Suppression of Unsteady Boundary-Layer Separation Using Sub-Optimal Control

A two-dimensional channel with localized suction from the upper surface is considered as a framework within which to consider sub-optimal control of an unsteady separating bound-ary layer. A quasi-steady (sub-optimal) approach is adopted in which the control input is optimized at each time as the unsteady flow evolves. Two cost functionals are implemented and compared; they both use a boundary-based performance measure that minimizes the difference between the wall shear stress and a target distribution corresponding to the unseparated boundary layer. The two control mechanisms considered, with corresponding penalty functions in the respective cost functionals, are a domain-based control, involv-ing a body force throughout the boundary layer, and a boundary-based control, involving the normal wall velocity. Both control mechanisms are successful in eliminating unsteady separation, and the relative effectiveness of each approach is compared. I