Dynamic interlinking between near- and far-field wakes behind a pitching–heaving airfoil

Abstract

This study investigates the transitional wake dynamics of a simultaneously pitching– heaving airfoil in the low Reynolds number regime. The transition from Kármán to reverse Kármán wakes and the subsequent wake deflection are known to take place entirely in the periodic regime as the dynamic heave velocity $\kappa h$ (proportionally, the amplitude-based Strouhal number $St_A$ ) is gradually increased. However, further increase in $\kappa h$ may result in the loss of dynamic stability of the deflected vortex street and an eventual transition to chaos. This phenomenon has largely remained unexplored in the existing literature. The present study attempts to fill this gap and aims to establish a dynamic link between the near- and far-field wake transitions. It is shown that the deflected jet undergoes a switching of deflection direction in the far-field as the near-field encounters a quasi-periodic transition with the increase in $\kappa h$ . The quasi-periodic behaviour of the near-field is seen to get interspersed with intermittent aperiodic windows, resulting in a complete reversal of the deflection direction through flipping of the immediate vortex couple. Eventually, the wake topology becomes fully chaotic through a series of rapid aperiodic jet-switching. To the best of the authors’ knowledge, this is the first study that investigates the role of this aperiodic jet-switching in ushering in chaos in the wake of a pitch–heave flapping system. The mechanism of jet-switching and the role of leading-edge vortex are also revealed. Flow field dynamics during these changes and the underlying vortex interactions are analysed using nonlinear dynamical tools.