When a water soluble granular fertilizer, such as potash, is wetted and then dried during storage and transportation processes, clumps or cakes often form in the material even when the maximum moisture content is less than 1% by mass. In order to avoid or decrease these occurred cakes, it is essential to characterize cake strength and to explore the process of cake formulation or caking through theoretical/numerical analysis. In this thesis, both experimental measurements of cake strength and theoretical/numerical simulations for recrystallization near a contact point are used to investigate the relationship between the caking process and the cake strength for important factors such as initial moisture content and drying time. <p>In this research, a centrifugal loading method has been developed to determine cake strength in a caked ring specimen of potash fertilizer where internal tensile stresses dominate. Research on fracture mechanics states that brittle materials, such as caked potash, fail at randomly positioned fracture surfaces in tension so the centrifuge test method is well suited to provide good data. A two-dimensional plane stress analysis was used to determine the area-averaged tensile stress at the speed of the centrifuge when each specimen fractures. Repeated tests and uncertainty calculations give data with a narrow range of uncertainty. <p>The centrifuge test facility was used for a series of tests in which the initial moisture content, drying time, particle size and chemical composition (i.e. magnesium content) of the samples were varied. For particle sizes in the range from 0.85 to 3.35 mm, experimental data show that the cake strength increased linearly with initial moisture content for each drying method and particle size, and decreased with increasing particle size for each initial moisture content and drying method. As well, it was also found that cake strength will increase essentially linearly with magnesium content from 0.02% to 0.1% for samples with the same initial moisture content, particle size and drying method. All data show that potash samples tend to form a stronger cake with a slower drying process. <p>A theoretical/numerical model is presented in this thesis to simulate ion diffusion and crystallization near one contact point between two potash (KCl) particles during a typical drying process. The effects of three independent factors are investigated: initial moisture content; evaporation rate; and degree of supersaturation on the surface surrounding the contact point. The numerical results show that the mass of crystal deposition near the contact point will increase with increased initial moisture content and decreased evaporation rate. These numerical predictions for recrystallization near the contact point are consistent with the experimental data for the cake strength of test samples of particle beds. With variations in the solid crystal surface degree of supersaturation near the contact point, simulations showed up to 5 times the increase in the crystal mass deposition near the contact point. This prediction of increased roughness is consistent with another experimental investigation which showed that the surface roughness of NaCl and KCl surfaces increased by a factor of five after one wetting and drying process.

Surface patterns of bead defects such as humping, gouged and rippling after solidification during laser and electron processing and different welding processes are systematically and quantitatively studied in this project. These defects usually accompanying with porosity, undercut, segregation, stress concentration, etc. seriously reduce the properties and strength of the surface heat treatment and weld joint. In order to improve quality, assure mass production and repeatability and reduce costs, it is necessary to understand their mechanisms. Although the defects have been extensively studied in the past, systematical, penetrative and quantitative understanding of their formation from thermal, physics, and pattern selection viewpoints are limited.The study include thermocapillary force, evaporation, and phase changes between solid-liquid and liquid-gas phases by introducing energy equation and interfacial and kinematic boundary conditions to simulate realistic processes.

In this research, least-squares based finite element formulations and their applications in fluid mechanics are presented. Least-squares formulations offer several computational and theoretical advantages for Newtonian as well as non-Newtonian fluid flows. Most notably, these formulations circumvent the inf-sup condition of Ladyzhenskaya-Babuska- Brezzi (LBB) such that the choice of approximating space is not subject to any compatibility condition. Also, the resulting coefficient matrix is symmetric and positive-definite. It has been observed that pressure and velocities are not strongly coupled in traditional leastsquares based finite element formulations. Penalty based least-squares formulations that fix the pressure-velocity coupling problem are proposed, implemented in a computational scheme, and evaluated in this study. The continuity equation is treated as a constraint on the velocity field and the constraint is enforced using the penalty method. These penalty based formulations produce accurate results for even low penalty parameters (in the range of 10-50 penalty parameter). A stress based least-squares formulation is also being proposed to couple pressure and velocities. Stress components are introduced as independent variables to make the system first order. The continuity equation is eliminated from the system with suitable modifications. Least-squares formulations are also developed for viscoelastic flows and moving boundary flows. All the formulations developed in this study are tested using several benchmark problems. All of the finite element models developed in this study performed well in all cases. A method to exploit orthogonality of modal bases to avoid numerical integration and have a fast computation is also developed during this study. The entries of the coefficient matrix are calculated analytically. The properties of Jacobi polynomials are used and most of the entries of the coefficient matrix are recast so that they can be evaluated analytically.

