A New Type of Water Hammer in Gas-Liquid Two-Phase Fluid Lines

As far as the author is aware there has been no previous work on the problem addressed in the present paper, namely water hammer analysis in two-phase flow pipes in which a bubble-bubble interaction, deformation of the tube cross-section, shear stress, and compressibility of liquid phase play a significant role. In this paper, new mathematical model that couples the generalized inhomogeneous wave equation of Lighthill-type with the generalized Rayleigh-Plesset equation is derived to simulate unsteady, quasi-one-dimensional bubbly flows. We should stress that all of above mentioned effects have been included in the formulation deduced from proposed theory. A high effective and accurate finite difference technique for the exact solution of governing equations and new parallel program by using MPI are developed. Based on the developed algorithm and computer parallel program various numerical experiments have been carried out to investigate the major fluid dynamical features of the water hammer in horizontal pipes. It is found from these computations that the advantages of our model and numerical technique are evident especially in the area of hydraulic transients dominated by bubble dynamics. We have revealed the oscillatory water hammer with fine structure and the low-amplitude high-frequency wave called the precursor.