Aeroacoustic analysis based on FW–H analogy to predict low-frequency in-plane harmonic noise of a helicopter rotor in hover

Abstract

The integral formulation of the Ffowcs-Williams and Hawkings (FW–H) analogy, developed by Farassat (known as Farassat’s formulation 1A), is implemented to study the sound generation and propagation of rotating slender bodies. The general post-processing numerical code utilizes the linear acoustic theory to predict the thickness and loading noise terms for bodies in subsonic motion. The developed numerical code is validated for elementary acoustic sources (rotating monopole and dipole) against analytical solutions. The validated code is then applied for prediction of lowfrequency in-plane harmonic noise (LF-IPH) of a model helicopter rotor of Sargent and Schmitz in a low-thrust hover with full-scale tip Mach number. The required loading distribution of the rotor blade is obtained with CFD (RANS) and Blade Element Momentum Theory (BEMT) methods and also validated against literature data. The developed acoustic code, supplemented by CFD and BEMT loading analyses, allows for a detailed comparison (thickness and loading, near- and far-field, etc.) of the LFIPH noise of a helicopter rotor in both, time and frequency domains. The predicted (FW–H) acoustic signals are compared not only with the reference code solutions, but also with the experimental data. Moreover, the paper quantifies the impact of computational grid density and time-step size (used by CFD and FW–H codes) on the final solution accuracy. Additionally, a simplified analytical code is developed (based on elementary dipole solutions, compact chord assumption and BEMT method) allowing for the initial loading noise analysis with highly reduced computational resources. The acquired results are fully compatible with the classical FW–H analysis in terms of the impact of the in-plane and out-of-plane forces on the generated noise. The FW–H code predictions of the acoustic pressure and its components are in satisfactory agreement with the reference and experimental data of Sargent and Schmitz.