Abstract
The leading-edge separation bubble 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 nonzero incidence, instead, the underlying scale governing bubble length is not clear. To investigate, we undertake a critical review of experimental and theoretical studies and 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≳104, Rec≳105. 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=πσα2, 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.
Highlights
The leading-edge separation bubble (LESB) is a flow feature that occurs on wings, blades, and sails when the leadingedge (LE) is sharp, promoting flow separation, and the angle of attack is sufficiently small to enable reattachment
IV A), we review past experiments showing that the reattachment length tends to become independent of the Reynolds number as this increases, but it strongly depends on the angle of attack
We investigate the characteristic length of the turbulent leading-edge bubble, a feature that occurs at the sharp edge of thin wings in moderate and high Reynolds number conditions
Summary
The leading-edge separation bubble (LESB) is a flow feature that occurs on wings, blades, and sails when the leadingedge (LE) is sharp, promoting flow separation, and the angle of attack is sufficiently small to enable reattachment. Consider a thin foil at a non zero incidence to a free stream velocity (Fig. 1). An attached boundary layer develops from the stagnation point, which is located on the pressure side, towards both sides of the foil. At sufficiently small angles of attack, the flow is observed to reattach further aft the foil surface. This paper aims to identify a predictive model of the reattachment length xR, which is the distance between the point of separation and that of reattachment (Fig. 1)
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