Number density of turbulent vortices in the entire energy spectrum

Abstract

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. © 2014 The Authors AIChE Journal published by Wiley Periodicals, Inc. on behalf of American Institute of Chemical Engineers AIChE J, 60: 3989–3995, 2014