A methodology for optimal laminar flow control: Application to the damping of Tollmien-Schlichting waves in a boundary layer

A methodology for determining the optimal steady suction distribution for the delay of transition in a boundary layer is presented. The flow state is obtained from the coupled system of boundary layer equations and parabolized stability equations (PSE), to account for the spatially developing nature of the flow. The wall suction is defined by an optimal control procedure based on the iterative solution of the equations for the state and the dual state; the latter is available from the adjoint boundary layer equations and the adjoint PSE. The technique is applied to the control of two-dimensional Tollmien-Schlichting (TS) waves. Results show that the onset of the instability can be significantly postponed and/or the growth rate considerably reduced by applying an appropriate suction through the whole wall length, in a wide frequency band. Control over panels of finite length completes the study and brings useful, preliminary information on the practicality of the approach in view of implementation. Finally, a simplified methodology which does not rely on the PSE is discussed, based on the minimization of the shape factor. Satisfactory results are achieved with this simpler approach which might, thus, constitute a method of choice when results are needed rapidly, i.e., during on-line control of TS waves. (C) 2003 American Institute of Physics.