A mathematical model for a diluted two-phase flow

The aim of this work is to model the forces exchanged by the liquid and aeriform phase in a two-phase flow. Assuming that the aeriform is constituted by spherical bubbles, far enough each other in order to exclude reciprocal interactions, introducing a suitable phase average operation and describing the motion of the bubbles, relative to the liquid phase, the forces exchanged by the two phases can be finalyy expressed as functions depending on the macroscopic parameters of the motion. Accounting for such forces in motion equations, a partial differential system describing the evolution of the two-phase flow is obtained. The mathematical model is then applied in order to simulate water hammer experimental results. The comparison between numerical and experimental results is good, indicating that the modeling of the inter phase momentum exchange term has been correctly performed.