Méthode particulaire anisotrope pour des écoulements de fluide visqueuxAnisotropic particle method for viscous flows

The anisotropic particle method has been extended to the case of viscous flows. The moment transport equation is modified to account for viscous effects. The diffusion term has been evaluated by using the PSE method and the particle moments. The modified transport equation includes geometrical moments for which a specific transport equation has been introduced. The study of the evolution of two corotating vortices allowed the comparison of the anisotropic particle method with the usual particle method. To cite this article: A. Beaudoin et al., C. R. Mecanique 332 (2004).     

A harmonic balance method for the non-linear vibration of viscoelastic shellsVibrations non linéaires des structures viscoélastiques par une méthode de la balance harmonique

In this Note, we deal with the non-linear vibration of viscoelastic shell structures. Coupling a harmonic balance method with a one mode Galerkin's procedure, one obtains an amplitude equation depending on two complex coefficients. These are determined by solving a classical eigenvalue problem and two linear problems. This permits us to characterize the evolution of the loss factor with the vibration amplitude. To validate our approach, the amplitude-frequency and the amplitude-loss factor relationships are illustrated in the case of a circular ring. To cite this article: E.H. Boutyour et al., C. R. Mecanique 334 (2006).     

Evolution de la fonction de répartition d'un gaz de tourbillons 2D en présence d'un bruitEvolution of the repartition function of 2D vortex gaz in presence of noise

In this work, we study the motion of N localized vortices in the presence of ‘noise’. To apply the methods of statistical mechanics, we determine the evolution equation for the probability density function of vortices in which the presence of the ‘noise’ is accounted for by as a term similar to viscosity. This equation is isomorph to the system of equations which describe 2D turbulence with viscosity. The advantage of this formulation is that it can be numerically implemented at very large Reynolds numbers. To cite this article: S. Decossin, V. Pavlov, C. R. Mecanique 331 (2003).     

Modélisation des problèmes d'impact avec dissipation d'énergie par frottement

The bi-potential method has been successfully applied for the modeling of frictional contact problems in static cases. This paper presents the application of this method for dynamic analysis of impact problems with multiple deformable bodies. A first order algorithm is applied for numerical integration of the time-discretized equation of motion. The numerical results show clearly the physical energy dissipation introduced by frictional effects between the solids in contact. To cite this article: B. Magnain et al., C. R. Mecanique 333 (2005).     

Amortissement visqueux d'un résonateur mécanique en environnement gazeuxViscous damping of a mechanical resonator in a gaseous environment

We study dissipation phenomena due to the presence of a gaseous environment, leading to the damping of the oscillations in vibrating systems such as mechanical resonators. In the so-called “viscous” pressure region (p ranging between 10^?3 mbar and 1 bar), we suggest a simple model allowing an order of magnitude analysis of the dissipation mechanisms. This model, based on the classical form of the energy conservation equation in fluid mechanics, leads to a p^1/2 variation scale for the dissipation. In addition, we present experimental results that are found to be in good agreement with the predictions of the model. To cite this article: D. Perret et al., C. R. Mecanique 331 (2003).     

Selection of two-dimensional nonlinear strain waves in micro-structured mediaSelection d'ondes de déformation non linéaires à deux dimensions dans des milieux à microstructure

It is shown that the micro-displacement gradient allows the propagation of two-dimensional localized long nonlinear strain waves in a medium with microstructure. These waves may exist even in the presence of dissipation and energy input in the microstructured medium but with selected values of the wave amplitude and velocity. An increase or a decrease in the wave amplitude and velocity happens faster at the initial stage than that of the plane localized wave. However, their steady values selected by the energy input/output, are higher for the plane waves. To cite this article: A.V. Porubov et al., C. R. Mecanique 332 (2004).     

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).     

Stabilité linéaire d'écoulements symétriques presque parallèles en canalLinear stability of nearly parallel symmetric flows in a channel.

In this Note, we present a temporal linear stability analysis of symmetric developing flows slightly perturbed from Poiseuille flow. The Chebyshev spectral collocation method is used to resolve the Orr–Sommerfeld equation. For the main flow, the solution considered is analytic. The results of the stability study depend essentially on the shape and amplitude of the velocity profiles imposed at the channel entry. To cite this article: A. Hifdi et al., C. R. Mecanique 332 (2004).     

An advanced design method for propellers behind bodies of revolutionCalcul de l'hélice fonctionnant en arrière d'un corps à symétrie axiale

The flow around the unshrouded marine propellers operating in the wake of an axisymmetric body is rotational and tridimensional. An inverse method based on the model of inviscid and rotational fluid and coupling two complementary steps (axisymmetric computation + 3D panel method) is proposed for the design of the marine propellers. The meridional flow computation leads to the determination of axisymmetrical stream sheets as well as the approximate camber surface of the blades and gives a good estimation of the surface of the free vortex wake. The new aspects developed in this method are the involvement of the contraction and the stretching of the free vortex wake, the rotational character of the incoming flow in the axisymmetric computation with tridimensional effects due to 3D panel method. To cite this article: N. Settou, B. Viney, C. R. Mecanique 331 (2003).     

