Analyse mathématique de l'équation de Galbrun en écoulement uniforme

We consider Galbrun's equation, used in linear aeroacoustics. For a simple case (rigid duct with uniform flow) in the time harmonic regime, we show that an approach based on a regularized variational formulation of the problem ensures the convergence of a nodal finite-element method.     

Modélisation de l'effet de portance dans un écoulement à bulles

We propose here a lift coefficient modeling in a turbulent bubbly boundary layer under the assumption of bidimensional stationary and vertical upward fully developed flow. The basic frame of this approach is to consider that the volumetric flux of bubbles is composed of the convective flux by the liquid, the contribution by the gravitational field and those of the lift force and the bubble dispersion terms. A discussion of results completes this study.     

Représentation de la ligne de contact mobile dans les équations de la mécanique des fluides

Although the contact angle at equilibrium has a well understood theory for the case of flat homogeneous solid surfaces, the displacement of the contact line is still not well understood. We propose to introduce in the dynamics of the contact line a mobility relation between the deviation of the contact angle out of its equilibrium value and the speed of the line on the solid. When the line slides on the solid thanks to an evaporation/condensation process, this introduces a dynamical Arrhenius factor that may be sufficiently small to make the mobility of the contact line the limiting factor of the dynamics in many physical situations. Then, the shape of the liquid/vapor interface will be in quasi equilibrium giving a contact angle that will define ultimately the speed of the contact line.     

Sur la nature de la transition à l'instationnaire d'un écoulement de convection naturelle en cavité différentiellement chauffée à grands écarts de température

Natural convection of air inside a rectangular cavity, differentially heated under large temperature gradients, is considered. The low Mach approximation equations are those obtained by Paolucci allowing for filtering of sound waves. Transition to unsteadiness is studied with numerical simulation, with a finite volume code based on a fractional time step method derived from projection methods used for incompressible flows. When the fluid physical properties are prescribed constants, transition to unsteadiness follows the classical scheme of a Hopf bifurcation. The transition is quite different when viscosity obeys Sutherland's law while the Prandtl number is kept constant. There is evidence of hysteresis, therefore the transition seems to be subcritical. In the vicinity of the transition, on the large amplitude branch, an intermittent solution is observed, with periodic bursts separating quasi-steady states.     

Interprétation géométrique de la décomposition des équations de compatibilité en grandes déformations

In this paper, we establish compatibility equations satisfied by the right Cauchy–Green stress tensor by annihiling the associated curvature and torsion. The cancelation of torsion, using variables introduced by the polar decomposition, is not trivial as is usually the case. This point is the key to the decomposition of compatibility conditions in two first-order EDPs.     

Caractéristiques rhéologiques,coéfficient de frottement et écoulement en situation réelle de fluides à seuil

Résumé Ce travail porte sur l'étude de solutions diluées d'un polymère de l'acide acrylique dans l'eau (concentration en poids 0,1%). Ce fluide présente des effets de seuil. La mesure du champ de vitesse par vélocimétrie laser permet une détermination précise de l'indice rhéologique,n, étant un paramètre essentiel de la loi de comportement proposée: . Les autres constantes peuvent être déduites d'essais rhéologiques classiques, à fort taux de cisaillement. Il est possible de corriger le gradient de pression mesuréP/L, afin d'obtenir la valeur véritable de ce gradient, notéedp/dz. L'analyse de l'écoulement dans un élargissement brusque montre que le seuil a une forte influence sur les zones de recirculation.

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This work deals with the study of very dilute solutions of polyacrylic acid in water (weight concentration about 0.1%). These fluids seem to exhibit a yield effect. The determination of the fully developed velocity field by laser velocimetry allows us an accurate determination of the rheological indexn which is an essential parameter for the proposed rheological relationship: . Other constants can be determined from classical rheological experiments (high shear strain). It is possible to correct the experimental pressure gradientP/L so as to get the real value, noted asdp/dz. An analysis of the flow in an abrupt expansion shows that the yield effect strongly influences the recirculation zones.

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D, d m diamètre intérieur d'une conduite cylindrique - C % concentration en poids - _s Pa seuil de contrainte - K consistance - gradient de vitesse axiale - gradient pariétal de vitesse axiale - Pa s viscosité pour - Pa contrainte de cisaillement - m/s vitesse débitante - n indice de structure - dp/dz Pa/m gradient longitudinal de pression - z m abscisse longitudinale - u m/s vitesse axiale - écart entre le gradient de pression effectif et le gradient mesuré en Pa - P Pa différence de pression mesurée - L m distance entre 2 prises de pression - A Pa constante intervenant dans l'expression de - B 10^–3 Pa s constante intervenant dans l'expression de     

Méthode de Le Verrier–Souriau et équations différentielles linéaires

A crucial step of algorithms allowing the study of discrete mechanical system vibrations is the determination of eigenmodes and eigenvalues. The accuracy of the results is of great importance because the stability study of the system depends on them. Eigenvalues can be found with a very good precision, however the eigenmodes determination is awkward: their direction could present significant instabilities. We proposed a method which avoids the necessity of doing eigenmodes research and so the attendant instabilities. It is based on Le Verrier–Souriau algorithm usually reserved for the resolution of linear algebraic systems.     

