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:
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.
In this article, the two-phase water hammer theoretical and numerical simulation are provided. A mathematical formulation is presented to describe the transient one-dimensional flow of bubbly gas-liquid mixtures without phase change in an horizontal pipe. The features of the two-fluid model for simulating water hammer flows are investigated. The governing equations were obtained from mass and momentum conservation laws combined with interfacial interaction correlations. The obtained system of equations for steady-state is solved through the Runge-Kutta method. On the other hand, the transient flow equation solutions are provided by the Newton-Raphson methods. A laborious calculation was carried out to determine the common pressure of the two phases. In order to improve the robustness and efficiency of the Richtmeyer-Lax-Wendroff method in solving the two-fluid model, a flux corrected transport technique was proposed. The results obtained by the proposed model are compared successfully to the corresponding homogeneous equilibrium model and the experimental ones provided by the literature.
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