The importance of quadrupole sources in prediction of transonic tip speed propeller noise

Abstract

SUMMARYA theoretical analysis is presented for the harmonic noise of high speed, open rotors.Far field acoustic radiation equations based on the Ffowcs-Williams/Hawkings theory are derived for a static rotor with thin blades and zero lift.Near the plane of rotation, the dominant sources are the volume displacement and the pu2 quadrupole, where u is the disturbance velocity component in the direction of blade motion. These sources are compared in both the time domain and the frequency domain using twodimensional airfoil theories valid in the subsonic, transonic, and supersonic speed ranges.For nonlifting parabolic arc blades, the two sources are equally important at speeds between the section critical Mach number and a Mach number of one. However, for moderately subsonic or fully supersonic flow over thin blade sections, the quadrupole term is negligible.It is therefore concluded for thin blades that significant quadrupole noise radiation is strictly a transonic phenomenon and that it can be suppressed with blade sweep. Noise calculations are presented for two rotors, one simulating a helicopter main rotor and the other a model propeller tested at United Technologies Corporation.For the latter, agreement with test data was substantially improved by including the quadrupole source term.

Spectral Conditioning of Propeller Noise From Broadband Sources

“…This is a non-linear process but one which can be modelled exactly. The noise generated by a propeller is related to its geometry and to the on-blade pressure, quadrupole sources being negligible for the thin, highly swept blades used in this study [18]. A model based on linear acoustic theory is used which incorporates unsteady loading and asymmetric convection.…”

A Procedure for the Evaluation of Installed Propeller Noise

“…The "rst of these is related to the displacement of #uid by the propeller blade and is proportional to L , the momentum injection at the blade surface, while the loading term is related to the force applied by the blade on the #uid. The third term is only of importance when strong non-linear e!ects are present and can be neglected for subsonic propellers [30]. Equation (1) can be solved using the Green function given by Garrick and Watkins [31] for acoustic radiation in a uniform #ow,…”

Comparison of Computational Aeroacoustic Prediction Methods for Transonic Rotor Noise

“…The quadrupole source, on the other hand, is a volume distribution of sources (indicated by the Heaviside function H(f )). The importance of the quadrupole term has long been recognized [8,9]. However, the quadrupole source has often been neglected in rotor noise prediction because of the computational demands of computing the ow eld with sucient accuracy and integrating over a volume in the acoustic prediction.…”