Radial planetary vorticity tilting in the leading-edge vortex of revolving wings

Abstract

Previous studies suggested that Coriolis acceleration and spanwise flow both played key roles in stabilizing the leading-edge vortex (LEV) in revolving wings. The current study examined a mechanism that relates the effects of Coriolis acceleration, spanwise flow, and the tilting of the planetary vorticity on removing the radial component of LEV vorticity. Specifically, the fluid particles moving with the spanwise flow toward the wing tip are expected to experience tangential Coriolis acceleration in the wing-fixed rotating frame; therefore, a vertical gradient in spanwise flow can create a vertical gradient in the Coriolis acceleration, which will in turn produce oppositely signed radial vorticity within the LEV. This gradient of Coriolis acceleration corresponds to the radial component of planetary vorticity tilting (PVTr) that reorients the planetary vorticity into the spanwise (radial) direction, therefore producing oppositely signed radial vorticity. Using an in-house, immersed-boundary-method flow solver, this mechanism was investigated alongside the other vorticity dynamics for revolving wings of varying aspect ratio (AR = 3, 5, and 7) and Reynolds number (Re = 110 and 1400). Analyses of vorticity dynamics showed that the PVTr consistently produced oppositely signed vorticity for all values of AR and Re investigated, although other three-dimensional phenomena play a similar but more dominant role when Re = 1400. In addition, the relative strength of the PVTr increased with increasing AR due to a decrease in the magnitude of advection. Finally, a dimensional analysis was performed on the advection and PVTr for the different AR and Re.