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).     

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).     

High-order evolution equation for nonlinear wave-packet propagation with surface tension accountingÉquation d'évolution d'ordre élevé de groupes d'ondes non linéaires en présence de tension superficielle

The nonlinear problem for propagation of wave-packets along the interface of two semi-infinite fluids is solved on the basis of multiple scale asymptotic expansions. Unlike all previous investigations dealing only with third-order approximations, here fourth-order approximation is developed. The corresponding solvability condition is obtained and the evolution equation in the case away from the cut-off wave number is derived. As a result, the nonlinear higher-order Schrödinger equation is obtained which contains the nonlinear part in a compact form. This equation is valid for a wide range of wave numbers. The stability diagram shows regions of stability and instability of capillary-gravity wave-packets. To cite this article: I. Selezov et al., C. R. Mecanique 331 (2003).     

Contrôle par rotation ou par aspiration de l'écoulement autour d'un cylindre calculé par Simulation des Grandes Échelles

Control of the flow around a circular cylinder is studied using Large Eddy Simulation. The influence of control by rotation and suction on the flow characteristics is considered for several Reynolds numbers. Comparisons with experiments were conducted at $\mathit{Re}={10}^5$ for the flow with and without control. A drag reduction up to 30% is obtained for an usual suction intensity. To cite this article: G. Fournier et al., C. R. Mecanique 333 (2005).     

Bifurcations et solutions multiples en cavité 3D différentiellement chaufféeBifurcations and multiple solutions in a differentially heated cubic cavity

In this paper, a differentially heated square/cubic cavity is studied by performing three-dimensional direct numerical simulations. The first bifurcation observed at $\text{R}{}_{\mathrm{a}}\text{≈3.2×10}{}^7$ is due to the 3D vortex structures generated at the end regions of vertical boundary layers near the median plane. The main results of this Note are that the flow returns to a steady state for higher values of the Rayleigh number $\text{R}{}_{\mathrm{a}}$ (7×10⁷ and 10⁸ for example) still exhibiting these 3D vortex structures, and that multiple steady flows which differ by their symmetry properties, are obtained for $\text{R}{}_{\mathrm{a}}\text{=10}{}^8$. However, the flow reverts to unsteadiness for $\text{R}{}_{\mathrm{a}}\text{=3×10}{}^8$. In this latter case, the instability is due to the vertical boundary layers. To cite this article: G. de Gassowski et al., C. R. Mecanique 331 (2003).     

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).     

Model equations for the Eiffel Tower profile: historical perspective and new results

Model equations for the shape of the Eiffel Tower are investigated. One model purported to be based on Eiffel's writing does not give a tower with the correct curvature. A second popular model not connected with Eiffel's writings provides a fair approximation to the tower's skyline profile of 29 contiguous panels. Reported here is a third model derived from Eiffel's concern about wind loads on the tower, as documented in his communication to the French Civil Engineering Society on 30 March 1885. The result is a nonlinear, integro-differential equation which is solved to yield an exponential tower profile. It is further verified that, as Eiffel wrote, “in reality the curve exterior of the tower reproduces, at a determined scale, the same curve of the moments produced by the wind”. An analysis of the actual tower profile shows that it is composed of two piecewise continuous exponentials with different growth rates. This is explained by specific safety factors for wind loading that Eiffel & Company incorporated in the design of the free-standing tower. To cite this article: P. Weidman, I. Pinelis, C. R. Mecanique 332 (2004).     

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).