Book Description
The problem of controlling turbulent boundary layers was studied using techniques employed in control system analysis and design. During the last three years, the linearized Navier-Stokes equations were modified to include a boundary input of blowing/suction along the wall. By a Galerkin method, the modified linearized Navier-Stokes equations were converted into a temporal control theoretical model, to which modern control synthesis can be applied. The resulting state space model allows a multivariable feedback design combining an array of sensors with an array of actuators along the wall. Based on this spectral decomposition, a parallel architecture for the implementation of temporal controllers allows significant decrease in computational bandwidth. For each wavenumber linear- quadratic-Gaussian multivariable synthesis and model reduction techniques are used to derive robust feedback controllers. Controller performance was tested on a direct numerical simulation of a fully developed turbulent channel flow. Controller performance for the nonlinear flow was surprisingly good, suggesting that linear systems can be used as a basis for developing controllers for near-wall turbulence. Controllers are being developed on the basis of the three dimensional linearized Navier-Stokes equations. Both spanwise and streamwise shear sensors are considered. By a Galerkin method, a temporal state space model is determined where, for every wave number pair, a 500 state system is obtained with two inputs and four outputs. Model reduction techniques are used to reduce the state space drastically, and wave number pairs that produce the largest shear stress amplification for uncertainty induced at the wall are investigated.
