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

详细信息    查看全文

• 作者：Jannike Solsvik ; Hugo A. Jakobsen
• 刊名：Industrial & Engineering Chemistry Research
• 出版年：2016
• 出版时间：February 10, 2016
• 年：2016
• 卷：55
• 期：5
• 页码：1449-1460
• 全文大小：526K
• ISSN：1520-5045

文摘

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 numerically; thus, an approximate algebraic model is proposed in this work for computing the second-order longitudinal structure function to reduce the computational costs for solving the complete population balance equation. The novel modeling procedure is illustrated extending a few of the more popular drop and bubble breakage frequency and collision rate kernel (coalescence) closures to the complete range of scales in the spectrum of isotropic turbulence. The predictions of the extended closure laws are compared to those of the original model versions of the number density of vortices, breakage frequency, daughter size distribution, and collision rate which are limited to the inertial range of isotropic turbulence at infinite integral scale Reynolds numbers.