Numerical investigation of the flow dynamics past a three-element aerofoil

Abstract

AbstractA numerical investigation of the flow dynamics around a two-dimensional high-lift configuration was carried out by means of a zonal detached eddy simulation (ZDES) technique for flow conditions corresponding to aircraft approach. Both slat and flap regions have been scrutinized and compared with experimental data available in the literature. It is shown that slat and flap coves behave like shallow cavities. The distance between the upstream cusp and the downstream edge is the relevant length scale for each cove taken separately. Consistently with previous findings, this study indicates that the maximum of the broadband spectrum of slat (respectively flap) pressure fluctuations occurs for Strouhal numbers $0. 5\leq \mathit{St}\leq 4$ when based on slat chord (respectively on flap chord) and free-stream velocity. It is shown that mode $(n)$ of the slat cove and mode $(n+ 1)$ of the flap cove are very close making a coherent phase relationship possible. A large-scale coupled self-sustained oscillations mechanism between slat and flap cavities, evidenced by spectral analysis, occurs at a Strouhal number $\mathit{St}= 3{\unicode{x2013}} 6$ based on the main wing chord and free-stream velocity. This yields to an acoustic feedback mechanism characterized by a normalized frequency depending on the free stream Mach number like $\mathit{St}= (1- { M}_{0}^{2} )/ 2{M}_{0} $. The present result appears to line up with the findings by Hein et al. (J. Fluid Mech., vol. 582, 2007, pp. 179–202) who showed that two types of resonance could exist: surface waves ones, scaling with the total aerofoil length and longitudinal cavity-type resonances, scaling with the slat cove length.