Modeling Rotor Unsteady Forces and Sound Due to Homogeneous Turbulence Ingestion

Abstract

An analytical approach is presented to model the broadband unsteady force cross-correlations exerted on a rotor due to a spatially homogeneous turbulent inflow. In addition, the rotor unsteady force cross-correlation matrix is treated as a set of correlated, compact dipole acoustic sources to predict the low-frequency radiated sound field of a subsonic rotor ingesting a turbulent flow. It is shown that turbulence-induced rotor forces in the radial and axial directions are uncorrelated for the special condition when spatially homogeneous turbulence is ingested, and further it is shown that radial-to-axial force correlation can exist when the turbulent inflow velocity field contains a coherent once-per-revolution variation. Equations to estimate rotor turbulence ingestion sound from noncompact dipole sources are also developed for situations when the compact acoustic assumption is invalid. A numerical simulation of the turbulence force and acoustic response for a 10-bladed rotor ingesting a spatially homogeneous turbulent inflow closely match an available experimental data set. A numerical simulation was also performed for a variation in rotor blade pitch, which indicated that radial force dipole source strength becomes nearly comparable to axial force dipole source strength when the blade-tip pitch angle reaches a value of .