Séminaire de Mécanique d'Orsay
Jeudi 6 octobre à 14h au LIMSI
Open-loop control of instabilities in open flows
Denis Sipp
ONERA DAFE
 

The objective of this talk is to present three different approaches to the stabilization or de-stabilization of unstable flows. First, we consider the case of an oscillator flow, the super-critical open cavity. After briefly recalling the case of a steady forcing targetting directly the modification of the base-flow (Marquet et al. 2008), we present the case of a harmonic forcing modifying the dynamics of an unstable global eigenmode thanks to non-linear interactions. For this, an amplitude equation is sought based on a weakly non-linear approach and a multiple time-scale analysis. The frequency ranges for maximal stabilization or destabilization are sought and validated against a forced Direct Numerical Simulation. Secondly, we consider an amplifier flow, a leading-edge boundary layer characterized by Re=600000 (based on the length of the plate and the upstream velocity). We will first characterize the dynamics of such a flow by computing the singular values/vectors of the resolvant operator: it will be shown that the TS instabilities and Lift-Up instabilities are nicely characterized by such an approach. The effect of a steady forcing on this flow will then be evaluated thanks to an adjoint approach: the gradient of a singular value (and not a global mode!) with respect to the introduction of a steady forcing will show where to introduce a small control cylinder to stabilize the TS and Lift-up instabilities.