A unifying model for fluid flow and elastic solid deformation : a novel approach for fluid-structure interaction and wave propagation

Le modèle compressible multiphasique proposé, permettant de gérer dans un même système des phases fluides (compressibles) et solides (élastiques), est basé sur les équations classiques de conservation de masse, de quantité de mouvement et de flux de chaleur. Sa spécificité réside dans la prise en compte dans l’équation de Cauchy, définie sous sa forme Lagrangienne, de la pression p à l’instant t, explicitement définie à partir de la pression p0 à l’instant t0=t-dt, des coefficients thermodynamiques et des divergences de vitesse et de flux de chaleur de l’instant t. De façon similaire, la température T est explicitement définie dans l’équation de conservation des flux de chaleur. Les champs de vitesses et de flux de chaleur alors obtenus par la résolution du système d’équations de conservation permettent le calcul explicite de la pression p et de la température T contribuant à la fermeture du système. Notons que dans ce modèle, la masse volumique n’est plus déduite d’une équation d’état, mais est directement déterminée du calcul de la divergence de la vitesse. C’est dans une étape ultérieure que les différents champs scalaires et vectoriels sont advectés à partir de leur dérivée totale pour une résolution Eulérienne. Ce modèle compressible est dans un premier temps validé par plusieurs cas test comme : 1) la compression de systèmes monophasés fluide ou solides ; 2) la compression d’un système diphasé fluide/solide à interface plane ; 3) la propagation d’ondes de compression et de cisaillement dans un solide élastique pour le calcul de la vitesse des ondes sonores. Dans un second temps, est abordée l’étude d’un cas complexe 3D consistant en l’injection d’un fluide sur un solide élastique. La déformation de l’interface fluide/solide ainsi que l’évolution de la pression en des points caractéristiques des deux phases de l’instant initial à l’état stationnaire sont analysées

The impact of fluctuations on the sintering kinetics of two particles demonstrated through Monte Carlo simulation

In the field of particle sintering involving viscous bulk flow, this paper shows, using Monte Carlo modelling, that energy fluctuations influence particles sintering kinetics. These fluctuations are considered to be responsible for the non-linear mass transport behaviour during the sintering of two cylinders. In the case where these fluctuations are considered negligible, the Newtonian viscous flow regime is shown to be the main mechanism

Numerical study of a hard sphere wetted by a spherical viscoelastic particle

The wetting process of a hard sphere by a fluid particle is numerically studied using a Monte Carlo approach. A methodology different to that based on the Potts model is being developed in the framework of an energetic potential, which explicitly accounts for the interfacial energies as well as a cohesive energy of the fluid particle. The minimisation of the potential through random changes of the particle configuration enables the quantification of stress gradients within the particle induced by the surface curvature gradients as well as the induced mass fluxes. The physical constants considered for the calculation of the energetic potential correspond to a wetting angle equal to 30°, and ensure that the rheological behaviour, which is implicitly generated during the Monte Carlo procedure, is viscoelastic. An insight into the stress gradients and mass fluxes within the fluid particle at different stages of the wetting process is presented. The wetting kinetics are analysed and compared to the kinetics of the co-sintering process of two fluid particles

Numerical modeling of diffusion-controlled phase transformation using the Darken method: Application to the dissolution/precipitation processes in materials

Many material phase transformations are controlled by mass transport induced by diffusion. To better understand such transformations, numerous modeling strategies at the scale of the moving interfaces exist, with their strengths and weaknesses. Phase-field approaches are based on diffuse interfaces that do not require any interface tracking, as opposed to those based on fixed-grid sharp interface tracking. In the case of binary two-phase systems, in this paper we address the key point of the mass balance equation at the interface involving a concentration jump, which determines the interface moving velocity. We propose a unique diffusion equation for both phases and their interface, based on the component’s chemical potentials which are continuous through the interface and a smooth volume-of-fluid phase representation. This model is achieved in the framework of the Darken method, which involves intrinsic diffusion of components and a drift velocity to which all compounds are subjected. This drift velocity is shown to be that of the interface displacement as well. This methodology is verified for 1D and 3D dissolution/precipitation problems and has a first-order spatial convergence. The 3D simulations of precipitation and dissolution processes of more complex microstructures clearly show a bifurcation of the particle morphology from the initial spherical shape when the diffusion edges of each particle interact with each other. An extension of the diffusion potential to mechanical driving forces should make it possible to deal with mechano-chemical coupling of mass transport

3D original modelling of phase transformation/mechanics coupling : Effects of internal and external applied stresses on particle growth

