Phase sensitivity analysis of post-stall airfoil wakes.

Phase reduction analysis of time-periodic flows reveals perturbation dynamics with respect to the base flow scalar phase variable. Synchronization properties of the unsteady flows can be derived from the high-fidelity phase sensitivity fields (Z ) obtained from the adjoint-based phase reduction analysis. We use this technique to determine the influence of perturbations around post-stall airfoils on their phase dynamics. We consider symmetric airfoils of different thicknesses at post-stall angles of attack (α) for Re = 100. We observe that the influence of α on Z is significant compared to that of thickness. For lower α, the phase can be altered with less actuation input as reflected in the large magnitudes of Z around the airfoil. This follows from the wake dynamics as perturbing the large vortices formed at higher α requires larger actuation input. The Z fields are found to scale with the lift force with high sensitivity around the leading and trailing edges. The present approach can support open loop unsteady flow control strategies by accelerating or decelerating vortex shedding over different bodies.