Influence of airfoil thickness on unsteady aerodynamic loads on pitching airfoils

Abstract

The influence of the airfoil thickness on aerodynamic loads is investigated numerically for harmonically pitching airfoils at low incidence, under the incompressible and inviscid flow approximation. Force coefficients obtained from finite-volume unsteady simulations of symmetrical 4-digit NACA airfoils are found to depart from the linear Theodorsen model of an oscillating flat plate. In particular, the value of the reduced frequency resulting in the inversion – from clockwise to counter-clockwise – of the lift/angle-of-attack hysteresis curve is found to increase with the airfoil thickness. Both the magnitude and direction of the velocity vector due to pitching over the airfoil surface differ from their flat-plate values. During the upstroke, namely nose-up rotation, phase, this results in a decrease (increase) of the normal velocity magnitude over the upper (lower) surface of the airfoil. The opposite occurs during the downstroke phase. This is confirmed by comparing the computed pressure distribution to the flat-plate linear Küssner model. Therefore, beyond the inversion frequency, the lift coefficient of a finite-thickness airfoil is higher during upstroke and lower during downstroke than its flat-plate counterpart. A similar dependence is also found for the quarter-chord moment coefficient. Accordingly, a modification to the classical Theodorsen model is proposed to take into account the effects of the airfoil thickness on unsteady loads. The new model is found to accurately predict the unsteady aerodynamics of a thick symmetric and a slightly cambered airfoil with a maximum thickness in the range 4–24 %. The limits of the present inviscid flow analysis are assessed by means of numerical simulation of high Reynolds number ($\mathit{Re}=10^{6}$) flows.