Higher-order Statistical Metrics for Characterizing Rotor Acoustics.

Abstract

A number of well established higher-order statistical metrics are used to evaluate the significance of acoustic waveform nonlinearities in the sound field of a coaxial, co-rotating rotor in hover. These comprise the magnitude-squared coherence, skewness and kurtosis of the pressure waveform and its time derivative, number of zero crossings per rotation, a wave steepening factor, and the quadrature spectral density and its integral. A unique feature of the coaxial, co-rotating rotor, as well as distributed rotor propulsion systems for that matter, is the constructive and destructive interference of sound waves produced by neighboring blades, which are incubators for signal distortion effects; these effects are not captured using traditional metrics like overall sound pressure level and the sound pressure spectrum level. Waveform distortions are evaluated here using higher-order metrics for changes to the index angle and separation distance between the upper and lower rotors, as well as changes to rotor speed for different observer positions. Significant sensitivities in the kurtosis of the pressure waveform and its time derivative, the number of zero crossings, and the integral of the quadrature spectral density are shown for changes in rotor index angle, observer position and rotor speed; stacking distance appears less important at effecting changes to these metrics. The trade space between these metrics and rotor figure of merit demonstrates how relatively small changes in rotor performance can effect large changes in acoustic waveform nonlinearities. A common obstacle to the development of a ‘quiet’ rotor is the establishment of a firm connection between the rotor’s aerodynamic performance and the level of annoyance or detection that is observed in the acoustic far-field. An improved understanding of these higher-order effects could prove useful in narrowing this gap.