Direct simulation of the motion of neutrally buoyant balls in a three-dimensional Poiseuille flow

In a previous article the authors introduced a Lagrange multiplier based fictitious domain method. Their goal in the present article is to apply a generalization of the above method to: (i) the numerical simulation of the motion of neutrally buoyant particles in a three-dimensional Poiseuille flow; (ii) study – via direct numerical simulations – the migration of neutrally buoyant balls in the tube Poiseuille flow of an incompressible Newtonian viscous fluid. Simulations made with one and several particles show that, as expected, the Segré–Silberberg effect takes place. To cite this article: T.-W. Pan, R. Glowinski, C. R. Mecanique 333 (2005).     

On the slow gravity-driven migration of arbitrary clusters of small solid particles

A new approach is advocated to compute at a low cpu time cost the rigid-body motions of settling solid particles when inertial effects are negligible. In addition to the relevant boundary-integral equations, the numerical implementation and a few convincing benchmark tests we address two configurations of equivalent spheres and spheroids, i.e. that exhibit when isolated the same settling velocity. To cite this article: A. Sellier, C. R. Mecanique 332 (2004).

Résumé

On propose une approche originale pour déterminer le mouvement d'une assemblée de particules solides et de formes arbitraires soumise à l'action de la pesanteur dans l'approximation de Stokes. Outre les intégrales de frontière et la méthode numérique associées on présente quelques comparaisons et examine le cas de deux configurations de sphères et ellipsoides de révolution équivalents, c'est-à-dire dotés lorsqu'ils sont seuls de la même vitesse de sédimentation. Pour citer cet article : A. Sellier, C. R. Mecanique 332 (2004).     

Missing boundary data recovering for the Helmholtz problem

This Note is dedicated to the numerical treatment of the ill-posed Cauchy–Helmholtz problem. Resorting to the domain decomposition tools, these missing boundary data are rephrased through an ‘interfacial’ equation. This equation is solved via a preconditioned Richardson algorithm with dynamic relaxation. The efficiency of the proposed method is illustrated by some numerical experiments. To cite this article: R. Ben Fatma et al., C. R. Mecanique 335 (2007).     

Effective flow of a viscous liquid through a helical pipe

We study the flow of a viscous fluid through a pipe with helical shape parameterized with , where the small parameter stands for the distance between two coils of the helix. The pipe has small cross-section of size . Using the asymptotic analysis of the microscopic flow described by the Navier–Stokes system, with respect to the small parameter that tends to zero, we find the effective fluid flow described by an explicit formula of the Poisseuile type including a small distorsion due to the particular geometry of the pipe. To cite this article: E. Marušić-Paloka, I. Pažanin, C. R. Mecanique 332 (2004).

Résumé

On considère un écoulement dans un tube de section circulaire et de forme hélicoïdale paramétré par , où est la distance entre deux tours de la spirale. Le rayon de la section du tube est lui aussi supposé égal à . A partir de l'écoulement microscopique décrit par le système de Navier–Stokes et en utilisant l'analyse asymptotique par rapport à ce petit paramètre on obtient l'écoulemment effectif décrit par une formule explicite de type Poiseuille associée à une petite déviation due à la géometrie du tube. Pour citer cet article : E. Marušić-Paloka, I. Pažanin, C. R. Mecanique 332 (2004).     

Apparent viscosity of a mixture of a Newtonian fluid and interacting particles

We investigate the behavior of fluid–particle mixtures subject to shear stress, by mean of direct simulation. This approach is meant to give some hints to explain the influence of interacting red cells on the global behavior of the blood. We concentrate on the apparent viscosity, which we define as a macroscopic quantity which characterizes the resistance of a mixture against externally imposed shear motion. Our main purpose is to explain the non-monotonous variations of this apparent viscosity when a mixture of fluid and interacting particles is submitted to shear stress during a certain time interval. Our analysis of these variations is based on preliminary theoretical remarks, and some computations for some well-chosen static configurations. To cite this article: A. Lefebvre, B. Maury, C. R. Mecanique 333 (2005).     

Espaces d'écoulements dits « universels », 3

Universal motions with uniform steady vorticity form a corolla of linear spaces derived from rigid body motions. Closely related to potential flows, they satisfy two extensions of Lagrange theorem, are investigated with the help of complex functions, as stand celebrated when be plane. They take place in hydrodynamics, aerodynamics, geophysics, astrophysics, turbulence, physics of plasmas and superfluid helium. In all the cases, arbitrary unsteady span-wise translations permit to generalise as well as to exhibit helical or 3D universal motions. Three misunderstood periodic flows illustrate our purpose, as they approach shear instabilities in numerous fluids. To cite this article: M. Bouthier, C. R. Mecanique 332 (2004).     

