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).     

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).     

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).     

A criterion of the continuous spectrum for elasticity and other self-adjoint systems on sharp peak-shaped domains

The spectra of the elasticity and piezo-electricity systems for a solid with a sharp peak point on the boundary, which is free of traction, are not discrete. An algebraic criterion of non-empty continuous spectrum is found for the Neumann problem for rather arbitrary formally self-adjoint elliptic systems of second-order differential equations on a sharp peak-shaped domain. To cite this article: S.A. Nazarov, 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).     

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).     

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).     

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).     

Asymptotics of eigenfrequencies of an elastic body with a heavy and hard peak-shaped inclusion

A heavy and hard peak-shaped inclusion in an elastic body provokes to concentration of eigenvalues in the low-frequency range of the spectrum and localization of the corresponding eigenmodes near the peak tip. To cite this article: S.A. Nazarov, C. R. Mecanique 335 (2007).     

On the confinement of a viscous fluid by means of a feedback external field

In this work we consider a planar stationary flow of an incompressible viscous fluid in a semi-infinite strip governed by the standard Stokes system. We show how this fluid can be stopped at a finite distance from the entrance of the semi-infinite strip by means of a feedback source depending in a sublinear way on the velocity field. This localization effect is proved by reducing the problem to a non-linear biharmonic type one for which the localization of solutions is obtained through the application of an energy method, in the spirit of the monograph by S.N. Antontsev, J.I. Díaz and S.I. Shmarev (Energy Methods for Free Boundary Problems: Applications to Non-Linear PDEs and Fluid Mechanics, Birkäuser, Boston, 2002). Since the presence of the non-linear terms defined by the source is not standard in fluid mechanics literature, we give also some results about the existence and uniqueness of weak solutions for this problem. To cite this article: S.N. Antontsev et al., C. R. Mecanique 330 (2002) 797–802.     

Analytical development of disturbed matrix eigenvalue problem applied to mixed convection stability analysis in Darcy media

This work consists in evaluating algebraically and numerically the influence of a disturbance on the spectral values of a diagonalizable matrix. Thus, two approaches will be possible; to use the theorem of disturbances of a matrix depending on a parameter, due to Lidskii and primarily based on the structure of Jordan of the no disturbed matrix. The second approach consists in factorizing the matrix system, and then carrying out a numerical calculation of the roots of the disturbances matrix characteristic polynomial. This problem can be a standard model in the equations of the continuous media mechanics. During this work, we chose to use the second approach and in order to illustrate the application, we choose the Rayleigh–Bénard problem in Darcy media, disturbed by a filtering through flow. The matrix form of the problem is calculated starting from a linear stability analysis by a finite elements method. We show that it is possible to break up the general phenomenon into other elementary ones described respectively by a disturbed matrix and a disturbance. A good agreement between the two methods was seen. To cite this article: H.B. Hamed, R. Bennacer, C. R. Mecanique 336 (2008).     

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).     

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).     

Using data assimilation in numerical simulations of experimental geophysical flows

Data assimilation is used to couple numerical simulations and laboratory experiments of unsteady fluid flows in a stratified, rotating fluid. The experiments are performed on the large Coriolis turntable (Grenoble) and the simulations are performed with a multi-layer shallow water model. Sequential assimilation of high-resolution CIV (Correlation Image Velocimetry) measurements drives the numerical model close to the experimental flow and provides an estimation of all the flow variables at each time and each point. It is then possible (i) to analyse the flow dynamics in details, (ii) to determine the model errors starting from a realistic initial condition and (iii) to test the assimilation scheme when a reduced set of data is assimilated. To illustrate this, some results on the baroclinic instability of a two-layer vortex are presented. To cite this article: M. Galmiche et al., C. R. Mecanique 331 (2003).     

Transition of unsteady flows of evaporation to steady state

We investigate the half-space problem of evaporation and condensation in the scope of discrete kinetic theory. Exact solutions are found to the boundary value problem and the initial boundary value problems of the flow in the half space for a discrete velocity model. The results are used to analyze the transition of the unsteady solutions towards steady states. To cite this article: A. d'Almeida, C. R. Mecanique 336 (2008).     

Relevance of a thermal contact resistance depending on the solid/liquid phase change transition for sprayed composite metal/ceramic powder by direct current plasma jets

The thermal contact between layers plays a key role in the behaviour of composite particles (mechanofused) subjected to a high temperature jet (example of two layers metal/ceramic particles under plasma spraying). This work underlines the interest of considering a thermal contact resistance varying with the melting state of the two components along the full process. The computational model considers the time-dependent state of the particle during its flight with coupled transfers and solid/liquid/vapor phase changes. To cite this article: M. Bouneder et al., C. R. Mecanique 336 (2008).     

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).     

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).     

Experimental observation of frequency doubling in a viscoelastic mixing layer

An experimental mixing layer in water at Reynolds number 440 is investigated. A colored viscoelastic solution is introduced in the shear layer before the roll-up dynamics. On the basis of flow visualization and local velocity measurements, it is found that compared to the Newtonian case, the roll-up process is affected by the non-Newtonian behavior of the viscoelastic solution. The effect consists of the appearance of secondary eddies in the mixing layer corresponding to the production of higher harmonics in the vorticity distribution. Consequently, there is a frequency doubling of the local velocity oscillations in the mixing layer. To cite this article: F. Sausset et al., C. R. Mecanique 332 (2004).

Résumé

Une étude expérimentale de la couche de mélange à un nombre de Reynolds de 440 est réalisée. Une solution viscoélastique colorée est introduite dans la couche cisaillée stationnaire juste avant la formation des tourbillons. En utilisant un mesure locale de la vitesse et une technique de visualisation par fluorescence, il est montré que la formation tourbillonnaire est affectée par le comportement non-Newtonien de la solution viscoélastique par rapport au cas Newtonien. Cet effet correspond à la formation de tourbillons secondaires produisant un harmonique supérieur dans la répartition spatiale de vorticité. En conséquence, un doublement de la fréquence des oscillations de la vitesse locale dans la couche de mélange est observé. Pour citer cet article : F. Sausset et al., C. R. Mecanique 332 (2004).