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<p>Understanding the drying of droplets is of interest for processes such as spray drying, where particulate materials are produced by evaporating moisture. Even though spray-drying is a widely used method, there are still challenges, such as undesired agglomeration or controlling the morphology and size of the final dried product. This dissertation develops a physics based model that is used to examine the droplet dynamics and drying kinetics at large and small scales.  In addition, the model simulates the internal motion of insoluble particles and  is used to better understand particle formation during spray drying type processes.</p> <p><br></p> <p>The first part of this work examines the effect of droplet-droplet collisions on evaporation and the size distribution at a large scale. Droplet collision dynamics are implemented into an Eulerian-Lagrangian framework, where droplets are tracked in the Lagrangian frame, and the background gas is modeled as a continuum. The modeling framework includes fully coupled interphase heat and momentum transfer between the droplet and gas phases. Binary collision of droplets could result in coalescence, reduction in surface area, or separation of droplets, resulting in the generation of satellite droplets and an increase in total surface area. By capturing the change in size distribution due to the collision of particles, our results show a linear relationship between the Weber number and the evaporation rate at low droplet number densities. Further, it is shown that droplet number density is a critical factor influencing the evaporation rate. At high droplet number densities, the relationship between the evaporation rate and the Weber number becomes non-linear, and at extremely high droplet number densities, the evaporation rate decreases even at high Weber numbers.</p> <p><br></p> <p>In the next part of this dissertation, the drying of a single droplet containing insoluble solid particles is investigated. Using a volume-of-fluid framework coupled with the Lagrangian phase, we study the particle transport within a droplet, and how it is affected by airflow, phase properties (e.g., viscosity and density of each phase), surface tension, and evaporation. Unlike the traditional one-dimensional modeling approach, our multi-dimensional model can capture the generation of internal flow patterns due to shear flow and the accumulation of solid particles on the surface of the drying droplet. Our results show that the surface tension effect is more pronounced at larger droplet diameters and low airflow velocities. Our approach also provides a quantitative method for modeling crust growth and formation. </p> <p>Our results show that increasing solids mass fraction, and decreasing particle diameter, slow down the internal transport of solid particles, leading to a more quick accumulation near the surface of the droplet. Further, despite the droplet undergoing a constant-rate drying stage, the accumulation of solids near the surface is non-linear. In addition, the inclusion of solids within the droplet drastically reshapes the formation of internal vortices compared to the uncoupled case, which determines solids distribution.</p>

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The collisions frequency of dispersed phases (particles, droplets, bubbles) in a turbulent carrier phase is a fundamental quantity that is needed for modeling multiphase flows with applications to chemical processes, minerals flotation, food science, and many other industries. In this dissertation, numerical simulations are performed to determine collisions frequency of bi-dispersed particles (solid particles and bubbles) in homogeneous isotropic turbulence. Both direct numerical simulations (DNS) and Large Eddy simulations (LES) are conducted to determine velocity fluctuations of the carrier phase. The DNS results are used to validate existing theoretical models as well as the LES results. The dissertation also presents a CFD-based flotation model for predicting the pulp recovery rate in froth flotation machines. In the direct numerical simulations work, particles and bubbles suspended in homogeneous isotropic turbulence are tracked and their collisions frequency is determined as a function of particle Stokes number. The effects of the dispersed phases on the carrier phase are neglected. Particles and bubbles of sizes on the order of Kolmogorov length scale are treated as point masses. Equations of motion of dispersed phases are integrated simultaneously with the equations of the carrier phase using the same time stepping scheme. In addition to Stokes drag, the pressure gradient in the carrier phase and added-mass forces are also included. The collision model used here allows overlap of particles and bubbles. Collisions kernel, radial relative velocity, and radial distribution function found by DNS are compared to theoretical models over a range of particle Stokes number. In general, good agreement between DNS and recent theoretical models is obtained for radial relative velocity for both particle-particle and particle-bubble collisions. The DNS results show that around Stokes number of unity particles of the same group undergo expected preferential concentration while particles and bubbles are segregated. The segregation behavior of particles and bubbles leads to a radial distribution function that is less than one. Existing theoretical models do not account for effects of this segregation behavior of particles and bubbles on the radial distribution function. In the large-eddy simulations efforts, the dissertation addresses the importance of the subgrid fluctuations on the collisions frequency and investigates techniques for predicting those fluctuations. The cases studied are of particles-particles and particles-bubbles collisions at Reynolds number Re_λ = 96. A study is conducted first by neglecting the effects of subgrid velocity fluctuations on particles and bubbles motions. It is found that around Stokes number of unity solid particles of the same group undergo the well known preferential concentration as observed in the DNS. Effects of pressure gradient on the particles are negligible due to their small sizes. Bubbles as a low inertia particles are very sensitive to subgrid velocity and acceleration fields where the effects of pressure gradient in the carrier phase are dominant. However, particle-bubble radial distribution functions from LES are not as low as that from DNS. To account for the effects of subgrid field on the dispersion of particles and bubbles, a new multifractal methodology has been developed to construct a subgrid vorticity field from the resolved vorticity field in frame work of LES. A Poisson's solver is used to obtain the subgrid velocity field from the subgrid vorticity field. Accounting for the subgrid velocity fluctuations (but neglecting pressure gradient) produced minor changes in the radial distribution function for particle-particle and particle-bubble collisions. We conclude from this study that for accurate particle tracking in LES the subgrid velocity fluctuations must be dynamically realizable field (temporally and spatially correlated with the large scale motion). Adding random SGS velocity fluctuations is not enough to capture the correct radial distribution functions of dispersed phases especially for bubbles-particles collisions where the pressure gradient term ( or acceleration Du_f′/Dt) is responsible for particle-bubble segregation around particle Stokes number near one. A CFD-based model for minerals flotation machines has been developed in this dissertation. The objective of flotation models is to predict the recovery rate of minerals from a flotation cell. The developed model advances the state-of-the-art of pulp recovery rate prediction by incorporating validated theoretical collisions frequency models and detailed hydrodynamics from two-phase flow simulations. Spatial distributions of dissipation rate and air volume fraction are determined by the two-phase hydrodynamic simulations. Knowing these parameters throughout the machine is essential in understanding the effectiveness of different components of flotation machine (rotor, stator or disperser, jets) on the flotation efficiency. The developed model not only predicts the average pulp recovery rate but also it indicates regions of high/low recovery rates. The CFD-based flotation model presented here can be used to determine the dependence of recovery rate constant at any locality within the pulp based on particle diameter, particle specfic gravity, contact angle, and surface tension. / Ph. D.

