Influence du comportement élastique non-linéaire des conduites dans les écoulements transitoires avec cavitation de vapeur

A numerical model is presented to study the influence of the non-linear elastic behaviour of the pipe wall in transient flows with vapour cavitation. The application of mass and momentum conservation laws yields to a system of two hyperbolic partial differential equations. The obtained system is resolved by a two-step finite differences numerical scheme. By analogy with the gas release phenomenon, when the liquid pressure in the pipe drops below the vapour pressure, vapour will be released from the liquid according to Henry's law. To put in evidence the fluid-structure interaction, a relationship between pressure and pipe section has been introduced. Computation results permit to study the influence of the pipe wall deformation on the evolution of water hammer and vapour cavitation phenomena. The presented mathematical formulation is validated while comparing these results to those experimental obtained from relevant literature.