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Direct numerical simulations of forced and unforced separation bubbles on an airfoil at incidence. (English) Zbl 1144.76050
Summary: We present direct numerical simulations (DNS) of laminar separation bubbles on a NACA-0012 airfoil at \(Re_{c}=5\times 10^{4}\) and incidence 5\(^\circ\). Initially volume forcing is introduced in order to promote transition to turbulence. After obtaining sufficient data from this forced case, the explicitly added disturbances are removed and the simulation run further. With no forcing the turbulence is observed to self-sustain, with increased turbulence intensity in the reattachment region. A comparison of the forced and unforced cases shows that the forcing improves the aerodynamic performance whilst requiring little energy input. Classical linear stability analysis is performed upon the time-averaged flow field; however no absolute instability is observed that could explain the presence of self-sustaining turbulence. Finally, a series of simplified DNS are presented that illustrate a three-dimensional absolute instability of the two-dimensional vortex shedding that occurs naturally. Three-dimensional perturbations are amplified in the braid region of developing vortices, and subsequently convected upstream by local regions of reverse flow, within which the upstream velocity magnitude greatly exceeds that of the time-average. The perturbations are convected into the braid region of the next developing vortex, where they are amplified further, hence the cycle repeats with increasing amplitude. The fact that this transition process is independent of upstream disturbances has implications for modelling separation bubbles.

MSC:
76N15 Gas dynamics, general
76E09 Stability and instability of nonparallel flows in hydrodynamic stability
76F06 Transition to turbulence
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