Optimal waveform for fast entrainment of airfoil wakes

Phase synchronization analysis for time-periodic flows can be characterized using phase reduction analysis. Phase reduction method reduces high-dimensional flow physics to single scalar phase dynamics. The synchronization of phase dynamics to external forcing and optimal waveform of forcing could be obtained from phase sensitivity analysis. We assess the receptivity of the wake through the spatial phase sensitivity fields for laminar flows over symmetric airfoils at high angles of attack. We discuss the framework to obtain the optimal waveform for promoting synchronization of post-stall airfoil wakes to periodic actuation inputs. We investigate the influence of the angle of attack on phase coupling functions and find optimal waveforms based on the spatial phase-sensitivity fields. We observe that phase synchronization becomes harder to achieve for high angle of attack and the corresponding optimal actuation waveform becomes non-sinusoidal. The present analysis for phase synchronization of time-varying flows reveals critical insights for modifying unsteady vortex dynamics with special care toward the time-adaptive nature of actuation.

This work is supported by the US Air Force Office of Scientific Research (FA9550-21-1-0178) and the US National Science Foundation (2129639).