Dynamic stall with circulation pulse and hysteresis for NACA 0012 and VR-12 airfoils

Airfoils undergoing dynamic stall often display a secondary lift peak after the lift has begun to decrease. A study of this phenomenon for the NACA 0012 and VR-12 airfoils shows that the secondary peak is followed by a damped oscillation in lift. It is found that this under-damped lift can be modeled by an ONERA type equation for secondary lift that is driven by a simple pulse. It is speculated that the physical basis of this pulse is the attaching of a secondary vortex to the airfoil. The onset and duration of this pulse can be predicted in terms of angle of attack in a general time-domain simulation. When added to the present Ahaus-Peters stall equations, this new stall equation gives a total finite-state model for dynamic stall simulation that can include the secondary stall peak.