Dynamic stall at high Reynolds numbers induced by ramp-type pitching motions

Abstract

The transient pressure field around a moderately thick airfoil is studied as it undergoes ramp-type pitching motions at high Reynolds numbers and low Mach numbers. A unique set of laboratory experiments were performed in a high-pressure wind tunnel to investigate dynamic stall at chord Reynolds numbers in the range of $0.5\times 10^6\leq Re _c\leq 5.5\times 10^6$ in the absence of compressibility effects. In addition to variations of mean angle and amplitude, pitching manoeuvres at reduced frequencies in the range of $0.01\leq k\leq 0.40$ were studied by means of surface-pressure measurements. Independently of the parameter variations, all test cases exhibit a nearly identical stall behaviour characterized by a gradual trailing-edge stall, in which the dynamic stall vortex forms approximately at mid-chord. The location of the pitching window with respect to the Reynolds-number-dependent static stall angle is found to define the temporal development of the stall process. The time until stall onset is characterized by a power law, where a small excess of the static stall angle results in a drastically prolonged stall delay. The reduced frequency exhibits a decrease in impact on the stall development in the case of angle-limited pitching manoeuvres. Beyond a critical reduced frequency, both load magnitudes and vortex evolution become reduced frequency independent and instead depend on the geometry of the motion and the convective time scale, respectively. Overall, the characteristics of vortex evolution induced by dynamic stall show remarkable similarities to the framework of optimal vortex formation reported in Gharib et al. (J. Fluid Mech., vol. 360, 1998, pp. 121–140). The data from this study are publicly available at https://doi.org/10.34770/b3vq-sw14.

Time scales of dynamic stall development on a vertical-axis wind turbine blade

“…Note that we subtract the time at which the static stall angle is exceeded t ss to realign subsequent stall events, in accordance with results presented by Buchner et al (2018). When we express the upwind stall delay (light green + green) in terms of convective times, the stall delay does not depend on the tip-speed ratio and converges to approximately 4.5 convective times, which matches standard vortex formation times found in the literature (Dabiri, 2009;Dunne, Schmid, & McKeon, 2016;Gharib, Rambod, & Shariff, 1998;Kiefer, Brunner, Hansen, & Hultmark, 2022). The combination of the upwind and downwind stalled stages also reaches similar values for all tip-speed ratios, although the distribution between the two stages varies.…”

Laminar separation bubble formation and bursting on a finite wing

“…Examination of individual runs for the airfoil at α = 9 • revealed significant local maxima after the initial decrease in lift coefficient, and the absence of a local maximum in the ensemble-averaged lift coefficient during the ramp down for the airfoil α = 9 • is the result of higher variability between runs at this angle of attack. Although not presented here for conciseness, non-monotonicity was also observed in the transient drag coefficients, with a local maximum in drag coefficient occurring at the same time as the initial decrease in lift coefficient, similar to that observed during dynamic stall at higher Reynolds numbers (Kiefer et al 2022).…”

Comparison of dynamic stall on an airfoil undergoing sinusoidal and VAWT-shaped pitch motions

“…In [21] static data from this setup was corrected for blockage and aspect ratio and showed good agreement with previous studies of this airfoil. The reader is referred to [21] and [9] for more details on the experimental setup. Pitch motions corresponding to a sinusoidal shape as well as to several VAWT-shaped motions were tested.…”

“…For λ = 1.4 in figure 3, the upstroke is decelerated and therefore significantly longer than the accelerated downstroke. The yellow regions indicate the maximum suction peaks, while the dark red regions at x/c ≈ 0.5 mark the dynamic stall vortices convecting downstream [9]. Because the static stall angle is passed later in time at λ = 1.4, stall occurs slightly later in time.…”

“…If the angle of attack fluctuations are large enough that the maximum angle of attack significantly exceeds the static stall angle of the airfoil, a phenomenon known as dynamic stall occurs [8,9]. Dynamic stall leads to an overshoot in the lift force as the flow momentarily remains attached beyond the static stall angle, followed by drastic stall as a vortex forms on the suction side of the airfoil and convects downstream.…”