Scattering of entropy waves into sound by isolated aerofoils

This article presents a modelling approach to predict the low-frequency sound generated by entropy fluctuations interacting with isolated aerofoils. A model of the acoustic field is obtained based on a linearisation of the compressible Euler equations about a steady, potential, compressible mean flow. Mean flow variations of velocity and density are accounted for in the source term, but are neglected in the sound propagation. Using a Lorentz-type transformation, the problem is reduced to solving a Helmholtz equation. This equation is recast in integral form and a solution is obtained using a compact Green's function method. This approach places no restrictions on the entropy wavelength, while assuming that the acoustic wavelength is large compared to the profile chord and spacing. The source term is further simplified by assuming that the steady flow is a small perturbation to a uniform flow. The model is illustrated using a symmetric aerofoil and its performance is assessed against numerical simulations of the compressible Euler equations. Good agreement is found for all the frequencies of validity of the theory and for all the range of subsonic Mach numbers. The solution for a symmetric aerofoil interacting with plane entropy waves corresponds to the combination of a dipole along the horizontal axis and a monopole. The dipole originates from the unsteady drag experienced by the aerofoil owing to the fluctuations of density and the monopole from the strong local acceleration of the flow at the leading edge. The monopole term becomes negligible for low Mach numbers

Estimation et contrôle des amplificateurs de bruit avec des stratégies basées sur les données

This work aims to provide new modelling strategies for noise amplifier flows using data-based techniques. This kind of flow is particularly difficult to model since the upstream noise environment, triggering the flow via a receptivity process, is not known. We propose a system-identification approach, rather than a classical Galerkin technique, to extract the model from time-synchronous velocity snapshots and wall-shear stress measurements. The technique is illustrated using the case of a transitional flat-plate boundary layer, where the snapshots of the flow are obtained from direct numerical simulations. Particular attention is directed to limiting the processed data to data that would be readily available in experiments, thus making the technique applicable to an experimental setup. The proposed approach combines a reduction of the degrees of freedom of the system by projection of the velocity snapshots onto a POD basis combined with a system-identification technique to obtain a state-space model. This model is then used in a feed-forward control setup to significantly reduce the kinetic energy of the perturbation field and thus successfully delay transition.In the second part of this work, the extracted model is used to determine coherent structures of the flow that are inherent to the system and not a representation of the external driving noise. The global modes and frequency response of the reduced-order model are qualitatively compared to global modes of the full-order boundary layer reported previously in the literature.Finally, the estimator obtained using system identification is compared to an estimator obtained using a projection technique together with a Kalman filter (this method is exact but it cannot be applied in experimental setups). Here, the influence that different parameters have on the quality of the estimation has been analysed: noise in the estimation sensor, number of internal states of the reduced order model and the position of the sensor with respect to the position of the window measuring the velocity field.Ce travail est consacré à la modélisation des écoulements laminaires et incompressibles de type amplificateur de bruit avec des stratégies basées sur les données. Ce type d'écoulement est particulièrement difficile à modéliser car le bruit en amont gouvernant l'écoulement n'est pas connu. On propose ici une stratégie basée sur l'identification de systèmes (plutôt qu’une technique classique de projection Galerkin) pour extraire un modèle à partir de clichés de champ de vitesse et de mesures d'un capteur situé à l'amont de l'écoulement. La technique est appliquée dans le cas d'une couche limite sur une plaque plane, avec des clichés de vitesse obtenus d'une simulation numérique des équations de Navier-Stokes. Le principe de la méthode consiste à déterminer au préalable les modes POD du champ de perturbation, de projeter les clichés de l'écoulement à chaque instant sur cette base et d'apprendre la dynamique de ces modes par des techniques d'identification. Le modèle résultant peut ensuite être utilisé pour contrôler cette dynamique de manière à supprimer les instabilités du système. Dans la première partie de cette thèse, la méthode est présentée en détail et la qualité des modèles est évaluée. La deuxième partie, propose d'exploiter la technique décrite ci-dessus pour extraire la dynamique intrinsèque d'un écoulement de type amplificateur de bruit. On montre que la technique utilisée traditionnellement par la communauté (Dynamic Mode Decomposition) présente un biais pour ce type d'écoulement, du fait qu'elle néglige les termes de forçage, présents de façon inhérente dans ces écoulements. On propose alors d'utiliser la technique d'identification pour estimer les modes globaux de l'écoulement de façon juste et d’extraire la fonction de transfert entre le capteur amont et l'énergie cinétique des perturbations dans le champ.La dernière partie compare de façon exhaustive les performances des modèles obtenus par la technique d'identification aux performances des modèles obtenus par une méthode de projection avec un filtre de Kalman (méthodes exactes mais non applicables dans un contexte expérimental). Différents paramètres sont analysés ici : bruit de capteur, nombre d'états dans le modèle réduit par rapport au nombre de modes POD estimés et position du capteur par rapport à la fenêtre des clichés de champ de vitesse

