Open-loop control of a separated boundary layer

Édouard Boujo; François Gallaire; Uwe Ehrenstein

doi:10.1016/j.crme.2014.01.014

Separation flow control

Open-loop control of a separated boundary layer

Édouard Boujo ¹ ; François Gallaire ¹; Uwe Ehrenstein ²

¹ Laboratory of Fluid Mechanics and Instabilities, École polytechnique fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
² Aix–Marseille Université, CNRS, Centrale Marseille, IRPHE UMR 7342, 13384, Marseille, France

Comptes Rendus. Mécanique, Flow separation control, Volume 342 (2014) no. 6-7, pp. 403-409.

Abstract
Résumé

Linear optimal gains $G_{opt} (ω)$ are computed for the separated boundary-layer flow past a two-dimensional bump in the subcritical regime. Very large values are found, making it possible for small-amplitude noise to be strongly amplified and to destabilize the flow. Next, a variational technique is used to compute the sensitivity of $G_{opt} (ω)$ to steady control (volume force in the flow, or blowing/suction at the wall). The bump summit is identified as the region the most sensitive to wall control. Based on these (linear) sensitivity results, a simple open-loop control strategy is designed, with steady wall suction at the bump summit. Calculations on non-linear base flows confirm that optimal gains can be significantly reduced at all frequencies using this control. Finally, sensitivity analysis is applied to the length of the recirculation region $l_{c}$ and reveals that the above control configuration is also the most efficient to shorten the recirculation region. This suggests that $l_{c}$ is a relevant macroscopic parameter to characterize wall-bounded separated flows, which could be used as a proxy for energy amplification when designing steady open-loop control.

Le gain optimal linéaire $G_{opt} (ω)$ est calculé pour un écoulement de couche limite décollée en aval d'une bosse bidimensionnelle, en régime sous-critique. De très grandes valeurs sont obtenues. Un bruit de faible amplitude peut donc être fortement amplifié et déstabiliser l'écoulement. Une technique variationnelle est utilisée pour calculer la sensibilité de $G_{opt} (ω)$ à un contrôle stationnaire (force volumique dans l'écoulement, ou soufflage/aspiration à la paroi). Le sommet de la bosse est identifié comme la région la plus sensible au contrôle pariétal. À partir de ces résultats (linéaires), une stratégie simple de contrôle en boucle ouverte est développée, avec aspiration stationnaire au sommet de la bosse. Des calculs sur des champs de base non linéaires confirment que ce contrôle réduit significativement le gain optimal à toutes les fréquences. Enfin, l'analyse de sensibilité est appliquée à la longueur de la zone de recirculation $l_{c}$ et révèle que la configuration de contrôle ci-dessus est aussi la plus efficace pour raccourcir la zone de recirculation. Cela suggère que $l_{c}$ est un paramètre macroscopique pertinent pour caractériser les écoulements décollés près d'une paroi, qui pourrait être utilisé comme alternative à l'amplification d'énergie lors de l'élaboration d'un contrôle stationnaire en boucle ouverte.

Received: 2013-09-02
Accepted: 2014-01-14
Published online: 2014-06-01

DOI: 10.1016/j.crme.2014.01.014

Keywords: Separated flow, Flow instability, Flow control
Mots-clés : Ecoulements décollés, Instabilité des écoulements, Contrôle des écoulements

Author's affiliations:

Édouard Boujo ¹; François Gallaire ¹; Uwe Ehrenstein ²

¹ Laboratory of Fluid Mechanics and Instabilities, École polytechnique fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
² Aix–Marseille Université, CNRS, Centrale Marseille, IRPHE UMR 7342, 13384, Marseille, France

@article{CRMECA_2014__342_6-7_403_0,
     author = {\'Edouard Boujo and Fran\c{c}ois Gallaire and Uwe Ehrenstein},
     title = {Open-loop control of a separated boundary layer},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {403--409},
     publisher = {Elsevier},
     volume = {342},
     number = {6-7},
     year = {2014},
     doi = {10.1016/j.crme.2014.01.014},
     language = {en},
}

TY  - JOUR
AU  - Édouard Boujo
AU  - François Gallaire
AU  - Uwe Ehrenstein
TI  - Open-loop control of a separated boundary layer
JO  - Comptes Rendus. Mécanique
PY  - 2014
SP  - 403
EP  - 409
VL  - 342
IS  - 6-7
PB  - Elsevier
DO  - 10.1016/j.crme.2014.01.014
LA  - en
ID  - CRMECA_2014__342_6-7_403_0
ER  -

