An inviscid model of unsteady separated vortical flow for a moving plate

Abstract

An inviscid vortex shedding model for separated vortices from a solid body is studied. The model describes the separated vortices by vortex sheets and the attached flow via conformal mapping. We develop a computational model to simulate the vortex shedding of a moving body, with varying angle. An unsteady Kutta condition is imposed on the edges of the plate to determine the edge circulations and velocities. The force on the plate is obtained by integrating the unsteady Blasius equation. We apply the model to two representative cases of an accelerated plate, with impulsive start and uniform acceleration, and investigate the dynamics for large angles of attack. For both cases, the vortex force is dominant in the lift over times. The lift coefficients are initially high and decrease in four chord lengths of displacement, in general. For large angles of attack, the appearance of a peak of lift at an early time depends on the power-law velocity, which differs from the behavior for small angles of attack. The lift and drag from the model are in agreement with the Navier–Stokes simulation and experiment for moderate Reynolds numbers. We also demonstrate the vortex shedding of hovering and flapping plates. In the hovering motion, the large increase in lift at the early backward translation is due to the combined effect of the vortex force and added mass force. In the flapping plate, our model provides an improvement in the prediction for the induced force than other shedding models.