Reynolds Number Validation of Stall Hysteresis Hypothesis

Wind tunnel tests were undertaken at the United States Air Force Academy’s (USAFA’s) Sub-Sonic wind tunnel (SWT) to validate or refute the previous hypothesis for stall hysteresis [0]. An explanation for the difference in separation and reattachment angle during stall on two-dimensional airfoils was offered in previous work [0], utilizing stall prediction theory [1] and potential flow theory [2,3] and was supported by follow-up work [4]. It is observed, at moderate to high Reynolds numbers, when an airfoil’s angle of attack is increased beyond the angle for (catastrophic) stall, the flow does not reattach at the same angle when lowering the angle of attack again. For this work, the reattachment angle is defined as the angle where the stall-dominated flow regime is convected downstream, replaced by an attached flow state, while decreasing the angle of attack. By contrast, the separation or catastrophe angle is the stall angle encountered when increasing the angle of attack from an attached flow state to a stall-dominated state. The difference between the separation angle and the reattachment angle is the size of the hysteresis loop. Within the clockwise hysteresis loop there exist two distinct airfoil geometries: the physical and the effective. The physical, or actual airfoil geometry, dominates the behavior of the pre-catastrophic lift-curve – albeit somewhat modified by the boundary layer at higher angles. The much longer effective body dominates the hysteresis loop from catastrophic stall to reattachment. The effective body (encompassing the physical body) is what the flow “sees” from the potential flow perspective. Longer, and therefore thinner, airfoils stall at lower angles than comparatively thicker ones. Previous investigations [1,4] demonstrate support for current hypothesis for the NACA 0012 at Re = 4.75 x 10^5 (corresponding effective body Re ~ 1.3M). This current work extends investigations to higher Reynolds number on the NACA 0012 (~3/4M) and the associated effective body (~2.0M) with good agreement. Future tests will include other geometries, as well. However, due to the lengthening from the physical to the effective body (chordwise increase), combined with a minimum Reynolds number (~1/2M) to record a large enough hysteresis loop to investigate, difficulties arise with having wind tunnels capable of testing effective bodies – hence it is concluded to conduct parallel computational investigations in the future. Finally, an additional hypothesis for prediction of the general effective body shape is offered based on the current results.