On the leading-edge suction and stagnation-point location in unsteady flows past thin aerofoils

Variation of leading-edge suction during stall for unsteady aerofoil motions

“…For pitch motions, the calculation of is more complicated because the velocity due to the pitch rate varies along the chord depending on the distance from the pivot location. In the search for a theoretical basis for the velocity contribution due to the pitch rate, we get some direction from the expression for from quasi-steady thin-aerofoil theory (QSTAT) (Leishman 2002; Ramesh 2020). This theory provides expressions for the thin-aerofoil theory Fourier terms, lift and pitching-moment coefficients by applying the quasi-steady assumptions of negligible contributions from the wake vorticity.…”

“…This theory provides expressions for the thin-aerofoil theory Fourier terms, lift and pitching-moment coefficients by applying the quasi-steady assumptions of negligible contributions from the wake vorticity. From Ramesh (2020) we get the expression for for a symmetric aerofoil at a pitch angle of undergoing unsteady motion with a time-varying forward velocity, , upward plunge velocity, , and pitch rate about a non-dimensional pivot location as …”

“…Ramesh et al (2014) observed that the determining factor for the leading-edge suction and the flow velocity at the leading edge () for an aerofoil is the circulation at the leading edge, , which is represented by the first coefficient . Furthermore, using matched asymptotic expansion, Ramesh (2020) showed that is directly proportional to the coefficient in (2.1) as where is the aerofoil leading-edge radius non-dimensionalized by the chord. It may therefore be argued that the instantaneous value could serve as the LESP.…”

Boundary layer vortex sheet evolution around an accelerating and rotating cylinder

“…Furthermore, the results may offer a possibility to explain the downwards trend observed in the LESP criterion during vortex shedding as reported by Deparday & Mulleners (2019) and He & Williams (2020). The expansion of the velocity singularity around the leading edge by Ramesh (2020) links the LESP criterion directly to the leading edge velocity. In potential flow, the boundary layer edge velocity can in turn be straightforwardly linked to the vortex sheet strength used in the present study.…”

“…Even though the LESP is often calculated directly from the leading edge pressure, it is intrinsically linked to the boundary layer vorticity and can be calculated from this (Eldredge 2019). Ramesh (2020) further shows that the LESP can be related to the leading edge velocity by expanding the singularity using asymptotic matching of an outer solution, based on thin linear airfoil theory, and an inner solution, formed by evaluating flow past a parabola. Whilst the LESP has been shown to be successful at predicting flow detachment, trailing edge separation (Ramesh et al 2018) and increased airfoil pitch rates (Deparday & Mulleners 2019) can modify the critical value at which unsteady separation occurs.…”