A systems theory approach to control of transitional and turbulent flows

Various linear optimal controllers based on a systems theory approach are designed and applied to transitional channel flow for suppressing the disturbance wall-shear stress. Linear Quadratic Regulator (LQR) controllers based on the Single-Input-Single-Output (SISO) and Multi-Input-Multi-Output (MIMO) system model are not only able to stabilize a transitional flow, but also robust to the uncertainty of Reynolds number. A practical Linear Quadratic Gaussian (LQG) controller/estimator which requires only the wall information also stabilizes a transitional flow.; A realistic two-dimensional controller is designed using both the modern technique of reducing the order of system and the modern optimal control technique, LQG ($H2$)/Loop Transfer Recovery (LTR) synthesis. The robust reduced-order linear controller applied at the wall efficiently reduces the finite near-wall disturbances in a two-dimensional channel flow at Re = 1500. It also produces a substantial drag reduction. In a secondary instability flow, it attenuates the two-dimensional disturbance energy rapidly, so that it inhibits transition to turbulence.; The two-dimensional robust reduced-order linear controller is applied to a fully-developed turbulent flow for drag reduction. Depending on the streamwise disturbance wall-shear stress, it reduces the skin-friction by 10% in direct numerical simulation of a low Reynolds number turbulent channel flow. The two-dimensional controller reinforced with a simple ad-hoc control scheme enhances the drag reduction by 17%. The turbulence intensity and the Reynolds stress are also significantly reduced throughout the channel. The ad-hoc control creates streamwise vorticity at the wall that counteracts near-wall streamwise vorticity, thereby enhancing the drag reduction further.