Mode and regime identification for a static NACA0012 airfoil at transitional Reynolds numbers

This work examines the flow structure modes in the boundary layer and in the wake of a NACA0012 airfoil in static conditions at transitional chord-based Reynolds numbers (Rec), for small angles of attack (α). A laminar mode, with a laminar separation of the boundary layer and laminar Kármán streets in the wake, was first observed for Rec < 61400 and α = 0°. For 77 000 < Rec < 118600, which corresponds to a regime between laminar and transitional mode called subcritical mode, the boundary layer exhibited a long separation bubble reattached close to the trailing edge, and the wake showed a turbulent Kármán street. Finally, for higher Rec and α, a critical transition mode consisted of a long bubble followed by a turbulent separation, and a less structured vortex street in the wake of the airfoil.

Numerical study of a turbulent separation bubble with sweep

Direct numerical simulation (DNS) is used to study a separated and rapidly reattached turbulent boundary layer over an idealized $35^{\circ }$ infinite swept wing. The separation and reattachment are induced by a transpiration profile at fixed distance above the layer, with the pressure gradient applied to a well-defined, fully developed, zero-pressure-gradient (ZPG) collateral state. To isolate the influence of the sweep, results are compared with one of our earlier DNS of an unswept flow, with the same chordwise transpiration distribution and appropriate upstream momentum thickness. The independence principle (IP) traditionally proposed for swept wings, which is exact for laminar flows, is found to be close to valid in some regions (bridging the separation/reattachment zone) and to fail in others (in the ZPG layers upstream and downstream of the separation). This is assessed primarily through the skin friction and integral thicknesses. The regions in which the IP is approximately valid correspond to regions of diminished Reynolds-stress divergence, compared to the pressure-gradient magnitude. The mean-velocity profiles exhibit significant skewing as the flow develops, while the velocity magnitude departs only slightly from the ZPG logarithmic profile, even above the separation zone. Implications for Reynolds-averaged turbulence modelling are discussed.