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).     

A fourth order accurate finite volume scheme for numerical simulations of turbulent Rayleigh–Bénard convection in cylindrical containers

A finite volume scheme, which is based on fourth order accurate central differences in spatial directions and on a hybrid explicit/semi-implicit time stepping scheme, was developed to solve the incompressible Navier–Stokes and energy equations on cylindrical staggered grids. This includes a new fourth order accurate discretization of the velocity and temperature fields at the singularity of the cylindrical coordinate system and a new stability condition [J. Appl. Numer. Anal. Comput. Math. 1 (2004) 315–326]. The method was applied in direct numerical simulations of turbulent Rayleigh–Bénard convection for different Rayleigh numbers $\mathit{Ra}={10}^{\gamma }$, $\gamma =5\text{,}\dots \text{,}8$, in wide cylinders with the aspect ratios $a\equiv H/R=0.2$ and $a=0.4$ (where R denotes the radius and H – the height of the cylinder). To cite this article: O. Shishkina, C. Wagner, C. R. Mecanique 333 (2005).     

Écoulement turbulent dans une cavité rotor–stator fermée de grand rapport d'aspect

A direct numerical simulation is combined with laboratory study to describe the turbulent flow in an annular high speed rotor–stator cavity. Comparisons are made for a turbulent flow characterized by a Reynolds number $\mathit{Re}=\Omega R_2^2/\nu =9.5\times {10}^4$ in a shrouded cavity of large aspect ratio $G=(R_2?R_1)/h=18.32$, where $R_1$ and $R_2$ are the inner and outer radii of the rotating disk, and h is the inter-disk space. A close agreement is found between the computed results and the experimental data for the mean and turbulent fields.? To cite this article: S. Poncet, A. Randriamampianina, C. R. Mecanique 333 (2005).     

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).     

Two-phase flow patterns and size distribution of droplets in a microfluidic T-junction: Experimental observations in the squeezing regime

Generating micrometer sized droplets has been studied in a microfluidic system with T-junction geometry 250 μm in internal diameter and with PTFE capillary tubing. Several experiments were conducted by varying the flow rate of the dispersed phase from $2.78\cdot {10}^{-11}{\text{ m}}^3/\text{s}$ to $5.28\cdot {10}^{-9}{\text{ m}}^3/\text{s}$ and that of the continuous phase from $2.78\cdot {10}^{-10}{\text{ m}}^3/\text{s}$ to $1.94\cdot {10}^{-9}{\text{ m}}^3/\text{s}$. The visualization of different flow regimes (drop, plug, and annular) was carried out for three configurations (not inverted in a horizontal position, inverted in a horizontal position, and inverted in a vertical position) for low capillary numbers. The model of Gauss was also chosen for a droplet size distribution in the dispersed phase, with the flow quality x varying from 0.016 to 0.44. The evolution of the drop size distribution as a function of the flow quality in the dispersed phase shows that the variation coefficient of the droplet's diameter is inversely proportional to the flow quality.     

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).     

Propagation of weak waves in elastic-plastic and elastic-viscoplastic solids with interfaces

A numerical technique based on the method of singular surfaces has been developed for the computation of wave propagation in solids exhibiting rate-independent elastic-plastic or rate-dependent elastic-viscoplastic behavior. The von Mises yield condition and associated flow rule is taken to represent the rate-independent behavior, while the Perzyna dynamic overstress model is taken to represent the rate-dependent behavior. For 1100-0 Al, a good empirical fit with published experimental data was found to be: $J_2{}^{1/2}?\kappa \left(W^p\right)=\left({\tau }_0/{\gamma }_0\right)\left(\stackrel{0}{W^p}/J_2{}^{1/2}\right)$ where:J₂ is the second invariant of the stress deviator;_k(W^p) is the static hardening curve;W^p is the plastic work and the parameter (τ₀/γ₀) = 0 (rate-independent model) or (80)^?1 to (70)^?1 MPa · s. In the numerical technique, the “connection equations” which provide relations between discontinuities in space and time derivatives lend themselves naturally to finite difference representations. A five-point space-time grid (center point coincident with the instantaneous location of the singular surface) is sufficient for the differenced form of the connection equations and suggests a natural marching scheme for the calculation of all necessary variables at each time step. Supplementing these equations which hold in the interior of the specimen are interface equations which assure continuity in stress and velocity across boundaries which separate materials with dissimilar properties. Application of the technique is made to wave propagation in pure shear for the purpose of comparing numerical predictions with relevant experimental data. The measurements of Duffyet al.[10] which are obtained from the torsional Kolsky apparatus (one dimensional torsional shear wave propagation in a thin-walled tube) were compared with predictions obtained numerically. By using the experimental input pulse history and the constitutive equation reported above, excellent agreement between the predicted and observed histories of reflected and transmitted pulses was obtained when the viscoplastic model was used. Poorer agreement was observed when the rate-independent model (τ₀/γ₀=0) was used. It is concluded that the Perzyna model gives good results for the behavior of 1100-0 Al at high rates of strain.     

Asymptotic analysis of layered elastic beams

We consider an elastic beam formed by three layers, fixed at one end and loaded at the free end. We call adherents the upper and lower layers ${\Omega }_{+}^{?}$ and ${\Omega }_{?}^{?}$ and an adhesive layer ${\Omega }_m^{?}$. We denote by $?h_{\pm ,m}$ the thickness of each layer and we suppose that the stiffness of the adhesive layer is ${?}^2$, with respect to that of the adherents. By an asymptotic analysis we obtain the zeroth order limit problem and the form of the second order displacements. To cite this article: M. Serpilli, C. R. Mecanique 333 (2005).