Transient gas flow simulation using an Adaptive Method of LinesSimulation d'écoulements dans un gazoduc par la méthode adaptative de lignes

Designing natural gas pipelines to safely and efficiently handle unsteady flows, requires knowledge of pressure drop, flowrate and temperature distribution throughout the system. The accurate prediction of these parameters is essential in order to achieve optimum cumulative deliverability, and safe and reliable operation. An Adaptive Method of Lines algorithm is formulated for the solution of Euler system of equations, which fully simulates slow and fast transients. Two test cases present the improvement of the numerical solution from grid adaptation. Good results are obtained both for slow and fast transients simulations proving that the suggested numerical procedure is appropriate for such predictions. To cite this article: E. Tentis et al., C. R. Mecanique 331 (2003).     

Numerical approximation of a viscoelastic frictional contact problemApproximation numérique d'un problème viscoélastique de contact avec frottement

We consider a fully discrete scheme for a quasistatic frictional contact problem between a viscoelastic body and an obstacle. The contact is bilateral, the friction is modeled with Tresca's law and the behavior of the material is described with a viscoelastic constitutive law with long memory. We state an existence and uniqueness result for the discrete solution, followed by error estimate results. Then, we present numerical simulations in the study of a two-dimensional test example. To cite this article: Á. Rodríguez-Arós et al., C. R. Mecanique 334 (2006).     

Comparison of numerical methods and combustion models for LES of a ramjet

Ramjets are very sensitive to instabilities and their numerical predictions can only be addressed adequately by Large Eddy Simulation (LES). With this technique, solvers can be implicit or explicit and handle structured, unstructured or hybrid meshes, etc. Turbulence and combustion models are other sources of differences. The impact of these options is here investigated for the ONERA ramjet burner. To do so, two LES codes developed by ONERA and CERFACS compute one stable operating condition. Preliminary LES results of the two codes underline the overall robustness of LES. Mean flow features at the various critical sections are reasonably well predicted by both codes. Disagreement mainly appear in the chamber where combustion positions differ pointing to the importance of the combustion and subgrid mixing models. The two LES produce different energy containing motions. With CEDRE, a low frequency dominates while AVBP produces different ranges of low frequencies that can be linked with acoustic modes of the configuration. To cite this article: A. Roux et al., C. R. Mecanique 337 (2009).     

A competitive transport across polymeric membranes. Study of complexation and separation of ions

The removal and separation of Cu(II), Zn(II) and Ni(II) from nitrate aqueous solutions were studied by competitive transport across cellulose triacetate plasticized membranes modified with polyelectrolytes: polyethyleneimine (PEI) and polyethyleneglycol (PEG). Competitive transport of trace ions from aqueous solutions across polymer inclusion membranes containing a mixture of the three polymers (cellulose triacetate as the support) and tris(2-ethylhexyl-phosphate) (TEHP) as the plasticizer provide the selectivity order: Cu(II) > Ni(II) > Zn(II). A long-term transport experiment was carried out to demonstrate the durability of polymer inclusion membranes. A separation of bivalents cations (Cu²⁺, Ni²⁺, Zn²⁺) and monovalent cations (K⁺ and Na⁺) is achieved.     

Effects of conductivity jumps in the envelope of a kinematic dynamo flowInfluence des discontinuités de conductivité dans l'enveloppe de l'écoulement d'une dynamo cinématique

This Note reports on numerical simulations of the kinematic dynamo action in a test flow modeling the Von Kármán Sodium (VKS) experiment performed at CEA-Cadarache. We show that the conductivity of the vessel greatly influences the critical magnetic Reynolds number. These effects are dramatically amplified as the ratio of the conductivity of the vessel to that of the sodium increases from 1 to 5. To cite this article: R. Laguerre et al., C. R. Mecanique 334 (2006).     

A time-integration scheme for thermomechanical evolutions of shape-memory alloysUn algorithme d'intégration en temps pour l'évolution thermomécanique des alliages à mémoire de forme

This Note presents a time-integration strategy for computing the evolution of structures embedding shape-memory alloys in a thermomechanical setting. A variational formulation is associated with the scheme proposed, which allows one to study the existence and unicity of solutions depending on the material model considered. A numerical example is presented to illustrate the method and discuss the influence of the thermomechanical coupling. To cite this article: M. Peigney, C. R. Mecanique 334 (2006).     

Dynamics of a particle with friction and delay

We are interested in the motion of a simple mechanical system having a finite number of degrees of freedom subjected to a unilateral constraint with dry friction and delay effects (with maximal duration $\tau >0$). At the contact point, we characterize the friction by a Coulomb law associated with a friction cone. Starting from a formulation of the problem that was given by Jean-Jacques Moreau in the form of a second-order differential inclusion in the sense of measures, we consider a sweeping process algorithm that converges towards a solution to the dynamical contact problem. The mathematical machinery as well as the general plan of the existence proof may seem much too heavy in order to treat just this simple case, but they have proved useful in more complex settings.     

Numerical analysis of a quasistatic piezoelectric problem with damage

The quasistatic evolution of the mechanical state of a piezoelectric body with damage is numerically studied in this paper. Both damage and piezoelectric effects are included into the model. The variational formulation leads to a coupled system composed of two linear variational equations for the displacement field and the electric potential, and a nonlinear parabolic variational equation for the damage field. The existence of a unique weak solution is stated. Then, a fully discrete scheme is introduced by using a finite element method to approximate the spatial variable and an Euler scheme to discretize the time derivatives. Error estimates are derived on the approximate solutions, from which the linear convergence of the algorithm is deduced under suitable regularity conditions. Finally, a two-dimensional example is presented to demonstrate the behaviour of the solution. To cite this article: J.R. Fernández et al., C. R. Mecanique 336 (2008).     

Modeling force transmission in granular materials

The probability density function of contact forces in granular materials has been extensively studied and modeled as an outstanding signature of granular microstructure. Arguing that particle environments play a fundamental role in force transmission, we analyze the effects of steric constraints with respect to force balance condition and show that each force may be considered as resulting from a balance between lower and larger forces in proportions that mainly depend on steric effects. This idea leads to a general model that predicts an analytical expression of force density with a single free parameter. This expression fits well our simulation data and generically predicts the exponential fall-off of strong forces, a small peak below the mean force and the non-zero probability of vanishingly small forces.