Lift Hysteresis of an Oscillating Slender Ellipse

A theoretical investigation has been conducted to determine the timewise variation of lift on a slender elliptic cylinder moving at uniform speed but oscillating in pitch. The analysis couples a potential flow calculation, including the effect of a vortical wake, for the flow past the cylinder with a calculation of the unsteady, twodimensional, laminar boundary layer on the surfaces of the pitching ellipse. The coupling is achieved by matching the rate at which boundary-layer-developed vorticity is shed into the wake with the time rate of circulation about the ellipse. The unsteady lift is determined from an integration of the unsteady pressure distribution on the body. The effects of mean angle of attack and oscillation frequency on the lift hysteresis loops are determined. It is shown that the hysteresis loops change direction as the mean angle of attack is increased through the angle of attack corresponding to maximum steady lift.