A force reduced-order approach for optimal control of turbulent analysis and perturbation method

In this article, a forced reduced-order modeling approach, suitable for active optimal control of uid dynamical systems, based on the Proper Orthogonal Decomposition and perturbation method on the Reynolds-Averaged Navier-Stokes equations, is presented. Numerical simulation of turbulent ow equations is too costly for the purpose of optimization and control of unsteady ows. As a result, the POD/Galerkin projection and perturbation method on the RANS equations is considered. Using the perturbation method, the controlling parameter shows up explicitly in the forced reduced-order system. The feedback control of the controlling parameter is one of the objectives of this study. With the perturbation method, the eect of the controller is sensed by the uid ow at each time step. The eectiveness of this method has been shown on optimal control of the re-circulation problem for a turbulent ow over a step with blowing/suction controlling jets. Actuators are positioned at two dierent locations; blowing/suction jets at the foot and edge of the step, and blowing/suction jets at the wall of the step. Results show that the perturbation method is fast and accurate in estimating the re-circulated turbulent ow over a step. It is concluded that blowing/suction jets at the wall of the step are more ecient in mitigating ow separation.