Closed-Loop Control of Transition by Local Dynamic Surface Modification

Direct numerical simulations (DNSs) were carried out in order reproduce the generation and control of transition on a flat plate by means of local dynamic surface modification. The configurations and flow conditions duplicate those of previous numerical investigations, and are similar to an experimental arrangement, which employed piezoelectrically driven actuators to impart small amplitude local deformation of the plate surface. In those studies, one actuator was located in the upstream plate region, and oscillated at the most unstable frequency of 250 Hz in order to generate small disturbances, which amplified Tollmien–Schlichting instabilities. A second actuator placed downstream, was then oscillated at the same frequency, but with appropriate amplitudes in order to mitigate disturbance growth and delay the evolution of transition. Prior simulations employed an empirical process to determine optimal values of the control parameters. In the current effort, this process is replaced with a closed-loop control law. Numerical solutions are obtained to the two-dimensional and three-dimensional compressible Navier–Stokes equations, utilizing a high-fidelity numerical scheme and an implicit time-marching approach. Local surface modification of the plate is enforced via grid deformation. Results of the simulations are presented, and features of the flowfields are described. Comparisons are made between results obtained with the two control methods, and effectiveness of the closed-loop approach is evaluated.