Stabilité de l'écoulement de Hartmann chauffé par le basStability of the Hartmann flow heated from below

A numerical study is conducted in order to determine the influence of a vertical magnetic field, the Reynolds number and a temperature stratification on the instabilities occurring in the Hartmann flow heated from below. For $\mathit{Pr}=0.001$ and $\mathit{Ha}?2.5$, the results show that the vertical magnetic field has a stabilizing effect on both transverse oscillatory travelling waves $(T)$ and longitudinal stationary rolls $(L)$. The temperature stratification is responsible of a destabilization of the transverse $(T)$ modes and the appearance of longitudinal $(L)$ modes non-existent for the isothermal Hartmann flow. Moreover, the extent of the domains of Re where the transverse modes $(T)$ prevail is found to narrow when Ha increases and to widen when Ra increases for a given value of Ha. On the other hand, for the $(L)$ modes, the extent of the domains of Re where they prevail increases when Ha grows. To cite this article: W. Fakhfakh et al., C. R. Mecanique 334 (2006).     

Experimental determination of the concentration Probability Density Function for a saltating particle layerDétermination expérimentale de la densité de probabilité de concentration d'une couche de particules en saltation

A horizontal saltation layer of glass particles in air was investigated experimentally in a wind tunnel. Particle concentrations are measured by light scattering diffusion and image processing and all the statistical characteristics were evaluated and thus the probability density function. Our experimental results confirm that the mean concentration decreases exponentially with height, the mean Eulerian dispersion height H being a characteristic lengthscale and that the instantaneous concentration distribution $\stackrel{?}{c}(\overrightarrow{x},t)$ is a random variable following quite well a lognormal distribution. To cite this article: X. Zhang et al., C. R. Mecanique 334 (2006).     

The stochastic energy-Casimir methodLa méthode d'énergie-Casimir stochastique

In this paper, we extend the energy-Casimir stability method for deterministic Lie–Poisson Hamiltonian systems to provide sufficient conditions for stability in probability of stochastic dynamical systems with symmetries. We illustrate this theory with classical examples of coadjoint motion, including the rigid body, the heavy top, and the compressible Euler equation in two dimensions. The main result is that stable deterministic equilibria remain stable in probability up to a certain stopping time that depends on the amplitude of the noise for finite-dimensional systems and on the amplitude of the spatial derivative of the noise for infinite-dimensional systems.     

Utilisation de la phase stationnaire pour localiser la provenance du bruit sur l'axe d'une structure élastique à symétrie de révolutionUse of the stationary phase method to localize the source of noise on the axis of an axisymmetric elastic structure

Consider the problem numbered (1) in the text. Along the axis, the pressure may be expressed as a combination of axisymmetric modes only. For high wave numbers, the method of stationary phase may be used to show that the pressure on the axis comes only from the vicinities of a few parallels. Generally, only the parallel constituting the points nearest to this axis point is to be considered. For low circumferential mode numbers (especially $n=0$), the curvature greatly influences the wavelength of the modes of the structure in vacuo: thus, the method of stationary phase can be applied, for most aeronautical airborne structures, even from the first axisymmetric mode and not only above the coincidence frequency. Using an expression established earlier, we can give an expression for the pressure on the axis of an axisymmetric enclosure. To cite this article: D. Brenot, C. R. Mecanique 334 (2006).     

Étude numérique du couplage de la convection naturelle avec le rayonnement de surfaces en cavité carrée remplie d'airNumerical study of natural convection-surface radiation coupling in air-filled square cavities

A numerical tool is developed for coupling natural convection in cavities with surface radiation and computations are performed for an air-filled square cavity whose four walls have the same emissivity. Compared to the adiabatic case without radiation, the top wall is cooled, the bottom wall is heated, air flow along the horizontal walls are reinforced and thermal stratification in cavity core is reduced. Detailed analysis shows that net radiative heat flux is linear with ΔT if $\mathrm{\Delta }T?T_0$, which is the case at low Rayleigh number, and that radiative Nusselt number is a linear function of the cavity height. Surface radiation induces an early transition to time-dependent flows: for $?=0.2$ and a cavity height of 0.335 m the critical Rayleigh number is equal to $9.3\times {10}^6$ and the corresponding Hopf bifurcation is supercritical. Furthermore, multiple periodic solutions are observed between $\mathit{Ra}=1.2\times {10}^7$ and $1.3\times {10}^7$. To cite this article: H. Wang et al., C. R. Mecanique 334 (2006).     

