Dynamic stall reattachment revisited

TL;DR

The paper investigates dynamic stall reattachment on a sinusoidally pitching airfoil using time-resolved PIV and surface pressure data to uncover the sequence of recovery events. It reveals that reattachment is delayed below the static stall angle $\alpha_{\mathrm{ss}}$ and is governed by a critical leading-edge suction parameter $A_{0}^{*}$, with recovery progressing through three stages: reaction delay, wave propagation, and relaxation. The authors quantify stage time-scales (e.g., $2.7$ convective times for wave propagation and $1.7$ for relaxation) and establish a practical criterion for onset via $A_{0}^{*}$, largely independent of pitch rate. These findings provide concrete diagnostics to improve semi-empirical dynamic stall models and to design control strategies for gust-mensitive wings and blades.

Abstract

Dynamic stall on airfoils is an undesirable and potentially dangerous phenomenon. The motto for aerodynamic systems with unsteadily moving wings, such as helicopters or wind turbines, is that prevention beats recovery. In case prevention fails or is not feasible, we need to know when recovery starts, how long it takes, and how we can improve it. This study revisits dynamic stall reattachment to identify the sequence of events during flow and load recovery and to characterise key observable features in the pressure, force, and flow field. Our analysis is based on time-resolved velocity field and surface pressure data obtained experimentally for a two-dimensional, sinusoidally pitching thin airfoil. Stall recovery is a transient process that does not start immediately when the angle of attack falls below the critical stall angle. The onset of recovery is delayed to angles below the critical stall angle and the duration of the reattachment delay decreases with increasing unsteadiness of the pitching motion. An angle of attack below the critical angle is a necessary, but not sufficient condition to initiate the stall recovery process. We identified a critical value of the leading-edge suction parameter, independent of the pitch rate, that is a threshold beyond which reattachment consistently initiates. Based on prominent changes in the evolution of the shear layer, the leading-edge suction, and the lift deficit due to stall, we divided the reattachment process into three stages: the reaction delay, wave propagation, and the relaxation stage, and extracted the characteristic features and time-scales for each stage.

Figures (12)

• Figure 1: Spatio-temporal evolution of the suction-side surface pressure coefficient (a) and temporal evolution of the lift coefficient (b) for a selected pitching cycle indicated by the solid black line (${\alpha}_{\hbox{0}}=\ang{20}$, ${\alpha}_{\hbox{1}}=\ang{8}$, $k=0.05$, ${\dot{\alpha}}_{\hbox{ss}}=0.0135$). The shaded gray bands in the lift evolution represent the area between the minimum and maximum envelopes obtained from 39.0 recorded cycles. The thick dashed line shows the quasi-static evolution of the lift coefficient ${C}_{\hbox{l,qs}}$. Vertical dashed lines indicate the moment the static stall angle is exceeded during pitch-up (${t}_{\hbox{ss $\nearrow$}}$) and the moment the angle of attack falls below the static stall angle during pitch-down (${t}_{\hbox{ss $\searrow$}}$). The extra axis on top indicated the angle of attack variation for the cycle. The extra axis below indicated the non-dimenional time variation shifted based on the instant the geometric angle of attack falls below the critical static stall angle during the pitch-down motion (${t}_{\hbox{ss $\searrow$}}$).
• Figure 2: Combined visualisation of the instantaneous chord wise surface pressure distribution on the suction side and the nFTLE and pFTLE ridges for three selected time instants immediately following dynamic stall onset for the sinusoidal pitching motion presented in \ref{['fig:forcepanel']} ($\alpha=\ang{27.2}$ (a), $\alpha=\ang{27.3}$ (b), $\alpha=\ang{27.4}$ (c)). The pressure distribution is visualised by arrows normal to the surface, where the length of arrow indicates the magnitude of the pressure coefficient. Only negative pressure coefficients are displayed. The intersection of the nFTLE (red) and pFTLE (blue) ridges indicates the location of a saddle point.
• Figure 3: (a) Temporal evolution of the lift deficit due to stall $({C}_{\hbox{l,qs}} - {C}_{\hbox{l}})$ and selected snapshots of the vorticity and nFTLE fields during dynamic stall reattachment for the selected pitching cycle in \ref{['fig:forcepanel']}. Snapshots (b1)-(b5) correspond to the marked instants b1-b5 on the lift deficit, ranging from the angle of attack dropping below the static stall angle (b1) to the point where the lift deficit converges to zero (b5). The range from (b1) to (b5) is highlighted by the shaded region and marks the entire dynamic stall reattachment process.
• Figure 4: (a-c) All nFTLE ridges extracted during the reattachment process, grouped into three time intervals. Ridges are coloured based on the timing and angle of attack of the instantaneous snapshots from which they were extracted. (d) Schematic illustration of the definitions of the angle of attack $\alpha$, ridge angle relative to the chord $\beta$, and ridge angle relative to the incoming flow $\gamma = (\beta - \alpha$). (e) Temporal evolution of the shear layer angle relative to the chord $\beta$, for the selected cycle. (f) Temporal evolution of the shear layer angle relative to the incoming flow direction ($\gamma$). The shaded areas in (e) and (f) correspond to the duration of the three intervals indicated in (a)-(c) for the selected pitch cycle.
• Figure 5: (a) Example snapshot of the nFTLE ridge and horizontal velocity component ($u/{\textrm{U}}_{\hbox{$\infty$}}$) during the reattachment process ($\alpha=\ang{17.3}$, $t/T=0.81$). The transition points identified by the surface velocity reversal point (${u}_{\hbox{surf}}=0$) and the nFTLE ridge intersection are marked on the airfoil. (b) Temporal evolution of the transition points overlaid on the surface pressure field during the pitch-down part of the cycle.