Abstract
A unified supersonic/hypersonic theory is given of flow past a pitching oscillating double wedge airfoil at arbitrary mean angle of attack. The amplitude and the (reduced) frequency parameter of the oscillation are assumed small and a perturbation method is employed. Closed form formulae are obtained for the stiffness and damping-in-pitch derivatives. They are exact with respect to the free stream Mach number, angle of attack and body thickness etc., provided only that the bow shock is attached to the leading edge. The theory predicts negative damping (instability) if the angle of attack, or the airfoil thickness is sufficiently large, or if the free stream Mach number is sufficiently low. It is shown to be in good agreement with experiments of Scruton et. al. Comparisons with Van Dyke second order potential theory and with Lighthill piston theory are also given. Finally the theory may easily be extended to arbitrary smooth airfoils.
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