Effect of coupling with internal and external fluids on the mechanical behavior of aerostats

International audienceIn the context of the simulation of aerostats in flight, we are interested here in the coupling between a deformable structure, the fluid contained inside and the fluid flow outside. To study the dynamic stability of such systems, the fluid-structure coupled equations are linearized around an equilibrium position and, by assuming that the fluid flow perturbations are potential, the loads exerted by the fluids on the moving structure can be decomposed in terms proportional, respectively, to the displacement, velocity and acceleration fields of the structure, representing what are generally called the added stiffness, damping and mass effects of the fluid on the structure. In this work, a focus is made on the added mass because, for such lightweight structures, its effect is of prime importance. A Boundary Element Method (BEM) is proposed to compute the fluid added mass operators, for external and internal fluids, and for any structure deformation field. Numerical and experimental validations are conducted on an axisymmetric ellipsoid mockup immerged in water and subject to rigid motions. Variations of the imposed movement amplitude and velocity have also helped to evaluate the validity domain of this model

Influence de la gravité sur les vibrations linéaires d'une structure élastique partiellement remplie par un liquide incompressible

The present study deals with the low frequency vibrational analysis of the fluid-structure interactions in an elastic tank partially filled with an incompressible inviscid liquid. The originality of this work is to keep the contribution of all terms depending on gravity in the modelling, in order to represent the strong coupling between the sloshing of the liquid and the hydroelastic deformations of the structure, whereas the classical models study this two phenomena on two distinct frequency domains using some simplifying assumptions. Since gravity effects can be considered as prestresses in structure and fluid, we use a "large displacement" formalism in lagrangian coordinates. The non linear terms of the symmetric variational formulation are linearized to exhibit a stiffness operator depending on the gravity, named \emph{elastogravity} operator. The study of this operator and its rigid body modes shows that taking the gravity into account in the hydroelastic model allows to correctly predict the body motions of a free-free fluid-structure system, in opposition to the classical modelling. After finite element discretization, this method is validated with some test cases and applied to a semi-industrial problem.L'étude présentée dans ce document a pour objet l'analyse vibratoire basse fréquence des interactions fluide-structure dans un réservoir déformable partiellement rempli par un liquide incompressible non visqueux. L'originalité de ce travail est de conserver l'intégralité des effets de la gravité dans la modélisation afin de tenir compte du couplage fort entre le ballottement de la surface libre du liquide et les déformations hydroélastiques du réservoir, alors que les méthodes traditionnelles appréhendent ces deux phénomènes sur des plages de fréquence supposées distinctes et sous certaines hypothèses réductrices. La gravité agissant comme une précontrainte dans la structure et dans le fluide, le formalisme "grands déplacements" en coordonnées lagrangiennes est utilisé. La linéarisation des termes non linéaires obtenus dans la formulation variationnelle symétrique du problème fait apparaitre un opérateur de rigidité dépendant de la gravité, appelé opérateur d'élastogravité. L'étude de cet opérateur et de ses modes rigides a montré que la prise en compte de la gravité dans la modélisation hydroélastique permet d'obtenir des résultats cohérents dans le calcul des mouvements d'ensemble d'un système fluide-structure libre dans l'espace, ce qui n'était pas le cas avec les méthodes classiques. Après discrétisation par éléments finis, la méthode est validée sur différents cas tests et appliquée sur un modèle semi-industriel

Modal analysis of liquid-structure interaction

International audienceThe computation of the linear vibrations of structures partially filled with liquids is of prime importance in various industries such as aerospace, naval, civil and nuclear engineering. It is proposed here to present a formulation for the modal analysis of incompressible liquids in elastic tanks taking into account sloshing, pressurization and elastogravity effects obtained through an adapted procedure of linearization. A corresponding Finite Element formulation is then presented

Vibrations of structures containing fluids. Elastogravity operator. Compressibility effects

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Modal analysis of vibrations of liquids coupled with structures

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Incompressible hydroelastic vibrations: Finite element modelling of the elastogravity operator

International audienceThis paper deals with the low frequency vibratory analysis of fluid-structure interactions in an elastic tank partially filled with an incompressible inviscid liquid. The originality of this work is to give an exact expression of the gravity interface operator whereas other standard hydroelastic formulations treat this effect through approximations. The properties of this so-called elastogravity operator will be studied here from theoretical and numerical point of view. Experimental measurements will validate the computational model and allow to quantify the effect of coupling between the liquid sloshing and the hydroelastic deformations of the structure

Damped vibrations of structures containing liquids

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Amortissement du ballottement d'un liquide dans un réservoir élastique

National audienceOn présente ici une formulation d’un problème couplé fluide - structure linéarisé amorti :il s’agit dans un premier temps d’introduire un modèle d’amortissement diagonal dans les équationsréduites du problème hydroélastique avec ballottement. Le système couplé dissipatif obtenu est alorsnon symétrique. En projetant sur ses modes propres complexes, on construit les réponses fréquentielleset temporelles pour différents types d’excitation

Linear vibrations of the structures containing viscous liquids

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RESOLUTION OF FLUID-STRUCTURE COUPLED PROBLEMS WITH FLOW USING THE BOUNDARY ELEMENT METHOD

Effects of fluid-structure coupling on the dynamic behaviour of flexible airship can be modelled with a potential, incompressible, inviscid flow. A new formalism to study linear variations of the flow induced on the fluid-structure interface in a time dependent ambient flow is introduced. The features of the Boundary Element Method used to solve this problem numerically are exhibited. Numerical results of the linear model are compared with analytical and non linear numerical results, assessing the validity and the limitations of the approach