Effect of turbulent kinetic energy dissipation rate on the prediction of droplet size distribution in stirred tanks

In this work the capabilities of Two Fluid Model simulations coupled with a Population Balance Model solved with the Quadrature Method of Moments in predicting the turbulent kinetic energy dissipation rate and the droplet size distribution in a dilute liquid-liquid stirred tank are investigated. For a strict evaluation of the numerical and modelling approximations, original two-phase flow fields and droplet size distributions are collected by Particle Image Velocimetry and a laser diffraction technique, respectively. The spatial discretization requirements for achieving grid independent and reliable predictions of the turbulent variables already observed in RANS-based simulations of single-phase stirred tanks are confirmed also for the investigated dilute two-phase system, for which the effect of the dispersed phase on the continuous liquid is negligible. Besides, better prediction of the droplet size distribution is apparently obtained with poorly predicted turbulent kinetic energy dissipation rate, showing that the usually adopted parameters of the breakup kernel have been tuned for coarse grids. A way to derive grid independent breakup kernel parameters and a correction based on the spatial distribution of turbulent dissipation rate are proposed to account for the underestimation of the turbulent variables in the RANS simulation of industrial scale equipment.