In this dissertation, we explore direct-forcing immersed boundary methods (IBM) under the framework of the lattice Boltzmann method (LBM), which is called the direct-forcing immersed boundary-lattice Boltzmann method (IB-LBM). First, we derive the direct-forcing formula based on the split-forcing lattice Boltzmann equation, which recovers the Navier-Stokes equation with second-order accuracy and enables us to develop a simple and accurate formula due to its kinetic nature. Then, we assess the various interface schemes under the derived direct-forcing formula. We consider not only diffuse interface schemes but also a sharp interface scheme. All tested schemes show a second-order overall accuracy. In the simulation of stationary complex boundary flows, we can observe that the sharper the interface scheme is, the more accurate the results are. The interface schemes are also applied to moving boundary problems. The sharp interface scheme shows better accuracy than the diffuse interface schemes but generates spurious oscillation in the boundary forcing terms due to the discontinuous change of nodes for the interpolation. In contrast, the diffuse interface schemes show smooth change in the boundary forcing terms but less accurate results because of discrete delta functions. Hence, the diffuse interface scheme with a corrected radius can be adopted to obtain both accurate and smooth results. Finally, a direct-forcing immersed boundary method (IBM) for the thermal lattice Boltzmann method (TLBM) is proposed to simulate non-isothermal flows. The direct-forcing IBM formulas for thermal equations are derived based on two TLBM models: a double-population model with a simplified thermal lattice Boltzmann equation (Model 1) and a hybrid model with an advection-diffusion equation of temperature (Model 2). The proposed methods are validated through natural convection problems with stationary and moving boundaries. In terms of accuracy, the results obtained from the IBMs based on both models are comparable and show a good agreement with those from other numerical methods. In contrast, the IBM based on Model 2 is more numerically efficient than the IBM based on Model 1. Overall, this study serves to establish the feasibility of the direct-forcing IB-LBM as a viable tool for computing various complex and/or moving boundary flow problems.

Finite element solution of solidification process in 2-D Cartesian and axisymmetric geometries is investigated. The use of finite element may result in spurious increase of temperature in the field and the selection of the mushy zone range when used as a numerical tool along with the selection of the mesh size results in large errors in the predicted solidification time. The approach works best for problems where the mushy zone range is finite and the thermal conductivities of both phases are high.

MODELING AND NUMERICAL ANALYSIS OF SINGLE DROPLET DRYING DALMAZ, Nesip M.Sc., Department of Chemical Engineering Supervisor: Prof. Dr. H. &Ouml / nder &Ouml / ZBELGE Co-Supervisor: Asst. Prof. Dr. Yusuf ULUDAg August 2005, 120 pages A new single droplet drying model is developed that can be used as a part of computational modeling of a typical spray drier. It is aimed to describe the drying behavior of a single droplet both in constant and falling rate periods using receding evaporation front approach coupled with the utilization of heat and mass transfer equations. A special attention is addressed to develop two different numerical solution methods, namely the Variable Grid Network (VGN) algorithm for constant rate period and the Variable Time Step (VTS) algorithm for falling rate period, with the requirement of moving boundary analysis. For the assessment of the validity of the model, experimental weight and temperature histories of colloidal silica (SiO2), skimmed milk and sodium sulfate decahydrate (Na2SO4&amp / #8901 / 10H2O) droplets are compared with the model predictions. Further, proper choices of the numerical parameters are sought in order to have successful iteration loops. The model successfully estimated the weight and temperature histories of colloidal silica, dried at air temperatures of 101oC and 178oC, and skimmed milk, dried at air temperatures of 50oC and 90oC, droplets. However, the model failed to predict both the weight and the temperature histories of Na2SO4&amp / #8901 / 10H2O droplets dried at air temperatures of 90oC and 110oC. Using the vapor pressure expression of pure water, which neglects the non-idealities introduced by solid-liquid interactions, in model calculations is addressed to be the main reason of the model resulting poor estimations. However, the developed model gives the flexibility to use a proper vapor pressure expression without much effort for estimation of the drying history of droplets having highly soluble solids with strong solid-liquid interactions. Initial droplet diameters, which were calculated based on the estimations of the critical droplet weights, were predicted in the range of 1.5-2.0 mm, which are in good agreement with the experimental measurements. It is concluded that the study has resulted a new reliable drying model that can be used to predict the drying histories of different materials.

