Calcul de l'écoulement autour d'un cylindre semi-circulaire par une méthode de collocationNumerical study of the flow over a half-circular cylinder by a diffuse approximation-based collocation method

A diffuse approximation based collocation method is used for the study of the flow over a half-circular cylinder. We give some results on the instationary wake at a Reynolds number Re=65. To cite this article: T. Sophy et al., C. R. Mecanique 330 (2002) 193–198.     

Développement en polynômes de chaos d'un modèle lagrangien d'écoulement autour d'un profilPolynomial chaos expansion of a Lagrangian model for the flow around an airfoil

A polynomial chaos (PC) expansion a the Lagrangian model for the stochastic incompressible inviscid flow around an airfoil is presented. The flow field is modeled using a distribution of lumped vortices on the airfoil surface while the wake is modeled with Lagrangian point vortices. An original technique is proposed for the computation of the PC coefficients of the velocities induced by the vortices. Two computational examples for random airfoil motions are provided to illustrate the capability of the method to deal with complex situations. To cite this article: O. Le Maître, C. R. Mecanique 334 (2006).     

A symmetry-preserving Cartesian grid method for computing a viscous flow past a circular cylinder

This article deals with a numerical method for solving the unsteady, incompressible Navier–Stokes equations in domains with arbitrarily-shaped boundaries, where the boundary is represented using the Cartesian grid approach. We introduce a novel cut-cell discretization which preserves the spectral properties of convection and diffusion. Here, convection is discretized by a skew-symmetric operator and diffusion is approximated by a symmetric, positive-definite coefficient matrix. Such a symmetry-preserving discretization conserves the kinetic energy (if the dissipation is turned off) and is stable on any grid. The method is successfully tested for an incompressible, unsteady flow around a circular cylinder at $\mathit{Re}=100$. To cite this article: R. Verstappen, M. Dröge, C. R. Mecanique 333 (2005).     

Stabilité linéaire d'écoulements symétriques presque parallèles en canalLinear stability of nearly parallel symmetric flows in a channel.

In this Note, we present a temporal linear stability analysis of symmetric developing flows slightly perturbed from Poiseuille flow. The Chebyshev spectral collocation method is used to resolve the Orr–Sommerfeld equation. For the main flow, the solution considered is analytic. The results of the stability study depend essentially on the shape and amplitude of the velocity profiles imposed at the channel entry. To cite this article: A. Hifdi et al., C. R. Mecanique 332 (2004).     

Verification of higher-order discontinuous Galerkin method for hexahedral elements

A high-order implementation of the Discontinuous Galerkin (dg) method is presented for solving the three-dimensional Linearized Euler Equations on an unstructured hexahedral grid. The method is based on a quadrature free implementation and the high-order accuracy is obtained by employing higher-degree polynomials as basis functions. The present implementation is up to fourth-order accurate in space. For the time discretization a four-stage Runge–Kutta scheme is used which is fourth-order accurate. Non-reflecting boundary conditions are implemented at the boundaries of the computational domain.The method is verified for the case of the convection of a 1D compact acoustic disturbance. The numerical results show that the rate of convergence of the method is of order $p+1$ in the mesh size, with p the order of the basis functions. This observation is in agreement with analysis presented in the literature. To cite this article: H. Özdemir et al., C. R. Mecanique 333 (2005).     

Cylindre transverse isotrope poroélastique chargé cycliquement : application à un ostéonCyclic loading of a transverse isotropic poroelastic cylinder: a model for the osteon

The poroelastic problem associated with a hollow cylinder under cyclic loading is solved. Both fluid and solid phases are supposed compressible. Solid matrix is modeled as an elastic transverse isotropic material. An explicit close-form solution for the steady state is obtained. This cylinder is considered as a model for an osteon, the basic unit of cortical bone. The fluid flow distribution as a function of poroelastic properties and cyclic loading is discussed, as this could influence bone remodeling. To cite this article: A. Rémond, S. Naili, 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).     

