Direct numerical simulation of transition to turbulence in an oscillatory channel flowSimulation numérique de la transition vers la turbulence d'un ecoulement oscillant dans une conduite bi-dimensionnelle

In this Note, we present results of the numerical simulation of transition to turbulence for a purely oscillatory channel flow. These simulations were performed for various values of the Reynolds number, the so-called Stokes parameter being equal to 4. The methodology used for the flow simulation relies on a combination of finite element space approximations with time-discretization by operator splitting; it has shown to be very effective, even when it is applied to relatively complex domains with strong expansions at the inlet and outlet of the channel. The numerical results obtained agree qualitatively well with previous experiments by other investigators. To cite this article: L.H. Juárez, E. Ramos, C. R. Mecanique 331 (2003).     

Base minimale pour les corrélations pression-déformationMinimal basis for the pressure-strain correlations

The pressure-strain correlation tensor can be specified by means of five scalar functions in a reduced basis. In this basis, realisability and geostrophic constraints can be easily obtained, and the resulting realisable model is consistent with rapid distorsion theory. To cite this article: J. Piquet, C. R. Mecanique 330 (2002) 167–173.     

Stability of roll waves in open channel flowsStabilité de trains d'ondes dans un canal découvert

The stability of finite amplitude roll waves that may develop at a liquid free surface in inclined open channels of arbitrary cross-section is studied. In the framework of shallow water theory with turbulent friction the modulation equations for wave series are derived and a nonlinear stability criterion is obtained. To cite this article: A. Boudlal, V.Yu. Liapidevskii, C. R. Mecanique 330 (2002) 291–295.     

Instabilité et particularités de l'évolution d'une nappe tourbillonnaireInstability and features of vortex sheet evolution

The instability and the features of vortex sheet evolution are studied. We consider the self-organization of localized vortices (in two-dimensional flows) into clusters-like and spiral-like structures and show that quasi-final states do not ‘forget’ conditions of their initial origin. We discuss the physical significance of the obtained results. To cite this article: V. Pavlov et al., C. R. Mecanique 330 (2002) 757–762.     

Champ de vitesse dans un échangeur à vortex en régime turbulentHeat exchanger velocity field with turbulent inlet condition

We consider the isothermal flow through a cylindrical flat chamber, a model of some particular heat exchanger, for which LDV measurements and a numerical simulation have been performed. Experimental results show the establishment of an important vortex zone, the secondary flow extending all along the chamber radius. This observation leads to an expected significant increase of the fluid mixing. Results issued from the numerical simulation appear to be in close agreement with experimental data. Nevertheless, the k–ε model used here must be improved to obtain a better approach near the vortex centre. To cite this article: S. Petitot et al., C. R. Mecanique 330 (2002) 593–599.     

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).     

Eléments finis stochastiques en élasticité linéaireA stochastic finite element method in linear mechanics

The stochastic finite element method presented in this Note consists in representing in a probabilistic form the response of a linear mechanical system whose material properties and loading are random. Each input random variable is expanded into a Hermite polynomial series in standard normal random variables. The response (e.g., the nodal displacement vector) is expanded onto the so-called polynomial chaos. The coefficients of the expansion are obtained by a Galerkin-type method in the space of probability. To cite this article: B. Sudret et al., C. R. Mecanique 332 (2004).     

Visualisation de l'écoulement de Taylor–Dean ouvert

Results of flow visualisation in a Taylor–Dean open device are given. Observations made at the inlet, the core and the outlet of the flow show that different flow patterns can develop simultaneously. The formation and the growth of the structures observed versus control parameters are described. To cite this article: A. Ait Aider et al., C. R. Mecanique 333 (2005).     

Injection de bulles en paroi d'un écoulement cisaillé visqueuxBubble injection at the wall of a viscous shear flow

Air bubble injection at the wall of a viscous shear flow is filmed using a high speed video camera. The temporal evolution of the bubbles equivalent radius and the position of their centre of mass throughout their growth are determined from image processing. The experimental results are then used to validate a model of forces acting on the bubbles during their growth and after their detachment within the limit of small bubble Reynolds numbers. To cite this article: G. Duhar, C. Colin, C. R. Mecanique 331 (2003).     

Justification of the kinematic assumptions for thin-walled rods with shallow profile

In this Note we present a justification of the kinematic assumptions for thin-walled rods with shallow profile. These assumptions are fundamental to writing the one-dimensional equilibrium equations for such structures. The obtained kinematics are different from the Vlassov case, which is only valid for strongly curved profiles. They are also different from the that classically used in shell theory. The justification given in this Note is based on an asymptotic approach. To cite this article: L. Grillet et al., C. R. Mecanique 333 (2005).     

Écart à la réciprocité et identification de fissures en thermoélasticité isotrope transitoireReciprocity gap and identification of cracks in transitory isotropic thermoelasticity

We consider a three-dimensional homogeneous isotropic elastic solid containing a family of planar cracks submitted to a time-dependent thermal loading. The displacement and surface traction fields are measured over the whole external boundary of the solid. We propose in this Note to define and exploit a reciprocity gap, based only on the mechanical quantities available on the boundary, and which enables us to derive explicit formula for the location of the plane where the cracks are lying. Boundary conditions on the cracks can be of any nature provided they ensure that the normal heat flux and surface traction vector are continuous across the crack surfaces. To cite this article: S. Andrieux, H.D. Bui, C. R. Mecanique 334 (2006).     

