A Hypothesis of Stall Hysteresis - Why the reattachment angle is less than the separation stall angle

摘要

An explanation for the difference in separation and reattachment angle during stall on two-dimensional airfoils is offered here, utilizing stall prediction theory [1] and potential flow theory [2]. It is observed when an airfoil's angle of attack is increased beyond the angle for stall that the flow does not reattach at the same (separation) angle when lowering the angle of attack again. Here, the reattachment angle is defined as where the stalled flow regime is convected away, reestablishing an attached flow state. Whereas, the separation angle is the stall angle encountered when increasing the angle of attack during an attached flow state. The difference between the separation angle and the reattachment angle, or the size of the hysteresis loop, grows with Reynolds number. It is proposed that in 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. The effective body dominates the hysteresis loop from catastrophic stall to reattachment. The effective body, from the potential flow perspective, is the physical airfoil along with the recirculating wake behind it. This effective body "appears" as a longer, and therefore thinner airfoil, with possibly some negative camber. Numerical simulations are run to determine the shape of the effective body via minimum shear compared to the freestream. Stall prediction theory and experimental data are used to determine the stall angle of the effective body. It is found that, where hysteresis data is available for comparison, the reattachment angle of a given airfoil geometry agrees with the stall/separation angle of the associated effective body to within a fraction of a degree. Wind tunnel tests of the effective body of a NACA 0012 at Re = 4.75xl05 were conducted at the Doryland Wind Tunnel at Embry-Riddle Aeronautical University (ERAU) with excellent agreement. More tests are in progress for other Reynolds number on the NACA 0012. Future tests will include other geometries.