Three-dimensional Rayleigh–Bénard instability in a supercritical fluidInstabilité tridimensionnelle de Rayleigh–Bénard dans un fluide supercritique

This paper describes the unsteady convective flow of a supercritical fluid in the Rayleigh–Bénard configuration. Two-dimensional earlier studies reported fast temperature equilibrium due to the piston effect and the development of a convective instability when the local Rayleigh number exceeds a critical value. In the present work, a high order 3D finite volume method has been developed and optimized, and to our knowledge, we show for the first time a three-dimensional convective instability in a supercritical fluid. Inspecting the time-evolution of temperature field patterns, we exhibit corner effects and a three-dimensional behavior of the flow. To cite this article: G. Accary et al., C. R. Mecanique 332 (2004).     

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).     

Multiple-scale modelling of acoustic sources in low Mach-number flow

The main difficulty in the calculation of sound generated by fluid flow at low Mach numbers is the occurrence of different scales. The fluid flow is characterized by small spatial structures containing a large amount of energy that may propagate with a small convective velocity, such as small vortices in a turbulent flow. The radiated acoustic waves have small amplitudes and carry a small amount of energy, but have a long wavelength due to their fast propagation velocity. In this paper a perturbation method is used to calculate noise generation and propagation in combination with fluid flow based on the incompressible equations. The idea for the numerical modelling is to introduce a fine grid for the resolution of the fluid flow that is embedded into a larger acoustical domain with a coarse grid adapted to the long wavelength acoustics. To get an appropriate restriction of the acoustic source terms from the fine CFD-grid to the coarse CAA-grid, a multi-scale expansion with one time and two space scales is introduced. To cite this article: C.-D. Munz et al., C. R. Mecanique 333 (2005).     

Instabilité d'une nappe de vorticité étirée instationnaireInstability of an unsteady stretched vortex layer

We consider how the Kelvin–Helmholtz instability is affected by an external hyperbolic strain flow. The basic flow being unsteady, the inviscid evolution of perturbations is studied within the framework of a non-normal analysis in which the maximum amplification is computed for any given time. A positive or negative stretching is shown to enhance or reduce, respectively, the instability even for weak stretching rates. To cite this article: T. Gomez, M. Rossi, C. R. Mecanique 331 (2003).     

On the stability of a Bingham fluid flow in an annular channelSur la stabilité de l'écoulement d'un fluide de Bingham dans une conduite annulaire

Linear stability of a fully developed Bingham fluid flow between two coaxial cylinders subject to infinitesimal axisymetric perturbations is investigated. The analysis leads to two uncoupled Orr–Sommerfeld equations with appropriate boundary conditions. The numerical solution is obtained using fourth order finite difference scheme. The computations were performed for various plug flow dimensions and radii ratios. Within the range of the parameters considered in this paper, the Poiseuille flow of Bingham fluid is found to be linearly stable. To cite this article: N. Kabouya, C. Nouar, C. R. Mecanique 331 (2003).     

Approche analytique de la convection forcée des fluides de Bingham dans un tubeAnalytical approach for forced convection of Bingham fluids in a tube

The asymptotic behaviour of laminar forced convection for Bingham fluid in a circular tube subjected to an axially varying wall heat flux is studied analytically. The effect of viscous dissipation is taken into account while the axial heat conduction in the fluid is considered as negligible. The asymptotic temperature profile and the asymptotic Nusselt number are determined for various axial wall heat flux distributions which yield a thermally developed region. The results obtained show a diminution in asymptotic Nusselt number when the Brinkman number and the dimensionless radius of the plug flow region increase. Comparisons with the results in the literature for Newtonian fluids show the validity of the present analysis. To cite this article: R. Khatyr et al., C. R. Mecanique 330 (2002) 69–75.     

Singular nature of nonlinear macroscale effects in high-rate flow through porous mediaNature singulière des effets macroscopiques non linéaires dans un écoulement à hautes vitesses en milieux poreux

The quadratic law of laminar flow through porous media at high Reynolds numbers, which is well confirmed by the multiple experimental data, is shown to give rise to three fundamental paradoxes. All them can be resolved by assuming the singular structure of flow. The singularity is produced by the formation of jet brunches which invade the stagnant zones and sharply loss their kinetic energy. The numerical simulation confirms this effect. To cite this article: M. Panfilov et al., C. R. Mecanique 331 (2003).     

