An Analysis of the Turbulent Dispersion of Concentrations of Non-Stokesian Particles (Transport, Low Reynolds Number, Uniform Distributions)
Hardy, Bruce John
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https://hdl.handle.net/2142/70904
Description
Title
An Analysis of the Turbulent Dispersion of Concentrations of Non-Stokesian Particles (Transport, Low Reynolds Number, Uniform Distributions)
Author(s)
Hardy, Bruce John
Issue Date
1985
Department of Study
Nuclear Engineering
Discipline
Nuclear Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Engineering, Nuclear
Abstract
A theoretical model for the turbulent dispersion of a concentration of non-Stokesian particles has been developed. The basic assumptions for the fluid are that the turbulence is Gaussian, homogeneous, and ergodic. The assumptions for the particle suspension are that the spatial distribution of particles is uniform, the particle Reynolds number is sufficiently large that the asymptotic matching technique used in the theory is valid, the particle diameters are small relative to the macroscale of the turbulence, and the volumetric concentration of particles, (phi), and the particle Reynolds number, Re(,pf), are such that E (DBLTURN) 9.25(phi)/Re(,pf)('3/5) is small.
The theory in the current work is based on the modeling of terms in Tchen's (1947) equation for the unsteady motion of a single Stokesian particle. The current modifications extend Tchen's equation to apply to a concentration of particles and model the drag force on the particle as a non-Stokesian drag. Further, the added mass acceleration of a particle is modeled so that it applies to the particle pair configuration, observed by Gronager (1978), in the range of particle volumetric concentrations 0 0.01.
The current theoretical model includes the particle free fall velocity in the equation of motion for the particle. Therefore, the effect of a constant drift imposed on a heavy particle by the gravitational force is taken into account.
In order to apply the theory developed in this work one needs to know the particle radius, the volumetric concentration of particles, the free fall velocity of the particles, the particle density and the fluid density. Further, one needs to know the Lagrangian energy density spectrum of the fluid. The particle concentrations addressed in this study are assumed to be sufficiently low that the Lagrangian energy density spectrum of the fluid containing the particle suspension is approximated by that for the fluid in the absence of the particles.
The predictions made by the current theory are in good agreement with the experimental data of Souza (1981). An examination of the predicted energy density spectrum of the particle reveals a shift towards lower frequencies as the particle density increases. This shift may be attributed to both inertial and crossing trajectories effects since the particle free fall velocity is included in the equation of motion. (Abstract shortened with permission of author.)
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