Neutral Damping Boundary in the Transonic Regime
Linearized theory for supersonic flow past oscillating profiles indicates the possibility of instability of pitching oscillations for low frequencies. If the Mach number M∞ approaches one, linearized theory fails. The influence of the thickness ratio cannot be neglected. Even the second-order theory becomes unreliable, when the bow shock wave detaches. In order to get results for this regime an approximate method similar to that of the “local linearization method” for the steady case has been developed. For M∞ = 1, a linear parabolic differential equation has been already established; now for M∞ > 1 a linear hyperbolic differential equation will be derived. The neutral damping boundary will be discussed as a function of the thickness ratio and of the Mach number.
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