INTERPHASE MOMENTUM INTERACTION EFFECTS IN THE AVERAGED MULTIFIELD MODEL .2. KINEMATIC WAVES AND INTERFACIAL DRAG IN BUBBLY FLOWS

The model proposed in Part I for bubbly flows is extended to include the effect of velocity distributions around bubbles and the Riemann invariants are calculated to demonstrate that the void fraction is the conserved quantity that propagates along the faster characteristics. It is shown that kinematic wave velocities based on a constant interfacial friction coefficient propagate with velocities close to but slightly greater than that for the faster characteristic and are weakly unstable. Neutral stability of kinematic waves is found to imply a form of the interfacial friction coefficient in remarkable agreement with experiment. Wall friction has a negligible effect on these results for the usual range of parameters. Bubble interactions as described by a bubble-in-cell model do not affect the results up to a void fraction of 0. 1. Beyond these void fractions the cell model predicts significant effects but experimental data suggest that the effects may be overestimated. Turbulence is shown to provide axial dispersion of void fraction which stabilizes the system of bubbly flow equations.