Subgrid models preserving the symmetry group of the Navier–Stokes equations

In order to preserve the physical properties of the flow (scaling laws, conservation laws, …) during the simulation, a class of subgrid models respecting the symmetry group of the Navier–Stokes equations is built. The class is then refined such that models satisfy the second law of thermodynamics and are suited to take into account the inverse energy cascade. A simple model belonging to the class is tested and a better result than those provided by Smagorinsky and dynamic models is obtained. To cite this article: D. Razafindralandy, A. Hamdouni, C. R. Mecanique 333 (2005).     

Fermetures entropiques pour les systèmes bifluides à sept équations

In this Note, we propose a way to obtain two-fluid two-pressures multiphase models that satisfy an entropy inequality. We first notice that the continuous model associated to the discrete model of Abgrall and Saurel (2003) satisfies the entropy principles. Thanks to this, we show how to modify existing models in order to achieve the second law of thermodynamics. To cite this article: M. Papin, R. Abgrall, C. R. Mecanique 333 (2005).     

Un modèle paramétrique d'évolution de surface pour matériaux contraints : modélisationA parametric model of surface evolution for materials under constraint; part I: modeling

We present a model describing the surface changes of an elastic preconstrained material which is valid for large deformations. The surface profile is described by a parametric curve that allows the emergence of infinite tangents and back return point as the surface evolves. The proposed model covers a number of classic models: Spencer (1994), Yang (1993), Kassner (1994), Chiu (1994). These latter models were limited to surface profiles with one-to-one representations and low amplitudes of deformation. To cite this article: M. Carrive, J. Grilhé, C. R. Mecanique 334 (2006).     

A two scale method for modulated vibration modes of large,nearly repetitive,structuresUne méthode asymptotique à deux échelles pour les modes de vibrations modulés des longues structures presque répétitives

Nearly repetitive structures can present at least two kinds of vibration modes: localized modes and modulated ones. In this Note, the multiple scale method is applied to characterize a packet of modulated modes. In this respect, only small size problems are to be solved: periodic problems posed on a few basic cells and amplitude equations, which define a sort of homogenized model for this type of modes. It is established that the influence of the non-repetitive part of the structure is accounted by a boundary condition. To cite this article: E.M. Daya et al., C. R. Mecanique 331 (2003).     

Phenomenological nonlinear modelling of glassy polymers

Compared with the numerous works into the constitutive equations for the mechanical behaviour of metals, very little attention has been devoted to those of polymers. However, a model is required to describe both the complex shape of the stress–strain curves and strain rate sensitivity of glassy polymers. In this Note, a unified viscoelastic-viscoplastic model is presented in which the nonlinear pre-yield behaviour, the strain softening and the strain hardening are described by internal variables, in analogy with the models developed for metals. In order to check the predictive capability of the model, the numerical results are compared with the experimental data (monotone, creep and relaxation tests) of a typical amorphous glassy polymer. To cite this article: F. Zaïri et al., C. R. Mecanique 333 (2005).     

Mixing and coherent vortices in turbulent coaxial jets

Direct numerical simulations associated with mixing in constant-density round coaxial jets are performed. They are validated by comparison against laboratory experiments. The mixing process is studied by seeding a passive tracer first in the outer annular jet, then in the inner jet. We demonstrate the important role played by coherent vortices in the mixing mechanisms. The turbulent mixing exhibits an intermittent character as a consequence of fluid ejections caused by the counter-rotating streamwise vortices. We quantify also the domination of the outer jet and show that the fluid issuing from the central jet remains confined. To cite this article: G. Balarac, M. Si-Ameur, C. R. Mecanique 333 (2005).     

Cut-off analysis of coherent vortical structure identification in a three-dimensional external flow

Vortical structure identification has more recently been applied in the study of the transport of vortical structures in low Reynolds number three-dimensional complex geometry flows. An important issue in this identification procedure is to choose an appropriate cut-off value ${\lambda }_2$ which takes into consideration the finite precision vortex interfaces. This cut-off choice is studied in this Note and applied to an external flow around a curved cylinder. The vortex identification technique at different cut-off values is compared to the threshold of the vorticity field showing the efficiency of choosing the optimal tolerance gap. The computations are performed with a fully three-dimensional spectral/hp element method. To cite this article: A. Miliou et al., C. R. Mecanique 333 (2005).     

