The scales of the leading-edge separation bubble*

We discuss the length scales of the leading-edge separation bubble that occurs at the sharp edge of bluff and streamlined bodies at an angle of attack with the stream. We consider a flat plate with a blunt leading edge and with the chord aligned with the stream, and a thin plate at an angle of attack. We suggest predictive models of the reattachment length based on the free-streamline theory and the growth ratio of the mixing layer. The model predictions compare well with experimental data of various authors. We focus on turbulent flow conditions, where transition occurs in the separated shear layer at a negligible distance from the point of separation, viz. at thickness- and chord-based Reynolds numbers of 10⁴ and 10⁵, respectively. For a plate with thickness t aligned with the stream, we show that the reattachment length x_R increases with the chord (c) up to x_R ≈ 4.8t for c / t > 12. For a plate at an angle of attack (α), we find that x_R / c = π σ α², where σ ≈ 7.9 is the inverse of the growth rate of a turbulent mixing layer. These results provide new insights on the governing mechanism underlying flow reattachment, and allow the prediction in the first approximation of the reattachment length of separated shear layers on bluff and streamlined bodies.