Seuils d'instabilités des écoulements de type rotor–stator avec flux axialInstability thresholds of rotor–stator flows with axial throughflow

This experimental study deals with the stability of rotor–stator flows subjected to an axial inward or outward throughflow. Stability diagrams have been established by flow visualizations according to the rotational Reynolds number Re and to $V_z^1$ the dimensionless axial velocity in the radial gap between the rotor and the shroud. Three aspect ratios G of the cavity have been considered to take into account both Batchelor type of flows with separated boundary layers and torsional Couette type of flows with joined boundary layers. We show then the influence of rotation, geometry and most of all of the superimposed throughflow on the appearance and disappearance thresholds of instabilities. Some new structures have also been observed to be compared to the case of a closed cavity. To cite this article: S. Poncet, M.-P. Chauve, C. R. Mecanique 334 (2006).     

On some features of the effective behaviour of porous solids with J2- and J3-dependent yielding matrix behaviourSur quelques effets de l'angle de Lode sur les caractéristiques macroscopiques de matériaux en rupture ductile

Some features od the constitutive behaviour of voided materials taking into account possible effects of the Lode angle in the yielding behaviour of the matrix are discussed. The Gurson approach is used to this end. After providing a parametric representation of the effective behaviour of such materials, some closed-form results are given for pure shear stress states and also at very high stress triaxialities. In the former case corresponding to a zero macroscopic mean stress, the contour of the yield domain in the π-plane has exactly the shape of the yield surface of the matrix in the deviatoric plane, but a size reduced by a factor $1?f$, with f the porosity of the voided material. In the latter, effective yield stresses for the voided material are slightly different from the Gurson result and found to be set by the yield stress at a microscopic stress Lode angle $\frac{\pi }{3}$ for very high positive triaxiality and by the yield stress at a microscopic stress Lode angle 0 for very high negative triaxiality. This last result is extended for porous materials with yielding depending further on the hydrostatic stress, fully exhibiting the interaction between volumetric and shear interactions on the yielding behaviour of isotropic porous materials. Applications to many usual yielding criteria for the matrix are also provided.     

Kinematic regimes of convection at high Prandtl number in a shallow cavityRégimes cinématiques de la convection à haut nombre de Prandtl dans une cavité allongée.

We consider free convection in a horizontal shallow cavity with different end temperatures, filled with a high Prandtl number fluid. From scaling analysis, we find two kinematic regimes resulting from the competition of heat transfer by conduction and by convection. Numerical simulations realized for a large range of Rayleigh number and aspect ratio confirm the phenomenological analysis and provide the threshold between the two regimes. The conductive and convective regimes occur at $\mathit{Ra}{A}^2$ smaller and larger than 443 respectively, where Ra is the Rayleigh number and A is the aspect ratio. In the convective regime, the characteristic velocity is independent of depth of the cavity. To cite this article: J.-M. Flesselles, F. Pigeonneau, C. R. Mecanique 332 (2004).     

Estimation of aerodynamic noise generated by forced compressible round jetsEstimation du bruit d'origine aérodynamique rayonné par des jets ronds forcés compressibles

An acoustic numerical code based on Ligthill's analogy is combined with large-eddy simulations techniques in order to evaluate the noise emitted by subsonic $(M=0.7)$ and supersonic $(M=1.4)$ round jets. We show first that, for centerline Mach number $M=0.9$ and Reynolds number $\mathit{Re}=3.6\times {10}^3$, acoustic intensities compare satisfactorily with experimental data of the literature in terms of levels and directivity. Afterwards, high Reynolds number $(\mathit{Re}=3.6\times {10}^4)$ free and forced jets at Mach 0.7 and 1.4 are studied. Numerical results show that the jet noise intensity depends on the nature of the upstream mixing layer. Indeed, the subsonic jet is 4 dB quieter than the free jet when acting on this shear layer by superposing inlet varicose and flapping perturbations at preferred and first subharmonic frequency, respectively. The maximal acoustic level of the supersonic jet is, on the other hand, 3 dB lower than the free one with a flapping upstream perturbation at the second subharmonic. The results reported in this paper confirm previous works presented in the literature demonstrating that jet noise may be modified according to the inlet conditions. To cite this article: M. Maidi, C. R. Mecanique 334 (2006).     

Détonabilité de mélanges stoechiométriques méthane–hydrogène–oxygène–azoteDetonation characteristics of stoichiometric mixtures of methane–hydrogen–oxygen–nitrogen

The goal of this Note is to determine the influence of H₂ addition on the detonation and detonability of stoichiometric CH₄/O₂/N₂ mixtures for three values of the nitrogen dilution $\beta ={\mathrm{N}}_2/{\mathrm{O}}_2$ ($\beta =0$ (oxygen); 2; 3.76 (air)) and also of the influence of the initial temperature. It is based on the measurement of the mean cell size of the steady self-sustained detonation in these mixtures, this characteristic length being representative of the mixture detonability. Results indicate that the detonability of the (CH₄H₂) mixture is mainly controlled by the heavier fuel, i.e., CH₄ and for instance the detonability of the mixture where 20% of CH₄ volume has been replaced by H₂ is nearly the same as that of the mixture where CH₄ is the only fuel. The influence of the initial temperature on the detonability depends on N₂ concentration. To cite this article: C. Matignon et al., C. R. Mecanique 334 (2006).     

