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).     

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).     

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).     

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).     

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).     

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).     

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.     

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).     

“Tepid” Geysers above salt cavernsGeysers tièdes au-dessus des cavités salines

The formation of a brine geyser erupting from the wellhead of a large underground salt cavern is described. In most cases, the brine outflow from an opened cavern is slow; it results from the cavern creep closure and the thermal expansion of the cavern brine. These two processes are smooth; however, the brine outflow often is bumpy, as it is modulated by atmospheric pressure variations that generate an elastic increase (or decrease) of both cavern and brine volumes. In addition, when the flow is fast enough, the brine thermodynamic behavior in the wellbore is adiabatic. The cold brine expelled from the cavern wellhead is substituted with warm brine entering the borehole bottom, resulting in a lighter brine column. The brine outflow increases. In some cases, the flow becomes so fast that inertia terms must be taken into account. A geyser forms, coming to an end when the pressure in the cavern has dropped sufficiently. A better picture is obtained when head losses are considered. A closed-form solution can be reached. This proves that two cases must be distinguished, depending on whether the cold brine initially contained in the wellbore is expelled fully or not. It can also be shown that geyser formation is a rare event, as it requires both that the wellbore be narrow and that the cavern be very compressible. This study stemmed from an actual example in which a geyser was observed. However, scarce information is available, making any definite interpretation difficult.     

Reversibles und irreversibles Fließen von Hochmolekularen

Zusammenfassung Es wird gezeigt, daß zwischen der Platzwechseltheorie und der linearen phänomenologischen Relaxationstheorie für das plastisch-elastische Verhalten keine Widersprüche bestehen. Die Platzwechseltheorie führt zu nichtlinearen Beziehungen, und die bekannten Gleichungen ergeben sich, indem statt der hyperbolischen Beziehungen jeweils die ersten Näherungen verwendet werden. Fließvorgänge, die durch verminderte Entropie (Änderung der Verteilung auf die vorgegebenen möglichen Lagen) und durch molekulare Haftstellen gekennzeichnet sind und die nach Aufhören einer äußeren Beeinflussung wieder rückläufig verlaufen, sind von solchen, bei denen eine Änderung der molekularen Verteilung auf die im Mittel unverändert bleibenden möglichen Plätze nicht erfolgt, zu unterscheiden. Es empfiehlt sich, neben den Ortskurven den Verlauf von tan in Abhängigkeit von der Frequenz zu zeichnen, um nähere Auskunft über den zugrundeliegenden Fließmechanismus zu erhalten.     

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.     

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).