On an Uniform Rotor-Stator Wake-Interaction Noise Model Based on a Mode-Matching Technique

F2 -Tonal Noise Modelling

The work addresses the noise generated as rotor wakes impinge on a row of outlet guide vanes in a ducted subsonic axial-flow fan architecture. That noise, referred to as wake-interaction noise, is a dominant contributor to the total aerodynamic noise of a fan. Its prediction requires a substantial, most often not affordable, effort using numerical approaches. The present analytical approach is believed a consistent alternative, especially at the early design stage. Previous analytical works based on a single-airfoil response function cannot reproduce the cascade effect of the stator. Conversely existing cascade-response functions lead to mathematical complexity and cannot be declined easily in a cylindrical coordinate system for which they require approximations. The proposed new approach allows introducing simply the cascade effect, both in an unwrapped representation in Cartesian coordinates and in cylindrical coordinates. The problem is formulated in the frequency domain. Only its declination in a two-dimensional Cartesian coordinate system (axial and tangential) is detailed in the paper for the sake of illustration. The three-dimensional generalization is straightforward though more complicated.
A linear and non-viscous analysis is considered, for which the vortical and acoustic modes of oscillation in a gas are uncoupled except at solid boundaries. The velocity disturbances associated to the wakes are expanded in oblique sinusoidal vortical gusts. Each gust is frozen and characterized by its vorticity. Its impingement on the stator front-face generates acoustic modes which propagate upstream and are also transmitted downstream in the inter-vane channels. The latter are assimilated to a periodic array of bifurcated waveguides. The front-face (and similarly the back-face) of the stator is considered as an interface on both sides of which field variables are matched relying on continuity conditions. The continuity of pressure and of axial velocity is commonly used in the literature of acoustic wave transmission. The same is retained here. Furthermore the vorticity is also assumed continuous across the interface. This allows deriving an infinite set of equations that is solved by modal projections and matrix inversion. The acoustic waves are directly determined from the incident gust. The acoustic field is uniformly obtained in the whole domain.
The interest and the robustness of the approach for further fan broadband-noise modelling are discussed.