The dissipation rate of turbulent kinetic energy and its relation to pumping power in inline rotor-stator mixers

The theoretical understanding of inline rotor-stator mixer (RSM) efficiency, described in terms of the dissipation rate of turbulent kinetic energy as a function of mixer design and operation, is still poor. As opposed to the correlations for shaft power draw, where a substantial amount of experimental support for the suggested correlations exists, the previously suggested correlations for the dissipation rate of turbulent kinetic energy have not been experimentally validated based on primary hydrodynamic measurements. This study uses energy conservation to reformulate the previously suggested dissipation rate correlations in terms of pumping power which allows for empirical testing. The dimensionless pumping power of three investigated geometrically dissimilar inline RSMs were found to be qualitatively similar to that of centrifugal pumps and decrease linearly with the inline RSM flow number. The previously suggested models for turbulent dissipation in inline RSMs are inconsistent with this observation. Using this reformulation approach, the previously suggested correlation for power-draw is extended to a correlation for dissipation. A new model is suggested based on conservation of energy and angular momentum, and the empiric pumping power relationship. The new model compares well to CFD simulations of total dissiaption and show reasonable agreement to emulsification drop size scaling. (C) 2017 Elsevier B.V. All rights reserved.