Longueteau F., Brazier J.

Noise from high-lift devices, such as flaps and slats, can contribute significantly to the overall aircraft noise, particularly during approach. The acoustic spectrum of the sound radiated from slats exhibit two features. A broadband component in the low to mid-frequency band (0-500 Hz), a tonal one in the high frequencies (around 4-5 kHz). URANS/LES computations from ONERA and experiments from DLR (W. Dobrzynski, AIAA Paper 2001-2158) of the flow around the slat show a large scale unsteady vortex in the slat cove and a vortex shedding in the wake of the slat trailing edge. It has been found that broadband noise is related to the slat cove vortex and tonal noise to the vortex shedding. While LES computations are able to give a global resolution, stability analysis can give, at small computing costs, an original insight concerning the mechanisms underlying the physics of the flow and a validation of LES post-treatments. The aim of this study is to predict the frequency of the vortex shedding with stability analysis tools in order to confirm the link between the former and the tonal noise. We assume the flow to be inviscid, quasi-parallel and slowly varying in the streamwise direction. The formulation of the stability problem from the Linearized Euler Equations, leads to a generalized eigenvalue problem which is solved by a spectral collocation scheme based on the Tchebichev's polynomials. Then, the stability of three velocity profiles extracted from a RANS computation in the wake of a 1/10th-scale slat trailing edge is examined. The vortex shedding frequency is obtained thanks to the 'Absolute Instability Criterion', as the real part of the dimensioned absolute pulsation. The value found near 40 kHz is in good agreement with the existing experiments and computations.