Centre-Manifold Reduction of Bifurcating Flows

In this paper we describe a general and systematic approach to the centre-manifold reduction and normal form computation of flows undergoing complicated bifurcations. The proposed algorithm is based on the theoretical work of Coullet & Spiegel (SIAM J. Appl. Maths, vol. 43(4), 1983, pp. 776821) and can be used to approximate centre manifolds of arbitrary dimension for large-scale dynamical systems depending on a scalar parameter. Compared with the classical multiple-scale technique frequently employed in hydrodynamic stability, the proposed method can be coded in a rather general way without any need to resort to the introduction and tuning of additional time scales. The method is applied to the dynamical system described by the incompressible NavierStokes equations showing that high-order, weakly nonlinear models of bifurcating flows can be derived automatically, even for multiple codimension bifurcations. We first validate the method on the primary Hopf bifurcation of the flow past a circular cylinderand after we illustrate its application to a codimension-two bifurcation arising in the flow past two side-by-side circular cylinder

First Instability and Structural Sensitivity of the Flow Past Two Side-by-Side Cylinders

The onset of two-dimensional instabilities in the flow past two side-by-side circular cylinders is numerically investigated in the ranges 0.1 <= 6 <= 3 and Re < 100, with g being the non-dimensional gap spacing between the surfaces of the two cylinders and Re the Reynolds number. A comprehensive, global stability analysis of the symmetric base flow is carried out, indicating that three harmonic modes and one steady antisymmetric mode become unstable at different values of g and Re. These modes are known to promote distinct flow regimes at increasing values of g: single bluff-body, asymmetric, in-phase and antiphase synchronized vortex shedding. For each mode, the inherent structural sensitivity is examined in order to identify the core region of the related instability mechanism. In addition, by exploiting the structural sensitivity analysis to base flow modifications, a passive control strategy is proposed for the simultaneous suppression of the two synchronized shedding modes using two small secondary cylinders. Its effectiveness is then validated a posteriori by means of direct numerical simulations

On the Origin of the Flip-Flop Instability of two Side-by-Side Cylinder Wakes

In this work the flip-flop instability occurring in the flow past two side-by-side circular cylinders is numerically investigated within the range of non-dimensional gap spacing 0.6<g<1.4 and Reynolds number 50<Re\leq 90. The inherent two-dimensional flow pattern is characterized by an asymmetric unsteady wake (with respect to the horizontal axis of symmetry) with the gap flow being deflected alternatively toward one of the cylinders. Such behaviour has been ascribed by other authors to a bistability of the flow, and therefore termed flip-flop. In contrast, the simulations performed herein provide new evidence that at low Reynolds numbers the flip-flopping state develops through an instability of the in-phase synchronized vortex shedding between the two cylinder wakes. This new scenario is confirmed and explained by means of a linear global stability investigation of the in-phase periodic base flow. The Floquet analysis reveals indeed that a pair of complex-conjugate multipliers becomes unstable having the same low frequency as the gap flow flip-over. The neutral curve of this secondary instability is tracked within the above range of gap spacing. The spatiotemporal shape of the unstable Floquet mode is then analysed and its structural sensitivity is considered in order to identify the 'core' region of the flip-flop instability mechanism

Analyse aérodynamique et acoustique d'une architecture boxwing dans le cadre du projet PARSIFAL

International audienceThe present paper summarizes the main results obtained from the CFD analysis of a reference boxwing configuration designed during the initial phase of the PARSIFAL project, with focus on the assessment of its aerodynamic performance in the transonic regime. For such purpose, high-fidelity RANS computations have been carried out and a detailed inspection of the different drag sources, induced, wave and viscous drag components, is presented. In addition, preliminary results from the acoustic analysis of such innovative aircraft configuration are also discussed, concerning the impact of the engine location

New approaches to the multiple functionalization of fullerene

2012/2013Fullerene C60 is a charming molecule, its beautiful symmetry and its unique properties are still intriguing scientific community after almost three decades from its discovery. Investigation of its properties and applications is still an active field. In our group we are interested especially in the biological aspect of fullerene sciences. In this field, polyfunctional derivatives are particularly attractive, for the increased solubility and for the possibility to attach different biologically active molecules on the same carbon cage. In the first project we studied different methods to control the site selectivity of the double 1,3-dipolar cycloaddition of azomethine ylides. To this purpose, we synthesized several bis-reactive templates with very different design, and we could obtain unusual fullerene-macrocyclic and fullerene-cyclophanes structures. A good degree of control of the site selectivity was achieved in some cases. A supramolecular approach to the control of the second cycloaddition was also developed. In the second part we focused our efforts in finding a feasible and scalable method to produce bis- or poly-functional fullerene derivatives from the easily accessible monoadduct. Triazine chemistry in combination with oxyethylenic chains allowed us to easily synthesize a library of polyfunctional, versatile and highly soluble derivatives. Some toxicological results indicate that this kind of compounds can be very useful carriers for drug delivery and some application in this sense are currently under investigation. Finally in a third part of the work we synthesized several fullerene-bipyridyl ligands and their ruthenium complexes. In this way we want to combine in the same molecule both the antiproliferative properties of ruthenium complexes and the photosensitizing effect of fullerene in order to obtain a synergistic effect against tumor cells.XXVI Ciclo198

Linear stability analysis of strongly coupled fluid–structure problems with the Arbitrary-Lagrangian–Eulerian method

International audienceThe stability analysis of elastic structures strongly coupled to incompressible viscous flows is investigated in this paper, based on a linearization of the governing equations formulated with the Arbitrary-Lagrangian–Eulerian method. The exact linearized formulation, previously derived to solve the unsteady non-linear equations with implicit temporal schemes, is used here to determine the physical linear stability of steady states. Once discretized with a standard finite-element method based on Lagrange elements, the leading eigenvalues/eigenmodes of the linearized operator are computed for three configurations representative for classical fluid–structure interaction instabilities: the vortex-induced vibrations of an elastic plate clamped to the rear of a rigid cylinder, the flutter instability of a flag immersed in a channel flow and the vortex shedding behind a three-dimensional plate bent by the steady flow. The results are in good agreement with instability thresholds reported in the literature and obtained with time-marching simulations, at a much lower computational cost. To further decrease this computational cost, the equations governing the solid perturbations are projected onto a reduced basis of free-vibration modes. This projection allows to eliminate the extension perturbation, a non-physical variable introduced in the ALE formalism to propagate the infinitesimal displacement of the fluid–solid interface into the fluid domain