Optimal control of a separated boundary-layer flow over a bump

The optimal control of a globally unstable two-dimensional separated boundary layer over a bump is considered using augmented Lagrangian optimization procedures. The present strategy allows of controlling the flow from a fully developed nonlinear state back to the steady state using a single actuator. The method makes use of a decomposition between the slow dynamics associated with the baseflow modification, and the fast dynamics characterized by a large scale oscillation of the recirculation region, known as flapping. Starting from a steady state forced by a suction actuator located near the separation point, the baseflow modification is shown to be controlled by a vanishing suction strategy. For weakly unstable flow regimes, this control law can be further optimized by means of direct-adjoint iterations of the nonlinear Navier-Stokes equations. In the absence of external noise, this novel approach proves to be capable of controlling the transient dynamics and the baseflow modification simultaneously.Comment: 27 pages, 11 figure

Optimal transient growth in thin-interface internal solitary waves

The dynamics of perturbations to large-amplitude Internal Solitary Waves (ISW) in two-layered flows with thin interfaces is analyzed by means of linear optimal transient growth methods. Optimal perturbations are computed through direct-adjoint iterations of the Navier-Stokes equations linearized around inviscid, steady ISWs obtained from the Dubreil-Jacotin-Long (DJL) equation. Optimal perturbations are found as a function of the ISW phase velocity $c$ (alternatively amplitude) for one representative stratification. These disturbances are found to be localized wave-like packets that originate just upstream of the ISW self-induced zone (for large enough $c$) of potentially unstable Richardson number, $Ri < 0.25$. They propagate through the base wave as coherent packets whose total energy gain increases rapidly with $c$. The optimal disturbances are also shown to be relevant to DJL solitary waves that have been modified by viscosity representative of laboratory experiments. The optimal disturbances are compared to the local WKB approximation for spatially growing Kelvin-Helmholtz (K-H) waves through the $Ri < 0.25$ zone. The WKB approach is able to capture properties (e.g., carrier frequency, wavenumber and energy gain) of the optimal disturbances except for an initial phase of non-normal growth due to the Orr mechanism. The non-normal growth can be a substantial portion of the total gain, especially for ISWs that are weakly unstable to K-H waves. The linear evolution of Gaussian packets of linear free waves with the same carrier frequency as the optimal disturbances is shown to result in less energy gain than found for either the optimal perturbations or the WKB approximation due to non-normal effects that cause absorption of disturbance energy into the leading face of the wave.Comment: 33 pages, 22 figure

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

International audienceThe 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

Response of a stratified boundary layer on a tilted wall to surface undulations

International audienceThe structure of a stratified boundary layer over a tilted bottom with a small streamwise undulation is studied theoretically and numerically. We show that the tilt of the boundary can induce strong density variations and wall-transverse velocities in the critical layer when the frequency of the forcing by the topography kU(z c) is equal to the transverse Brunt–Väisälä frequency N sin α (N being the vertical Brunt–Väisälä frequency). The viscous solution in the critical layer, obtained and compared with direct numerical simulation results, is in good agreement for both the scaling and the spatial structure. The amplitude of the transverse velocity response is also shown to exhibit quasi-resonance peaks when the stratification strength is varied

Optimisation et contrôle d'une couche limite décollée

Les écoulements décollés le long d'une paroi sont source de d'instabilités qui conduisent à une dégradation des performances aérodynamiques. L'exemple d'une couche limite laminaire au dessus d'une bosse produit une dynamique appropriée au contrôle en boucle fermée ainsi qu'à l'analyse des perturbations optimales. Une formulation de type Lagrangienne est mise en uvre afin de prendre en compte les aspects non linéaires du problème

A comparative study between kriging and adaptive sparse tensor-product methods for multi-dimensional approximation problems in aerodynamics design

International audienceThe performances of two multivariate interpolation procedures are compared using functions that are either synthetic or coming from a shape optimization problem in aerodynamics. The aim is to evaluate the efficiency of adaptive sparse interpolation algorithms [2] and compare them with the kriging approach developed for the design and analysis of computer experiment (DACE) [21]. The accuracy and computational time of the two methods are examined as the number N of samples used in the interpolation increases. It appears in our test cases that both methods perform equivalently, in terms of precision. However, as the dimension d increases, the computational time involved in the enrichement of the kriging sample becomes intractable for large values of N. This problem is circumvented in the case of the sparse interpolation procedure for which the computational time scales linearly with N and d.Nous comparons les performances de deux méthodes d'interpolation en grande dimension, aussi bien sur des fonctions synthétiques que pour celles issues d'un problème d'optimisation de forme en aérodynamique. L'objectif est d'évaluer l'efficacité d'algorithmes adaptatifs d'interpolation parcimonieuse [2], et de les comparer avec l'approche du kriging développée dans le cadre design and analysis of computer experiment (DACE) [21]. La précision et le temps de calcul des deux méthodes sont étudiés lorsque le nombre N d'échantillons utilisés pour l'interpolation augmente. Les cas tests montrent que les deux méthodes sont comparables en terme de précision. Cependant, lorsque la dimension d augmente, le temps de calcul associé a l'enrichissement de l'échantillon pour le kriging devient prohibitif pour les grandes valeurs de N. Ce problème est contourné dans le cas de l'interpolation parcimonieuse pour lequel le temps de calcul est linéaire en N et d

Etude expérimentale de la dynamique basse fréquence d'une bulle de recirculation laminaire

Le décollement est intrinsèque aux écoulements le long des parois qu'elle qu'en soit la géométrie. Les bulles de recirculation ainsi formées sont sources de phénomènes d'instabilité. Cette étude expérimentale vise à quantifier les instabilités créées par une couche limite laminaire où le décollement est provoqué par une bosse optimisée à cet effet. La première partie consiste à étudier le mouvement transverse à l'intérieur de la bulle de recirculation. Dans une seconde partie, nous nous intéresserons au battement basse fréquence produit près du point de rattachement de l'écoulement