The elastic effects on particle growth were studied from a developed 3D original model that couples explicitly phase transformations and mechanical fields. This model is shown to be able to describe the time-evolution of both chemical and mechanical fields and their interactions in diffusive mass transport. In order to isolate and to analyse some generic effects of elastic fields, the model developed was applied to the growth of an initially single spherical precipitate into a supersaturated matrix in a finite media. We account for both internal and external applied stresses effects on the growth process including both thermo-kinetics and morphological aspects. In all cases studied, the elastic effects are shown to affect the transformation kinetics and equilibrium state. It is also demonstrated that the applied uniaxial compression loading induces an anisotropy of growth that affects both the morphological evolution and hence the equilibrium shape of the particle. This is shown to result to complex interactions between local pressure gradients and local composition gradients

3D original modelling of phase transformation/mechanics coupling : Effects of internal and external applied stresses on particle growth

The elastic effects on particle growth were studied from a developed 3D original model that couples explicitly phase transformations and mechanical fields. This model is shown to be able to describe the time-evolution of both chemical and mechanical fields and their interactions in diffusive mass transport. In order to isolate and to analyse some generic effects of elastic fields, the model developed was applied to the growth of an initially single spherical precipitate into a supersaturated matrix in a finite media. We account for both internal and external applied stresses effects on the growth process including both thermo-kinetics and morphological aspects. In all cases studied, the elastic effects are shown to affect the transformation kinetics and equilibrium state. It is also demonstrated that the applied uniaxial compression loading induces an anisotropy of growth that affects both the morphological evolution and hence the equilibrium shape of the particle. This is shown to result to complex interactions between local pressure gradients and local composition gradients

Full resolution of the Monte Carlo time scale demonstrated through the modelling of two-amorphous-particles sintering

Kinetics Monte Carlo approaches based on the discrete Potts model are shown to be limited for a complete resolution of the time scale for mesoscale problems. This is due to the inadequacy of a discrete modelling for a continuous physical problem. In the field of particle sintering involving viscous flow, it is shown how to overcome this limitation through the non-discrete Monte Carlo (NDMC) methodology, which is based on an energetic potential directly related to the energy scale of the system. In this paper is presented the last step in the complete resolution of the Monte Carlo time scale, counted in number of steps, into real time. The obtained conversion time scaling is defined as a function of materials physical properties and numerical parameters depending on the algorithm only. This resolution was based on the physical consistency of the sintering kinetics simulated using the NDMC. Actually, the NDMC kinetics was shown to perfectly match viscous sintering kinetics. This result was not straightforward since the sintering mechanism is not predetermined in the Monte Carlo methodology but implicitly generated as a function of mass transport probabilities

A unifiying model for fluid flow and elastic solid deformation: a novel approach for fluid-structure interaction

Fluid–structure coupling is addressed through a unified equation for compressible Newtonian fluid flow and elastic solid deformation. This is done by introducing thermodynamics within Cauchy׳s equation through the isothermal compressibility coefficient that is experimentally measurable for both fluids and solids. The vectorial resolution of the governing equation, where every component of velocity vectors and displacement variation vectors is calculated simultaneously in the overall multi-phase system, is characteristic of a monolithic resolution involving no iterative coupling. For system equation closure, mass density and pressure are both re-actualized from velocity vector divergence, when the shear stress tensor within the solid phase is re-actualized from the displacement variation vectors. This novel approach is first validated on a two-phase system, involving a plane fluid–solid interface, through the two following test cases: (i) steady-state compression and (ii) longitudinal and transverse elastic wave propagations. Then the 3D study of compressive fluid injection towards an elastic solid is analyzed from initial time to steady-state evolution

A multi-physics and multi-time scale approach for modeling fluid–solid interaction and heat transfer

A novel non-conservative formulation for equations governing thermo-mechanical phenomena is developed to address multi-material and multi-physics issues. The first key point is that this formulation achieves a unifying equation for compressible viscous fluid flow and elastic solid deformation. The second is that the thermo-mechanical equations are both written with velocity and thermal flux variables to solve them simultaneously. With that formulation, interaction conditions at the fluid–structure interface become implicit and state equation is no longer necessary. Multi-time scale problems are solved, from the time scale of acoustic and thermoacoustic wave propagation, to longer time scale of fluid flow and thermal diffusion

Improvent in the accuracy of calculated interface morphologies within Monte Carlo simulations of sintering processes

Non-discrete energetic Monte Carlo methodology applied to two-dimensional constrained or free sintering of an infinite row of particles, showed the relevance of such a model for an accurate evaluation of the interface morphologies. Calculated interface morphologies for equilibrium and quasi-equilibrium states match perfectly those obtained using direct analytical methods