Coupling multiphysics problems in transient regimes: application to liquid resin infusion process

Liquid resin infusion (LRI) process is widely considered in the aeronautics, due to its benefits (low void content and production of large parts), for high performance composite material forming. The main objective of the present work is to simulate nu- merically the LRI process, in a high performance computing framework, which consists in coupling fluid-solid mechanics. Hence, two fluid flow regimes are coupled with an ef- ficient ASGS stabilized monolithic finite element formulations: the resin flow in both a highly permeable distribution medium (Stokes) and low permeability fibrous orthotropic preforms (Darcy). Moreover, weak coupling algorithms are used along for coupling solid / fluid mechanics, solid / level-set problems and fluid / level-set problems; where the level-set method is used to capture the moving flow front and the Stokes-Darcy interface. To transfer the different physical variables between the above coupled problems, Message Passing Interface (MPI) library is chosen, to ensure the best data transfer performances

3D simulation of the matter transport by surface diffusion within a level-set context

International audienceWithin the framework of the sintering process simulation, this paper proposes a numerical strategy for the direct simulation of the matter transport by surface diffusion. A level-set method is used to describe the topological changes which arise at the free boundary of the sintering particles. The surface velocity is found to be proportional to the surface Laplacian of the curvature, that is, proportional to the fourth-order derivative of the level-set function. Consequently, both curvature and velocity must be computed carefully and with accuracy. Finally, three-dimensional simulations are shown and investigated

Techniques d'interaction fluide-structure et théories cinétiques pour la simulation des procédés de mélange des polymères

http://hdl.handle.net/2042/15970International audienceNous présentons une méthode d'interaction fluide-structure basée sur une approche monolithique eulérienne permettant d'étudier à différentes échelles les procédés de mélange sous leur aspect dispersif et distributif. Une approche macroscopique traitant de la résolution mécanique dans le procédé, où interviennent des outils tournants, est présentée, couplée à un modèle dispersif via une théorie cinétique = A fluid-structure interaction method, based on a eulerian monolithic approach is introduced to study mixing processes within a multiscale approachs. One investigates macroscopic flow resolution for the whole process, including moving tools, coupled through a kinetic theory for dispersive mixin

A P1/P1 Finite Element Framework for Taking Into Account Capillary Effects in Biphasic Flow Simulations

This work describes a computational strategy, based on a stabilised finite element method, to simulate bifluid flow with capillary effects in a fibrous microstructure. In this framework, triple junction equilibrium is imposed as a natural condition in the weak formulation of the Stokes problem. Two types of 2D microstructures are then considered, hexagonal and random, and studied in terms of numerical permeability and capillary pressure

Étude de la formation d'une structure de mousse par simulation directe de l'expansion de bulles dans une matrice liquide polymère

