In dispersed two-phase flows, the particle size is probably the most important parameter in determining the particle dynamics. Interphase forces, heat and mass transfers are all functions of the particle diameter. Diameters of the particles are unlikely to be uniform and for droplets and bubbles they can change continuously due to breakup and coalescence. Methods of moments have been used very successfully in modeling particle size distributions in dispersed two-phase flows. The model described in this paper is based on the method of moment. It contains models for droplet breakup and coalescence. γS
For breakup, the model considers the balance between disruptive forces (due to shear and turbulence) and restoring forces (due to surface tension) on the droplet. In laminar flows the viscous effects dominate hence we named this regime “viscous breakup”. In turbulence flows the interactions with turbulence eddies dominate and we named this regime “inertia breakup”. For coalescence, the model considers the probability of collisions of the droplets, the contact time of two colliding drops and the drainage time of the liquid film between the drops. Similar to the breakup model, we have the “viscous collision” regime in laminar flows and the “inertia collision” regime in turbulent flows. The drainage time is a function of the state of the droplet surface, whether it is fully or partially mobile or totally immobile. The model therefore considers the breakup and coalescence processes in great details.
The model was implemented in the Eulerian multiphase flow model in the commercial CFD software, STAR-CD. The model was applied to analyse the oil-water pipeline experiment of Simmons and Azzopardi (2001). It was found that droplet breakup was strongest near the pipe walls since turbulence and velocity gradient were strongest there. Since horizontal pipe flow was considered, some settling of the water droplets (the heavier phase) was observed as in the experiments. The predicted droplet size distribution was found to be relatively insensitive to the initial droplet diameter specified at the pipe inlet. The computed and the measured droplet size distributions at the pipe exit were presented and compared in form of cumulative frequency curves. Reasonable agreements between the two sets of curves were obtained.