Vorticity dynamics of revolving wings: The role of planetary vortex tilting on the stability of the leading-edge vortex

TL;DR

This study explores how planetary vortex tilting influences the stability of leading-edge vortices in revolving wings, revealing a mechanism involving Coriolis acceleration gradients that stabilizes LEVs across various wing aspect ratios and Reynolds numbers.

Contribution

It introduces a new mechanism linking planetary vortex tilting and Coriolis acceleration gradients to LEV stability, supported by detailed vorticity dynamics analysis.

Findings

PVTr consistently produces oppositely-signed vorticity across all tested conditions.

The strength of PVTr increases with wing aspect ratio due to reduced advection.

Other three-dimensional effects become more dominant at higher Reynolds numbers.

Abstract

This work investigated the vorticity dynamics and stability of leading-edge vortices (LEVs) in revolving wings. Previous studies suggested that Coriolis acceleration and spanwise flow both played key roles in stabilizing the LEV; however, the exact mechanism remains unclear. The current study examined a mechanism that relates the effects of Coriolis acceleration, spanwise flow, and the tilting of the planetary vortex on limiting the growth of the LEV. Specifically, this mechanism states that a vertical gradient in spanwise flow can create a vertical gradient in Coriolis acceleration, which will in turn produce oppositely-signed vorticity within the LEV. This gradient of Coriolis acceleration corresponds to the spanwise (radial) component of planetary vortex tilting (PVTr) that reorients the planetary vortex into the spanwise direction therefore creating oppositely-signed LEV 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, the effects of AR and Re on the vorticity dynamics and LEV stability were also investigated.