A simplified Mach number scaling law for helicopter rotor noise

Abstract

A simplified Mach number scaling law is obtained for rotational and high frequency broadband noise from helicopter rotors. These scaling laws are based on geometric parameters of the rotor. The existing theory of Lowson and Ollerhead is used in deriving the conventional M t 6 law for rotational noise of geometrically similar blades operating in similar flow environ. The effects of number of blades, forward speed and directionality are included in the scaling formula. The ambiguous state of the art regarding the origin and and nature of high frequency broadband noise does not permit such a straightforward scaling law for this frequency regime. The vortices are assumed to be shed at an unknown Strouhal frequency and the scaling law is derived by simply integrating the blade sectional velocity over the span. The resulting scaling law is a function of the spanwise correlation lengths, Mach number, advance ratio, and geometric parameters of the rotor. Use of stationary airfoil data for the correlation lengths leads to a M t 5·8 lawfor the sound pressure level of the high frequency broadband noise. Both scaling laws were experimentally verified by using a 4·17 foot model rotor operating in the M.I.T. 5 × 7 1 2 foot anechoic wind tunnel. A comparison of the peak frequency location of high frequency broadband noise for full scale rotors obtained by Leverton was made, with the predicted Strouhal frequency parameter being used, and the agreement was found to be highly favorable. However, the predicted sound pressure levels were higher than the measured full scale rotor data.