Inflow Velocity and Rotational Effects on Revolving and Translating Wings

Abstract

An aspect ratio 9.5 rectangular wing is articulated in revolving and translating motions at a 45-degree angle of incidence and Reynolds number Re = O(300). Four cases are considered while varying two salient aspects of rotational motion. Coriolis and centripetal accelerations are present in the rotating cases and absent in the translating cases, whereas uniform and linearly-varying inflow velocity profiles are imposed on instances of the rotating and translating cases. Each case exhibits distinct leading-edge vortex (LEV) growth and behavior. For the range of displacements studied (180 deg. rotation and corresponding translational displacement) a stably attached LEV is observed when rotational accelerations and/or a linearly-varying inflow velocity profile is present; however, the inflow velocity profile has a stronger effect on stability of the LEV. LEV vorticity magnitude and lift force are significantly augmented when both factors are included (i.e. the full revolving wing case). Vorticity transport analyses are conducted in a planar control region two chords from the axis of rotation, where three-dimensional vorticity transport is shown to be important in mitigating LEV growth, and at an equivalent distance from the wing root in the translating case. The revolving wing exhibits a substantially larger leading-edge shear-layer vorticity flux than the other cases. Inspection of the Coriolis tilting term demonstrates little relevance to LEV stability. In all cases, the surface diffusive flux and shear-layer vorticity flux contributions are found to be negatively correlated. Additionally, a correlation is found between the spanwise convective flux and tilting flux contributions in all cases. Decomposition of the spanwise convective flux reveals that the tilting flux is a constituent of it, demonstrating that the two phenomena are kinematically linked. Based on this result, a significantly simplified vorticity transport equation is developed in which all of the three-dimensional transport fluxes are consolidated into a single term, providing new physical interpretation of these terms.