Influence of the Mass ratio on the fluid-elastic instability of a flexible cylinder in a bundle of rigid tubes

Several linear lumped-parameter models were proposed in the past to identify the main mechanisms underlying the cross-flow instability of a single flexible cylinder in tube bundles. Basing on such models, we analyze the influence of the mass ratio when the cylinder vibrates in the transverse direction, without structural damping (corresponding to a zero Scruton number). For two selected mass ratios, we focus on this linear interaction plotting the poles of the fluid–structure system as a function of the reduced velocity (root locus). This asymptotic approach allows a better understanding of the combined influence of the transient fluidelastic coupling and the mass ratio

Density fluctuation correlations in free turbulent binary mixing

This paper is devoted to the analysis of the turbulent mass flux and, more generally, of the density fluctuation correlation (d.f.c.) effects in variable-density fluid motion. The situation is restricted to the free turbulent binary mixing of an inhomogeneous round jet discharging into a quiescent atmosphere. Based on conventional (Reynolds) averaging, a ternary regrouping of the correlations occurring in the statistical averaging of the open equations is first introduced. Then an exact algebraic relationship between the d.f.c. terms and the second-order moments is demonstrated. Some consequences of this result on the global behaviour of variable-density jets are analytically discussed. The effects of the d.f.c. terms are shown to give a qualitative explanation of the influence of the ratio of the densities of the inlet jet and ambient fluid on the centerline decay rates of mean velocity and mass fraction, the entrainment rate and the restructuring of the jet. Finally, the sensitivity of second-order modelling to the d.f.c. terms is illustrated and it is suggested that such terms should be considered as independent variables in the closing procedure

Anisotropic Organised Eddy Simulation for the prediction of non-equilibrium turbulent flows around bodies

The unsteady turbulent flow around bodies at high Reynolds number is predicted by an anisotropic eddy-viscosity model in the context of the Organised Eddy Simulation (OES). A tensorial eddy-viscosity concept is developed to reinforce turbulent stress anisotropy, that is a crucial characteristic of non-equilibrium turbulence in the near-region. The theoretical aspects of the modelling are investigated by means of a phase-averaged PIV in the flow around a circular cylinder at Reynolds number 1.4×10^5. A pronounced stress–strain misalignment is quantified in the near-wake region of the detached flow, that is well captured by a tensorial eddy-viscosity concept. This is achieved by modelling the turbulence stress anisotropy tensor by its projection onto the principal matrices of the strain-rate tensor. Additional transport equations for the projection coefficients are derived from a second-order moment closure scheme. The modification of the turbulence length scale yielded by OES is used in the Detached Eddy Simulation hybrid approach. The detached turbulent flows around a NACA0012 airfoil (2-D) and a circular cylinder (3-D) are studied at Reynolds numbers 105 and 1.4×10^5, respectively. The results compared to experimental ones emphasise the predictive capabilities of the OES approach concerning the flow physics capture for turbulent unsteady flows around bodies at high Reynolds numbers

Modélisation des jets subsoniques fortement chauffés

Après un retour sur les différentes alternatives de traitement statistique des équations d'évolution d'un fluide à masse volumique variable, une formulation qui explicite la contribution des flux turbulents de masse est adoptée. Celle-ci ne manipule en effet que des grandeurs statistiques centrées. Dans ce cadre, on discute la transposition des modélisations à masse volumique constante aux variables pondérées de l'écoulement non-isotherme. La discussion porte essentiellement sur les fermetures au premier et au second ordre pour les termes de diffusion. Le contenu des modèles usuels en variables de Favre est détaillé. On propose de conclure quant au potentiel de fermeture des alternatives de formulation initiales. On illustre ensuite l'intérêt de simulations numériques paraboliques par fermetures au premier et au second ordre de jets turbulents chauffés. La restitution de l'effet de densité sur les évolutions des grandeurs moyennes sur l'axe des jets est démontrée. La sensibilité de caractéristiques de la turbulence au rapport de densité initial est abordée. On apporte enfin quelques éléments pour juger de la qualité comparée des deux ordres de fermeture notamment pour la prédiction des flux turbulents de masse

Coherent and turbulent processes in the bistable regime around a tandem of cylinders including reattached flow dynamics by means of high-speed PIV

