Modeling water hammer in viscoelastic pipes using the wave characteristic method

Abstract

For the first time, the wave characteristic method (WCM) is used to simulate transient flow in viscoelastic pipes. The WCM is based on Newton's second law equating the change in momentum and net pressure forces applied on the liquid, which leads to the Joukowsky equation. The friction head loss within a pipe segment is replaced by an imaginary friction orifice with the same head loss. Here the Joukowsky equation is rederived for elastic pipes on the basis of the conservation of energy principle. Then the same method is used to derive a quadratic equation for the conservation of energy in viscoelastic pipes. Under a relaxation assumption, the square root of the energy equation yields a linear equation that is applicable with the superposition principle. The method developed is studied numerically and verified with experimental data from the literature. The water hammer in a simple pipe system consisting of a reservoir, a pipe, and a valve is demonstrated. Parameters calibrated with the method of characteristics are taken from the literature and used as essential input data for the proposed WCM. A constant friction coefficient of the pipe is considered. Even if a small number of friction orifices are selected, good agreement is found between the experimental data and the simulation results especially for the first pressure head cycles. Finally, the numerical results obtained with both the WCM and the method of characteristics are compared to investigate the effectiveness of the WCM. The WCM shows superior computational efficiency in determining the maximum pressure.