published_or_final_version / abstract / Mechanical Engineering / Master / Master of Philosophy

The principal objectives of the work described in this thesis were: 1. To develop an improved multiphase CFD model for classifying cyclones and further improve understanding of the separation mechanism based on fluid flow and turbulence inside the cyclone. 2. To develop an improved Empirical model of classifying cyclones, covering a wide range of design and operating conditions. The multi-phase CFD model developed in this work is based on the approach reported by Brennan et al (2002) and Brennan (2003) using Fluent, and involves individual models for the air-core, turbulence, and particle classification. Two-phase VOF and mixture models for an air/water system were used to predict the air-core and the pressure and flow fields on 3D fitted fine grids. The turbulence was resolved using both DRSM (QPS) and LES turbulence models. The predicted mean and turbulent flow field from the LES and DRSM turbulence models were compared with the LDA measurements of Hsieh (1988). The LES model predicts the experimental data more accurately than the DRSM model. The standard mixture model (Manninnen et al, 1996) and the modified mixture model for a water/air/solids system were used to predict cyclone performance. The standard mixture model was able to predict classification efficiency reasonably at low solids concentrations, but under-predicts the recovery of coarse size fractions to underflow. To improve the predictions at moderate to high feed solids, the author modified the slip velocity with additional Bagnold dispersive forces, Saffman lift forces, and a hindered settling correction for particle drag in the mixture model superimposed on an LES turbulence model. Several cyclone geometries were used for validating the multiphase CFD model. The modified mixture model improves prediction of the separation of coarse size particles, and the predicted closely matches the experimental in various cyclones. The particle classification mechanism has been further elucidated using the simulated particle concentration distributions. At high solids concentrations, the modified CFD model predicts the efficiency curve reasonably well, especially the cut-size of the cyclone, but prediction of fine particle recovery to overflow is poor compared to the experimental data. It appears that the fines are significantly affected by turbulent dispersion and the flow resistance due to the high viscosity of the slurry at the apex is not sufficiently accounted for in the modified Mixture model. The improved multi-phase CFD model was validated against two sets of experimental data available in the literature: particle concentrations measured by gamma ray tomography data in a dense medium cyclone (Subramanian, 2002), and particle size distribution inside a hydrocyclone (Renner, 1976). Large eddy simulation (LES) with the modified Mixture model, including medium with a feed size distribution appears to be promising in predicting medium segregation inside a dense medium cyclone. The CFD predicted sample size distributions at different positions are reasonably comparable with Renner’s (1976) experimental data near the wall and in the bottom cone, but differ considerably near the forced vortex region, and also near the tip of the vortex finder wall. The CFD model shows no air-core formation at the low operating pressure used by Renner, which suggests his experiments involved an unusual/unstable forced vortex based cyclone separation. The effect of turbulence on fluid and solid particle motion was also studied in this thesis. The resolved turbulent fluctuations from LES of the hydrocyclone at steady flow were analysed using ensemble averaging. The ratio of the effective turbulent acceleration of each particle size to the centrifugal acceleration was calculated for various cyclones, which showed that turbulent mixing becomes less important with larger particles. The trends in this ratio correlate with the equilibrium positions of the particles from the multiphase LES. The analysis indicates that the short-circuiting might be aggravated by turbulent mixing across the locus of zero vertical velocity (LZVV) against the classification force, and along the vortex finder wall into the inner upflow region of the cyclone. An experimental study of the “fish-hook” effect was pursued in various industrial scale cyclones to evaluate the effect of various cyclone parameters. The observed diameter at which fine particle recovery starts to increase is mainly affected by feed solids content and spigot diameter, but less influenced by feed pressure. The observed particle recovery to the underflow at the fishhook dip size, the bypass, is always higher than the underflow water split. Any cyclone variable that affects the underflow water split, will also affect the bypass value. CFD studies showing high particle Reynolds numbers for coarse particles were used to provide a qualitative mechanism for fines reporting to the underflow in the wakes behind the larger particles (Tang et all. 1992). The Frachon and Cilliers (1999) model was used to fit and evaluate the fishhook parameters. The variations of these fishhook parameters were quantified for changes in cyclone design and operating conditions. The development of an improved empirical hydrocyclone model was attempted by collecting extensive historical data covering a wide range of cyclones. Additional experiments on 10 and 20 inch Krebs cyclones were performed to fill the gaps in the database, especially at low to moderate feed solids concentration and with different cone sections. Tangential velocity, turbulent diffusion, slurry viscosity and particle hindered settling correlations were identified from CFD as the key inputs to the particle classification mechanism for the empirical model. A new cyclone model structure based on a dimensionless approach has been developed. The model for , , Q gives a very good fit to the data, while the model for separation sharpness gave reasonable correlations with the cyclone design and operating conditions. 208 additional data sets were used to validate the new hydrocyclone model.

We study systems of n dimensional diffusions whose drift and dispersion coefficients depend only on the relative ranking of the processes. We consider the question of how long it takes for a particle to go from one rank to another. It is argued that as n gets large, the distribution of particles satisfies a Porous Medium Equation. Using this, we derive a deterministic limit for the system of particles. This limit allows for direct calculation of the properties of the rank traversal time. The results are extended to the case of asymmetrically colliding particles. These models are of interest in the study of financial markets and economic inequality. In particular, we derive limits for the performance of some Functionally Generated Portfolios originating from Stochastic Portfolio Theory.

Accurate modeling and simulation of wave propagation in dispersive dielectrics such as water, human tissue and sand, among others, has a variety of applications. For example in medical imaging, electromagnetic waves are used to interrogate human tissue in a non-invasive manner to detect anomalies that could be cancerous. In non-destructive evaluation of materials, such interrogation is used to detect defects in these materials. In this thesis we present the construction and analysis of two novel operator splitting methods for Maxwell's equations in dispersive media of Debye type which are used to model wave propagation in polar materials like water and human tissue. We construct a sequential and a symmetrized operator splitting scheme which are first order, and second order, respectively, accurate in time. Both schemes are second order accurate in space. The operator splitting methods are shown to be unconditionally stable via energy techniques. Their accuracy and stability properties are compared to established schemes like the Yee or FDTD scheme and the Crank-Nicolson scheme. Finally, results of numerical simulations are presented that confirm the theoretical analysis. / Graduation date: 2012 / Access restricted to the OSU Community at author's request from June 20, 2012 - Dec. 20, 2012

University of Macau / Faculty of Science and Technology / Department of Electromechanical Engineering