Étude numérique de l'effet de la portance inverse pour un fluide de Bingham autour d'un obstacle

Ce travail porte sur la simulation numérique d'un écoulement de fluide non-Newtonien (Bingham) autour d'un obstacle en forme de profil hydrodynamique. La méthode des volumes finis avec un maillage orthogonale généralisée est utilisée. Les résultats du calcul montrent une portance inverse pour l'écoulement du fluide de Bingham en régime laminaire. Ceci est en accord avec des résultats expérimentaux concernant la portance inverse obtenus par B. Dollet et al. (Physical Review Letters, 2005) pour une solution mousseuse

Development of secondary flows in viscoelastic curved ducts and the influence of outlet region

International audienceThis paper presents numerical simulations of Newtonian and viscoelastic flows through a 180° curved duct of square cross section with a long straight outlet region. A particular attention is paid to the development of the flow in the output rectangular region after the curved part. The viscoelastic fluid is modeled using the constitutive equation proposed by Phan-Thien-Tanner (PTT). The numerical results, obtained with a finite-volume method, are shown for three different Dean numbers (125,137,150)(125,137,150) and for three Deborah numbers (0.1,0.2,0.3)(0.1,0.2,0.3). The necessary outlet length to impose boundary conditions is presented and discussed for these cases. Streamlines and vortex formation are shown to illustrate and analyze the evolution of the secondary flow in this region

IBN SĪNĀ'S APPROACH TO EQUALITY AND UNITY

Aristotle did not develop the quantification of the predicate, but, as shown in a recent paper by Hasnawi, Ibn Sīnā did. In fact, assuming the Aristotelian subject-predicate structure, Ibn Sīnā qualifies those propositions that carry a quantified predicate as deviating (muḥarrafa) propositions. A consequence of Ibn Sīnā's approach is that the second quantification is absorbed by the predicate term. The clear differentiation between a quantified subject, that settles the domain of quantification, and a predicative part, that builds a proposition over this domain, corresponds structurally to the distinction, made in constructive type theory, between the type of sets and the type of propositions. Neither did Aristotle combine his logical analysis of quantification with his ontological theory of relations or equality. But Ibn Sīnā makes use of syllogisms that require a logic of equality, and considered cases where quantification combines via equality with singular terms. Moreover these reflections provide the basis for his theory of numbers that is based on the interplay between the One and the Many. If we combine Ibn Sīnā's metaphysical theory of equality with his work on the quantification of the predicate, a logic of equality comes out naturally. Indeed, the interaction between quantification of the predicate and equality can be applied to Ibn Sīnā's own examples of syllogisms involving these notions. By using the formal instruments provided Martin-Löf's constructive type theory, the present paper establishes links between Ibn Sīnā's metaphysics and his logical work: links that have been discussed in relation to other topics by Thom and Street. Ibn Sīnā did not develop a logic of identity, but he did develop the conceptual means to do s

Mathematical study of viscoelastic fluid flows in singular domains

Cette thèse est consacrée à l’analyse mathématique de trois problèmes d’écoulements de fluides viscoélastiques de type Oldroyd. Tout d’abord, nous étudions des écoulements stationnaires faiblement compressibles dans un domaine borné avec des conditions au bord de type "rentrante-sortante". Nous étudions aussi le problème d’écoulements stationnaires faiblement compressibles dans un coin convexe. En utilisant une méthode de point fixe (premier et deuxième problèmes) et une décomposition de Helmoltz (deuxième problème), nous montrons des résultats d’existence et d’unicité des solutions. Nous étudions également le cas d’un écoulement non stationnaire. Nous montrons un résultat d’existence locale et un résultat d’existence globale, avec des conditions initiales suffisamment petites, pour des fluides compressibles. Nous démontrons aussi la convergence du modèle d’écoulement viscoélastique compressible à faible nombre de Mach vers le modèle incompressible lorsque les données initiales sont "bien préparées"In this PHD thesis, we study three problems for viscoelastic flows of Oldroyd type. First, we study steady flows of slightly compressible in a bounded domain with non-zero velocities on the boundary ; the pressure and the extra-stress tensor are prescribed on the part of the boundary corresponding to entering velocity. This causes a weak singularity in the solution at the junction of incoming and outgoing flows. We also study the problem of steady flows of slightly compressible fluids with zero boundary conditions in a domain with an isolated corner point. Using a method of fixed point (first and second problems) and a Helmoltz decomposition (second problem), we show some results of existence and uniqueness of solutions. In the last part, we study the case of a non-steady flow : we show some results of local and of global existence, with sufficiently small initial data, for compressible flows. The zero-Mach number limit is also establishe

Étude mathématique d’écoulements de fluides viscoélastiques dans des domaines singuliers

In this PHD thesis, we study three problems for viscoelastic flows of Oldroyd type. First, we study steady flows of slightly compressible in a bounded domain with non-zero velocities on the boundary ; the pressure and the extra-stress tensor are prescribed on the part of the boundary corresponding to entering velocity. This causes a weak singularity in the solution at the junction of incoming and outgoing flows. We also study the problem of steady flows of slightly compressible fluids with zero boundary conditions in a domain with an isolated corner point. Using a method of fixed point (first and second problems) and a Helmoltz decomposition (second problem), we show some results of existence and uniqueness of solutions. In the last part, we study the case of a non-steady flow : we show some results of local and of global existence, with sufficiently small initial data, for compressible flows. The zero-Mach number limit is also establishedCette thèse est consacrée à l’analyse mathématique de trois problèmes d’écoulements de fluides viscoélastiques de type Oldroyd. Tout d’abord, nous étudions des écoulements stationnaires faiblement compressibles dans un domaine borné avec des conditions au bord de type "rentrante-sortante". Nous étudions aussi le problème d’écoulements stationnaires faiblement compressibles dans un coin convexe. En utilisant une méthode de point fixe (premier et deuxième problèmes) et une décomposition de Helmoltz (deuxième problème), nous montrons des résultats d’existence et d’unicité des solutions. Nous étudions également le cas d’un écoulement non stationnaire. Nous montrons un résultat d’existence locale et un résultat d’existence globale, avec des conditions initiales suffisamment petites, pour des fluides compressibles. Nous démontrons aussi la convergence du modèle d’écoulement viscoélastique compressible à faible nombre de Mach vers le modèle incompressible lorsque les données initiales sont "bien préparées

FLOWS OF WEAKLY COMPRESSIBLE VISCOELASTIC FLUIDS THROUGH A REGULAR BOUNDED DOMAIN WITH INFLOW-OUTFLOW BOUNDARY CONDITIONS

International audienceWe study steady isothermal motions of a nonlinear weakly compressible viscoelastic fluids of Oldroyd type in a bounded domain Omega subset of R(2),with given non-zero velocities on the boundary of Omega. We suppose that the pressure p and the extra-stress tensor tau are prescribed on the part of the boundary corresponding to entering velocities. A uniqueness and existence result for the solution (u,p,tau) is established in W(2,q)(Omega)xW(1,q)(Omega)xW(1,q)(Omega) with