The present study aims at accounting for swirling mean flow effects on rotor trailingedge noise. Indeed, the mean flow in between the rotor and the stator of the fan or of a compressor stage is highly swirling. The extension of Ffowcs-Williams & Hawkings' acoustic analogy in a medium at rest with moving surfaces and of Goldstein's acoustic analogy in a circular duct with uniform mean flow to a swirling mean flow in an annular duct is introduced. It is first applied to tonal noise. In most cases, the swirl modifies the pressure distribution downstream of the fan. In several configurations, when the swirl is rather close to a solid body swirl, it is often sufficient to apply a simple Doppler effect correction when predicting the duct modes in uniform mean flow in order to predict accurately the noise radiated with swirl. However, in other realistic configurations, the swirling meanflow effect cannot be addressed using this simple Doppler effect correction. Second, a rotor trailing-edge noise model accounting for both the effects of the annular duct and the swirling mean flow is developed and applied to a realistic fan rotor with different swirling and sheared mean flows (and as a result different associated blade stagger angles). The benchmark cases are built from the Boeing 18-inch Fan Rig Broadband Noise Test. In all cases the swirling mean flow has an effect. In some cases the a simple Doppler effect may address it, but, in other realistic configurations our acoustic analogy with swirl is needed.
NomenclatureLatin characters A, D, M differential operators involved in Eq. (7) B blades number B m swirling mean flow factor in the duct wall boundary condition c 0 (r) non-dimensional local base-flow speed of sound c * 0 (R T ) base-flow speed of sound at R T c d0 (r) blade chord length at constant radius r C k numerical integration contour in the complex k plane C ± m,µ duct mode (m, µ) normalization factor D 0 /Dt base-flow time convective derivative E * energy per volume unit [kg.m −1 .s −2 ] E * S energy loss per time and volume unit [kg.function that defines the surface and the fluid locations F 6 th order partial differential non-dimensional operator acting on p F * ± m,µ (ω) duct mode acoustic power factor [kg −1 .m 4 .s 2 ] F * ± m,µ,U nif (ω) duct mode acoustic power factor in uniform mean flow [kg −1 .m 4 .s 2 ] G Green's function tailored to the rigid straight annular duct with swirling mean flowGreen's function tailored to the rigid straight annular duct with uniform mean flow G m time and axial Fourier transform of the m th azimuthal Fourier series component of G h non-dimensional hub radius, i.e. hub-to-tip ratio H(f ) Heaviside functionnon-dimensional axial wave-number of the sonic and nearly-convected modes k ± m,µ,cd non-dimensional chordwise wave-number of the sonic modes K (k, r 0 ) Kernel function that defines the modal eigenvalues k z cd,0 non-dimensional spanwise wavenumber L non-dimensional linearized operator acting on the perturbations L loading-noise source tensor l r non-dimensional spanwise...