Fluid structure interaction problems in large deformation

The present article deals with the simulation of fluid structure interaction problems in large deformation, and discusses two aspects of their numerical solution: (i) the derivation of energy conserving time integration schemes in presence of fluid structure coupling, moving grids, and nonlinear kinematic constraints such as incompressibility and contact, (ii) the introduction of adequate preconditioners efficiently chaining local fluid and structure solvers. Solutions are proposed, analyzed and tested using nonlinear energy correcting terms, and added mass based Dirichlet Neumann preconditioners. Numerical applications include nonlinear impact problems in elastodynamics and blood flows predictions within flexible arteries. To cite this article: P. Le Tallec et al., C. R. Mecanique 333 (2005).     

Large-Eddy Simulation of transcritical flows

The present study uses the LES code AVBP, developed at CERFACS, to simulate transcritical flows. Real gas effects are accounted for by the use of a cubic equation of state, in conjunction with appropriate viscosity and thermal conductivity coefficients. First a single nitrogen round jet at supercritical pressure injected in a gaseous reservoir is simulated. Two cases are considered, one demonstrating a transcritical injection (high density injection), the other being directly injected at supercritical temperature (lower density injection). Comparison with available measurements shows good agreement. Finally, the simulation of a reacting case from the Mascotte bench (ONERA) is performed, consisting in a single coaxial injector injecting transcritical oxygen and supercritical hydrogen in a 60 bar chamber. Mean flow characteristics are in good agreement with the experimental observations of OH^* emission, whereas temperature comparisons are more difficult to interpret. To cite this article: T. Schmitt et al., C. R. Mecanique 337 (2009).     

Modélisation du comportement thermique d'un outil de fraisage : approche par identification de système non entierThermal modelling of a milling tool: a noninteger system identification approach

In this work we present an experimental apparatus devoted to the thermal characterisation of a milling tool. The experimental device used thermistors, one for each insert. Each thermistor is located at a point in the tool close to the tip of the insert. The heat flux in each insert is expressed according to the temperature at the sensor from a non-integer model. The parameters of the model are identified from transient evolutions measurements of the temperature on the sensor and on the cutting edge. An application shows the difference in the behaviour of each insert during machining from the estimated heat fluxes. To cite this article: J.-L. Battaglia et al., C. R. Mecanique 330 (2002) 857–864.     

Homogenization of an elasticity problem in domains with a net of slender bars near surface

We consider an elasticity problem in a domain Ω⁽⁾=ΩF⁽⁾, where Ω is an open bounded domain in R³, F⁽⁾ is a connected nonperiodic set in Ω like a net of slender bars, and is a parameter characterizing the microstructure of the domain. We consider the case of a surface distribution of the set F⁽⁾, i.e., for sufficiently small , the set F⁽⁾ is concentrated in arbitrary small neighbourhood of a surface Γ. Under a hypothesis on the asymptotic behaviour of the energy functional, we obtain the macroscopic (homogenized) model. To cite this article: M. Goncharenko, L. Pankratov, C. R. Mecanique 331 (2003).     

A two-dimensional effective model describing fluid–structure interaction in blood flow: analysis, simulation and experimental validation

We derive a closed system of effective equations describing a time-dependent flow of a viscous incompressible Newtonian fluid through a long and narrow elastic tube. The 3D axially symmetric incompressible Navier–Stokes equations are used to model the flow. Two models are used to describe the tube wall: the linear membrane shell model and the linearly elastic membrane and the curved, linearly elastic Koiter shell model. We study the behavior of the coupled fluid–structure interaction problem in the limit when the ratio between the radius and the length of the tube, , tends to zero. We obtain the reduced equations that are of Biot type with memory. An interesting feature of the reduced equations is that the memory term explicitly captures the viscoelastic nature of the coupled problem. Our model provides significant improvement over the standard 1D approximations of the fluid–structure interaction problem, all of which assume an ad hoc closure assumption for the velocity profile. We performed experimental validation of the reduced model using a mock circulatory flow loop assembled at the Cardiovascular Research Laboratory at the Texas Heart Institute. Experimental results show excellent agreement with the numerically calculated solution. Major applications include blood flow through large human arteries. To cite this article: S. Čanić et al., C. R. Mecanique 333 (2005).     

Micromechanical computational modeling of expansive porous media

A modified Terzaghi principle is proposed to describe the influence of locally coupled electro-chemo-mechanical processes in highly compacted swelling clays upon the form of the macroscopic modified effective stress principle. The two-scale model is derived using the homogenization procedure to upscale the microscopic behavior of a two-phase system composed of clay particles saturated by a completely dissociated electrolyte aqueous solution. Numerical experiments are performed to illustrate the results in a particular cell geometry. To cite this article: M.A. Murad, C. Moyne, C. R. Mecanique 330 (2002) 865–870.     

