Reactive control of isolated unsteady streaks in a laminar boundary layer

Abstract

This study is motivated by controlling transient growth and subsequent bypass transition of the laminar boundary layer to turbulence. In experiments employing a model problem, an active roughness element is used to introduce steady/unsteady streak disturbances in a Blasius boundary layer. This tractable arrangement enables a systematic investigation of the evolution of the disturbances and of potential methods to control them in real time. The control strategy utilizes wall-shear-stress sensors, upstream and downstream of a plasma actuator, as inputs to a model-based controller. The controller is designed using empirical input/output data to determine the parameters of simple models, approximating the boundary layer dynamics. The models are used to tune feedforward and feedback controllers. The control effect is examined over a range of roughness-element heights, free stream velocities, feedback sensor positions, unsteady disturbance frequencies and control strategies; and is found to nearly completely cancel the steady-state disturbance at the downstream sensor location. The control of unsteady disturbances exhibits a limited bandwidth of less than 1.3 Hz. However, concurrent modelling demonstrates that substantially higher bandwidth is achievable by improving the feedforward controller and/or optimizing the feedback sensor location. Moreover, the model analysis shows that the difference in the convective time delay of the roughness- and actuator-induced disturbances over the control domain must be known with high accuracy for effective feedforward control. This poses a limitation for control effectiveness in a stochastic environment, such as in bypass transition beneath a turbulent free stream; nonetheless, feedback can remedy some of this limitation.