Modelling of steady-state two-phase bubbly flow through a sudden enlargement

A global formulation of the conservation laws (mass, momentum and energy) is applied to a two-phase, two-component flow through a sudden enlargement. The assumption of thermal equilibrium of the phases is acceptable. However, due to the difference in the mechanical inertia of the phases, the kinematic non-equilibrium effect has to be taken into account. In order to determine the role of mechanical non-equilibrium, two assumptions are made, which can be considered as two limited cases. Firstly, an infinite momentum transfer coefficient (mechanical equilibrium model) is assumed: an analytical solution can be obtained when the gas is ideal. Secondly, no momentum transfer can occur between phases (mechanical frozen model): an approximate analytical solution is obtained in this case. The comparison in terms of singular pressure variations between the results of these two models and the experimental data of other authors for air-water mixtures shows clearly that both models indeed simulate two extreme conditions. New experimental data were obtained for two-phase air-water bubbly flow through an axisymmetric and horizontal sudden enlargement. A new physical model approximately taking into account the effects of the interfacial drag of the bubbles is developed, and compared favourably with the data in the literature and the new data. This model shows a rather limited dependence with respect to the reduced bubble diameter.