Scattering of incident disturbances by an annular cascade in a swirling flow

Abstract

Analytical and numerical analyses are developed for the interaction and scattering of incident acoustic and vortical disturbances by an unloaded annular cascade in a swirling flow. The mathematical formulation uses the Euler equations linearized about an axial and swirling mean flow. The incident disturbances are decomposed into nearly sonic and nearly convected disturbances using the results of a normal-mode analysis, namely the unsteady pressure is predominantly associated with the former. Exact non-reflecting inflow/outflow conditions are derived in terms of the normal modes using the group velocity to segregate the modes propagating downstream and upstream. An inflow condition is also derived for the nearly convected disturbances. An explicit primitive-variable scheme is implemented and validated by comparison with the uniform flow and narrow annulus limits. Acoustic and aerodynamic results are presented to examine how swirl modifies the scattering from that of the uniform flow and narrow annulus limits and to determine the conditions leading to strong scattering. The results indicate that the swirl changes the physics of the scattering in three major ways: (i) it modifies the number of acoustic modes in the duct, (ii) it changes their duct radial profile, and (iii) it causes significant amplitude and radial phase variations of the incident disturbance. The results also show that when the radial phase of the incident disturbance is different from that of the duct modes, weak scattering into the duct acoustic modes occurs. These results suggest that analysis of the radial variation of the incident disturbance and duct modes can provide an indication of the efficiency of the scattering process.

Experimental Validation of a Cascade Response Function for Fan Broadband Noise Predictions

“…The emergence is around 3, 8, and 5 dB in the range of Strouhal numbers [1.75,29] for the configurations T1-C1, T2-C1, and T1-C2, respectively, and around 10 dB in [0. 9,29] for T2-C2, as shown in Fig. 7 for U x d 80 m=s.…”

“…It is so when using an acoustic analogy in rectilinear configuration (Green's function for rectilinear configuration) with the present model of blade loading. It would be so as well with a fully three-dimensional annular-cascade response function, accounting for the real geometry and applying the acoustic analogy in an annular duct, in the same way as with the three-dimensional seminumerical models of Namba [27] or Schulten [28], or with a code solving the three-dimensional linearized Euler equations [29]. Hanson's approximation does not exhibit any singularity, since its direct-radiation formulation is equivalent to an acoustic analogy in a rectilinear configuration and since the present unsteady blade loading is suited to rectilinear cascades.…”

The acoustic analogy in an annular duct with swirling mean flow

“…Several studies [1,2,3] have shown that the swirl modifies the number of acoustic modes in the duct, their radial profile and alters the incident disturbance in rotor-stator interaction. The present study is a part of an ongoing work dedicated to account for the swirling mean flow effect on rotor-stator fan noise prediction.…”

Random particle methods applied to broadband fan interaction noise

“…The incident turbulent flow consists in a uniform base flow and an isotropic, locally homogeneous fluctuating velocity field. The model has also been extended to include nonuniform base flows [8] and different energy spectra [9]. The fluctuating components of the inflow velocity field are described as a sum of Fourier modes and the propagation model is solved in the frequency domain.…”