Computation of the mean velocity field above a stack plate in a thermoacoustic refrigeratorSimulation numérique de la vitesse moyenne près d'une plaque de l'empilement d'un réfrigérateur thermoacoustique.

A numerical simulation of the unsteady flow above one stack plate in a thermoacoustic refrigerator was performed. The second order mean velocity field was computed. Two regions could be distinguished. In the first region, located at the plate extremities, the mean flow is essentially vortical and results from the resonator/plate transition. In the second region, located above the plate, the mean velocity field corresponds to a streaming flow which results from the interaction of the acoustic wave with the plate boundaries. The effects of stack plates spacing on the streaming flow pattern is studied. To cite this article: D. Marx, Ph. Blanc-Benon, C. R. Mecanique 332 (2004).     

Shape optimization of an accommodative intra-ocular lens

Cataract surgery consists in replacing the clouded or opacified crystalline lens by an Intra-Ocular Lens (IOL) having the same mean dioptrical power. Clear vision is then achieved at a given distance and glasses are needed in many situations. A new kind of IOL, potentially accommodative, is proposed. Its design is based on the deep understanding of the accommodation mechanism and on the mathematical modeling and the numerical simulation of the IOL's comportment in vivo. A preliminary version of this IOL is now commercialized by the company HumanOptics under the name ‘1CU’. In a second phase, shape optimization techniques equipped with strong mechanical and physiological constraints, are used to enhance the IOL performance and build a new design. To cite this article: F. Jouve, K. Hanna, C. R. Mecanique 333 (2005).     

Homogénéisation de coques minces piézoélectriques perforées

In this Note we establish the limit constitutive law of a piezoelectric material with periodically perforated microstructures and whose reference configuration is a thin shell with fixed thickness. The justification of the new associated model (we show that the limit global and local problems are more complicated than the intial one) is obtained using the periodic unfolding method introduced by Cioranescu, Damlamian and Griso. To cite this article: M. Ghergu et al., C. R. Mecanique 333 (2005).     

Derivation of a well-posed and multidimensional drift-flux model for boiling flows

In this Note, we derive a multidimensional drift-flux model for boiling flows. Within this framework, the distribution parameter is no longer a scalar but a tensor that might account for the medium anisotropy and the flow regime. A new model for the drift-velocity vector is also derived. It intrinsically takes into account the effect of the friction pressure loss on the buoyancy force. On the other hand, we show that most drift-flux models might exhibit a singularity for large void fraction. In order to avoid this singularity, a remedy based on a simplified three field approach is proposed. To cite this article: O. Grégoire, M. Martin, C. R. Mecanique 333 (2005).     

Piston Stokes flow in a semi-infinite channelL'écoulement de Stokes autour d'un piston dans un conduit semi-infini

The piston flow is bounded by rigid walls at y=±1, x>0 and generated by the uniform translation of the end wall x=0. After Katopodes, Davis and Stone [3] constructed a solution in terms of biorthogonal eigenfunctions, Meleshko and Krasnopolskaya [1] used a variation of an asymptotic technique developed by Meleshko and Gomilko [2] to examine the pointwise convergence of the non-orthogonal series. However, they overlooked the nonuniqueness of their solution and the consequent solvability condition which is shown here to necessitate a minor modification without significant harm to their contribution. To cite this article: A.M.J. Davis, C. R. Mecanique 330 (2002) 457–459.     

Une comparaison des schémas d'intégration temporelle explicites de Chung–Lee et Tchamwa–WielgoszA comparison between the Tchamwa–Wielgosz and the Chung–Lee explicit time integration algorithms.

Numerous effort during the past ten years have focused on developing explicit time integration algorithms for structural dynamics that include controllable numerical dissipation of the spurious oscillations. Stability and consistency of the Tchamwa–Wielgosz algorithm are analysed for the linear damped/undamped cases. Furthermore, numerical results are compared for this algorithm and the Chung–Lee explicit method. To cite this article: V. Grolleau et al., C. R. Mecanique 332 (2004).     

Mathematical modeling of an array of underground waste containersModélisation mathématique d'un réseau souterrain de stockage de déchets

We consider a mathematical model describing the behavior of an underground waste repository, once the containers start to leak. Due to the high contrast of the characteristic lengths, numerical simulations on a such model are unrealistic. After renormalization, a small parameter ε appears and the global model is obtained when ε tends to zero, by means of homogenization and boundary layers methods. The asymptotic model obtained could be used as a global repository model for large field numerical simulations. To cite this article: A. Bourgeat et al., C. R. Mecanique 330 (2002) 371–376.     

