Upstream-radiated rotor–stator interaction noise in mean swirling flow

Abstract

A major component of the noise in modern aeroengines is rotor-stator interaction noise generated when the wake from the rotating fan impinges on a stator row downstream. An analytically based model for the prediction of upstream-radiated rotor-stator interaction noise is described, and includes the important effect of mean swirling flow on both the rotor wake evolution and the acoustic response. The analytic nature of the model allows for the inclusion of all wake harmonics and enables the response at all blade passing frequencies to be determined.An asymptotic analysis based on large rotor blade number is used to model the evolution of the rotor wake downstream in a cylindrical duct carrying mean swirling flow. The equations governing the axial evolution of the wake simplify to three coupled first-order differential equations in the interior, while close to the duct walls, a boundary-layer correction is required in order to satisfy the impermeability conditions at the boundaries. At the stator location, the wake is used as input into a local linear cascade model at each radius. The interaction of each wake harmonic gives rise to acoustic waves of multiple azimuthal order which contribute to the pressure field radiated back upstream. This enables the total acoustic response to be determined in terms of cylindrical duct modes in mean swirling flow.The effect of stator blade geometry (thickness, camber, angle of attack) and rotorstator separation on the total upstream-radiated noise is determined. Blade geometry is shown to have a significant effect on the noise generated, and increasing the rotorstator gap can lead to large reductions in noise levels. Asymptotic treatment of the acoustic field, based on large azimuthal order, is also considered and used to identify the dominant contributions to the total pressure field resulting from the rotor-stator interaction. The ray structure of the acoustic modes in swirl is shown to be very different in some cases from that in uniform flow.

Numerical study of acoustic modes in ducted shear flow

“…Its validity will be verified against asymptotic results of the WKB type similar to what has been proposed by Envia [13] and Cooper & Peake [11].…”

“…In the eigenvalue problem (11,13,14) the excitation frequency ω and the circumferential wavenumber m are given parameters while the axial wavenumber k is the unknown spectral variable.…”

“…The relevant numerical procedure, which has also been used to integrate the generic problem (11,13,14), is described in the next Section. However, prior to proceeding to the numerical analysis, we briefly summarize here the main analytic results for the eigenvalue problem (15,16,17) reported in Vilenski & Rienstra [12].…”

“…The eigenvalue problem (11,13,14) was solved numerically using the following method. The field equation (11) was first rewritten in the form of a system of two first-order ordinary differential equations…”

“…Of amongst more recent numerical studies, especially with regards to swirling flows, the works by Golubev & Atassi [7], Tam & Auriault [8], Kousen [9], Nijboer [10], Cooper & Peake [11] should be mentioned.…”