Vorticity transport in the leading-edge vortex on a rotating blade

Abstract

Vorticity transport is analysed within the leading-edge vortex generated on a rectangular flat plate of aspect ratio 4 undergoing a starting rotation motion in a quiescent fluid. Two analyses are conducted on the inboard half of the blade to better understand the vorticity transport mechanisms responsible for maintaining the quasi-equilibrium state of the leading-edge vortex. An initial global analysis between the 25 and 50 % spanwise positions suggests that, although spanwise velocity is significant, spanwise convection of vorticity is insufficient to balance the flux of vorticity from the leading-edge shear layer. Subsequent detailed analyses of vorticity transport in planar control volumes at the 25 and 50 % spanwise positions verify this conclusion and demonstrate that vorticity annihilation due to interaction between the leading-edge vortex and the opposite-sign layer on the plate surface is an important, often dominant, mechanism for regulation of leading-edge-vortex circulation. Thus, it provides an important condition for maintenance of an attached leading-edge vortex on the inboard portion of the blade.

Determining the relative stability of leading-edge vortices on nominally two-dimensional flapping profiles

“…This analogy between the aspect ratio AR and the reduced frequency k of course neglects effects such as vorticity convection and vortex stretching, which have been shown here to also improve relative LEV stability. In addition to vorticity transport, Wojcik & Buchholz (2014) found that vorticity annihilation was a significant mechanism for regulating LEV growth and was generally much larger in magnitude than vorticity convection. However, as an extension to these findings, it has been shown here that relative LEV stability can be improved by moderating LEV growth through vorticity convection and vortex stretching.…”

“…The effect of vorticity convection on LEV circulation In addition to having a larger limiting length scale for a given circulation, as estimated by the reduced frequency k above, it is hypothesized that relative LEV stability can be improved by moderating circulation growth with vorticity convection. As done by Wojcik & Buchholz (2014), the rate of circulation change due to vorticity convection can be determined from the integral of the unsteady and spanwise convection terms of the vorticity-transport equation across the vortex-core area:…”

“…rotating cases often exhibit vortex stability, where both the convection speed of the LEV relative to the profile and the growth rate of the LEV are near zero, as observed by Ozen & Rockwell (2012), Cheng et al (2013) and Wojcik & Buchholz (2014), to name a few.…”

“…The vorticity generated in the leading-edge shear layer of a rotating profile must therefore be balanced by either the transport or annihilation of vorticity in order to limit vortex growth as a necessary condition for LEV stability. A recent study by Wojcik & Buchholz (2014) conducted a vorticity balance within the LEV on a rotating profile, utilizing direct measurements of the circulation transport through the leading-edge shear layer and via spanwise vorticity convection. It was concluded that spanwise vorticity convection was insufficient to balance vorticity production, and that the large residual in the vorticity balance must be accounted for by vorticity annihilation.…”

Large amplitude flow-induced oscillations and energy harvesting using a cyber-physical pitching plate

“…Recent studies that focused exclusively on characterization of the LEV formation have used predefined kinematic motion of a sharp-edged flat plate to explore the forces induced by pitching (Granlund et al, 2013;Jantzen et al, 2014), rotation (DeVoria and Ringuette, 2012;Wojcik and Buchholz, 2014), and plunging (Rival et al, 2009;Ford and Babinsky, 2013). Numerous studies on pitching and/or plunging wings with sufficient forcing have identified reduced frequency as the primary scaling parameter that determines the flow evolution and unsteady force (see, e.g., Baik et al, 2012;Jantzen et al, 2014).…”