Mécanique des fluides numérique Coup de bélier Fluides-structures Méthodes des caractéristiques Éléments finisWe present a numerical code for fluid-structure interactions to solve the problem of waterhammer in pipes with thin walls. The pipe is modeled by planar beams theory of Bernoulli-Euler in longitudinal and transverse vibrations. This code is the coupling of the finite element method combined with the Newmark algorithm for movement of the pipe wall, and, for the fluid, the method of characteristics. Unlike the classical theory, this code illustrates the side effects of fluid-structure interaction affecting parameters of waterhammer in elastic and viscoelastic pipe.

Les équations de base sont les relations classiques de conservation associées aux lois de comportement du fluide et de la paroi. Toutefois, afin de simplifier le problème tout en tenant compte, pour l'essentiel, du caractère bidimensionnel de l'écoulement, les hypothèses suivantes ont été faites: -fluide newtonien barotrope avec une compressibilité suffisamment faible pour être négligeable au niveau des termes de viscosité, -écoulement axisymétrique à trajectoires des particules fluides sensiblement rectilignes avec une vitesse du fluide très faible par rapport à celle de propagation des perturbations, -dans l'expression des contraintes visqueuses, les gradients longitudinaux de vitesses sont négligeables par rapport aux gradients transversaux, -conduite cylindrique circulaire ancrée à l'origine et dont le matériau constitutif a un comportement élastique linéaire.Avec ces hypothèses on a, sous forme adimensionnelle, comme équations concernant le fluide, un système linéaire tel que:

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We present a numerical code for calculating transient flow in plastic pipes, especially in the polyethylene pipe, to analysis water hammer phenomena. The set partial differential equations to be solved is obtained using conservation laws and behavior for the fluid and the pipe wall, associated with constitutive equations of the two media, and relationships compatibility of interfaces on velocities and stresses. Coupling due to Poisson's ratio is also incorporated in this model. A global digital processing is achieved using the method of characteristics. The results obtained are in good agreement with those found in the literature. a E m m = ( ) / / 0 1 2 ρ : Celerity of sound in the pipe wall

We present a numerical code for calculating transient flow in plastic pipes, especially in the polyethylene pipe, to analysis transient flow in a viscoelastic pipe such as polyethylene. The set partial differential equations to be solved is obtained using conservation laws and behavior for the fluid and the pipe wall, associated with constitutive equations of the two media. A global digital processing is achieved using the method of characteristics. The results obtained are in good agreement with those found in the literature.

This study is devoted to a numerical modeling of a transient pseudo plastic fluid flow in an elastic pipe. The set partial equations for both the fluid are derived from the law conservations of mass, momentum and energy for the fluid and Hooke’s law for the wall pipe. The system governing this problem is presented and then solved numerically. The non-Newtonian character behavior of the fluid s modeled by the power law. The coupled method of characteristics, finite differences and Runge Kutta are used for spatial and temporal discretization respec-tively. Some results obtained are in good agreement with those found in the literature.