A vorticity-based criterion to characterise leading edge dynamic stall onset

We propose a more conservative, physically-intuitive criterion, namely, the boundary enstrophy flux ($BEF$), to characterise leading-edge-type dynamic stall onset in incompressible flows. Our results are based on wall-resolved large-eddy simulations of pitching aerofoils, with fine spatial and temporal resolution around stall onset. We observe that $|BEF|$ reaches a maximum within the stall onset regime identified. By decomposing the contribution to $BEF$ from the flow field, we find that the dominant contribution arises from the laminar leading edge region, due to the combined effect of large clockwise vorticity and favourable pressure gradient. A relatively small contribution originates from the transitional/turbulent laminar separation bubble (LSB) region, due to LSB-induced counter-clockwise vorticity and adverse pressure gradient. This results in $BEF$ being nearly independent of the integration length as long as the region very close to the leading edge is included. This characteristic of $BEF$ yields a major advantage in that the effect of partial or complete inclusion of the noisy LSB region can be filtered out, without changing the $BEF$ peak location in time significantly. Next, we analytically relate $BEF$ to the net wall shear and show that its critical value ($=\max (|BEF|)$) corresponds to the instant of maximum net shear prevailing at the wall. Finally, we have also compared $BEF$ with the leading edge suction parameter ($LESP$) (Ramesh et al., J. Fluid Mech., vol. 751, 2014, pp. 500–538) and find that the former reaches its maximum value between $0.3^{\circ }$ and $0.8^{\circ }$ of rotation earlier.