Sur une méthode de pénalisation tensorielle pour la résolution des équations de Navier–Stokes

An original reformulation of the viscous stress tensor is proposed for the motion equations dedicated to an incompressible fluid. Four different tensors appear in this decomposition, associated with viscosities of compression, elongation, shearing and rotation. This new model allows us to build a numerical solver of the Navier–Stokes equations based on a technique of tensorial penalization which is generalized with all the stresses acting on a flow. The processing of incompressibility and the rotation of a rigid body in a flow are described thanks to the model. Several numerical applications are proposed to illustrate the abilities of the new penalization method.     

Inductions électromagnétiques en relativité générale et principe de Fermat

Sans résumé Mémoire transmis par A. Lichnerowicz     

Extension de la DRBEM à la propagation guidée en écoulement cisaillé

The present study aims to extend the Dual Reciprocity Boundary Element Method in order to solve acoustic wave propagation equations in the frequency domain for a parallel shear flow. The Linearized Euler Equations are written as a coupled pair of equations, which are second-order in terms of acoustic pressure and first-order in terms of normal acoustic velocity. Good agreement between numerical results and analytical solutions for a low Mach number shear flow (M<0.1) shows the interest of the method.     

Analyse de la répartition du potentiel électrique dans les flammes

Distribution of electrical potential is investigated for two kinds of flames: Bunsen burner and counterflow flames. Different electrode materials have been tested to determine these potentials. Measurable potentials and organized structures are found. Premixed Bunsen burner flames show a zero potential cone at their base just under the most intense potential region. One-dimensional counterflow diffusion flames are characterized by the stretch rate. The potential reaches its minimum value in the reaction zone and its absolute value decreases when stretch increases.     

Mise en évidence par granularité en lumière blanche de phénomènes de multilocalisation de la déformation pour les bétons de poudres réactives sollicités en traction

From kinematic observations by granularity in whiting light mode based on a technique of digital speckle images correlation, the behaviour in tension of a reactive powders concrete is studied. The measures show several localisation areas of the deformation fields and the role of the fibres in the transmission of the stresses in the neighbourhood of a damaged area.     

Un résultat d'absence de valeurs propres plongées pour le guide topographique élastique

In this work, we prove a nonexistence result about embedded eigenvalues for the elastic topographical waveguide. We give an answer to a question raised by Bonnet-Bendhia et al. (1999).     

Proposition d'un paramètre énergétique de rupture pour les matériaux dissipatifs

We suggest an energetic fracture parameter for non elastic materials. This one is presented in a domain integral, and founded on the release rate of the total mechanical energy received by a notched solid, using a domain derivation method. This parameter is proposed for a large class of loading and materials described by internal variables. It is shown that this parameter is reduced to the Rice–Cherepanov integral when the material is either elastic or elastoplastic and submitted to proportional loading.     

Étude du comportement d'une fissure humide soumise à une élévation de température

We have been interested in the role of water inside a material crack, during heating. We have established an original analytical solution giving, the liquid–vapour repartition in the crack and the crack tip stress intensity factor, as functions of crack's length, water molecules contained in the inner of the crack and temperature. Then, we are able to study the crack stability.     

Dissymétrie de comportement élastique anisotrope couplé ou non à l'endommagement

A thermodynamic framework is proposed to model anisotropic elasticity different in tension and in compression. Based on Kelvin decomposition of the compliance tensor, it applies to any 3D loading. Coupling with damage is made considering fourth- and second-order damage tensors. The proposed formulation automatically satisfies the continuity of the stress tensor and of the energy release rate tensor. The particular case of initially isotropic materials is exposed.     

Étude expérimentale et numérique de la convection thermomagnétique dans un fluide non électroconducteur

We present an experimental and numerical study of convection driven by a central heat source in a vertical and cylindrical cavity with a higth aspect ration, filled by air and submitted to the action of non homogeneous intence magnetic field. We show how the magnetization force applying on oxygene is able to intensify, reduce, stop or even reverse the natural convection fluid flow.     

Comportement thermomécanique de l'argile de Boom

Special attention has been recently paid on temperature effects on the behaviour of deep saturated clays, in relation with nuclear deep waste storage. However, few experimental data are presently available, and existing constitutive models need to be completed. This note is aimed at completing, both experimentally and theoretically, the understanding of the effects of the overconsolidation ratio on the thermal volume changes of Boom clay (Belgium). The experimental data obtained here are in a good agreement with existing data. As a complement to existing data, they are used to develop a new elastoplastic model. The adoption of a second coupled plastic mechanism provides good simulations on a complex thermo-mechanical path.     

Une méthode inverse à régularisation évanescente

A new resolution method for inverse Cauchy problems is presented. The proposed method is iterative. It possesses the advantage to not perturbe the problem neither by an operator modification nor by introduction of an a priori information on the solution. The presentation is made on a model problem for the Laplace's equation. Numerical simulations prove the method efficiency.