This paper extends an existing analytical model of the aeroacoustic response of a rectilinear cascade of flat-plate blades to three-dimensional incident vortical gusts, by providing closed-form expressions for the acoustic field inside the inter-blade channels, as well as for the pressure jump over the blades in subsonic flows. The extended formulation is dedicated to future implementation in a fan-broadband-noise-prediction tool. The intended applications include the modern turbofan engines, for which analytical modelling is believed to be a good alternative to more expensive numerical techniques. The initial model taken as a reference is based on the Wiener–Hopf technique. An analytical solution valid over the whole space is first derived by making an extensive use of the residue theorem. The accuracy of the model is shown by comparing with numerical predictions of benchmark configurations available in the literature. This full exact solution could be used as a reference for future assessment of numerical solvers, of linearized Euler equations for instance, in rectilinear or narrow-annulus configurations. In addition, the pressure jump is a key piece of information because it can be used as a source term in an acoustic analogy when the rectilinear-cascade model is applied to three-dimensional blade rows by resorting to a strip-theory approach. When used as such in a true rectilinear-cascade configuration, it reproduces the exact radiated field that can be derived directly. The solution is also compared to a classical single-airfoil formulation to highlight the cascade effect. This effect is found important when the blades of the cascade overlap significantly, but the cascade solution tends to the single-airfoil one as the overlap goes to zero. This suggests that both models can be used as the continuation of each other if needed.

The present study aims at developing an acoustic formulation for the sound generated by the interaction of solid surfaces (such as blades) with an unsteady flow in an annular duct with swirl. Indeed, the mean flow in between the rotor and the stator of the fan or of a compressor stage is highly swirling. As a result, in order to properly predict the rotor self-noise radiated downstream of the rotor or the rotor-stator interaction noise radiated upstream of the stator, the swirling mean flow effect must be accounted for, either in the source terms or in the differential operator in an acoustic analogy. The proposed approach here, is to develop an acoustic analogy with an operator accounting for the swirl. It can be seen as an extension of Goldstein formulation in uniform mean flow (Aeroacoustics, 1976). The Navier-Stokes equations are first recast to obtain the differential operator and the associated equivalent noise sources in space and time. Then, the Green's function tailored to the rigid annular duct with swirl is derived in the frequency domain. Finally, the formulation to be used in the fan noise context is outlined.

No abstract

No abstract