The effects of interphase coupling in a multiphase power system become important in the presence of network imbalances and unbalanced phase loadings. In grounded-wye systems, currents that flow in the earth can have significant effects on the system's behavior. Both these effects must be considered in an accurate multiphase power system model. A new treatment of multiphase power system modeling is presented. The treatment relies upon linear graph theory and produces a system multiport model. Mutual coupling effects, the effects of neutral and static conductors, the finite conductivity of earth, and various component models are considered. A reduction in the order of the multiport model also is presented. Multiphase load flow analysis is introduced. Special considerations that arise in multiphase analyses are discussed. Example solutions are presented. A convenient method of representing multiple slack ports is described which results from an application of the principle of superposition. Circulating power flow in multiphase loops is discussed. A procedure is proposed for conveniently representing common shunt and series faults that occur in power systems. The procedure is constructed for efficient computer modeling of multiple cases of various fault combinations in a particular system. / Doctor of Philosophy

Fluidized beds have widespread industrial applications ranging from chemical industries to power plants. The flow inside a fluidized bed system consists of two main phases, a particle phase and the fluid phase. The two phases are strongly coupled to each other through various forces like drag and pressure. Capturing this multiphase phenomenon requires modeling strategies that possess good fidelity over a range of scales. Discrete Element Modeling (DEM) coupled with Computational Fluid Dynamics (CFD) provides a good platform to analyze the complex coupled multiphase hydrodynamics inside fluidized bed systems. Conventional DEM-CFD framework suffers from contradictory spatial resolution requirements for the particle and fluid phases, respectively. This prevents the conventional DEM-CFD method to be applied to geometries that have features comparable to the particle diameter of the solid phase. The novelty of this work lies in the development and validation of a two-grid formulation that removes the resolution restrictions of the conventional DEM-CFD framework. The results obtained from this new framework agree reasonably well with the experiments showing the capability of the new scheme to simulate conditions not possible with conventional DEM-CFD framework. In addition, this research also focuses on performing both 2D and 3D jetting fluidized bed simulations having millions of particles; validate/compare results with experiments and to perform heat transfer studies in a jetting fluidized bed system. The results suggest convective and diffusive mixing for a single jet at higher superficial velocity to be better than the mixing obtained in a multiple jet framework. The comparison with experimental results obtained in a multiple jetting setup shows that a 2D simulation captures the essential jet characteristics near the distributor plate reasonably well while a 3D simulation is needed to capture proper bubble dynamics near the freeboard of the bed. These results give insight into the detailed dynamics of fluidized bed systems and provide a foundation for a better design of these systems. / Ph. D.

