Waterhammer in Flexible Pipes

Consideration is given in this paper to the numerical solution of the transient flow in highly flexible pipes such as rubber tubing and arterial system. The transient regime is provoked by the waterhammer phenomenon. A mathematical model constituted of continuity and motion equations is presented. In this model, the tube wall is assumed to be elastic and the compressibility of the liquid is neglected. To take into account the fluid-structure interaction, a nonlinear relationship between the pressure and the cross-section area of the pipe is developed. A system of two nonlinear partial differential equations of hyperbolic type is formulated. The irregular grid characteristics method is applied to solve this system. The numerical developed algorithm permits to get indications on the evolution of the pressure waves due to a valve fast closing at the downstream end of the flexible pipe. Computation results show that the pressure wave propagation is significantly influenced by the pipe wall elasticity.