A theoretical study on drop breakup modeling in turbulent flows: The inertial subrange versus the entire spectrum of isotropic turbulence

Abstract

The traditional model framework for drop breakup in turbulent flows is based on the inertial subrange of turbulence. That is, Kolmogorov's formulas for the energy spectrum and second-order longitudinal structure function are used. In recent literature the model framework has been extended to consider the wide energy spectrum (i.e. including the dissipation, inertial and energy-containing subranges of turbulence). In particular, two different formulas have recently been proposed for the second-order longitudinal structure function based on the wide energy spectrum. The comparison between these two formulas reveals significantly different predictions of the breakup phenomenon for particular conditions.It is important to use the Pope model energy spectrum (valid for the wide spectrum of turbulence) consistently (Pope, S.B., 2000. Turbulent Flows. Cambridge University Press, Cambridge). That is, parameter fitting must be performed on the parameters of the energy spectrum function when the physical conditions of the system is changed. Although the parameter values given in the original literature by Pope are valid only at sufficiently high Reynolds number, these parameter values have been employed at low Reynolds numbers by some researchers. With decreasing Reynolds numbers the difference between employing the original suggested values and re-fitted parameter values in models for breakage is increasingly significant.In the development of new models for the daughter size distribution function, the number and volume conservation properties should always be analyzed. Care should be taken when a change in the model parameter is performed, for example, the Jacobian relation in an integral is required for consistency. Precise notation regarding the function definitions is required in order to avoid model misinterpretations.