Acoustique d'un fluide au voisinage du point d'ébullition

International audienceDans une étude précédente (Boutin et Auriault 1993), la propagation d'ondes acoustiques dans un fluide à bulles en concentration finie était analysée au moyen de la méthode des échelles multiples. Trois comportements différents étaient mis en évidence suivant la taille des bulles, grande, moyenne ou petite. Dans la présente note, nous étendons cette étude par la prise en compte d'un possible changement de phase. Nous montrons que les effets de celui-ci sont négligeables dans le cas de grandes bulles, et modifient fortement le comportement des bulles moyennes en diminuant de plusieurs orders de grandeur la rigidité effective. Pour les petites bulles la capillarité devient le phénomène prépondérent

Waves in bubbly liquids with phase change

International audienceIn a previous paper (C. Boutin, J.-L. Auriault, Acoustics of a bubbly fluid at large bubble concentration, Eur. J. Mech. B/Fluids, 12(3) (1993) 367-399), the homogenization technique was used to investigate how acoustic waves propagate in a bubbly fluid at finite concentration. Three different equivalent macroscopic behaviours were shown to exist, for "large"-, "medium"- and "small"-size bubble systems, respectively. In the present paper, we extend the analysis by taking into consideration possible phase change effects. We show that phase change effects are negligible in the case of large-size bubbles, whereas they strongly modify the medium-size bubble system behaviour. For small-size bubbles capillarity dominates the process

Hydro-mechanical coupling in damaged porous media containing isolated cracks or/and vugs: model and computations

In this paper we present the development of the macroscopic model describing the hydro-mechanical coupling of damaged porous media containing cracks or/and vugs, by using the asymptotic expansion method. The analysis starts at the mesoscopic scale at which we assume a generic microstructure and the validity of the Biot model in the micro-porous domain saturated by a fluid. In the crack/vug domain the Stokes equation is assumed. After estimation of orders of magnitude of different terms, the description is rendered non-dimensional and the homogenization process is carried out. It leads to an extended Biot model that possesses the same mathematical structure as the initial Biot model. However, the macroscopic poro-elasticity and the macroscopic Darcy conductivity are modified. In order to illustrate the performance of the model, numerical computations of a macroscopic boundary value problem were performed. The results show practical importance of modifications introduced in the Biot model

Long wavelenght inner-resonance cut-off frequencies in elastic composite materials

International audienceWe revisit an ancient paper (Auriault and Bonnet, 1985) which points out the existence of cut-off frequencies for long acoustic wavelength in high-contrast elastic composite materials, i.e. when the wavelength is large with respect to the characteristic heterogeneity length. The separation of scales enables the use of the method of multiple scale expansions for periodic structures, a powerful upscaling technique from the heterogeneity scale to the wavelength scale. However, the results remain valid for non-periodic composite materials which show a Representative Elementary Volume (REV). The paper extends the previous investigations to three-component composite materials made of hard inclusions, coated with a soft material, both of arbitrary geometry, and embedded in a connected stiff material. The equivalent macroscopic models are rigorously established as well as their domains of validity. Provided that the stiffness contrast within the soft and the connected stiff materials is of the order of the squared separation of scales parameter, it is demonstrated (i) that the propagation of long wave may coincide with the resonance frequencies of the hard inclusions/soft material system and (ii) that the macroscopic model presents a series of cut-off frequencies given by an eigenvalue problem for the resonating domain in the cell. These results are illustrated in the case of stratified composites and the possible microstructures of heterogeneous media in which the inner dynamics phenomena may occur are discussed

Acoustics of a bubbly fluid at large bubble concentration

International audienceThe homogenization process is used to investigate how acoustic waves propagate in a bubbly fluid at finite concentration. This method involves the consideration of waves whose lengths are large compared with the bubble size. We focus on the linear domain, with viscous, thermal and capillary effects. It is shown that this medium displays three different macroscopic descriptions according to bubble diameter and wave frequency. For bubbles of small size, the capillary effect leads to a model where in acoustic waves are either propagative with low celerity or diffusive. On increasing the bubble diameter we obtain waves which are damped and dispersed by both viscous and thermal effects. Finally for large bubbles, we get biphasic undamped and dispersed waves. Moreover, the homogenization method allows us to predict the kind of behaviour and the accuracy of the model from a knowledge of the physical characteristics of the mixture. Applications of these results are presented in the case of water containing air bubbles in equal proportion

About non-Fickian hyperbolic diffusion

Fick's law expresses the proportionality of solute flux with respect to concentration gradient. Similar relations are Darcy's law for the fluid flow in porous media, Ohm's law for the electric flux and Fourier's law for heat transfers. When introduced in the corresponding balance equations, these flux laws yield diffusion equations of parabolic character. Different attempts have been made to obtain hyperbolic equations so as to point out propagative phenomena. This was done by adding a time derivative flux term to the flow law. In the paper we focus on solute transport. Two possible non-Fickian diffusion cases are addressed. We firstly investigate diffusion in fluids by a mechanistic approach. Secondly, we study the macroscopic diffusion law in composite materials with large contrast of diffusion coefficient. We show that the obtained diffusion law yields hyperbolicity for drastically small characteristic times or non-propagative waves, respectively

DOUBLE-POROSITY SOILS WITH HIGHLY CONDUCTIVE INCLUSIONS: MODELING OF WATER FLOW IN UNSATURATED CONDITIONS

Summary The homogenization method by asymptotic expansions was used to study water flow in a double-porosity soil. The gravity effect is included. The macroscopic flow model was found to be a single diffusion-type equation with two effective parameters. The effective conductivity tensor is defined as depending on the solution of a local boundary value problem within a period. The effective specific water capacity is found to be the volumetric average. Both parameters are functions of the capillary pressure head. A numerical example of water infiltration into initially dry soil is presented. The results of homogenization show good agreement with the reference fine scale solution

Modélisation de l'écoulement de fluides en loi puissance en milieux fibreux anisotropes

L'écoulement de fluide en loi puissance à travers des milieux fibreux anisotropes est étudié en s'appuyant sur les résultats théoriques obtenus par la méthode d'homogénéisation des structures périodiques. Afin de determiner la structure de la loi d'écoulement, des simulations numériques ont été réalisées sur des volumes élémentaires représentatifs d'un milieu fibreux modèle 2D constitué d'un arrangement carré de fibres parallèles de sections circulaires ou elliptiques. Enfin une méthodologie, basée sur l'étude de courbes d'iso-dissipation mécanique ainsi que la théorie de représentation des fonctions tensorielles, est proposée afin de formuler la loi d'écoulement macroscopique. Cette méthodologie est illustrée sur les résultats numériques obtenus

Etude des milieux pulvérulents non chargés dans l'hypothèse de la plasticité parfaite : application au problème d'une roue rigide reposant sur du sable

Université : Faculté des sciences de l'Université de Grenobl