Confined buckling of inextensible rods by convex difference algorithms

In this Note we present an approach to determine the local minima of a specific class of minimization problems. Attention is focused on the inextensibility condition of flexible rods expressed as a nonconvex constraint. Two algorithms are derived from a special splitting of the Lagrangian into the difference of two convex functions (DC). They are compared to the augmented Lagrangian methods used in this context. These DC formulations are easily extended to contact problems and applied to the determination of confined buckling shapes. To cite this article: P. Alart, S. Pagano, C. R. Mecanique 330 (2002) 819–824.     

Chaos synchronization on the N-torus and cryptography

A class of chaotic dynamical systems on the N-dimensional torus is proposed for masking some information in secure communications. The information is then recovered thanks to a chaos synchronization process. To cite this article: L. Rosier et al., C. R. Mecanique 332 (2004).

Résumé

Nous proposons une classe de systèmes chaotiques sur le tore N-dimensionnel pour masquer une information à transmettre dans une communication sécurisée. Cette information est ensuite reconstruite à l'aide d'un mécanisme de synchronisation du chaos. Pour citer cet article : L. Rosier et al., C. R. Mecanique 332 (2004).     

Use of Faraday instabilities to enhance fuel pulverisation in air-blast atomisers

The atomization of liquids into a spray is an important process in many industrial applications and particularly in the aero-engine sector. Conventional air-blast injectors in aircraft engines today use aerodynamic shearing effects to atomize the liquid fuel. However, at operating conditions where the air velocity is below 30 m/s (such as ground start and high altitude restart) the atomization quality is poor. Consequently combustion is less efficient with high pollutant emissions. The objective of this study is to validate a new concept of injector which couples the shearing effects with the principle of ultrasonic atomization. The latter consists of using piezoelectric actuators to generate the oscillations of a wall in contact with the liquid film. This excitation perpendicular to the liquid film surface creates Faraday instabilities at the liquid/air interface. Amplitudes higher than a defined threshold value induce the break-up of ligaments and the formation of droplets. To cite this article: M. Boukra et al., C. R. Mecanique 337 (2009).     

Weighted Korn inequalities for thin-walled elastic structures

Appropriate weighted norms in H¹ are presented such that the Korn type inequality is asymptotically sharp with respect to relative thickness and stiffness of the elastic plates. The weights depend crucially on the geometric structure of the plates' junction. To cite this article: O.V. Izotova et al., C. R. Mecanique 334 (2006).     

Numerical analysis of a quasistatic piezoelectric problem with damage

The quasistatic evolution of the mechanical state of a piezoelectric body with damage is numerically studied in this paper. Both damage and piezoelectric effects are included into the model. The variational formulation leads to a coupled system composed of two linear variational equations for the displacement field and the electric potential, and a nonlinear parabolic variational equation for the damage field. The existence of a unique weak solution is stated. Then, a fully discrete scheme is introduced by using a finite element method to approximate the spatial variable and an Euler scheme to discretize the time derivatives. Error estimates are derived on the approximate solutions, from which the linear convergence of the algorithm is deduced under suitable regularity conditions. Finally, a two-dimensional example is presented to demonstrate the behaviour of the solution. To cite this article: J.R. Fernández et al., C. R. Mecanique 336 (2008).     

Computing Green's function of elasticity in a half-plane with impedance boundary condition

This Note presents an effective and accurate method for numerical calculation of the Green's function G associated with the time harmonic elasticity system in a half-plane, where an impedance boundary condition is considered. The need to compute this function arises when studying wave propagation in underground mining and seismological engineering. To theoretically obtain this Green's function, we have drawn our inspiration from the paper by Durán et al. (2005), where the Green's function for the Helmholtz equation has been computed. The method consists in applying a partial Fourier transform, which allows an explicit calculation of the so-called spectral Green's function. In order to compute its inverse Fourier transform, we separate as a sum of two terms. The first is associated with the whole plane, whereas the second takes into account the half-plane and the boundary conditions. The first term corresponds to the Green's function of the well known time-harmonic elasticity system in (cf. J. Dompierre, Thesis). The second term is separated as a sum of three terms, where two of them contain singularities in the spectral variable (pseudo-poles and poles) and the other is regular and decreasing at infinity. The inverse Fourier transform of the singular terms are analytically computed, whereas the regular one is numerically obtained via an FFT algorithm. We present a numerical result. Moreover, we show that, under some conditions, a fourth additional slowness appears and which could produce a new surface wave. To cite this article: M. Durán et al., C. R. Mecanique 334 (2006).     

A new formulation of immiscible compressible two-phase flow in porous media

A new formulation is proposed to describe immiscible compressible two-phase flow in porous media. The main feature of this formulation is the introduction of a global pressure. The resulting equations are written in a fractional flow formulation and lead to a coupled system which consists of a nonlinear parabolic (the global pressure equation) and a nonlinear diffusion–convection one (the saturation equation) which can be efficiently solved numerically. To cite this article: B. Amaziane, M. Jurak, C. R. Mecanique 336 (2008).