In this contribution, a numerical tool is developed in order to simulate the inflation of a polymer foam. A sample of foam is considered as a set of gas bubbles growing in a polymer matrix. This growth is due to a difference of pressure. A velocity - pressure formulation is established over the liquid and the gaseous parts. The computation of the gas pressure, uniform in each bubble, requires to follow individually each bubble: our approach is multidomain. In an eulerian framework, each domain is represented by its characteristic function, which is solution of a transport equation. A space-time discontinuous Galerkin method has been developed to solve this kind of purely convective equations. The stability of this implicit method does not depend on the time step. Furthermore, the interface location is improved by a r-adaptation technique. Finally, in order to preserve the amount of liquid along the expansion, a global expansion motion is introduced: the computation volume grows with the foam. Using this methodology, the formation of a foam structure can be simulated: bubbles, occupying initially few percents of the whole volume, grow to occupy, finally, more than 80% of this volume. The liquid is then trapped between bubbles, creating polyhedric cells. This local approach is used to determinate evolution laws of the viscosity and growth rate of a foam sample, with respect to its structure. Using a micro-macro transition, these laws are employed to simulate the macroscopic expansion of a polymer foam.Ce travail est consacré au développement d'un outil numérique simulant l'expansion d'une mousse polymère. Un volume de mousse est décrit par un ensemble de bulles de gaz évoluant dans une matrice polymère. Son expansion est provoquée par la surpression du gaz. Un système d'équations décrivant les champs de vitesse et de pression est établi dans le liquide et dans le gaz. Le calcul de la pression du gaz, homogène dans chaque bulle, nécessite de connaître individuellement l'emplacement de chaque bulle: notre approche est multidomaine. Dans un contexte eulérien, chaque domaine est suivi par sa fonction caractéristique, laquelle est solution d'une équation de transport. Cette équation, purement convective, est résolue par une méthode éléments finis espace-temps Galerkin discontinu. Cette méthode est implicite: sa stabilité ne dépend pas du pas de temps. Une technique de r-adaptation de maillage diminue la diffusion liée à la discrétisation, et améliore la description des interfaces. Enfin, le domaine de calcul croît avec les bulles. Cette expansion globale préserve la géométrie du domaine, ainsi que la quantité de liquide contenue dans ce domaine. Cette méthodologie permet de simuler la formation d'une structure cellulaire: le taux de gaz passe de quelques pourcent à 80%, le liquide est piégé entre les bulles, et les cellules adoptent des formes polyédriques. L'approche locale développée est appliquée pour établir l'évolution de la viscosité et de la vitesse d'expansion d'un échantillon de mousse en fonction de sa structure. Un passage micro-macro permet d'utiliser ces lois pour simuler l'expansion macroscopique d'une mousse

Etude de la formation d'une structure de mousse par simulation directe de l'expansion de bulles dans une matrice liquide polymère

PARIS-MINES ParisTech (751062310) / SudocSOPHIA ANTIPOLIS-Mines ParisTech (061522302) / SudocSudocFranceF

A numerical strategy for the direct 3D simulation of the expansion of bubbles into a molten polymer during a foaming process

International audienceIn the framework of the foam process modelling, this paper presents a numerical strategy for the direct 3D simulation of the expansion of gas bubbles into a molten polymer. This expansion is due to a gas overpressure. The polymer is assumed to be incompressible and to behave as a pseudo-plastic fluid. Each bubble is governed by a simple ideal gas law. The velocity and the pressure fields, defined in the liquid by a Stokes system, are subsequently extended to each bubble in a way of not perturbing the interface velocity. Hence, a global velocity-pressure-mixed system is solved over the whole computational domain, thanks to a discretization based on an unstructured first-order finite element. Since dealing with an Eulerian approach, an interface capturing method is used to follow the bubble evolution. For each bubble, a pure advection equation is solved by using a space-time discontinuous-Galerkin method, coupled with an r-adaptation technique. Finally, the numerical strategy is achieved by considering a global mesh expansion motion, which conserves the amount of liquid into the computational domain during the expansion. The expansion of one bubble is firstly considered, and the simulations are compared with an analytical model. The formation of a cellular structure is then investigated by considering the expansion of 64 bubbles in 2D and the expansion of 400 bubbles in 3D

Using a signed distance function for the simulation of metal forming processes : Formulation of the contact condition and mesh adaptation. From a Lagrangian approach to an Eulerian approach

International audienceThis paper proposes to use the metric properties of the distance function between two bodies in contact (or gap function) in simulations involving contact problems. First, the normal vectors, which are involved in the formulation of the contact condition, are defined through the gradient of this distance function. This definition avoids to deal with the numerical penetration parameter, which is generally introduced otherwise. Furthermore, it allows the contact problem to be extended in a simple way to an Eulerian formulation. Second, this paper investigates two mesh adaptation strategies based on the properties of the distance function. The first strategy consists in building a size map according to the values of this function, in order to refine locally the mesh, and consequently to improve the description of the contact surface. The second strategy consists in adapting locally the mesh to the geometry of the contact surface. This anisotropic adaptation is performed by constructing a metric map that allows the mesh size to be imposed in the direction of the distance function gradient. A lot of elements are saved when compared with the isotropic case. Throughout this paper, many numerical simulations are presented in the context of the forging process: the deformable material is pressed between two rigid tools. Furthermore, the algorithm used to calculate the signed distance to a surface mesh is detailed in appendix of this paper