Control of a separated boundary layer: reduced-order modeling using global modes revisited

Abstract

To cite this version:Uwe Ehrenstein, Pierre-Yves Passaggia, Francois Gallaire. Control of a separated boundary layer: Reduced-order modeling using global modes revisited. Theoretical and Computational Fluid Dynamics, Springer Verlag, 2011, 25 (1), pp.195-207. 10.1007/s00162-010-0195-5. hal-00433158 Abstract The possibility of model reduction using global modes is readdressed, aiming at the controlling of a globally unstable separation bubble induced by a bump geometry. A combined oblique and orthogonal projection approach is proposed to design an estimator and controller in a Riccati-type feedback setting. An input-output criterion is used to appropriately select the modes of the projection basis. The full-state linear instability dynamics is shown to be successfully controlled by the feedback coupling with controllers of moderate degrees of freedom.

Open-loop control of a separated boundary layer

“…Very large optimal gain values were found, confirming the strong non-normal character already observed with large transient growth [10,11] and the potential for large noise amplification. Sensitivity analysis applied to G opt (ω) identified the bump summit as the region the most sensitive to wall control.…”

“…The bump geometry y = y b (x) is shown in figure 1 and is the same as in Marquillie and Ehrenstein [12] and following studies [10,11,13]. The incoming flow has a Blasius boundary layer profile, of displacement thickness δ * at the reference position x = 0.…”

“…In this study, the flow past a wall-mounted bump is considered (section 2). This separated flow is characterized by a long recirculation region, high shear, strong backflow, and exhibits large transient growth [10,11]. Optimal gains are computed at different frequencies (sec.…”

Open-loop control of noise amplification in a separated boundary layer flow

“…The bump geometry y = y b (x) is shown in figure 1 and is the same as in Bernard, Foucaut, Dupont and Stanislas 30 , Marquillie and Ehrenstein 31 and following studies 11,29,32 . The incoming flow has a Blasius boundary layer profile, characterized by its displacement thickness δ * at the reference position x = 0.…”

Reduced order models for closed loop control: comparison between POD, BPOD, and global modes

“…Relative H∞-error norm as a function of the number p of included modes, using global (d ), POD (e), and BPOD modes (f ) sensitive to the action of the actuator when the ROM is constructed using a bi-orthogonal projection [8]. To overcome this feature, alternative projection techniques have been considered [9].…”