Asymptotic theory of propeller noise. I - Subsonic single-rotation propeller

Asymptotic expressions for the harmonic amplitudes and phases of the far- field acoustic pressure generated by a single-rotation propeller operating at subsonic tip relative Mach number are presented. These expressions are found from asymptotic approximations to integrals of the steady-loading distribution and of the blade thickness distribution over the surface of one blade, under the assumption that the number of blades B is large (but the harmonic number m is arbitrary). The asymptotics demonstrate rigorously that in this limit the noise of subsonic propellers is entirely tip generated, and described by very simple formulas giving explicit dependence on harmonic number, Mach number, and radiation angle. Excellent agreements is found between the asymptotic prediction and full numerical evaluation of the acoustic field (and between the latter and experimental data taken by Rolls-Royce in flyovers of a Gannet aircraft). Numerous trends and observations noted in the literature are explained by the asymptotic formulas, which are also extended to predict the acoustic benefit of sweep at subsonic conditions. (Author)