ASYMPTOTIC THEORY OF PROPELLER NOISE .2. SUPERSONIC SINGLE-ROTATION PROPELLER

This paper gives analytical formulas for the far-field harmonic components of the acoustic radiation from a B-bladed supersonic single-rotation propeller, in the asymptotic limit B --> infinity. The dominant source, for radiation in a given direction, is identified as located at the Mach radius along the blade span, the radius that approaches the observer at precisely sonic speed, once in each rotation. Favorable agreement is found between the asymptotic prediction and the results of full numerical evaluation of the radiation integrals. Singular surfaces in the field are identified from the asymptotic formulas, which are extended to include chordwise noncompactness effects. These show, among other things, that supersonic propeller noise is an algebraically decreasing function of tip Mach number, once chordwise noncompactness effects are taken into account. in contrast to the exponential increase with tip Mach number of subsonic propeller noise.