Assessment of prevalent vortex-center detection criteria for the compensation of wandering motion of wingtip vortices

Abstract

Vortex wandering, characterized as low-frequency displacements of vortex core locations, significantly affects the quantification of vortex statistics. To mitigate this impact, re-centering correction is a commonly employed method for post-processing velocity-field datasets being measured by particle image velocimetry (PIV). One of the key problems in this method is how to precisely detect instantaneous vortex centers. In this paper, eight prevalent vortex-center detection criteria are empirically evaluated, with the purpose of finding the most practical criterion for the compensation of vortex wandering. Cross-stream velocity fields in the near-wake and middle-wake regions of either an isolated vortex or a counter-rotating vortex pair, being measured by time-resolved stereoscopic PIV, are post-processed by re-centering correction with various vortex-center detection criteria, which are categorized as local or non-local methods with velocity-based or velocity-gradient-based measures. The yielded instantaneous vortex centers and vortex kinematical statistics, including mean velocity profiles and turbulent statistics, are compared in detail. It is found that the pseudo-circulation criterion, which is a velocity-based non-local method, outperforms all the other tested criteria. Once applying the pseudo-circulation criterion to decompose the instantaneous velocity field into triple components, i.e., mean component, large-scale motion and small-scale turbulent fluctuation, the pseudo-fluctuation from vortex wandering can be effectively peeled off from small-scale turbulent fluctuation, resulting in the most compact vortex profile, as well as the lowest level of small-scale turbulent kinetic energy and Reynolds shear stress in the vortex core region. Such an advance makes it an ideal vortex-center detection criterion to study either wingtip vortex instability or energy transfer characteristics associated with the vortex wandering motion.