ASYMPTOTIC THEORY OF SUPERSONIC PROPELLER NOISE

An asymptotic theory for predicting noise radiation from supersonic propellers with realistic blade geometries is presented. The theory, which utilizes a large-blade-count approximation, provides simple closed-form expressions for the radiation efficiency integrals of all three types of propeller noise sources. Comparisons with a method that uses numerical integration of the radiation efficiency integrals indicate that sound levels predicted by the asymptotic theory are quite accurate. Asymptotic calculations also confirm the conclusions by earlier investigators that for high-speed propellers the noise radiated by the Lighthill quadrupole source is substantial when compared with the noise radiated by blade thickness and loading sources. Furthermore, the theory predicts that the propeller peak sound pressure level (SPL) increases monotonically below a critical tip helical Mach number but reaches a plateau and does not increase further above that critical Mach number. Both the predicted SPL trend and critical Mach number are in good agreement with experimental observations.