Effect of time-dependent piston velocity program on vortex ring formation in a piston/cylinder arrangement

An analytical model describing laminar vortex ring formation in a nozzle flow generator (piston/cylinder arrangement) proposed previously by the authors is extended to time-dependent velocity programs. The predictions of the model are in good agreement with the available numerical data for impulsive, linear, and trapezoidal velocity programs. We also show that properly scaled vortex circulation is another universal quantity, in addition to the dimensionless energy, related to vortex rings and verify this by comparing with available numerical simulations and experimental results.