The turbulent flow around two cylinders in tandem at the sub-critical Reynolds number range of order of 105 and pitch to diameter ratio of 3.7 is investigated by using time-resolved Particle Image Velocimetry (TRPIV) of 1 kHz and 8 kHz. The bi-stable flow regimes including a flow pattern I with a strong vortex shedding past the upstream and the downstream cylinder, as well as a flow pattern II corresponding to a weak alternating vortex shedding with reattachment past the upstream cylinder are investigated. The structure of this “reattachment regime” has been analyzed in association with the vortex dynamics past the downstream cylinder, by means of POD and phase-average decomposition. These elements allowed interconnection among all the measured PIV planes and hence analysis of the reattachment structure and the flow dynamics past both cylinders. The results highlight fundamental differences of the flow structure and dynamics around each cylinder and provide the ‘gap’ flow nature between the cylinders. Thanks to a high-speed camera of 8 kHz, the shear-layer vortices tracking has been possible downstream of the separation point and the quantification of their shedding frequency at the present high Reynolds number range has been achieved. This issue is important regarding fluid instabilities involved in the fluid–structure interaction of cylinder arrays in nuclear reactor systems, as well as acoustic noise generated from the tandem cylinders of a landing gear in aeronautics

Etude numérique des effets de densité dans un jet de mélange turbulent en microgravité.

L'objet de cet article est de mettre en évidence, par le calcul, les effets de densité sur les caractéristiques d'un mélange hétérogène dans un jet turbulent libre en microgravité. Les effets de densité sur les grandeurs moyennes, l'entraînement, l'expansion et les moments d'ordre deux sont présentés en fonction du paramètre S caractérisant le rapport de densité entre le jet et le milieu ambiant. La plage de variation de ce paramètre s'étend de 0,14 à 5,11. Ces résultats de simulation, basés sur des modèles de fermeture en un point au second ordre, sont alors discutés en comparaison avec des données d'expériences ainsi que des considérations asymptotiques. On montre, en particulier, les effets du rapport de densité sur le développement du jet qui s'estompent dans la zone lointaine, conduisant à des profils de similitude indépendants du rapport de densité (similitude totale au sens de George [1]

Anisotropic eddy-viscosity concept for strongly detached unsteady flows

The accurate prediction of the flow physics around bodies at high Reynolds number is a challenge in aerodynamics nowadays. In the context of turbulent flow modeling, recent advances like large eddy simulation (LES) and hybrid methods [detached eddy simulation (DES)] have considerably improved the physical relevance of the numerical simulation. However, the LES approach is still limited to the low-Reynolds-number range concerning wall flows. The unsteady Reynolds-averaged Navier–Stokes (URANS) approach remains a widespread and robust methodology for complex flow computation, especially in the near-wall region. Complex statistical models like second-order closure schemes [differential Reynolds stress modeling (DRSM)] improve the prediction of these properties and can provide an efficient simulationofturbulent stresses. Fromacomputational pointofview, the main drawbacks of such approaches are a higher cost, especially in unsteady 3-D flows and above all, numerical instabilities

Numerical simulation of the fluid–structure interaction in a tube array under cross flow at moderate and high Reynolds number

The unsteady loads in a tube bundle are studied at moderate and high Reynolds number by means of URANS and hybrid (DDES) modelling. The onset of fluid-elastic instability is analysed for different structural parameters, Scruton number and reduced velocity. The simulations have been carried out with the code NSMB (Navier–Stokes Multi Block) by using turbulence modelling methods URANS and DDES (Delayed Detached Eddy Simulation). The CEA-DIVA configuration is considered for the cylinders array for an inter-tube Reynolds number 60 000. The study is carried out for a configuration of (4×5) cylinders in static conditions as well as for the vertical free motion of one of the central cylinders in one DOF (Degree Of Freedom).The inter-tube Reynolds number is 60 000. It is found that this cylinder spontaneously displays an oscillatory motion which first corresponds to Vortex Induced Vibration (VIV), associated to a lock-in mechanism for low values of the reduced velocity and secondly develops Movement Induced Vibration, MIV, for higher values of the reduced velocity. The variation of the cylinder׳s oscillations frequency, of the unsteady loads and the structure׳s displacement are studied as a function of the reduced velocity for low and high values of the Scruton number. The increase of the phase-lag between the forces and the displacement is predicted and discussed for different Scruton number values and reduced velocities

Analyse du sillage et de l'écoulement décollé autour d'une plaque en incidence par PIV Tomographique

L'écoulement autour d'une plaque plane d'envergure finie en incidence est étudié au nombre de Reynolds de 200000 par expériences physiques en soufflerie S4 de l'IMFT. Les champs de vitesse statiques, bi- et tridimensionnels ont été mesurés par PIV et Tomo-PIV. La dynamique tourbillonnaire est analysée à l'aide entre autres de l'approche POD sur une maquette rigide et déformable à l'aire d'alliages à mémoire de forme

Simulation de l'interaction fluide - structure dans un faisceau de tubes à nombre de Reynolds élevé

L'interaction fluide-structure dans un faisceau de tubes est analysée par les approches de modélisation de la turbulence OES (Organised Eddy Simulation) et DES (Detached Eddy Simulation). Les origines d'apparition des instabilités de flottement fluide-elastique sont étudiées. Les contributions du mouvement de la structure et de la turbulence dans cette interaction sont quantifiées