Acoustic source terms study for non-isothermal flows using an aeroacoustic hybrid approach

This paper presents a numerical study of noise source term in non-isothermal flows in the context of an aeroacoustic hybrid technique at low Mach numbers. Asymptotic analysis applied to the fully compressible Navier–Stokes equations provides separated sets of equations for the dynamic of the flow and the production and propagation of acoustic waves. Comparisons with analytical dipole and quadrupole distributions are performed, confirming the dipole type of non-isothermal source distribution. This paper is a preliminary work for some more extensive studies on the topic. To cite this article: F. Golanski, C. Prax, C. R. Mecanique 333 (2005).     

Modified fixed point algorithm in fluid–structure interactionAccélération avec des conditions de transpiration d'un algorithme de point fixe en interaction fluide–structure

In this work, we address the numerical solution of some non-linear problems arising in the time discretization of fluid–structure interaction problems with fully implicit schemes. At each time step, we have to solve a highly non-linear coupled system, since the fluid domain depends on the unknown displacement of the structure. We propose a modified fixed-point algorithm which combines the Block-Gauss–Seidel iterations with a transpiration formulation. Numerical experiments show the great improvement in computing time with respect to the standard method. To cite this article: S. Deparis et al., C. R. Mecanique 331 (2003).     

Computational aeroacoustics applications based on a discontinuous Galerkin method

caa simulation requires the calculation of the propagation of acoustic waves with low numerical dissipation and dispersion error, and to take into account complex geometries. To give, at the same time, an answer to both challenges, a Discontinuous Galerkin Method is developed for Computational AeroAcoustics. Euler's linearized equations are solved with the Discontinuous Galerkin Method using flux splitting technics. Boundary conditions are established for rigid wall, non-reflective boundary and imposed values. A first validation, for induct propagation is realized. Then, applications illustrate: the Chu and Kovasznay's decomposition of perturbation inside uniform flow in term of independent acoustic and rotational modes, Kelvin–Helmholtz instability and acoustic diffraction by an air wing. To cite this article: Ph. Delorme et al., C. R. Mecanique 333 (2005).     

Approximation uniformément valable pour l'écoulement de Falkner–SkanA uniformly valid approximation for a Falkner–Skan flow

In the context of the laminar steady two-dimensional flow of an incompressible Newtonian fluid, we propose a uniformly valid approximation in the whole domain of the flow over a flat plate with incidence. The solution is built from the asymptotic method of matched expansions at order one and has been compared with the classical boundary layer solution and the potential solution. It allows a better approximation of basic flow near the leading edge of the flat plate. The solution has been established at order two for the flow without incidence. These more realistic solutions should be employed when analysing the receptivity and the ensuing destabilisation of boundary layers. To cite this article: S. Saintlos, J. Bretteville, C. R. Mecanique 330 (2002) 673–682.     

Prolongation of two phases in the model of fluid displacement through a capillaryProlongement de deux phases dans le modèle du déplacement d'un fluide dans un capillaire

The problem of a piston-like displacement of a fluid by another in a capillary is examined. It is suggested that each fluid is prolonged into the domain occupied by the other fluid. This enables the replacement of the two-phase flow problem by a transient single-phase flow problem, with discontinuity in velocity and pressure on a film interface. The problems related to the triple point are solved by introducing a limit fluid near the pore wall. The demonstration of the Washburn equation contributes to the physical justification of our model. To cite this article: Y. Lucas et al., C. R. Mecanique 334 (2006).     

Flow in wavy tube structure: asymptotic analysis and numerical simulationÉcoulement dans une structure tubulaire ondulée : analyse asymptotique et résolution numérique

This paper deals with the study of the stationary, incompressible, 2D flow of a fluid in a thin wavy tube. In this work, we consider a domain which is the union of two wavy tubes depending on a small parameter. The asymptotic expansion is constructed. The method of partial asymptotic decomposition is applied. The numerical implementation of this method for the extrusion process is developed. The new physical effects are discussed. To cite this article: A. Ainser et al., C. R. Mecanique 331 (2003).     