%0 Journal Article
%A Édouard Boujo
%A François Gallaire
%A Uwe Ehrenstein
%T Open-loop control of a separated boundary layer
%J Comptes Rendus. Mécanique
%D 2014
%P 403-409
%V 342
%N 6-7
%I Elsevier
%R 10.1016/j.crme.2014.01.014
%G en
%F CRMECA_2014__342_6-7_403_0

Édouard Boujo; François Gallaire; Uwe Ehrenstein. Open-loop control of a separated boundary layer. Comptes Rendus. Mécanique, Flow separation control, Volume 342 (2014) no. 6-7, pp. 403-409. doi : 10.1016/j.crme.2014.01.014. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2014.01.014/

References
Cited by

[1] P.J. Schmid; D.S. Henningson Stability and Transition in Shear Flows, Springer, 2001

[2] L.N. Trefethen; A.E. Trefethen; S.C. Reddy; T.A. Driscoll Hydrodynamic stability without eigenvalues, Science, Volume 261 (1993) no. 5121, pp. 578-584

[3] K.M. Butler; B.F. Farrell Three-dimensional optimal perturbations in viscous shear flow, Phys. Fluids A, Fluid Dyn., Volume 4 (1992) no. 8, pp. 1637-1650

[4] J.-M. Chomaz Global instabilities in spatially developing flows: Non-normality and nonlinearity, Annu. Rev. Fluid Mech., Volume 37 (2005), pp. 357-392

[5] P. Corbett; A. Bottaro Optimal control of nonmodal disturbances in boundary layers, Theor. Comput. Fluid Dyn., Volume 15 (2001) no. 2, pp. 65-81

[6] E. Åkervik; U. Ehrenstein; F. Gallaire; D.S. Henningson Global two-dimensional stability measures of the flat plate boundary-layer flow, Eur. J. Mech. B, Fluids, Volume 27 (2008) no. 5, pp. 501-513

[7] F. Alizard; S. Cherubini; J.-C. Robinet Sensitivity and optimal forcing response in separated boundary layer flows, Phys. Fluids, Volume 21 (2009) no. 6, p. 064108

[8] X. Garnaud; L. Lesshafft; P.J. Schmid; P. Huerre The preferred mode of incompressible jets: linear frequency response analysis, J. Fluid Mech., Volume 716 (2013), pp. 189-202

[9] L. Brandt; D. Sipp; J.O. Pralits; O. Marquet Effect of base-flow variation in noise amplifiers: the flat-plate boundary layer, J. Fluid Mech., Volume 687 (2011), pp. 503-528

[10] U. Ehrenstein; F. Gallaire Two-dimensional global low-frequency oscillations in a separating boundary-layer flow, J. Fluid Mech., Volume 614 (2008), pp. 315-327

[11] U. Ehrenstein; P.-Y. Passaggia; F. Gallaire Control of a separated boundary layer: reduced-order modeling using global modes revisited, Theor. Comput. Fluid Dyn., Volume 25 (2011) no. 1–4, pp. 195-207

[12] M. Marquillie; U. Ehrenstein On the onset of nonlinear oscillations in a separating boundary-layer flow, J. Fluid Mech., Volume 490 (2003), pp. 169-188

[13] P.-Y. Passaggia; T. Leweke; U. Ehrenstein Transverse instability and low-frequency flapping in incompressible separated boundary layer flows: an experimental study, J. Fluid Mech., Volume 703 (2012), pp. 363-373

[14] F. Gallaire; M. Marquillie; U. Ehrenstein Three dimensional transverse instabilities in detached boundary layers, J. Fluid Mech., Volume 571 (2007), pp. 221-233

[15] E. Boujo; F. Gallaire Controlled reattachment in separated flows: a variational approach to recirculation length reduction, J. Fluid Mech., Volume 742 (2014), pp. 618-635 | DOI

[16] S. Taneda Experimental investigation of the wakes behind cylinders and plates at low Reynolds numbers, J. Phys. Soc. Jpn. (1956)

[17] D. Barkley; M. Gabriela M. Gomes; R.D. Henderson Three-dimensional instability in flow over a backward-facing step, J. Fluid Mech., Volume 473 (2002), pp. 167-190

[18] E. Boujo; U. Ehrenstein; F. Gallaire Open-loop control of noise amplification in a separated boundary layer flow, Phys. Fluids, Volume 25 (2013), p. 124106 | DOI

Cited by Sources:

Comments - Policy