A droplet transport model for channel and pipe flow based on particle kinetic theory and a stress–ω turbulence model
A model for droplet transport in turbulent gas–liquid flow in horizontal channels or pipes is developed. We invoke the kinetic theory of Reeks and co-workers for inertial particles, and the Reynolds stress– ω model of Wilcox for the gas turbulence. We introduce a suitable turbulence boundary condition at the gas–liquid interface. The full kinetic model is compared to experimental data using high density SF 6 gas and Exxsol oil, and the model gives a good prediction of the droplet distribution. A simplified “first order model” that adopts a diameter-averaged eddy diffusivity from the full turbulence model, and that ignores the variation of the turbulence over the cross section, gives reasonable order of magnitude estimates of the droplet concentration profiles. There is, however, a clear tendency to overestimate the droplet concentration near the interface (and hence the axial droplet transport rate). Furthermore, the classical single phase pipe flow diffusivity (0.075 Ru * ) underestimates the averaged eddy diffusivity by a factor of about two (giving too small concentration and transport rate). The strength of the full kinetic model is that it correctly predicts a droplet diffusivity that accounts for the droplet inertia. This is important for the larger droplets close to the interface which contribute the most to the axial droplet transport rate. Hence, a simple eddy diffusivity will not correctly predict the droplet transport rate, since the droplet inertia is then ignored. The droplet concentration in the upper half of the flow volume is dominated by the smaller droplets, and these are in contrast subject to the scalar eddy diffusivity. An elevated concentration close to the upper wall may be accounted for by a double-vortex secondary flow perpendicular to the axial mean flow.