Effect of radius of gyration on a wing rotating at low Reynolds number: a computational study

This computational study analyzes the effect of variation of the radius of gyration (rg), expressed as the Rossby number Ro=rg/C, with C the chord, on the aerodynamics of a rotating wing at a Reynolds number of 1400. The wing is represented as an aspect-ratio-unity rectangular flat plate aligned at 45. This plate is accelerated near impulsively to a constant rotational velocity and the flow is allowed to develop. Flow structures are analyzed and force coefficients evaluated. Trends in velocity field degradation with increasing Ro are consistent with previous experimental studies. At low Ro the flow structure generated initially is mostly retained with a strong laminar leading-edge vortex (LEV) and tip vortex (TV). As both Ro and travel distance increase, the flow structure degrades such that at high Ro it begins to resemble that of a translating wing. Additionally, the present study has shown the following. (i) At low Ro the LEV and TV structure is laminar and steady; as Ro increases this structure breaks down, and the location at which it breaks down shifts closer to the wing root. (ii) For moderate Ro of 1.4 and higher, the LEV is no longer steady but enters a shedding regime fed by the leading-edge shear layer. (iii) At the lowest Ro of 0.7 the lift force rises during start-up and then stabilizes, consistent with the flow structure being retained, while for higher Ro a force peak occurs after the initial acceleration is complete, followed by a reduction in lift which appears to correspond to shedding of excess leading-edge vorticity generated during start-up. (iv) All rotating wings produced greater lift than a translating wing, this increase varied from ∼65% at the lowest Ro=0.7 down to ∼5% for the highest Ro examined of 9.1.