A data-based, reduced-order, dynamic estimator for reconstruction of non-linear flows exhibiting limit-cycle oscillations

We apply a data-based, linear dynamic estimator to reconstruct the velocity field from measurements at a single sensor point in the wake of an aerofoil. In particular, we consider a NACA0012 aerofoil at Re = 600 and 16◦ angle of attack. Under these conditions, the flow exhibits a vortex shedding limit cycle. A reduced order model (ROM) of the flow field is extracted using proper orthogonal decomposition (POD). Subsequently, a subspace system identification algorithm (N4SID) is applied to extract directly the estimator matrices from the reduced output of the system (the POD coefficients). We explore systematically the effect of the number of states of the estimator, the sensor location, the type of sensor measurements (one or both velocity components), and the number of POD modes to be recovered. When the signal of a single velocity component (in the stream wise or cross stream directions) is measured, the reconstruction of the first two dominant POD modes strongly depends on the sensor location. We explore this behaviour and provide a physical explanation based on the non-linear mode interaction and the spatial distribution of the modes. When however, both components are measured, the performance is very robust, and is almost independent of the sensor location when the optimal number of estimator states is used. Reconstruction of the less energetic modes is more difficult, but still possible. Finally, we assess the robustness of the estimator at off-design conditions, at Re = 550 and 650.

Sound generation by entropy perturbations passing through a sudden flow expansion

Entropy perturbations generate sound when accelerated/decelerated by a non-uniform flow. Current analytical models provide a good prediction of this entropy noise when the flow cross-sectional area changes are gradual, as is the case for nozzle flows. However, they typically rely on quasi-1-D and isentropic assumptions, and their predictions differ significantly from experimental measurements when sudden area increases are involved. This work uses a theoretical approach to quantitatively identify the main mechanisms responsible for the mismatch. A new form of the acoustic analogy is derived in which the entropy-related source terms are systematically identified for the first time. The theory includes three-dimensional and non-isentropic effects. The approach is applied to the flow through a sudden area expansion, for which the large-scale flow separation creates a recirculation zone. The derived acoustic analogy is simplified for low Mach numbers and frequencies, and solved using a Green's function method. The results provide the first quantitative evidence that the presence and spatial extent of the recirculation zone, rather than the flow non-isentropicity, is the dominant factor causing deviation from predictions from quasi-1-D, isentropic theory

Tying a Molecular Overhand Knot of Single Handedness and Asymmetric Catalysis with the Corresponding Pseudo-D-3-Symmetric Trefoil Knot

We report the stereoselective synthesis of a left-handed trefoil knot from a tris(2,6-pyridinedicarboxamide) oligomer with six chiral centers using a lanthanide(III) ion template. The oligomer folds around the lanthanide ion to form an overhand knot complex of single handedness. Subsequent joining of the overhand knot end groups by ring-closing olefin metathesis affords a single enantiomer of the trefoil knot in 90% yield. The knot topology and handedness were confirmed by NMR spectroscopy, mass spectrometry, and X-ray crystallography. The pseudo-D3-symmetric knot was employed as an asymmetric catalyst in Mukaiyama aldol reactions, generating enantioselectivities of up to 83:17 er, which are significantly higher than those obtained with a comparable unknotted ligand complex

Search for New Particles in Two-Jet Final States in 7 TeV Proton-Proton Collisions with the ATLAS Detector at the LHC

A search for new heavy particles manifested as resonances in two-jet final states is presented. The data were produced in 7 TeV proton-proton collisions by the LHC and correspond to an integrated luminosity of 315 nb(-1) collected by the ATLAS detector. No resonances were observed. Upper limits were set on the product of cross section and signal acceptance for excited-quark (q*) production as a function of q* mass. These exclude at the 95% C. L. the q* mass interval 0: 30< m(q)*< 1:26 TeV, extending the reach of previous experiments