Étude numérique du champ de vitesse dans un échangeur à vortexNumerical study of the velocity field in a vortex heat exchanger

Flow through a cylindrical flat chamber, a model of some particular heat exchanger, is investigated numerically using the CFD-ACE code. Turbulence is modelled using the classical k–ε model. A better understanding of the secondary flow is then obtained: the k–ε model shows a strong dependence of the secondary flow velocity field with Reynolds number as was pointed out with precedent experimental results. Variations of the number of vortexes composing the secondary flow, giving a symmetrical or asymmetrical aspect, will influence the fluid particle trajectories and time residence. To cite this article: S. Petitot et al., C. R. Mecanique 330 (2002) 749–756.     

A penalization method applied to the wave equation

In this Note we investigate the mathematical properties of the volume penalization method applied to the one-dimensional wave equation. Generally speaking, the penalization method allows one to handle complex geometries by simply adding a term to the equation to impose the boundary conditions. We study the convergence of the method with regards to the penalization parameter and we present error and stability analyses for the wave equation. Numerical simulations using a finite difference scheme illustrate the results. To cite this article: A. Paccou et al., C. R. Mecanique 333 (2005).     

Présentation d'une méthode d'étude de la stabilité linéaire d'écoulements instationnairesPresentation of a method for linear stability analysis of unsteady flow

We propose a linear stability analysis of unsteady viscous flow. We apply this method to an oscillatory pipe flow with an axisymetric 2D perturbation which has received considerable attention. The numerical results are relevant. To cite this article: M. Siouffi et al., C. R. Mecanique 330 (2002) 641–645.     

Simulation du front d'écoulement dans les procédés de moulage des composites liquides

This work proposes a procedure of finite difference discretized in a system of curvilinear coordinates adapted to the shape of the saturated zone, to simulate a flow in the LCM (Liquid Composites Molding) process. Formulation and the numerical application of the procedure are described. We describe two configurations of injections. A good agreement is found between numerical, analytical and literature experimental results. To cite this article: M. Hattabi et al., C. R. Mecanique 333 (2005).     

High-order LES modeling of turbulent incompressible flow

This article presents the high-order algorithms that we have developed for large-eddy simulation of incompressible flows, and the results that have been obtained for the 3D turbulent wake of a cylinder at a Reynolds number of $\mathit{Re}=3900$. To cite this article: R. Pasquetti, C. R. Mecanique 333 (2005).     

Transient gas flow simulation using an Adaptive Method of LinesSimulation d'écoulements dans un gazoduc par la méthode adaptative de lignes

Designing natural gas pipelines to safely and efficiently handle unsteady flows, requires knowledge of pressure drop, flowrate and temperature distribution throughout the system. The accurate prediction of these parameters is essential in order to achieve optimum cumulative deliverability, and safe and reliable operation. An Adaptive Method of Lines algorithm is formulated for the solution of Euler system of equations, which fully simulates slow and fast transients. Two test cases present the improvement of the numerical solution from grid adaptation. Good results are obtained both for slow and fast transients simulations proving that the suggested numerical procedure is appropriate for such predictions. To cite this article: E. Tentis et al., C. R. Mecanique 331 (2003).     

Piston Stokes flow in a semi-infinite channelL'écoulement de Stokes autour d'un piston dans un conduit semi-infini

The piston flow is bounded by rigid walls at y=±1, x>0 and generated by the uniform translation of the end wall x=0. After Katopodes, Davis and Stone [3] constructed a solution in terms of biorthogonal eigenfunctions, Meleshko and Krasnopolskaya [1] used a variation of an asymptotic technique developed by Meleshko and Gomilko [2] to examine the pointwise convergence of the non-orthogonal series. However, they overlooked the nonuniqueness of their solution and the consequent solvability condition which is shown here to necessitate a minor modification without significant harm to their contribution. To cite this article: A.M.J. Davis, C. R. Mecanique 330 (2002) 457–459.     

Numerical simulation of expansion/compression effect on shock induced turbulent flow

The interaction of homogeneous and isotropic turbulence with a shock wave is observed by solving the Reynolds-averaged Navier–Stokes equations with the k–? turbulence model. All turbulent fluctuations are measured at the period of expansion in the turbulent field and during compression by the reflected shock on turbulent field, and it is observed that the longitudinal turbulent velocity fluctuation is enhanced more at the period of expansion due to incident shock wave movement far from the turbulent field. The amplification of the turbulent kinetic energy (TKE) level in the shock/turbulence interaction depends on the shock wave strength and the longitudinal velocity difference across the shock wave. On decreasing the longitudinal velocity difference across the shock, the turbulent kinetic energy (TKE) level is less amplified. The TKE level is amplified by the factor of 1.5–1.8 in the shock/turbulence interaction where the dissipation rate of TKE decreases in all cases of shock/turbulence interaction. After the shock/turbulence interaction, the turbulent dissipative-length scale is amplified slightly and the amplification of the length scales decreases when increasing the shock strength. To cite this article: M.A. Jinnah, K. Takayama, C. R. Mecanique 333 (2005).     

Influence d'une polarisation électrique sur l'instabilité d'une interface liquide/liquide

One studies the influence of the surface tension on the stability of a liquid electrolyte/liquid metal interface. The control of this parameter is obtained by an electric polarization imposed on the liquid metal. The flow is carried out in a cylindrical cavity with turning lid and fixed bottom on the level of which a annular drain filled with liquid gallium is set. One analyzes the phenomenon of appearance of the waves of instability according to the surface tension. The experimental results are compared with a Kelvin–Helmholtz model, purely non-viscous or corrected by taking into account the normal component of the viscous constraints. To cite this article: M. Al Radi et al., C. R. Mecanique 333 (2005).