Dispersion de particules solides en mouvement de saltation dans un écoulement turbulentDispersion of solid saltating particles in a turbulent flow

The solid particle dispersion in saltating motion is studied in an homogeneous turbulence and in a turbulent boundary layer. The fluid velocity along the particle trajectory is estimated using a continuous stochastic differential equation in which the correlation integral time takes into account gravity and inertia effects. As far as the boundary layer is concerned, the aerodynamic entrainment of particles and the rebound are modelised as random variables with Gaussian probability density functions. Compared with experimental results, the numerical results show good agreement for dispersion, although velocity fluctuations are slightly under evaluated. To cite this article: C. Aguirre et al., C. R. Mecanique 332 (2004).     

Ablative Rayleigh–Taylor instability in the limit of an infinitely large density ratio

The instability of ablation fronts strongly accelerated toward the dense medium under the conditions of inertial confinement fusion (ICF) is addressed in the limit of an infinitely large density ratio. The analysis serves to demonstrate that the flow is irrotational to first order, reducing the nonlinear analysis to solve a two-potential flows problem. Vorticity appears at the following orders in the perturbation analysis. This result simplifies greatly the analysis. The possibility for using boundary integral methods opens new perspectives in the nonlinear theory of the ablative RT instability in ICF. A few examples are given at the end of the Note. To cite this article: P. Clavin, C. Almarcha, C. R. Mecanique 333 (2005).     

Subgrid models preserving the symmetry group of the Navier–Stokes equations

In order to preserve the physical properties of the flow (scaling laws, conservation laws, …) during the simulation, a class of subgrid models respecting the symmetry group of the Navier–Stokes equations is built. The class is then refined such that models satisfy the second law of thermodynamics and are suited to take into account the inverse energy cascade. A simple model belonging to the class is tested and a better result than those provided by Smagorinsky and dynamic models is obtained. To cite this article: D. Razafindralandy, A. Hamdouni, C. R. Mecanique 333 (2005).     

Non-Darcian Bénard convection in eccentric annuli containing spherical particles

In this paper, a numerical investigation of natural convection in a porous medium confined by two horizontal eccentric cylinders is presented. The cylinders are impermeable to fluid motion and retained at uniform different temperatures. While, the annular porous layer is packed with glass spheres and fully-saturated with air, and the cylindrical packed bed is under the condition of local thermal non-equilibrium. The mathematical model describing the thermal and hydrodynamic phenomena consists of the two-phase energy model coupled by the Brinkman-Forchheimer-extended Darcy model under the Boussinesq approximation. The non-dimensional derived system of formulations is numerically discretised and solved using the spectral-element method. The investigation is conducted for a constant cylinder/particle diameter ratio ($D_i/d$) = 30, porosity ($\epsilon$) = 0.5, and solid/fluid thermal conductivity ratio ($k_r$) = 38.6. The effects of the vertical, horizontal and diagonal heat source eccentricity (−0.8 $⩽e⩽$0.8) and the annulus radius ratio (1.5 $⩽\mathit{RR}⩽$ 5.0) on the temperature and velocity distributions as well as the overall heat dissipation within both the fluid and solid phases, for a broad range of Rayleigh number (10⁴ $⩽$ Ra $⩽$ 8 $\times {10}^7$). The results show that uni-cellular, bi-cellular and tri-cellular flow regimes appear in the vertical eccentric annulus at the higher positive eccentricity e = 0.8 as Rayleigh number increases. However, in the diagonal eccentric annulus, the multi-cellular flow regimes are shown to be deformed and the isotherms are particularly distorted when Rayleigh number increases. In contrast, in the horizontal eccentric annulus, it is found that whatever the Rayleigh number is only an uni-cellular flow regime is seen. In addition, it is shown that the fluid flow is always unstable in the diagonal eccentric geometry at e = 0.8 for moderate and higher Rayleigh numbers. However, it loses its stability in the vertical eccentric geometry only at two particular cases, while it is always stable in the horizontal eccentric geometry, for all eccentricities and Rayleigh numbers.