Un nouveau préconditionneur pour les problèmes elliptiques à coefficients variablesA new preconditonner for general elleptic problems

In this Note we describe a preconditionner for iteratively solving the linear system arising from the discretization of a general nonseparable elliptic problem by spectral element method. This preconditionner is constructed from approximating the original problem with the closest (in some sense) separable elliptic problem. A direct method is then used to invert the preconditionner. To cite this article: M. Azaïez et al., C. R. Mecanique 331 (2003).     

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).     

Symmetry-breaking in periodic gravity waves with weak surface tension and gravity-capillary waves on deep waterBrisure de symétrie dans les vagues de gravité avec une faible tension de surface et les vagues de gravité-capillarité périodiques en eau profonde

The method developed by Debiane and Kharif for the calculation of symmetric gravity-capillary waves on infinite depth is extended to the general case of non-symmetric solutions. We have calculated non-symmetric steady periodic gravity-capillary waves on deep water. It is found that they appear via bifurcations from a family of symmetric waves. On the other hand we found that the symmetry-breaking bifurcation of periodic steady class 1 gravity wave on deep water is possible when it approaches the limiting profile, if it is very weakly influenced by surface tension effects. To cite this article: R. Aider, M. Debiane, C. R. Mecanique 332 (2004).     

Dispersion de Taylor généralisée à un fluide à propriétés physiques variablesGeneralized Taylor dispersion for heterogeneous fluid

The investigation of non-reactive miscible solute dispersion in a vertical Hele–Shaw cell is considered. An asymptotic method is used to extend Taylor model to the case of the fluid density, the dynamic viscosity and the molecular diffusion coefficient are solute concentration-dependent. It is demonstrated that the averaged variables over the gap are governed by a convection–dispersion equation in which the dispersion tensor is concentration-dependent. To cite this article: C. Felder et al., C. R. Mecanique 332 (2004).     

High-order LES modeling of turbulent incompressible flow

This article presents the high-order algorithms that we have developed for large-eddy simulation of incompressible flows, and the results that have been obtained for the 3D turbulent wake of a cylinder at a Reynolds number of $\mathit{Re}=3900$. To cite this article: R. Pasquetti, C. R. Mecanique 333 (2005).     

Interaction soliton–sable dans un canal en eau peu profonde

Interaction between solitons and a sandy bed in shallow water is investigated. In our experiments, solitons are generated on the background of a harmonic wave, in a wave flume used in resonant mode. It is found that the sand ripples formed by the solitons propagation induce a significant decrease of solitons amplitude and of the phase shift between the soliton and the harmonic wave. However, the amplitude of the harmonic wave is approximately constant. The possible physical processes of such behaviour for the soliton amplitude and for the harmonic wave amplitude are discussed. To cite this article: F. Marin et al., C. R. Mecanique 333 (2005).     

Evolution de configurations de tourbillons avec les mêmes invariants globauxEvolution of configurations of vortices with the same global integral invariants.

In this Note, we address the question of the evolution of a distribution of N identical localized vortices. Using direct numerical simulation, (here the Runge–Kutta scheme of order 4), together with the localized-vortices model, we show that different initial distributions of vorticity with identical integral invariants may exist. We show that the initial configurations with the same invariants may evolve to totally different quasi-final states. To cite this article: E. Bécu, V. Pavlov, C. R. Mecanique 332 (2004).     

Stability of a hypersonic shock layer on a flat plateStabilité d'une couche de choc hypersonique sur une plaque plane.

Stability of a hypersonic shock layer on a flat plate is examined with allowance for disturbances conditions on the shock wave within the framework of the linear stability theory. The characteristics of the main flow are calculated on the basis of the Full Viscous Shock Layer model. Conditions for velocity, pressure, and temperature perturbations are derived from steady Rankine–Hugoniot relation on the shock wave. These conditions are used as boundary conditions on the shock wave for linear stability equations. The growth rates of disturbances and density fluctuations are compared with experimental data obtained at ITAM by the method of electron-beam fluorescence and with theoretical data of other authors. To cite this article: A.A. Maslov et al., C. R. Mecanique 332 (2004).     

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).     

Modelling of unsteady 2D cavity flows using the Logvinovich independence principleModélisation des écoulements cavitants bidimensionnels basée sur le principe d'indépendance de Logvinovich.

A simple model for two-dimensional cavity flows is presented. It is based upon the Logvinovich independence principle. Each section of the cavity is assumed to behave independently of the neighbouring ones. The equation of evolution of the cavity interface is derived. It mainly takes into account an added mass effect and is similar to the well-known Rayleigh–Plesset equation relative to spherical bubbles. The dynamics of the 2D cavity is controlled by the pressure difference between infinity and the cavity. The model proves to be in good agreement with Tulin's solution for a steady cavity flow and easily applicable to unsteady cavity flows. To cite this article: C. Pellone et al., C. R. Mecanique 332 (2004).