Identifying the route to chaos in the flow past a flapping airfoil

Chaotic wake patterns in the flow past flapping airfoils have been reported earlier for high plunge velocities. The present work focuses on analysing the dynamics and identifying the route to chaos in this phenomenon. The unsteady flow-field is investigated using an incompressible Navier–Stokes solver. A bifurcation analysis with the plunge amplitude as the control parameter reveals that, for high plunge amplitudes, periodic vortex patterns in the wake are interrupted by abrupt chaotic patterns. The frequency of occurrence of these chaotic patterns increases on further increasing the bifurcation parameter and eventually the flow-field becomes completely chaotic. This behaviour is typically observed in systems exhibiting intermittency route to chaos, and to the best of our knowledge this has not been reported for flows past flapping airfoils. The intermittency route to chaos is conclusively established using techniques from time series analysis, such as, phase space reconstruction and recurrence plots. A qualitative analysis of the patterns in the recurrence plots is used to identify the type of intermittency to be Type I. Moreover, the implication of Type I intermittency into the flow dynamics has been studied through various vortex interaction mechanisms and its effect on the thrust generation. Quantitative measures obtained from the recurrence plots provide more insights into the dynamics as well as an early indication for the onset of chaos.