Effect of different vortex models on the linear instability characteristics of wingtip vortex

Abstract

Different analytical vortex models have been developed to characterize the evolution of wingtip vortex. However, their effect on the instability characteristics has not been well recognized. In this paper, the wingtip vortex generated by an elliptical wing was first experimentally measured in the near-wake and far-wake regions by particle image velocimetry. Then, it was fitted to different one-scale and multiscale vortex models as the base flow for linear stability analysis. The results show that though the eigenvalue spectra by different vortex models exhibit a unified topology with an isolated point around ωi=0 and three continuous branches, the multiscale vortex models tend to overestimate the instability of the wingtip vortex nonphysically. Furthermore, structures of the most unstable eigenmodes (Mode C) also differ between one-scale and multiscale vortex models. On this basis, a meaningful parameter, penetration depth (dp), is defined to predict the instability behavior of one perturbation mode. It is found that the most unstable streamwise wavenumber coincides with the streamwise wavenumber, where 1−dp is the local minimum, regardless of vortex models. The negative correlation between ωi and 1−dp of Mode C indicates that the closer the perturbation vorticity to the vortex boundary, the larger the growth rate. This reminds us that the penetration length might be a candidate measure of the instability behavior of perturbation modes, which deserves to be further studied in a broader parameter space.