Effect of Root Cutout on Force Coefficients of Rotating Wings

摘要

Experiments were performed to evaluate the effect or root cutout on the lift and drag of an aspect ratio 2 rotating wing at a 45 deg angle of attack. Two local maxima were observed in the force coefficient histories for all root cutouts, the first of which occurred at the end of wing acceleration and was a result of noncirculatory effects. The magnitude and location of the second local maxima were found to vary with the root cutout. When forces were normalized using the root-relative method, in which the reference plane is defined at 75% of the distance from the wing root to the wing tip, the difference in average velocity across the span was removed by normalizing lift and drag by the integral of the velocity along the wingspan. As a result of this normalization, the force histories collapsed up to approximately 2.5 chord lengths of travel. As the motion progressed, the various root cutout cases diverged, with a decline in lift greater for increasing the root cutout. This intuitively comported with viewing the translating case as a rotation with a root cutout approaching infinity. One can surmise that the decline in lift was related to increasing three dimensionality in the flow, i.e., increased influence of the root and tip vortices, which took time to develop from the onset of motion or the end of the accelerating phase of the motion. Both methods of normalizations have their pros and cons. Using the axis-relative method, the force curves became similar after several chord lengths traveled, and thus this method is more relevant to a study of the steady-state behavior. Conversely, the root-relative method collapsed the curves during the lift transient near the start of the wing motion and is thus more useful for the analysis of low-amplitude wing strokes that are not expected to reach a steady state.