Homogenized model of reaction–diffusion in a porous mediumUn modèle homogénéisé de réaction–diffusion dans un milieu poreux

We study the initial boundary value problem for the reaction–diffusion equation,

$\text{?}{}_{\mathrm{t}}\text{u}{}^{\mathrm{\epsilon }}\text{??·(a}{}^{\mathrm{\epsilon }}\text{?u}{}^{\mathrm{\epsilon }}\text{)+g(u}{}^{\mathrm{\epsilon }}\text{)=h}{}^{\mathrm{\epsilon }}$

in a bounded domain $\text{Ω}$ with periodic microstructure $\text{F}{}^{\mathrm{(\epsilon )}}\text{∪}\text{M}{}^{\mathrm{(\epsilon )}}$, where a^ε(x) is of order 1 in $\text{F}{}^{\mathrm{(\epsilon )}}$ and κ(ε) in $\text{M}{}^{\mathrm{(\epsilon )}}$ with κ(ε)→0 as ε→0. Combining the method of two-scale convergence and the variational homogenization we obtain effective models which depend on the parameter θ=lim_ε→0κ(ε)/ε². In the case of strictly positive finite θ the effective problem is nonlocal in time that corresponds to the memory effect. To cite this article: L. Pankratov et al., C. R. Mecanique 331 (2003).     

A method for the calculation of nonsymmetric steady periodic capillary–gravity waves on water of arbitrary uniform depthUne méthode de calcul des ondes de gravité–capillarité périodiques et non-symétriques en profondeur arbitraire

In this Note the method developed by Aider and Debiane (2004) for the calculation of nonsymmetric water waves on infinite depth is extended to finite depth. The water-wave problem is reduced to a system of nonlinear algebraic equations which is solved by using Newton's method. Solutions are computed up to their limiting forms by decrementing the depth from the infinity to a value of the depth-wavelength ratio $h/\lambda$ less than 0.025. It is found that the waves become symmetric when the depth becomes very small. Relations giving some integral properties are derived. To cite this article: R. Aider, M. Debiane, C. R. Mecanique 334 (2006).     

Comportement thermomécanique de l'argile de Boom

Special attention has been recently paid on temperature effects on the behaviour of deep saturated clays, in relation with nuclear deep waste storage. However, few experimental data are presently available, and existing constitutive models need to be completed. This note is aimed at completing, both experimentally and theoretically, the understanding of the effects of the overconsolidation ratio on the thermal volume changes of Boom clay (Belgium). The experimental data obtained here are in a good agreement with existing data. As a complement to existing data, they are used to develop a new elastoplastic model. The adoption of a second coupled plastic mechanism provides good simulations on a complex thermo-mechanical path.     

Modélisation et simulation numérique du changement de phase liquide–vapeur en cavitéModeling and numerical simulation of liquid–vapor phase change in an enclosed cavity

A model for the simulation of boiling flow with phase change in a closed cavity is presented. A front-tracking method is used to deal with the liquid–vapor interface. The liquid phase is incompressible while the vapor phase is weakly compressible and obeys to the perfect gas law. This model can deal with large density ratio (${\rho }_l/{\rho }_v?1000$) flows while accounting for the saturation curve. Computations are performed on a 1D validation case, idealizing a pressure cooker. Results are compared with a low Mach number approximation. To cite this article: V. Daru et al., C. R. Mecanique 334 (2006).     

Mécanique de la rupture fragile en présence de plasticité : définition d'un taux de restitution d'énergie

This study aims at defining an energetic parameter which characterises progressive crack growth in a brittle elastoplastic medium. First, Francfort and Marigo's elastic fracture theory, based on a minimum energy principle, is recalled. Then, a link with the framework of generalised standard materials is exhibited and allows to introduce the new energetic contributions due to plasticity.     

On the instantaneous formation of cavitation in hydrodynamic lubricationSur la formation instantanée de la cavitation en lubrification hydrodynamique

We consider the Elrod–Adams model extending the classical lubrication Reynolds equation to the case of the possible presence of a cavitation region. We show that the behaviour of the pressure and saturation depends crucially on the behaviour of the separation $h(t,x,y)$ among the two surfaces. In particular, we exhibit some simple formulations for which we prove (rigorously) that a cavitation region is formed instantaneously (even for initially saturated flows). Some numerical experiences are also given. To cite this article: J.I. Díaz, S. Martin, C. R. Mecanique 334 (2006).