Propriétés élastiques non linéaires d'un milieu mésofissuréNonlinear elastic properties of a mesocracked medium

It is shown that the influence of closed frictionless cracks on overall elasticity can be evaluated by estimates based on Eshelby's theory. The idea consists in replacing the closed cracks by a ficticious material with shear modulus equal to 0 and a bulk modulus identical to that of the solid. Progressive crack closure is responsible for the nonlinearity of the overall elasticity. From this phenomenon, the distribution of crack density as a function of the initial aspect ratio can be determined. To cite this article: V. Deudé et al., C. R. Mecanique 330 (2002) 587–592.     

On perspective errors in endoscopic PIVSur les erreurs de perspective dans PIV endoscopique

Results are presented from a single and dual lens endoscopic PIV imaging system with a view to application of PIV where optical access is restricted such as internal flows. The dual lens PIV images were processed using cross-correlation, a cubic mapping function and standard stereoscopic relationships. For the single lens system, the images were processed using cross-correlation and a quadratic distortion-mapping function. Results have shown the single lens system to have in-plane errors an order of magnitude greater than the stereoscopic dual lens endoscopic PIV system. These errors are generated by perspective effects. Use of the stereo arrangement is therefore recommended wherever quantitative 3D velocimetry data is acquired using an endoscopic system. To cite this article: M. Reeves, N.J. Lawson, C. R. Mecanique 332 (2004).     

A dynamical strategy for approximation methodsUne stratégie dynamique pour les méthodes d'approximation

The numerical result provided by an approximation method is affected by a global error, which consists of both a truncation error and a round-off error. Let us consider the converging sequence generated by successively dividing by two the step size used. If computations are performed until, in the convergence zone, the difference between two successive approximations is only due to round-off errors, then the global error on the result obtained is minimal. Furthermore its significant bits which are not affected by round-off errors are in common with the exact result, up to one. To cite this article: F. Jézéquel, C. R. Mecanique 334 (2006).     

Experimental observation of the straining field responsible for vortex ring instabilityObservation expérimentale du champ responsable de l'instabilité du tourbillon torique

The aim of this work is to show experimentally the straining field responsible for the vortex ring instability. To do so, the velocity field in the neighbourhood of the core is measured with Particle Image Velocimetry. This field is compared with the one coming from theoretical work on a thin vortex ring in an ideal fluid. Theoretical and experimental data fit well. This indicates that the linear phase of the instability is weakly influenced by viscosity. To cite this article: A. Dazin et al., C. R. Mecanique 332 (2004).     

Proper Orthogonal Decomposition of the mixing layer flow into coherent structures and turbulent Gaussian fluctuations

The Proper Orthogonal Decomposition is used to decompose fluctuating turbulent flows into a coherent non-Gaussian component and background fluctuations. An application is performed from 2D experimental data of a turbulent plane mixing layer flow. The analyses of the energy spectra and the Probability Density Function of the velocity field show that POD extracts an incoherent part approaching the quasi-Gaussian distribution properties. The background fluctuations are homogeneous with small amplitude. New future applications are then conceivable like the modeling of the incoherent part for particular inflow condition generation methodology and the analysis of the cyclic velocity field variabilities in Internal Combustion engine flow. To cite this article: Ph. Druault et al., C. R. Mecanique 333 (2005).     

Cut-off analysis of coherent vortical structure identification in a three-dimensional external flow

Vortical structure identification has more recently been applied in the study of the transport of vortical structures in low Reynolds number three-dimensional complex geometry flows. An important issue in this identification procedure is to choose an appropriate cut-off value ${\lambda }_2$ which takes into consideration the finite precision vortex interfaces. This cut-off choice is studied in this Note and applied to an external flow around a curved cylinder. The vortex identification technique at different cut-off values is compared to the threshold of the vorticity field showing the efficiency of choosing the optimal tolerance gap. The computations are performed with a fully three-dimensional spectral/hp element method. To cite this article: A. Miliou et al., C. R. Mecanique 333 (2005).     

