L. Hadj-Ta¨eb∗ and E. Hadj-Ta¨eb∗ ı ı
Transient flow, vapour cavitation, viscoelastic pipe, finite differences, fluid-structure interaction Notation C Pressure wave celerity c Pipe constraint factor D Pipeline diameter E Modulus of elasticity of pipe material e Pipe wall thickness F Function G Function g Gravity acceleration i Grid points in the x-direction J Creep function j Kelvin-Voigt element number K Bulk modulus ∗ Unit´e de Recherche: M´ecanique des Fluides Appliqu´ee et Mod´elisation Enis, B.P. 1173 3038 Sfax, Tun
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 liquid– vapour 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.
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