Theoretical derivation of the interaction effects with an eccentric cell model and void fraction propagation in two-phase flow

This paper was concerned with the dilute dispersion of gas bubbles in a continuous liquid phase. The starting point in the present study was the three-dimensional, transient averaged transport equations for inviscid incompressible and isothermal two-phase ¯ow. For the eva- luation of the averaged description, potential ¯ow around bubbles was considered in order to get closure relationships, using an eccentric cell model approach. The resulting averaged equations are novel in the literature on two-phase ¯ow. The closure averaged model was used to describe the features of the propagation of void fraction waves, and to investigate the linear stability of bubble ¯ow regime. The hyperbolicity of the averaged wave equation was exam- ined and demonstrated that the model is stable when the void fraction is smaller or equal to 2/ 7.