Feedback control of laminar flow separation on NACA23012 airfoil by POD analysis and using perturbed Navier-Stokes equations

The main purpose of this article is to develop a forced reduced-order model based on the proper orthogonal decomposition (POD)/Galerkin projection (on isentropic Navier-Stokes equations) and perturbation method on the compressible Navier-Stokes equations. The resulting forced reduced-order model will be used in optimal control of the separated flow over a NACA23012 airfoil at Mach number of 0.2, Reynolds number of 800, and high incidence angle of 24 degrees. The main disadvantage of the POD/Galerkin projection method for control purposes is that controlling parameters do not show up explicitly in the resulting reduced-order system. The perturbation method and POD/Galerkin projection on the isentropic Navier-Stokes equations introduce a forced reduced-order model that can predict the time varying influence of the controlling parameters and the Navier-Stokes response to external excitations. An optimal control theory based on forced reduced-order system is used to design a control law for a nonlinear reduced-order system, which attempts to minimize the vorticity content in the flow field. The test bed is a laminar flow over NACA23012 airfoil actuated by a suction jet at 12% to 18% chord from leading edge and a pair of blowing/suction jets at 15% to 18% and 24% to 30% chord from leading edge, respectively. The results show that wall jet can significantly influence the flow field, remove separation bubbles, and increase the lift coefficient up to 22%, while the perturbation method can predict the flow field in an accurate manner.