Solutions périodiques et presque-périodiques des systèmes d'équations aux différences finies

Sans résumé Présenté par C. Iacob     

Contrôle passif d'écoulements incompressibles autour d'obstacles à l'aide de milieux poreux

Passive control of the flow behind a bluff-body is obtained by integrating porous area on the body. The penalisation method is used to modelize the flow in three different media. In fact each medium can be considered as a porous medium. The fluid is identified as a porous medium of infinite permeability and the solid is identified as a porous medium of zero permeability. This way, it is easy to compute the flow in each medium using the same parameter. Some benefical effects are due to the porous interface: the flow is smoothed, and the enstrophy and drag are significantly reduced.     

Extension du modèle d'échelles mixtes à la diffusivité de sous-maille

In the large-eddy simulation frame for non-isothermal turbulent flow, the Mixed Scale Model is extended to the subgrid diffusivity, in order to dissociate the computation of subgrid viscosity and diffusivity. The identification of the subgrid thermal dissipation term in the subgrid flux transport equation leads to an algebraic expression of the subgrid diffusivity. This diffusive model, as the Smagorinsky one, is weighted by a model based on scale similarity. This expression leads to satisfactory results when applied to a buoyant turbulent flow in a differentially heated cavity.     

Champ dynamique dans une cellule d'échangeur à vortex : 1. Régime d'entrée laminaire

Numerical simulation and LDV measurements are performed for laminar inlet flow condition in a vortex exchange chamber with isothermal conditions. Newtonian and non-Newtonian fluids were used. Experimental measurements are compared to results of numerical computations with good agreement. Both show the existence of a secondary flow generated by hydrodynamical instabilities due to streamline curvature. The main vortex flow appears then to be restricted by this secondary flow.     

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.     

Étude optique des processus d'écoulement de solutions viscoélastiques

Résumé On précise les caractères principaux des variations de la viscosité, de l'angle d'extinction et de la biréfringence des systèmes: laurate de potassium-chlorure de potassium/eau. On montre que dans l'ensemble, ces propriétés ne peuvent pas être interprétées à l'aide des modèles habituels de particules rigides indéformables ou de particules globulaires déformables. Par contre, au prix d'un petit nombre d'hypothèses simples, on peut rendre compte, au moins qualitativement des phénomènes observés par la considération du modèle d'une suspension de particules dissymétriques mais déformables à la manière d'un fluide anisotrope et non d'un solide élastique.

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Zusammenfassung Die wesentlichen Merkmale der Veränderungen der Viskosität, des Auslöschungswinkels und der Doppelbrechung von den Systemen: Kaliumlaurat-, Kaliumchlorid-Wasser können genau bestimmt werden. Diese Eigenschaften werden nicht mit Hilfe der gewöhnlichen Modelle von starren unverformbaren oder kugelförmigen Teilchen im Ganzen erklärt. Im Gegenteil, man kann mit einer kleinen Zahl von einfachen Voraussetzungen wenigstens in einer qualitativen Weise die beobachteten Phänomene durch die Betrachtung des Modells einer Suspension von dissymetrischen und sich wie eine anisotrope Flüssigkeit, nicht aber wie ein elastischer Festkörper fließenden verformbaren Teilchen erklären.

     

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.     

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.     

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.     

Modélisation du frottement pariétal dans un écoulement à bulles

In the present study, we propose a wall friction modeling in a vertical upward bubbly flow under the assumptions of bidimensional stationary and fully developed flow. This approach is based on the two-fluid model and on the hypothesis that the averaged flow is parallel to the wall. The turbulence modeling is an essential part in this model. Comparison with experimental data (presently available) exhibits satisfactory agreement. Other experimental studies, especially at a high void fraction, are desirable to examine further the model validity.     

Mécanique de la rupture fragile en présence de plasticité : définition d'un taux de restitution d'énergie

This study aims at defining an energetic parameter which characterises progressive crack growth in a brittle elastoplastic medium. First, Francfort and Marigo's elastic fracture theory, based on a minimum energy principle, is recalled. Then, a link with the framework of generalised standard materials is exhibited and allows to introduce the new energetic contributions due to plasticity.     

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.     

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.     

Inversion d'un écoulement plan de Stokes – application à l'écoulement à débit moyen nul entre deux plans parallèles

We present the interest and some characteristics of the inverse transformation of a 2D Stokes flow. This method is applied to the cellular flow between two parallel plates induced by a rotating cylinder to obtain the flow around two circular cylinders in contact placed in the centre of a rotating circular cylinder.     

La mécanique rationnelle sur un espace à trois dimensions dans un espace riemannien à quatre dimensions

Sans résumé     

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