Thickness noise of a propeller and its relation to blade sweep

Abstract

Linearized acoustic theory is applied to the calculation of the thickness noise produced by a supersonic propeller with sharp leading and trailing edges. The theoretical development is summarized and numerical calculations of the pressure-time waveform are presented. The erratic behaviour of previous time-domain calculations has been completely eliminated by careful numerical treatment of singular points, multiple singular points and nearly singular points that appear in the analysis. This allows a close inspection of the details of the calculated waveform and leads to the discovery of abrupt changes of slope in the pressure-time waveform, produced by singular points entering or leaving the blade at the tip. The behaviour of the pressure-time waveform is shown to be closely related to changes in the retarded rotor shape. Logarithmic singularities in the waveform are shown to be produced by regions on the blade edges that move towards the observer at sonic speed while at the same time having the edge normal to the line joining the source point and the observer. The logarithmic singularities are closely related to the shock waves produced by a swept airfoil in supersonic rectilinear motion, and they can be eliminated throughout the entire flow field by sweeping the rotor so that the Mach-number component normal to the leading and trailing edges is subsonic for all points on the rotor edges.