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).     

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).     

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).     

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).     

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).     

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).     

Instability of Navier slip flow of liquidsInstabilité des écoulements glissant de liquides.

We investigate the stability problem related to the basic slip flows of liquids in plane microchannels by using the Navier slip concept. We found that if the Navier slip parameter ($N_s$) equals 0.06, the critical Reynolds number (${\mathit{Re}}_{\mathrm{cr}}$) becomes 213.6. There are short-wave instabilities, however, when we further increase $N_s$ to 0.07 or 0.08. ${\mathit{Re}}_{\mathrm{cr}}$ becomes 132.9 for $N_s=0.08$ if we neglect the short-wave instability. To cite this article: A.K.-H. Chu, C. R. Mecanique 332 (2004).     

Modelling the transverse viscoelasticity of green wood using a combination of two parabolic elementsModélisation de la viscoélasticité transverse du bois vert à l'aide d'une combinaison de deux éléments paraboliques

The rigidity in radial compression at different levels of temperature and strain rate have been measured on green Boco, with a drastic softening around $\text{60}{}^{\mathrm{<mspace\; sp="0.2"\; width="2px"\; linebreak="nobreak"\; is="true"></mspace><mtext>°</mtext>}}$C attributed to the glassy transition of lignin. The representation of experimental results in an approximated complex diagram revealed a secondary viscoelastic process occurring at lower temperature. A multiparabolic model was used for the analysis. For convenience, each parabolic element was replaced by a generalised Maxwell model with a modified-Gaussian relaxation spectrum. This model fitted correctly the observed behaviour of wood in the time range of 0.05 to 50 sec and temperature between 10 to $\text{90}{}^{\mathrm{<mspace\; sp="0.2"\; width="2px"\; linebreak="nobreak"\; is="true"></mspace><mtext>°</mtext>}}$C. To cite this article: S. Bardet, J. Gril, C. R. Mecanique 330 (2002) 549–556.     

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.     

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).     

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.     

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.