Determining the strength of rotating broadband sources in ducts by inverse methods

Abstract

Aeroengine broadband fan noise is a major contributor to the community noise exposure from aircraft. It is currently believed that the dominant broadband noise mechanisms are due to interaction of the turbulent wake from the rotor with the stator, and interaction of the turbulent boundary layers on the rotor blades with their trailing edges. Currently there are no measurement techniques that allow the localisation and quantification of rotor-based broadband noise sources. This paper presents an inversion technique for estimating the broadband acoustic source strength distribution over a ducted rotor using pressure measurements made at the duct wall. It is shown that the rotation of acoustic sources in a duct prevents the use of standard acoustic inversion techniques. A new technique is presented here for inverting the strength of rotating broadband sources that makes use of a new Green function taking into account the effect of source rotation. The new Green function is used together with a modal decomposition technique to remove the effect of source rotation, thereby allowing an estimation of the rotor-based source strengths in the rotating reference frame. It is shown that the pressure measured at the sensors after application of this technique is identical to that measured by sensors rotating at the same speed as the rotor. Results from numerical simulations are presented to investigate the resolution limits of the inversion technique. The azimuthal resolution limit, namely the ability of the measurement technique to discriminate between sources on adjacent blades, is shown to improve as the speed of rotation increases. To improve the robustness of the inversion technique, a simplifying assumption is made whereby the sources on different blades are assumed to be identical. It is also shown that the accuracy and robustness of the inversion procedure improve as the axial separation between the rotor and sensors decreases. Simulation results demonstrate that for a 26-bladed fan, rotating with a blade tip Mach number of M t = 0.5 , the aerodynamic source strengths can be estimated with acceptable robustness and approximately 1 dB accuracy, when measurements are made approximately 0.1 acoustic wavelengths from the rotor.