Active Control and Modal Structures in Transitional Shear Flows

Abstract: Flow control of transitional shear flows is investigated by means of numerical simulations. The attenuation of three-dimensional wavepackets of Tollmien-Schlichting (TS) and streaks in the boundary layer is obtained using active control in combination with localised sensors and actuators distributed near the rigid wall. Due to the dimensions of the discretized Navier-Stokes operator, reduced-order models are identified, preserving the dynamics between the inputs and the outputs of the system. Balanced realizations of the system are computed using balanced truncation and system identification.We demonstrate that the energy growth of the perturbations is substantially and efficiently mitigated, using relatively few sensors and actuators. The robustness of the controller is analysed by varying the number of actuators and sensors, the Reynolds number, the pressure gradient and by investigating the nonlinear, transitional case. We show that delay of the transition from laminar to turbulent flow can be achieved despite the fully linear approach. This configuration can be reproduced in experiments, due to the localisation of sensing and actuation devices.The closed-loop system has been investigated for the corresponding twodimensional case by using full-dimensional optimal controllers computed by solving an iterative optimisation based on the Lagrangian approach. This strategy allows to compare the results achieved using open-loop model reduction with model-free controllers. Finally, a parametric analysis of the actuators/ sensors placement is carried-out to deepen the understanding of the inherent dynamics of the closed-loop. The distinction among two different classes of controllers – feedforward and feedback controllers - is highlighted.A second shear flow, a confined turbulent jet, is investigated using particle image velocimetry (PIV) measurements. Proper orthogonal decomposition (POD) modes and Koopman modes via dynamic mode decomposition (DMD) are computed and analysed for understanding the main features of the flow. The frequencies related to the dominating mechanisms are identified; the most energetic structures show temporal periodicity.