A mathematical model for 1D, bubbly flow

In this work a mathematical model for mono dimensional, two-phase, bubbly flow, is presented. The mathematical model consists of the motion equations (i.e. mass, momentum and energy balance equation) for each phase, obtained applying a suitable phase-average procedure. Such motion equations determine the evolution of the homogenized hydrodynamic variables and contain both the inter phase interaction terms and the dispersive terms too. The latter terms are usually calculated by means of closure relations or even neglected. In this work, introducing a suitable description for the local perturbation induced by the bubbles on the liquid phase motion, the inter phase momentum exchange terms are analytically calculated. Numerical simulations are performed in order to simulate an experimental case of water hammer. The agreement is good, although further work is needed on both dissipative and mass exchange terms.