Asymptotic modelling of weakly twisted electrostatic problemsModélisation asymptotique de problèmes électrostatiques faiblement torsadés

We present an analysis of an electrostatic field within a helicoidal structure with a twist, which is small compared to the characteristic size of the cross-section. The asymptotic results are checked against exact computations thanks to helicoidal coordinates, which preserve the intrinsically two-dimensional nature of the problem. The numerical studies are performed using the finite elements. To cite this article: A. Nicolet et al., C. R. Mecanique 334 (2006).     

DNS of premixed turbulent V-flame: coupling spectral and finite difference methods

To allow for a reliable examination of the interaction between velocity fluctuations, acoustics and combustion, a novel numerical procedure is discussed in which a spectral solution of the Navier–Stokes equations is directly associated to a high-order finite difference fully compressible DNS solver (sixth order PADE). Using this combination of high-order solvers with accurate boundary conditions, simulations have been performed where a turbulent premixed V-shape flame develops in grid turbulence. In the light of the DNS results, a sub-model for premixed turbulent combustion is analyzed. To cite this article: R. Hauguel et al., C. R. Mecanique 333 (2005).     

Characterization of a class of polycrystals whose effective elastic bulk moduli can be exactly determinedCaractérisation d'une classe de polycristaux dont les modules de compression isotrope effectifs peuvent exactement être déterminés

Necessary and sufficient conditions are established for the stress response of a linearly elastic material to an isotropic stain to be hydrostatic. In the 3D case, these conditions are satisfied not only by the isotropic and cubic materials but also by all other anisotropic materials provided appropriate restrictions are imposed. In the 2D case, only the isotropic and square materials have an isotropic stress response to an isotropic strain. Using a uniform field argument, the elastic bulk modulus of a polycrystal consisting of monocrystals compatible with the established conditions is shown to equal that of any constituent monocrystal. Thus, Hill's relevant result about a polycrystal composed of cubic monocrystals is generalized. To cite this article: Q.-C. He, C. R. Mecanique 331 (2003).     

Transition vers la turbulence géostrophique pour un écoulement d'air en cavité tournante différentiellement chaufféeTransition to geostrophic turbulence in an air-filled differentially heated rotating annulus

A direct numerical simulation is carried out to determine the transition to geostrophic turbulence in an air-filled differentially heated rotating annulus. The coupled Navier–Stokes and energy equations are solved numerically with a spectral method based on collocation Chebyshev and Fourier approximations associated with a second-order time accurate scheme. For a temperature difference fixed at ΔT=5 K, when increasing the rotation rate, we have obtained the successive occurrence of the different regimes as described in the literature. The route to turbulent flow, studied with respect to two principal dimensionless parameters, the Taylor number $\text{Ta}{}^1$ and the thermal Rossby number Θ, presents steady axisymmetric solution (S), periodic flow (P₁), quasi-periodic flow (QP), periodic flow (Pn), before transition to chaotic motion (NP). To cite this article: P. Maubert, A. Randriamampianina, C. R. Mecanique 330 (2002) 365–370.     

Homogénéisation de coques minces piézoélectriques perforées

In this Note we establish the limit constitutive law of a piezoelectric material with periodically perforated microstructures and whose reference configuration is a thin shell with fixed thickness. The justification of the new associated model (we show that the limit global and local problems are more complicated than the intial one) is obtained using the periodic unfolding method introduced by Cioranescu, Damlamian and Griso. To cite this article: M. Ghergu et al., C. R. Mecanique 333 (2005).     

Présentation d'une méthode d'étude de la stabilité linéaire d'écoulements instationnairesPresentation of a method for linear stability analysis of unsteady flow

We propose a linear stability analysis of unsteady viscous flow. We apply this method to an oscillatory pipe flow with an axisymetric 2D perturbation which has received considerable attention. The numerical results are relevant. To cite this article: M. Siouffi et al., C. R. Mecanique 330 (2002) 641–645.