Développement d''un modèle en vue de la prédiction du rallumage d''un foyer de turboréacteur à haute altitudeDevelopment of a model to predict the ignition performance of a turbojet engine at high altitude

Within the context of turbojet engine re-ignition after in-flight extinction, a thermo-diffusive model has been developed to describe the electrical ignition, at low pressure and low temperature, of a cluster of fuel droplets. The model involves the resolution of the conservation equations of mass, species and energy. It also takes into account the various physical and chemical phenomena occurring during the ignition process. This Note presents the ignition model and preliminary results of this model applied to an experimental configuration. To cite this article: V. Quintilla et al., C. R. Mecanique 330 (2002) 811–818.     

Stability of a hypersonic shock layer on a flat plateStabilité d'une couche de choc hypersonique sur une plaque plane.

Stability of a hypersonic shock layer on a flat plate is examined with allowance for disturbances conditions on the shock wave within the framework of the linear stability theory. The characteristics of the main flow are calculated on the basis of the Full Viscous Shock Layer model. Conditions for velocity, pressure, and temperature perturbations are derived from steady Rankine–Hugoniot relation on the shock wave. These conditions are used as boundary conditions on the shock wave for linear stability equations. The growth rates of disturbances and density fluctuations are compared with experimental data obtained at ITAM by the method of electron-beam fluorescence and with theoretical data of other authors. To cite this article: A.A. Maslov et al., C. R. Mecanique 332 (2004).     

Homogenization of an elastic medium reinforced by anisotropic fibersHomogénéisation d'un milieu élastique renforcé par des fibres anisotropes

We present results in this Note concerning a vector version in the framework of linearized elasticity (see A. Sili, Homogenization of an elastic medium reinforced by anisotropic fibers, in press), of our previous work in which we have studied the homogenization of a scalar nonlinear monotone problem posed on a fibered medium (see A. Sili, Homogenization of a nonlinear monotone problem in an anisotropic medium, in press). Here, we assume that parallel elastic anisotropic fibers, periodically distributed with a period of size ε in a cube $\text{Ω}$, are surrounded by a soft elastic material, the elasticity coefficients of this material being in the ratio ε² with those of the fibers. We prove that the homogenized problem is nonlocal and involves variables linked together with the anisotropy of the fibers. To cite this article: A. Sili, C. R. Mecanique 331 (2003).     

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.     

Homogénéisation de problèmes d''évolution dans une structure renforcée de fibresHomogenization of evolution problems in a fiber reinforced structure

We study the homogenization of evolution equations such as:

where the coefficient a is -periodic and takes very high values on a subset TΩ (fibered structure) of very small measure. We find a non-local effective equation deduced from a homogenized system of several equations. To cite this article: M. Bellieud, C. R. Mecanique 330 (2002) 843–848.     

Adaptive finite elements for the steady free fall of a body in a Newtonian fluid

The numerical simulation of the free fall of a solid body in a viscous fluid is a challenging task since it requires computational domains which usually need to be several order of magnitude larger than the solid body in order to avoid the influence of artificial boundaries. Toward an optimal mesh design in that context, we propose a method based on the weighted a posteriori error estimation of the finite element approximation of the fluid/body motion. A key ingredient for the proposed approach is the reformulation of the conservation and kinetic equations in the solid frame as well as the implicit treatment of the hydrodynamic forces and torque acting on the solid body in the weak formulation. Information given by the solution of an adequate dual problem allows one to control the discretization error of given functionals. The analysis encompasses the control of the free fall velocity, the orientation of the body, the hydrodynamic force and torque on the body. Numerical experiments for the two dimensional sedimentation problem validate the method. To cite this article: V. Heuveline, C. R. Mecanique 333 (2005).     

A two grid algorithm based on perturbation and homotopy methods

In this paper, we propose a new class of bi-grid algorithm to solve large scale linear algebraic equations. This method is based on homotopy, perturbation technique and Padé approximants. To cite this article: R. El Mokhtari et al., C. R. Mecanique 330 (2002) 825–830.     

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.     

Influence of mesoscale urban morphology on the spatial noise attenuation of flyover aircrafts

The influence of urban morphology of low-density built-up areas on spatial noise level attenuation of flyover aircrafts is investigated at a mesoscale. Six urban morphological parameters, including Building Plan Area Fraction, Complete Aspect Ratio, Building Surface Area to Plan Area Ratio, Building Frontal Area Index, Height-to-Width Ratio, and Horizontal Distance of First-row Building to Flight Path, have been selected and developed. Effects of flight altitude and horizontal flight path distance to site, on spatial aircraft noise attenuation, are examined, considering open areas and façades. Twenty sampled sites, each of 250 m * 250 m, are considered. The results show that within 1000 m horizontal distance of flight path to a site, urban morphology plays an important role in open areas, especially for the buildings with high sound absorption façades, where the variance of average noise level attenuation among different sites is about 4.6 dB at 3150 Hz. The effect of flight altitude of 200–400 ft on average noise level attenuation is not significant, within about 2 dB at both 630 Hz and1600 Hz in open areas. Urban morphological parameters influence the noise attenuation more in open areas than that on façades. Spatial noise attenuation of flyover aircrafts is mainly correlated to Building Frontal Area Index and Horizontal Distance of First-row Building to Flight Path.     

关于内接单形的不等式及其应用

应用解析方法和几何不等式理论研究了n维欧氏空间E~n中涉及n维单形Ω_n与其内接单形Ω′_n的几何不等式的问题,建立了涉及单形Ω_n及其内接单形Ω′_n的外接球半径与高线的一类几何不等式,作为其特例得到了著名的n维Euler不等式的一些推广.