Clapping propulsion and thin vortex rings: a computational study of vortex dynamics, energy equivalence, and core potential energy
We report a computational study of clapping propulsion using two thin rigid plates forming a 60-degree interplate cavity that generates a thrust-producing jet during closure. Plate kinematics are prescribed from experiments for two cases: dynamic and stationary, with forward motion constrained in the latter. The computations show that interplate pressure is higher in the stationary case compared to that in the dynamic case, resulting in differences in the thrust produced and in the evolution of wake vortices, with the stationary case forming triangular and Omega-shaped loops, while the dynamic case forms an elliptical loop for each plate. We examine the energy budget in the post-clapping phase, when the vortices are fully formed. The energy consists of kinetic energy and a component associated with vortex formation, whose sum approximately matches the work done on the fluid. This extra term, which we call the core potential energy, is found to be equal to the integral of pressure over the core volume of the vortex. This component is also checked using separate axisymmetric vortex ring simulations, where the kinetic energy is about 60% of the injected slug energy, and the remaining part is the core potential energy. Sullivan et al.(2008) had commented on this deficit for vortex rings and hypothesized the existence of a potential energy associated with the vortex structure.