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

W.J. Baars, Liam Bullard , Abdulghani Mohamed

Research output: Chapter in Book/Conference proceedings/Edited volumeConference contributionScientificpeer-review

## 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 $\theta \approx (10^\circ,-45^\circ)$, where $\theta = 0^\circ$ is the rotor plane and negative angles are in the direction of the rotor-induced flow. The strongest modulation appears around $\theta \approx -15^\circ$. 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.
Original language English AIAA Scitech 2021 Forum 11–15 & 19–21 January 2021Virtual/online event American Institute of Aeronautics and Astronautics Inc. (AIAA) 16 978-1-62410-609-5 https://doi.org/10.2514/6.2021-0713 Published - 2021 AIAA Scitech 2021 Forum - Virtual/online event due to COVID-19 , Virtual, OnlineDuration: 11 Jan 2021 → 21 Jan 2021

### Conference

Conference AIAA Scitech 2021 Forum Virtual, Online 11/01/21 → 21/01/21

### Bibliographical note

Virtual/online event due to COVID-19

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