Flow in wavy tube structure: asymptotic analysis and numerical simulationÉcoulement dans une structure tubulaire ondulée : analyse asymptotique et résolution numérique

This paper deals with the study of the stationary, incompressible, 2D flow of a fluid in a thin wavy tube. In this work, we consider a domain which is the union of two wavy tubes depending on a small parameter. The asymptotic expansion is constructed. The method of partial asymptotic decomposition is applied. The numerical implementation of this method for the extrusion process is developed. The new physical effects are discussed. To cite this article: A. Ainser et al., C. R. Mecanique 331 (2003).     

On the cavitation problem and the influence of the surface energy in a viscoplastic medium

In this Note, the solution for spherically symmetric cavitation in a viscoplastic material is analysed. To ensure of the reality of the physical behaviour of the material, the problem is studied by considering a hollow sphere whose matrix obeys to a modified Bodner and Partom model. This local phenomenon is understood in the sense of the rapid growth of a pre-existing void and a particular attention is made to understand the influence of the surface energy on the critical dilative stress. To cite this article: F. Zaïri et al., C. R. Mecanique 333 (2005).     

Simulation numérique directe de l'influence de la forme aval d'une plaque séparatrice sur une couche de mélangeDirect-numerical simulation of the splitting-plate downstream-shape influence upon a mixing layer

In this Note, we present direct numerical simulation results of a spatial mixing layer generated behind an upstream plate separating two boundary layers. The effect of the shape of the trailing edge of the plate is considered through comparisons between flows obtained from a bevelled or a blunt plate. In the former case, a spatial mixing layer consistent with previous experimental and numerical observations is obtained. In the latter case, the self-excited state that establishes in the near wake region dominates primary and secondary instability mechanisms while understating the importance of inflow perturbations. This behaviour is interpreted in terms of convective or absolute instability. The effects on turbulent statistics are also discussed. To cite this article: S. Laizet, E. Lamballais, C. R. Mecanique 334 (2006).     

Computational aeroacoustics applications based on a discontinuous Galerkin method

caa simulation requires the calculation of the propagation of acoustic waves with low numerical dissipation and dispersion error, and to take into account complex geometries. To give, at the same time, an answer to both challenges, a Discontinuous Galerkin Method is developed for Computational AeroAcoustics. Euler's linearized equations are solved with the Discontinuous Galerkin Method using flux splitting technics. Boundary conditions are established for rigid wall, non-reflective boundary and imposed values. A first validation, for induct propagation is realized. Then, applications illustrate: the Chu and Kovasznay's decomposition of perturbation inside uniform flow in term of independent acoustic and rotational modes, Kelvin–Helmholtz instability and acoustic diffraction by an air wing. To cite this article: Ph. Delorme et al., C. R. Mecanique 333 (2005).     

Écart à la réciprocité et identification de fissures en thermoélasticité isotrope transitoireReciprocity gap and identification of cracks in transitory isotropic thermoelasticity

We consider a three-dimensional homogeneous isotropic elastic solid containing a family of planar cracks submitted to a time-dependent thermal loading. The displacement and surface traction fields are measured over the whole external boundary of the solid. We propose in this Note to define and exploit a reciprocity gap, based only on the mechanical quantities available on the boundary, and which enables us to derive explicit formula for the location of the plane where the cracks are lying. Boundary conditions on the cracks can be of any nature provided they ensure that the normal heat flux and surface traction vector are continuous across the crack surfaces. To cite this article: S. Andrieux, H.D. Bui, C. R. Mecanique 334 (2006).     

Continuum modeling for the modulated vibration modes of large repetitive structuresModèle continu pour les modes de vibrations modulés des longues structures répétitives

By homogenization theory, one can predict the vibrations of long repetitive structures in the low frequency range. Beyond this range, many modes have a modulated shape. Based on a multiple scale analysis, a continuum model is presented, that is able to account for this class of modes. This model involves a real coefficient that can be computed from the finite element resolution of problems defined on a few basic cells. An application in 2D elasticity is presented. To cite this article: E.M. Daya et al., C. R. Mecanique 330 (2002) 333–338.