(155f) Modeling of Droplet Breakup in a Turbulent Flow

A model of droplet breakup in a turbulent flow is developed. The energy approach is employed: it is assumed that breakup occurs when the kinetic energy of a turbulence eddy interacting with a droplet exceeds a critical value proportional to an increase in the surface energy of newly formed droplets over the surface energy of an original droplet. The breakup event is assumed to be binary. Turbulence eddies are considered as spheres, whose velocities and concentrations are obtained based on the Kolmogoroff theory of isotropic turbulence. However, in contrast to the known models also based on the energy approach, the minimum scale of a turbulent eddy that is capable to break a droplet of a known size into fragments with a given volume ratio is not assumed but calculated. Also, a model of eddy - droplet interactions, different from that employed by majority of modelers, is developed. We suggest an approach, according to which the frequency of these interactions is calculated as a fluid fluctuation frequency, caused by eddies of different scales, in a given point of a computational domain. This approach is free of the strong conventionally used assumption, according to which a turbulent eddy at a moment preceding a collision with a droplet is considered as a sphere moving as whole with a certain velocity. Equations for both the droplet breakup rate and the daughter droplet size distribution are derived. The droplet size distribution function contains a single empirical parameter that is identified using an experimentally validated correlation for the maximum steady-state droplet size of stable non-coalescing droplet dispersion in a turbulent pipe flow. An equation for the droplet breakup rate also contains a parameter that should be identified from experimental data. A computed droplet size distribution is compared with experimental data available in literature.