Validation of two-fluid model for water hammer in elastic pipes

In this article, the two-phase water hammer theoretical and numerical simulation are provided. A mathematical formulation is presented to describe the transient one-dimensional flow of bubbly gas-liquid mixtures without phase change in an horizontal pipe. The features of the two-fluid model for simulating water hammer flows are investigated. The governing equations were obtained from mass and momentum conservation laws combined with interfacial interaction correlations. The obtained system of equations for steady-state is solved through the Runge-Kutta method. On the other hand, the transient flow equation solutions are provided by the Newton-Raphson methods. A laborious calculation was carried out to determine the common pressure of the two phases. In order to improve the robustness and efficiency of the Richtmeyer-Lax-Wendroff method in solving the two-fluid model, a flux corrected transport technique was proposed. The results obtained by the proposed model are compared successfully to the corresponding homogeneous equilibrium model and the experimental ones provided by the literature.