Feedback control of laminar flow behind backward-facing step by POD analysis and using perturbed Navier–Stokes equations

Abstract

The purpose of this article is to design a reduced order model based on the proper orthogonal decomposition/Galerkin projection and perturbation method to develop a non-autonomous model. The resulting model can be used in optimal control of flow over backward-facing step. The main disadvantage of the proper orthogonal decomposition approach for control purposes is that, controlling parameters or inputs do not show up explicitly in the resulting reduced order system. The perturbation method can solve this problem and insert control inputs in the resulting system. The resulting system captures the time-varying influence of the controlling parameters and precisely predicts the Navier–Stokes response to external excitations. At last, optimal control theory is introduced to design a control law for a non-linear forced reduced model, which attempts to minimize the vorticity content in the fluid domain. The test bed is laminar flow behind backward-facing step [Formula: see text] actuated by a pair of blowing/suction jets. Results show that the wall jet can significantly influence the flow field and delay separation, while the perturbation method can predict the flow field in an accurate manner. The method is also found to be fast and efficient in computational time.

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

“…The low‐order models that reduce computational complexity associated with Navier‐Stokes equations and capture the essential dynamics of system were required. The proper orthogonal decomposition (POD) has been extensively discussed in the literature as a reduced‐order model for control purposes . Therefore, POD is an attractive field for optimal control of fluid flows, which are governed by the Navier‐Stokes equations.…”

“…The purpose of this research is to design a forced reduced‐order model based on the POD/Galerkin projection and perturbation method to develop a nonautonomous system. The resulting method was used in optimal control of separated flow over backward facing by Zare et al They showed that perturbation method could predict the flow field in an accurate manner and the method was found to be fast and efficient in optimal control purposes.…”

“…The proper orthogonal decomposition (POD) has been extensively discussed in the literature as a reduced-order model for control purposes. [6][7][8][9][10][11][12][13][14] Therefore, POD is an attractive field for optimal control of fluid flows, which are governed by the Navier-Stokes equations. This method is inherently data based, and a great deal of information in the form of large data sets should be analyzed.…”