L. Hadj-Ta¨eb∗ and E. Hadj-Ta¨eb∗ ı ı
Fluid–structure interaction, transient flow, vapour cavitation, elastic pipe, finite differences Notation A Pipeline area B Function c Pipe constraint factor C Pressure wave celerity D Pipeline diameter E Modulus of elasticity of pipe material F Function e Pipe wall thickness G Function H Pressure head i grid points in the x-direction k grid points in the t-direction L Pipeline length N Large enough number ∗ Unit´e de Recherche: M´ecanique des fluides appliqu´ee et mod´elisation, E
The numerical vapour cavitation model presented in a previous work is extended and applied to study fluid–structure interaction in transient flows in elastic pipes. 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 the representation of pressures’ histories in different pipe sections, as well as the evolution of the cavitation zones in term of the elastic Young modulus.
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