A realizable data-driven approach to delay bypass transition with control theory

Abstract

The current work presents a realizable method to control streaky disturbances\nin boundary layer flows and delay transition to turbulence via active flow\ncontrol. Numerical simulations of the nonlinear transitional regime in a\nBlasius boundary layer are performed where streaks are excited in the boundary\nlayer via a high level of free-stream turbulence (FST). The occurring\ndisturbances are measured via localized wall sensors and damped via near-wall\nactuators resembling plasma actuators. The time-varying amplitude of the signal\nof each actuator is computed by processing signals from the sensors. This\nprocessing is the result of two control laws: the Linear Quadratic Gaussian\nregulator (LQG) and the Inverse Feed-Forward Control technique (IFFC). The use\nof the first, LQG, requires a state-space representation of the system\ndynamics, so the flow is described via an operator that captures only the most\nrelevant information of the dynamics and results in a reduced order model\n(ROM). The ROM is computed via the eigensystem realization algorithm, based on\nthe impulse responses of the real system. Collecting such impulse responses may\nbe unfeasible when considering FST because of the high dimensionality of the\ninput forcing needed for a precise description of such a phenomenon. Here, a\nnew method to identify the relevant system dynamics and generate the needed\nimpulse responses is proposed, in a data-driven approach that would be\nrealizable in experiments. Finally, the effectiveness of the technique in\ndelaying bypass transition is shown. The work (i) presents a systematic way to\ndeal with high dimensional disturbances to build ROMs for a control technique,\nand (ii) shows that even when considering constraints such as the type and size\nof actuators and sensors, it is possible to achieve at least as large delay of\nbypass transition as that obtained in more idealized cases found in literature.\n