Robust reduced-order control of turbulent channel flows via distributed sensors and actuators

Robust reduced-order feedback control of near-wall turbulence in a channel flow is investigated. Wall-transpiration is the means for suppressing near-wall disturbances. Measurements of wall-shear stress to be fed back to the controller are provided by sensors distributed along the wall of the channel. A quadratic cost function is composed of the wall-shear stress and the control effort. Linear-quadratic-Gaussian/loop-transfer-recovery synthesis, and model reduction techniques are used to derive robust feedback controllers from the linearized two-dimensional Navier-Stokes equations. Controllers' performance is first tested on a numerical simulation of infinitesimal three-dimensional disturbances in the presence of finite-amplitude two-dimensional perturbations. Controllers' performance is subsequently tested on a direct numerical simulation of a fully developed turbulent channel flow. Preliminary controllers' performance for the nonlinear flow was surprisingly good, suggesting that the linear system can be used as a basis for developing controllers for near-wall turbulence.