The scales of the leading-edge separation bubble

The leading-edge separation bubble (LESB) is a flow feature occurring on the suction side of thin foils as a result of separation at the sharp leading-edge followed by reattachment downstream along the chord. For a flat plate at zero angle of attack, the reattachment length of the bubble depends on the plate thickness t. At a non-zero incidence, instead, the underlying scale governing bubble length is not clear. To investigate, we undertake a critical review of experimental and theoretical studies, and we develop an analytical formulation to predict the reattachment length of plates both at zero and at small incidences. We focus on conditions where the bubble is turbulent, i.e. when transition occurs at a negligible distance from the point of separation. This occurs at thickness- and chord-based Reynolds numbers Ret=10,000, Rec=100,000. At angle of attack α = 0, we find that the reattachment length is xR ≈ 4.8t when the chord-to- thickness ratio is c/t > 12. At α > 0, we find that xR/c = πσα^2, where σ ≈ 7.9 is the inverse of the growth rate of a turbulent free shear layer. These results allow estimating xR on the thin wings of, for example, aerial vehicles and yacht sails.