Numerical simulation of transient flows in viscoelastic pipes with vapour cavitation

A mathematical model has been developed to calculate transient flows in viscoelastic pipes with vapour cavitation. This model takes into account both the viscoelastic behaviour of the pipe wall and the vapour cavitation phenomenon. When the liquid pressure falls below the vapour pressure, a bubbly cavitating flow of homogeneous liquidvapour mixture occurs in some parts of the pipeline. The mixture density is expressed by means of a non-linear expression of the liquid volume fraction. The pipe wall behaviour is simulated based on the mechanical principle, by introducing additional viscoelastic term into the mass balance fluid equation. The application of mass and momentum conservation laws yields to a system of hyperbolic partial differential equations. The later is resolved by a second order finite differences scheme. The proposed model is tested for transient flows with and without vapour cavitation. The obtained numerical results are discussed and compared with experimental data.