Numerical investigation of self-sustained oscillations of stall cells around a leading edge-separating airfoil

Abstract

The flow around a stalled airfoil is investigated using zonal detached-eddy simulation (mode 2), including transition effects through a coupling with the [Formula: see text] framework. The airfoil exhibits mixed trailing edge-leading edge stall type properties. The chord length-based Reynolds number and Mach number, respectively, amount to [Formula: see text] and 0.16. Two computations with different initial conditions are performed for 40 and 120 chord-passing durations, respectively (or equivalently [Formula: see text] and [Formula: see text]), allowing the capture of several periods of the low frequency dynamics of the flow—compared to typical von Kármán vortex shedding. A stall hysteresis is observed: the computation initiated from an attached flow remains thus, but the computation which starts from a separated flow yields a quasi-permanent low-frequency oscillatory behavior, which bifurcates to the previously attached topology after 90 chord-passing durations ([Formula: see text]). The oscillatory phase displays events of emergence and disappearance of stall cells. The partly- and fully attached flows are validated against experimental data. The oscillatory bistable flow is then analyzed with regard to the characteristics and frequency contents of both massive separation and partial transient reattachments. It is shown that the low-frequency separated shear layer flapping at the leading edge is forced by high-frequency fluctuations, which travel from the trailing edge upstream, close to the wall in the separated flow. The flapping phenomenon displays a Strouhal number based on the front-section height of the airfoil around [Formula: see text]. Conversely, the high-frequency fluctuations have Strouhal numbers closer to 3, which is in close agreement with leading-edge shear-layer instability frequencies. The spectral content of the flow is then explored in search of the source of these high-frequency fluctuations. It is proposed that they stem from the instability of the trailing edge shear layer between the pressure side boundary layer and the separated flow from the suction side. Finally, a scenario describing a cycle of the low-frequency oscillation of a stall cell is proposed.