Effect of vortex dynamics and instability characteristics on the induced drag of trailing vortices

In this paper, trailing vortices generated by three wingtip configurations, namely the M6 wing and the M6 wing with a blended or split winglet, are experimentally investigated using the Stereo Particle Image Velocimetry (SPIV) technology. Then, linear stability analysis is performed to investigate instability characteristics. Three corresponding trailing vortex patterns, including the isolated trailing vortex without wake (pattern v) and with wake (pattern v-w), co-rotating vortex pair (pattern v-v), are observed in experiments. The strength of trailing vortices, characterized by circulation, is reduced after installing winglets as expected, and the strength of pattern v-v can be further suppressed compared with pattern v-w. Moreover, instability characteristics, such as the eigenvalue spectrum and perturbation mode, are distinctive among these three vortex patterns. The distribution of eigenvalue spectrums indicates that pattern v and pattern v-w are temporally ‘‘marginally stable”, while pattern v-v is temporally ‘‘unstable.” The primary perturbation mode of pattern v and pattern v-w is the m = –1 helical mode, while |m|>1 for the case of pattern v-v. The effect of vortex dynamics and instability characteristics can be concluded in two aspects. Firstly, the value of induced drag is polluted by about 3% from vortex wandering since vortex wandering affects the tangential velocity and streamwise vorticity of trailing vortices. Secondly, the growth rate and penetration depth perturbation mode affect trailing vortex evolution and further affect induced drag. Specifically, the larger the growth rate and penetration depth are, the more turbulence injects inside the vortex core, thus leading to a quicker and more intense attenuation of trailing vortex, as well as a smaller induced drag. This finding can guide us to manipulate the induced drag in flow control.