Comptes Rendus
Separation flow control
Open-loop control of a separated boundary layer
Comptes Rendus. Mécanique, Volume 342 (2014) no. 6-7, pp. 403-409.

Linear optimal gains Gopt(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 Gopt(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 lc and reveals that the above control configuration is also the most efficient to shorten the recirculation region. This suggests that lc 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 Gopt(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 Gopt(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 lc et révèle que la configuration de contrôle ci-dessus est aussi la plus efficace pour raccourcir la zone de recirculation. Cela suggère que lc 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:
Accepted:
Published online:
DOI: 10.1016/j.crme.2014.01.014
Keywords: Separated flow, Flow instability, Flow control
Mot clés : Ecoulements décollés, Instabilité des écoulements, Contrôle des écoulements

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
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Édouard Boujo; François Gallaire; Uwe Ehrenstein. Open-loop control of a separated boundary layer. Comptes Rendus. Mécanique, 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/

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