A Methodology for the Automated Optimal Control of Flows including Transitional Flows

This paper describes a self-contained, automated methodology for active flow control which couples the time-dependent Navier-Stokes system with the adjoint Navier-Stokes system and optimality conditions from which optimal states, i.e., unsteady flow fields and controls (e.g., actuators), may be determined. The problem of boundary-layer instability suppression through wave cancellation is used as the initial validation case to test the methodology. Here, the objective of control is to match the wall-normal stress along a portion of the boundary to a given vector; instability suppression is achieved by choosing the given vector to be that of a steady base flow. Control is effected through the injection or suction of fluid through a single orifice on the boundary. The results demonstrate that instability suppression can be achieved without any a prior knowledge of the disturbance. The present methodology may potentially be applied to separation control, relaminarization, and turbulence control applications using one or more sensors and actuators.