Quantifying modulation in the acoustic field of a small-scale rotor using bispectral analysis

Abstract

This paper describes a methodology to quantify inter-frequency modulation in the acoustic field of a small-scale rotor. How the blade passing frequency modulates the intensity of the higher-frequency (broadband) noise content is of specific interest, as this modulation is a major factor in the human perception of rotor noise from advanced air mobility vehicles and drones. A proposed modulation-parameter is based on post-processing steps that are applicable to a single acoustic time series. First, an auto-bispectral analysis assesses the dominant nonlinear, quadratic inter-frequency coupling between the blade passing frequency and the higher-frequency noise content. Secondly, the degree of modulation is determined using a robust parameter: a correlation parameter between the (low-frequency) modulating BPF signal and an envelope of the (higher-frequency) carrier signal. Provided that a single parameter is obtained for a given acoustic time series, the directivity pattern of the modulation strength can be inferred from data available from standard acoustic measurement campaigns. For illustration, an 11 inch diameter single-rotor in hover is considered, with acoustic data taken at 420 microphone positions within a plane perpendicular to the rotor disk. It is revealed that modulation is confined to a sector θ ≈ (10 • , −45 • ), where θ = 0 • is the rotor plane and negative angles are in the direction of the rotor-induced flow. The strongest modulation appears around θ ≈ −15 • . This work aids in quantifying the phenomenological description of modulation, namely that it results from the periodic advance and retreat of certain rotor blade's noise sources, relative to a stationary observer.

Low-Frequency Intensity Modulation of High-Frequency Rotor Noise

“…In terms of source mechanisms, the working principle of BPFM may initially be thought of as a result of the harmonic variation in the source-receiver distance (as a direct result of the rotor spinning). But, if that were to be the case, the normalized modulation strength would be maximum at sideline angles; this is not observed in measurements [36]. As such, a proper quantification of BPFM and an identification of its source mechanisms is needed.…”

“…In this study, the time-and/or ensemble-averaged characterization of rotor noise is augmented by utilizing metrics that preserve the temporal variation in the intensity of high-frequency noise [36]. This intensity-variation is a nonlinear frequency-interaction and refers, in the context of our current work, to the phase-consistencies between the low-frequency BPF and higher-frequency noise.…”

Challenges and opportunities for low noise electric aircraft

“…197 To date, most rotor broadband noise analyses-whether predicted or measured-have focused on time-averaged broadband noise spectra, meaning that the broadband noise sound pressure level (SPL) spectrum is integrated over a time segment on the order of a rotor period. However, in the past 3 years, the time variation of rotor broadband noise has recently increased attention [202][203][204][205][206][207] due to its apparent importance to human perception of helicopter main rotor noise, as identified by Christian, Caston, and Greenwood. 106 As reviewed by Gan (Ref.…”

Characterization of the low-noise drone propeller with serrated Gurney flap

“…Frontiers in Aerospace Engineering frontiersin.org 07 noise depending on the noise measurement location (Baars et al, 2021). In addition, flow recirculation can affect the noise measurements in indoor experiments (Whelchel et al, 2020).…”