In coalescence and break-up modeling, vortex number density and size distributions of turbulent vortices are required to calculate the rate of interaction between continuous and dispersed phases. Existing number density models are only valid for the inertial subrange of the energy spectrum and no model of the vortex number density, valid for the entire energy spectrum, is available. The number density of the turbulent vortices were studied and modeled for the entire energy spectrum including the dissipative, inertial, and energy containing subranges. It was observed that the new number density model depends on vortex size, local turbulent kinetic energy, and dissipation rate. Moreover, the new number density model was validated by the number density distributions quantified in a turbulent pipe flow. The turbulent vortices of the pipe were identified and labeled using a vortex-tracking algorithm that was developed recently by the authors.
Many phenomena in chemical processes for example fast mixing, coalescence and break-up of bubbles and drops are not correctly described using average turbulence properties as the outcome is governed by the interaction with individual vortices. In this study, an efficient vortex-tracking algorithm has been developed to identify thousands of vortices and quantify properties of the individual vortices. The traditional algorithms identifying vortex-cores only capture a fraction of the total turbulent kinetic energy, which is often not sufficient for modeling of coalescence and break-up phenomena. In the present algorithm, turbulent vortex-cores are identified using normalized Q-criterion, and allowed to grow using morphological methods. The growth is constrained by estimating the influence from all neighboring vortices using the Biot-Sawart law. This new algorithm allows 82% of the total turbulent kinetic to be captured, at the same time the individual vortices can be tracked in time.
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