Hydraulic transients in two phase bubbly flows

We extend our mathematical model and develop a new solution method for two-phase bubbly flows in water hammer. The model involves the generalized inhomogeneous wave equation of Lighthill-type for host liquid phase, completed by the generalized Rayleigh-Lamb-Plesset equation for the gas phase, which takes into account multibubble interaction effects. In this paper, we propose a fourth order compact finite difference scheme, that is, it retains tridiagonal form of matrix that can be easily solved. The space differencing combined with implicit central second order time differencing. Accurate modeling is vital especially in the area of hydraulic transients dominated by bubble dynamics. Based on the developed algorithm and computer parallel program numerical experiments have been carried out to study water hammer events in pipes. The bubble pulsations crucial influence the development of the basic motion. We revealed three hydraulic transient evolution scenarios. Fundamentally new kinds of flow patterns are discovered. It is also shown that the frequency of interacting bubbles is shifted towards lower frequencies than expected from single-bubble dynamic considerations.