O seguinte trabalho procura estudar problemas de fronteira móvel, conhecidos por problemas de Stefan, bem como aproximar suas soluções. Aplicações de problemas de Stefan encontram-se, por exemplo, na física termal de mudança de estados, presente em diversos fenômenos físicos e químicos naturais e na indústria. Devido a não-linearidade, a maior parte destes problemas não possuem solução analítica conhecida e uma técnica comum para se aproximar soluções é o método de balanceamento integral, inicialmente estudado por Goodman (1958). Este método e suas variações propõem perfis de aproximação no domínio da solução e resolvem uma versão integral da equação diferencial. O problema se resume a resolver uma equação diferencial ordinária no tempo envolvendo a profundidade de penetração do calor e o perfil de aproximação proposto. O trabalho estuda tais métodos para problemas termais clássicos em primeiro lugar, de modo que a extensão para problemas de Stefan seja natural. Refinamentos são apresentados, bem como uma técnica de subdivisão do espaço que resulta num esquema numérico. A técnica de imobilização e fronteira é desenvolvida e aplicada em diversos momentos, a fim de simplificar a utilização dos métodos integrais. / The current work aims to study moving boundary problems, known as Stefan problems, and approximate their solutions. Applications of Stefan problems are found in situations where there is change of physical state, present in several natural and industrial physical and chemical phenomena. Due to their inherent nonlinearity, most of these problems have no known analytic solution and a common technique to approximate solutions is the heat balance integral method, originally studied by Goodman (1958). This method and its variations propose an approximating profile and solve an integral version of the differential equation. The problem is reduced to solving an ordinary differential equation in time involving the depth of heat penetration and the proposed profile. This work studies such classic methods to thermal problems first, in a way that the extension to Stefan problems is natural. Refinements are presented, as well as a technique of subdividing the space domain which results in a numerical scheme. The technique of boundary immobilization is developed and applied at different times in order to simplify the use of these methods.

Kyoto University (京都大学) / 0048 / 新制・課程博士 / 博士(工学) / 甲第17512号 / 工博第3671号 / 新制||工||1558(附属図書館) / 30278 / 京都大学大学院工学研究科機械理工学専攻 / (主査)教授 青木 一生, 教授 稲室 隆二, 教授 斧 髙一 / 学位規則第4条第1項該当

Using the Navier-Stokes equations along with a continuity equation, a one-dimensional model is developed to describe the spin coating process of thin polymeric films. The resulting model is a system of a parabolic partial differential equation coupled with an integral equation as well as with an ordinary differential equation describing the motion of a moving boundary. Viscosity and diffusivity are allowed to be varied in the model. To be able to perform the finite element approximation of the model equations, the moving boundary is fixed. Then the finite element method is applied along with the so called Method of Lines resulting in a semi-discrete problem, a large system of ordinary differential equations which is then solved with MATLAB. We present an existence and uniqueness result what concerns the semi-discrete solutions. Finally, we illustrate numerically the behavior of the solutions to our model.

京都大学 / 0048 / 新制・課程博士 / 博士(工学) / 甲第18271号 / 工博第3863号 / 新制||工||1592(附属図書館) / 31129 / 京都大学大学院工学研究科航空宇宙工学専攻 / (主査)教授 稲室 隆二, 教授 泉田 啓, 教授 青木 一生 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM