A scaling for vortex formation on swept and unswept pitching wings

Abstract

We examine the dynamics of the leading-edge vortex (LEV) on a rapidly pitching plate with the aim of elucidating the underlying flow physics that dictates the stability and circulation of the LEV. A wide variety of flow conditions is considered in the present study by systematically varying the leading-edge sweep angle ($\unicode[STIX]{x1D6EC}=0^{\circ }$, $11.3^{\circ }$, $16.7^{\circ }$) and the reduced frequency ($f^{\ast }=0.064{-}0.151$), while keeping the pitching amplitude and the Reynolds number fixed. Tomographic particle image velocimetry is used to characterise the three-dimensional fluid motion inside the vortex core and its relation to the LEV stability and growth. A series of control volume analyses are performed to quantify the relative importance of the vorticity transport phenomena taking place inside the LEV to the overall vortex development. We show that, near the wing apex where tip effects can be neglected, the vortex develops in a nominally two-dimensional manner, despite the presence of inherently three-dimensional vortex dynamics such as vortex stretching and compression. Furthermore, we demonstrate that the vortex formation time and circulation growth are well-described by the principles of optimal vortex formation number, and that the occurrence of vortex shedding is dictated by the relative energetics of the feeding shear layer and the resulting vortex.