-1- Compari son of analyti c al and num e ri c al pr e di c tion s of s tator van e pr e ss ur e di s tribution produ ce d by me an rotor wak e impinge m e nt Hélène Posson 1* , Frédéric Sicot 2 , Stéphane Moreau 1 , Nicolas Gourdain 3 1 Groupe d’Acoustique de l’Université de Sherbrooke (GAUS), Département de Génie Mécanique, Université de Sherbrooke 2500 Boulevard de l’Université, Sherbrooke, QC, J1H4X2, CANADA  Phone: +1-819-821-8000 ext:62085, FAX: +1-819-821-7163, E-mail: helene.posson@usherbrooke.ca 2 ONERA DADS/MS, Châtillon, FRANCE 3 CERFACS, Computational Fluid Dynamics Team, Toulouse, FRANCE 46 Copyright © 2010 by ISROMAC-13 ABSTRACT A recently developed analytical model for the predictions of the fan tonal and broadband noises has been tested by comparing the unsteady blade loading with results provided by numerical un- steady simulations on a realistic compressor rotor-stator configu- ration (CME2). Both a blade slice and the actual full blade span have been investigated with the URANS and Harmonic Balance methods. In the simpler case of the blade slice, both numerical methods compare very well up to the sixth harmonics, but show large fluctuations and variations close to the leading edge caused by a small local flow separation, which cannot be predicted by the analytical model and yield larger levels on the first and second harmonics. In the full 3D case, the better flow field behaviour on the blade triggers a better agreement between the URANS and the analytical model. A further comparison with a flat plate cascade improves the comparison for the first harmonics. INTRODUCTION Modern turbofan engines have a larger high bypass ratio in order to improve the aircraft performance while diminishing the fan rotational speed. Then the jet noise has been reduced and the fan noise becomes another important contribution to the total noise particularly at approach condition. In the latter conditions, the fan rotational speed is lower, and the blades and vanes operate under subsonic speeds for which the unsteady loading on the blades and vanes constitute the main noise sources. As pointed out by Prasad & Verdon (2002), the unsteady aerodynamic phenomena on blades and inside the cascade also have a critical role in the outbreak of sustained force vibrations, flutter and consequent fatigue of fan, compressor or gas turbine. Besides, the turbofans have a rather high solidity, compared to ventilators, which will affect both their aerodynamic and acoustic performances. Therefore accurate pre- diction schemes, involving notably cascade and three-dimensional geometry effects, become essential for the design of quieter fans. In preliminary industrial designs, analytical models can still provide faster results than numerical simulations of the real unsteady compressible three-dimensional flow around the actual fan and OGV geometries. These time-marching unsteady simulations, even inviscid, are still computationally memory and time-consuming. The present paper is the first part of a twofold study aimed at as- sessing a recently developed analytical model for the prediction of unsteady vane loading (Posson and Roger, 2007). It focuses on the impingement of mean rotor wakes in the context of tonal noise predictions. This unsteady vane loading is then used as an equiva- lent dipole source distribution in the framework of an acoustic analogy. The study addresses a comparison with two numerical methods: an Unsteady Reynolds Average Navier Stokes Simulation (URANS) and a Harmonic Balance Method (HB). The two simu- lations are used to outline the ability of the HB to accurately predict the detailed unsteady aerodynamics as it has already been shown to predict mean aerodynamic performances quite well while reducing the computational time. The analytical model and the numerical simulations are first presented. Then a comparison is performed in a narrow annulus configuration both with the real shape of the vanes and with flat plat vanes. Finally, the comparison is performed in the fully annular configuration to outline the three-dimensional effects and the abil- ity of the model to capture these phenomena. ANALYTICAL MODEL AND NUMERICAL SIMULATIONS Analyti c al mode l The noise prediction model is a strip-theory approach (Posson and Roger, 2008) based on a previously published formulation for the unsteady blade loading in rectilinear cascade (Posson and Roger, 2007). The latter follows Glegg's analytical work (1999) for the response of a swept blade row to a three-dimensional gust. This compressible linear unsteady model provides a continuously valid analytical formulation for the velocity potential produced by a three-dimensional gust impinging on a swept blade row of infinite span. That is obtained resorting to the Wiener-Hopf technique and extensively using the residue theorem. R ec tiline ar c asc ade mode l . The blade row modelled in Fig. 1 is taken as an equivalent rectilinear cascade of infinite span made of infinitely thin flat plates of finite chord c. The blades can be stag- gered at an angle  and swept at an angle . Fig. 1 Geometry of the rectilinear cascade: (a) side view; (b) three-dimensional view. The mean flow U 0 (vectorial sum of the chordwise U c and spanwise direction W c component) is assumed at a zero an-