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controlled by the heavier fuel, i.e., CH₄ and for instance the detonability of the mixture where 20% of CH₄ volume has been replaced by H₂ is nearly the same as that of the mixture where CH₄ is the only fuel.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).     

Déformation cumulée tensorielle dans le référentiel en rotation logarithmiqueCumulated tensorial strain measure in the logarithmic rotating frame.

The time integration of strain rate tensor $\stackrel{?}{\mathit{D}}$ is a central problem in large transformations even if it is often an underlying one. The cumulated tensorial strains, obtained by the time integration of strain rate tensor $\stackrel{?}{\mathit{D}}$, allow the tackling of this problem from a geometrical point of view, and independently of material behaviour considerations. The time integration here takes place in the local objective frame defined by the logarithmic spin proposed by Lehmann et al. and Xiao et al. The numerical results obtained in a closed deformation path are presented here. The advantages and drawbacks of this novel integration for the development of behaviour laws are described. To cite this article: V. Mora et al., C. R. Mecanique 332 (2004).     

Instabilité non linéaire dans un milieu en expansionNonlinear instability in a expanding medium

We consider nonlinear acoustical phenomena, explosive instabilities and a formation of localized structures in nonstationary environment. An example of such a medium is our Universe in expansion considered as a fluid submissive to a gravitational self-concorded force field and governed by the classical hydrodynamics equations. We show that the taking into account of the nonlinear effects allow us to understand the causes of the appearance of the specific nonlinear instability, which is calling explosive instability. This type of instability is more fast, $～\ln [{(t_0?t)}^{\mathrm{?1}}]$ for density fluctuation, that the habitual instability (exponential, $～{\mathrm{e}}^{\gamma t}$): at the end of a finite time, all spatial inhomogeneity of the initials conditions lead to a formation of singularities in the fields. This phenomena will be appear if certains conditions for the initials amplitudes and wavelengths of the fluctuations are observed. To cite this article: F. Henon, V. Pavlov, C. R. Mecanique 334 (2006).     

Étude numérique des instabilités de la phase fluide et de l'interface de solidification en croissance dirigée horizontale

Convective instabilities of low Prandtl number fluids are subject to various studies. The purpose here is an extension to hydrodynamic transitions in the fluid phase with a free or rigid surface under phase change and to construct the corresponding bifurcation diagram. Investigations interesting the process control by using the latent heat and the solid/liquid thermal conductivity difference are considered. The solution methodology is based on a front localisation approach showing a very good ability to describe convection regimes coupled to the phase change transition in the case of vertical solidification with confinement. To cite this article: E.A. Semma et al., C. R. Mecanique 331 (2003).     

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).     

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).     

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).     

Lagrangian–Eulerian simulation of slugging fluidized bed

This work studies gas–solid slugging fluidized beds with Type-D particles, using two-dimensional simulations based on discrete element model (DEM). DEM performance is quantitatively validated by two commonly accepted correlations for determining slugging behavior. The voidage profiles simulated with bed height corresponding to Baeyens and Geldart (1974) correlation for onset of slugging demonstrate a transitional flow pattern from free bubbling to slugging. The present calculated values for the maximum slugging bed height are in good agreement with the correlation from Matsen et al. (1969). Simulations show that fluidized beds with Type-D particles can operate in the round-nosed slugging regime and also shows that wall slugs and square-nosed slugs tend to be formed with increase in superficial gas velocity and in bed height, respectively.     

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).     

Suivi d'interface en maillages non structurés

We present a volume of fluid method, based on finite element analysis, for the 2D simulation of interfaces on an unstructured fixed mesh. Special techniques to reconstruct and advect the interface allows to track its evolution through this mesh.     

Mise en évidence par granularité en lumière blanche de phénomènes de multilocalisation de la déformation pour les bétons de poudres réactives sollicités en traction

From kinematic observations by granularity in whiting light mode based on a technique of digital speckle images correlation, the behaviour in tension of a reactive powders concrete is studied. The measures show several localisation areas of the deformation fields and the role of the fibres in the transmission of the stresses in the neighbourhood of a damaged area.     

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.     

Approche multi-échelle en fatigue polycyclique anisotherme

An extension of the macro-meso approach developed by Dang Van in isothermal high-cycle fatigue is established in the case of structures subjected to anisothermal cyclic loadings. The fatigue limits of such structures are assumed to be temperature-dependent. This proposal is based upon the assumption of elastic shakedown at macroscopic and mesoscopic scales. The use of a local shakedown condition established for structures with temperature-dependent yield limits leads to a thermomechanical formulation of the high-cycle fatigue criteria.     

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).     

Rhéologie des matériaux en cours de prise : Approche théorique

The rheological behavior of setting heterogeneous materials is studied from a theoretical approach by means of the homogenization technique of periodic medium. These materials considered as suspensions of gas bubbles at finite concentration in a viscoelastic matrix with low compressibility, present the macroscopic behavior of a compressible viscoelastic medium. The shear and volume macroscopic moduli are of the same order of magnitude and directly proportional to that of the fluid. The effective compressibility of the gas (out of thermal equilibrium) is added to these fluid contributions.     

Euler–Lagrange simulation of high pressure shock waves

This paper presents the numerical simulation of overdriven detonation (or O.D.D.) that occurs when a high velocity object impacts an explosive. The pressure and the velocity at this state are higher than those of the Chapman–Jouguet (C–J) state. First, before the simulation of this event, a study of PBX air blast by using multi-material Eulerian method is presented. Pressure peaks are computed for several distances from the explosive. Second, the O.D.D. phenomenon is modeled by the Euler–Lagrange penalty coupling, which permits to couple a Lagrangian mesh of the flyer plate to multi-material Eulerian mesh of explosives and air. This coupling gives us the high detonation velocities in the acceptor explosive and demonstrates that it is able to handle shock–structure interaction problems.     

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).     

Numerical simulation of a compressible vortex–wall interaction

The wall interaction of isolated compressible vortices generated from a short driver section shock tube has been simulated numerically by solving the Navier–Stokes equations in axisymmetric form. The dynamics of shock-free (incident shock Mach number \(M = 1.36\)) and shock-embedded \((M = 1.57)\) compressible vortices near the wall has been studied in detail. The AUSM+ scheme with a fifth-order upwind interpolation formula is used for the convective fluxes. Time integration is performed using a low dissipative and dispersive fourth-order six-stage Runge–Kutta scheme. The evolution of primary and wall vortices has been shown using the velocity field, vorticity field, and numerical schlierens. The vortex impingement, shocklets, wall vortices, and their lift-off are clearly identified from the wall pressure time history. It has been observed that the maximum vorticity of the wall vortices reaches close to 30 % of the primary vortex for \(M = 1.36\) and it reaches up to 60 % for \(M = 1.57\). The net pressure force on the wall due to incident shock impingement is dominant compared to the compressible vortex impingement and their evolution.