Modeling of droplet dispersion in a turbulent Taylor-Couette flow

- A model of droplet dispersion in a turbulent Taylor-Couette flow was developed.
- Both droplet breakup and coalescence were taken into account.
- Modeling results were compared with experimental data.
- Performance of the dispersion model was illustrated by numerical examples.

A process of dispersion of droplets in a developed turbulent Taylor-Couette flow is modeled. An apparatus, where the inner cylinder rotates whereas outer one is immobile, is considered. To exclude the effect of Taylor vorticities on a turbulent flow pattern, only flow regimes characterized by relatively high Reynolds numbers (>13,000) are investigated. Relatively dilute dispersions are modeled: the maximum droplet volume fraction does not exceed 10%. The time-dependent droplet size distribution in a Taylor-Couette device is described by an advection-diffusion equation containing a population balance term. Both breakup and coalescence of droplets are taken into account. An experimentally verified engineering model of a turbulent Taylor-Couette flow, based on the Prandtl mixing length theory, is used for calculating velocity, eddy diffusivity and turbulence energy dissipation rate distributions across a Taylor-Couette device gap. The known breakup and coalescence models of Coulaloglou and Tavlarides are employed for population balance modeling. However, the breakup model has been modified to account more accurately for turbulence - droplet interactions.The governing model equations are solved numerically. The computed droplet size distributions are compared with those obtained in the laboratory Taylor-Couette device in the presence of emulsion stabilizing surfactants for different rotation speeds and stirring durations. The dispersion process in a Taylor-Couette flow in both the presence and absence of surfactants is illustrated by numerical examples. The results of simulations and experiments are critically analyzed.