In this thesis a nonlinear optimal control algorithm is designed to suppress bypass transition in a zero pressure gradient boundary layer subjected to free stream vortical disturbances using direct numerical simulation (DNS). The inflow condition is a superposition of the Blasius velocity profile and two modes of the continuous spectrum of the Orr- Sommerfeld and Squire equations. Transition is realised through the outer secondary instability mode, which results from the interaction between the elevated low speed streaks and the high frequency mode in the free stream. The optimal control problem is solved using a Lagrange variational technique that results in a set of linearised adjoint equations. The optimal wall actuation (blowing and suction from a control slot located in the transition region) is found by solving iteratively the nonlinear Navier-Stokes and the adjoint equations in a forward/backward loop over a finite time horizon.
The optimal controller is effective in reducing the flow energy in a single optimisation horizon. It is found that the optimal control velocity has mean positive value (indicating net blowing) when there is no constraint on mass flow rate and its distribution reflects the flow above the control slot during the short optimisation time. Optimisation over longer time is limited by adjoint instability due to the chaotic nature of the uncontrolled flow. A receding horizon approach is used in order to compute the control velocity for longer time. A different control mechanism is observed as the optimisation time covers the full transition process and the optimal control reacts to it. Zero mass flow rate constraint enforces negative control velocity in the upstream side of the slot. The results show that the resulting adverse pressure gradient (due to suction) leads to abrupt transition in the upstream side of the slot, and control with this constraint is less efficient.