming at the plate edges and reconnecting with stopping vortex tubes to form triangular vortex loops in the rear wake, along with two sideways-oriented ringlets. In dynamic cases, the starting vortex tubes slide backward and reconnect with bound-vorticity threads shed from the outer surface of the plates, forming elliptical loops that reconnect circumferentially. Referring to Sullivan et al. (JFM, 2008), we quantify the energy deficit in isolated axisymmetric vortex rings using separate simulations and propose a model for the potential energy in the vortex core at the formation time. Using this model, we show that the total wake energy (kinetic + potential) equals the initial slug energy for the vortex ring, and in clapping, it equals the work done on the fluid by the pressure torque on the plates.