Jet engines often operate under dirty conditions where large amounts of particulate matter can be ingested, especially, sand, ash and dirt. Particulate matter in different engine components can lead to degradation in performance. The objective of this dissertation is to investigate sand transport and deposition in the internal cooling passages of turbine blades. A simplified rectangular geometry is simulated to mimic the flow field, heat transfer and particle transport in a two pass internal cooling geometry. Two major challenges are identified while trying to simulate particle deposition. First, no reliable particle-wall collision model is available to calculate energy losses during a particle wall interaction. Second, available deposition models for particle deposition do not take into consideration all the impact parameters like impact velocity, impact angle, and particle temperature. These challenges led to the development of particle wall collision and deposition models in the current study. First a preliminary simulation is carried out to investigate sand transport and impingement patterns in the two pass geometry by using an idealized elastic collision model with the walls of the duct without any deposition. Wall Modeled Large Eddy Simulations (WMLES) are carried to calculate the flow field and a Lagrangian approach is used for particle transport. The outcome of these simulations was to get a qualitative comparison with experimental visualizations of the impingement patterns in the two pass geometry. The results showed good agreement with experimental distributions and identified surfaces most prone to deposition in the two pass geometry. The initial study is followed by the development of a particle-wall collision model based on elastic-plastic deformation and adhesion forces by building on available theories of deformation and adhesion for a spherical contact with a flat surface. The model calculates deformation losses and adhesion losses from particle-wall material properties and impact parameters and is broadly applicable to spherical particles undergoing oblique impact with a rigid wall. The model is shown to successfully predict the general trends observed in experiments. To address the issue of predicting deposition, an improved physical model based on the critical viscosity approach and energy losses during particle-wall collisions is developed to predict the sand deposition at high temperatures in gas turbine components. The model calculates a sticking or deposition probability based on the energy lost during particle collision and the proximity of the particle temperature to the softening temperature. For validation purposes, the deposition of sand particles is computed for particle laden jet impingement on a coupon and compared with experiments conducted at Virginia Tech. Large Eddy Simulations are used to calculate the flow field and heat transfer and particle dynamics is modeled using a Lagrangian approach. The results showed good agreement with the experiments for the range of jet temperatures investigated. Finally the two pass geometry is revisited with the developed particle-wall collision and deposition model. Sand transport and deposition is investigated in a two pass internal cooling geometry at realistic engine conditions. LES calculations are carried out for bulk Reynolds number of 25,000 to calculate flow and temperature field. Three different wall temperature boundary conditions of 950 oC, 1000 oC and 1050 oC are considered. Particle sizes in the range 5-25 microns are considered, with a mean particle diameter of 6 microns. Calculated impingement and deposition patterns are discussed for different exposed surfaces in the two pass geometry. It is evident from this study that at high temperatures, heavy deposition occurs in the bend region and in the region immediately downstream of the bend. The models and tools developed in this study have a wide range of applicability in assessing erosion and deposition in gas turbine components. / Ph. D.

A finite element model is developed for multiphase flow through soil involving three immiscible fluids: namely air, water, and an organic fluid. A variational method is employed for the finite element formulation corresponding to the coupled differential equations governing the flow of the three fluid phase porous medium system with constant air phase pressure. Constitutive relationships for fluid conductivities and saturations as functions of fluid pressures which may be calibrated from two-phase laboratory measurements, are employed in the finite element program. The solution procedure uses iteration by a modified Picard method to handle the nonlinear properties and the backward method for a stable time integration. Laboratory experiments involving soil columns initially saturated with water and displaced by p-cymene (benzene-derivative hydrocarbon) under constant pressure were simulated by the finite element model to validate the numerical model and formulation for constitutive properties. Transient water outflow predicted using independently measured capillary head-saturation data agreed well with observed outflow data. Two-dimensional simulations are presented for eleven hypothetical field cases involving introduction of an organic fluid near the soil surface due to leakage from an underground storage tank. The subsequent transport of the organic fluid in the variably saturated vadose and ground water zones is analysed. / Ph. D.

Published Article / The paper reports on a Learn 2.0 technology that was used to support the continuing professional development of mathematics teachers at a secondary school. Design Based Research methods were used within a Multiphase Mixed Methods research framework to create professional development opportunities that were subsequently monitored by Social Network Analysis techniques. We demonstrate that Learn 2.0 technologies can indeed support the continuing professional development of teachers and improve their performance, and also that Social Network Analysis is an effective method to describe, comprehend, clarify and transparently monitor teacher engagement during online professional development activities. We identify 'participation' as a key pre-determinant to success.