Development of Fluid Particle Breakup and Coalescence Closure Models for the Complete Energy Spectrum of Isotropic Turbulence

Abstract

The constitutive equations proposed in the literature for describing the fluid particle (i.e., bubble and drop) breakage and coalescence phenomena created by turbulence mechanisms are generally limited to the inertial range of scales and infinite Reynolds numbers. A consistent approach for extending these breakage and coalescence kernels to the complete energy spectrum of isotropic turbulence (i.e., the energy-containing, inertial, and dissipation subranges) and for a larger range of integral scale Reynolds numbers is proposed in this study. The model energy spectrum for the complete range of scales of isotropic turbulence proposed by Pope (Turbulent Flows; Cambridge University Press: Cambridge, 2000) is employed in this work. A corresponding integral relation for the second-order longitudinal structure function model can be deduced from the model energy spectrum through the use of a Fourier transform pair via the scalar velocity correlation function. However, this integral relation is cumbersome to solve...