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On a uniformly valid analytical rectilinear cascade response function

Published online by Cambridge University Press:  27 September 2010

HELENE POSSON ,
M. ROGER  and
S. MOREAU
HELENE POSSON*
Affiliation:
Laboratoire de Mécanique des Fluides et Acoustique, École Centrale de Lyon, 69134 Écully CEDEX, France
M. ROGER
Affiliation:
Laboratoire de Mécanique des Fluides et Acoustique, École Centrale de Lyon, 69134 Écully CEDEX, France
S. MOREAU
Affiliation:
G.A.U.S., Mechanical Engineering Department, Université de Sherbrooke, Sherbrooke, QC, CanadaJ1K 2R1
*
†Present address: G.A.U.S., Mechanical Engineering Department, Université de Sherbrooke, Sherbrooke, QC, CanadaJ1K 2R1. Email address for correspondence: helene.posson@gmail.com
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Abstract

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.

JFM classification

Acoustics: Aeroacoustics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 663 , 25 November 2010 , pp. 22 - 52
Copyright
Copyright © Cambridge University Press 2010

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