A force reduced-order approach for optimal control of turbulent flow over backward-facing step using POD analysis and perturbation method

Abstract

In this article, a forced reduced-order modeling approach, suitable for active optimal control of fluid dynamical systems based on the Proper Orthogonal Decomposition and perturbation method on the Reynolds-Averaged Navier-Stokes equations is presented. Numerical simulation of turbulent flow equations is too costly for the purpose of optimization and control of unsteady flows. As a result, POD/Galerkin projection and perturbation method on the RANS equations is considered. Using 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 effect of the controller is sensed by fluid flow in each time step. The effectiveness of this method has been shown on optimal control of re-circulation problem for the turbulent flow over step with blowing/suction controlling jets. Actuators are positioned at two different 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 perturbation method is fast and accurate in estimating the re-circulated turbulent flow over step. It is concluded that blowing/suction jets at the wall of the step are more efficient in mitigating flow separation.