A natural low-frequency oscillation of the flow over an airfoil near stalling conditions

Abstract

An unusually low-frequency oscillation in the flow over an airfoil is studied experimentally as well as computationally. Wind-tunnel measurements are carried out with two-dimensional airfoil models in the chord Reynolds number (Rc) range of 0.15 × 105−3.0 × 105. During deep stall, at α [gsim ] 18°, the usual ‘bluff-body shedding’ occurs at a Strouhal number, Sts ≈ 0.2. But at the onset of static stall around α = 15°, a low-frequency periodic oscillation is observed, the corresponding Sts being an order of magnitude lower. The phenomenon apparently takes place only with a transitional state of the separating boundary layer. Thus, on the one hand, it is not readily observed with a smooth airfoil in a clean wind tunnel, while on the other, it is easily removed by appropriate ‘acoustic tripping’. Details of the flow field for a typical case are compared with a case of bluff-body shedding. The flow field is different in many ways from the latter case and does not involve a Kármán Vortex street. The origin of the flow fluctuations traces to the upper surface of the airfoil and is associated with a periodic switching between stalled and unstalled states. The mechanism of the frequency selection remains unresolved, but any connection to blower instabilities, acoustic standing waves or structural resonances has been ruled out.A similar result has been encountered computationally using a two-dimensional Navier–Stokes code. While with the assumption of laminar flow, wake oscillation akin to the bluff-body shedding has been observed previously, the Sts is found to drop to about 0.03 when a ‘turbulent’ boundary layer is assumed. Details of the flow field and unsteady forces, computed for the same conditions as in the experiment, compare reasonably well with the experimental data.The phenomenon produces intense flow fluctuations imparting much larger unsteady forces to the airfoil than that experienced in bluff-body shedding, and may represent the primary aerodynamics of stall flutter of blades and wings.

On the birth of stall cells on airfoils

“…On the other hand, the absence of an explanation for the low-frequency flapping in the present laminar flow reconstruction is in line with the conclusión of Zaman et al [32] and Yon and Katz [31], who related it to turbulent shear-layers.…”

“…In their experimental measurements Yon and Katz identified different frequencies on the pressure signal, one related to the wake instability (St ~ 0.15) and another with high amplitude and low frequency St ~ 0.04. Both Yon and Katz [31] and Zaman et al [32] concluded independently that the low frequency fluctuations are related to a violent motion of the leading edge shear-layer, termed shear-layer flapping, resulting from a transitional or turbulent state of the separated shear-layer. Here, the oscillatory behaviour of the flow could be explained in the context of a modal linear instability analysis with the inclusión of the other less-amplified but still unstable oscillatory modes that were recovered in the BiGlobal instability analysis (see Fig.…”

Numerical Simulation of Flow over an Airfoil with a Cavity

“…It is likely that this low-frequency behavior is very sensitive to three-dimensional effects and turbulence, which could be a reason why it may not be observed in experiments. There is, however, evidence of similar behavior in literature, but this was reported for airfoils near stall conditions [11].…”

Response of a laminar separation bubble to impulsive forcing

“…Two regions of increased fluctuation can be identified, the first extending along the displacement thickness, upstream ofx h . In this region, small variations in the shear layer distance from the wall due to the flapping mechanism (Zaman et al 1989) result in substantial changes in the value of u. Flapping does not affect the wall-normal velocity to the same extent, thus this region is absent in the σ v field. In contrast, the second region of elevated fluctuations is evident in both standard deviation fields downstream ofx h .…”

“…Marxen & Henningson (2011) argued that, if irregular disturbances are present in the incoming flow, such as freestream turbulence in free flight or wind-tunnel experiments, the aforementioned feedback loop may explain the occurrence of an intermittent shear layer fluctuation associated with LSBs, often referred to as "flapping" (e.g. Zaman et al 1989). Adding to this argumentation, significant reduction of the flapping behaviour due to artificial monochromatic forcing has been noted by Dovgal & Boiko (1994) and Sandham (2008), related to the locking of the bubble dynamics to modes of constant amplitude.…”