Adaptive control of low-Reynolds number aerodynamics in uncertain environments: Part 2. Vortex dynamics and system modeling under stall

A major challenge in unsteady aerodynamics is to handle uncertain free-stream and maintain desired performance. Closed-loop flow control provides substantial opportunities to help accomplish this goal. Effective control of unsteady aerodynamics can substantially benefit from proper pairing of system modeling and control law so that the system nonlinearity can be adequately addressed. In this second part of the paper, the low-Reynolds number airfoil equipped with the dielectric barrier discharge (DBD) actuator is investigated to shed light on both flow physics and system dynamics. In this flow regime, combined with unsteady free-stream, the evolution of separation bubble can significantly influence the force evolution. Specifically, anisotropic bubble expansion, namely, rapid bubble spread, is explored and linked to the temporal and spatial scales caused by the free-stream disturbances. The initiation and duration of the spread as well as bubble's convection speed are closely related to the slope and magnitude of the disturbance. In addition, two criteria about static stall angle match well with the disturbance regimes proposed in the first part of the paper. Furthermore, the system's nonlinearity is assessed utilizing parameter estimate techniques, suggesting both stall vortex evolution and free-vortex shedding stages accompany significant changes in system parameter estimates.