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.

The ongoing process of deregulation in energy markets changes the market from a monopoly into a complex one, in which large utilities and independent power producers are no longer suppliers with guaranteed returns but enterprisers which have to compete. This competence has forced utilities to improve their efficiency. In effect, they must still manage the challenges of physical delivery while operating in a complex market characterized by significant volatility, volumetric uncertainty and credit risk. In such an environment, risk management gains more importance than ever. In order to manage risk, first it must be measured and then this quantified risk must be utilized optimally. Using stochastic programming to construct a model for an energy company in liberalized markets is useful since it provides a generic framework to model the uncertainties and enable decisions that will perform well. However, the resulting stochastic programming problem is a large-scale one and decomposition techniques are needed to solve them.

In this thesis, the Generalized Finite Difference (GFD) method is applied to analyze the elastoplastic deformation behavior of a long functionally graded (FGM) tube subjected to internal pressure. First, the method is explained in detail by considering the elastic response of a rotating FGM tube. Then, the pressurized tube problem is treated. A long FGM tube with fixed ends (axially constrained ends) is taken into consideration. The two cases in which the modulus of elasticity only and both the modulus of elasticity and the yield limit are graded properties are analyzed. The plastic model here is based on incremental theory of plasticity, Tresca&#039 / s yield criterion and its associated flow rule. The numerical results are compared to those of analytical ones. Furthermore, the elastic response of an FGM tube with free ends is studied considering graded modulus of elasticity and Poisson&#039 / s ratio. The results of these computations are compared to those of Shooting solutions. In the light of analyses and comparisons stated above, the applicability of the GFD method to the solution of similar problems is discussed. It is observed that, in purely elastic deformations the accuracy of the method is sufficient. However, in case of elastic-plastic deformations, the discrepancies between numerical and analytical results may increase in determining plastic displacements. It is also noteworthy that the predictions for tubes with two graded properties, i. e. the modulus of elasticity and the yield limit, turn out to be better than those with one graded property in this regard.

A non-iterative pressure based algorithm which consists of splitting the solution of momentum energy and species equations into a sequence of predictor-corrector stages was developed for the simulation of transient reacting radiating flows. A semi-discrete approach called the Method of Lines (MOL) which enables implicit time-integration at all splitting stages was used for the solution of conservation equations. The solution of elliptic pressure equation for the determination of pressure field was performed by a multi-grid solver (MUDPACK package). Radiation calculations were carried out by coupling previously developed gray and non-gray radiation models with the algorithm. A first order (global) reaction mechanism was employed to account for the chemistry. The predictions of the algorithm for the following test cases: i) non-isothermal turbulent pipe flow and ii) laminar methane-air diffusion flame / were benchmarked against experimental data and numerical solutions available in the literature and the capability of the code to predict transient solutions was demonstrated on these test cases. Favorable agreements were obtained for both test cases. The effect of radiation and non-gray treatment of the radiative properties were investigated on the second test case. It was found that incorporation of radiation has significant effect on Temeprature and velocity fields but its effect is limited in species predictions. Executions with both radiation models revealed that the non-gray radiation model considered in the present study produces similar results with the gray model at a considerably higher computational cost. The algorithm developed was found to be an efficient and versatile tool for the timedependent simulation of different flow scenarios constitutes the initial steps towards the computation of transient turbulent combustion.

In this research, the Alternating Cell Direction Implicit method is used in temporal discretisation of the incompressible Navier-Stokes equations and compared with the well known and widely used Point Gauss Seidel scheme on structured and quadrilateral unstructured meshes. A two dimensional, laminar and incompressible Navier-Stokes solver is developed for this purpose using the artificial compressibility formulation. The developed solver is used to obtain steady-state solutions with implicit time stepping methods and a third order data reconstruction scheme (U-MUSCL) is added to obtain high order spatial accuracy. The Alternating Cell Directions Implicit method and Point Gauss Seidel scheme is compared in terms of convergence iteration number and total computation time using test cases with growing complexity, including laminar flat plate, single and multi-element airfoil calculations. Both structured and quadrilateral unstructured grids are used in single element airfoil calculations. In these test cases, it is seen that a reduction between 13% and 20% is obtained in total computation time by usage of Alternating Cell Directions Implicit method when compared with the Point Gauss Seidel method.

The aim of this study is to develop a two-dimensional pressure-based Navier-Stokes solver for incompressible/compressible flows. Main variables are Cartesian velocity components, pressure and temperature while density is linked to pressure via equation of state. Modified SIMPLE algorithm is used to achieve pressure-velocity coupling. Finite Volume discretisation is performed on non-orthogonal and boundary-fitted grids. Collocated variable arrangement is preferred because of its advantage on staggered arrangement in non-orthogonal meshes. Face velocities are calculated using Rhie-Chow momentum interpolation scheme to avoid pressure checkerboarding effect. The solver is validated by solving a number of benchmark problems.

We consider the reaction-diffusion-advection (RDA) equations resulting in air pollution mod- eling problems. We employ the finite element method (FEM) for solving the RDA equations in two dimensions. Linear triangular finite elements are used in the discretization of problem domains. The instabilities occuring in the solution when the standard Galerkin finite element method is used, in advection or reaction dominated cases, are eliminated by using an adap- tive stabilized finite element method. In transient problems the unconditionally stable Crank- Nicolson scheme is used for the temporal discretization. The stabilization is also applied for reaction or advection dominant case in the time dependent problems. It is found that the stabilization in FEM makes it possible to solve RDA problems for very small diffusivity constants. However, for transient RDA problems, although the stabilization improves the solution for the case of reaction or advection dominance, it is not that pronounced as in the steady problems. Numerical results are presented in terms of graphics for some test steady and unsteady RDA problems. Solution of an air pollution model problem is also provided.

Regulatory processes and history dependent behavior appear in many dynamical systems in nature and technology. For modeling regulatory processes, hybrid systems offer several advances. From this point of view, to observe the capability of hybrid systems in a history dependent system is a strong motivation. In this thesis, we developed functional hybrid systems which exhibit memory dependent behavior such that the dynamics of the system is determined by both the location of the state vector and the memory. This property was explained by various examples. We used the hybrid system with memory in modeling the gene regulatory network of human immune response to Influenza A virus infection. We investigated the sensitivity of the piecewise linear model with memory. We introduced how the model can be developed in future.

In this thesis, the two-dimensional initial and boundary value problems (IBVPs) and the one-dimensional Cauchy problems defined by the nonlinear reaction- diffusion and wave equations are numerically solved. The dual reciprocity boundary element method (DRBEM) is used to discretize the IBVPs defined by single and system of nonlinear reaction-diffusion equations and nonlinear wave equation, spatially. The advantage of DRBEM for the exterior regions is made use of for the latter problem. The differential quadrature method (DQM) is used for the spatial discretization of IBVPs and Cauchy problems defined by the nonlinear reaction-diffusion and wave equations. The DRBEM and DQM applications result in first and second order system of ordinary differential equations in time. These systems are solved with three different time integration methods, the finite difference method (FDM), the least squares method (LSM) and the finite element method (FEM) and comparisons among the methods are made. In the FDM a relaxation parameter is used to smooth the solution between the consecutive time levels. It is found that DRBEM+FEM procedure gives better accuracy for the IBVPs defined by nonlinear reaction-diffusion equation. The DRBEM+LSM procedure with exponential and rational radial basis functions is found suitable for exterior wave problem. The same result is also valid when DQM is used for space discretization instead of DRBEM for Cauchy and IBVPs defined by nonlinear reaction-diffusion and wave equations.

Semi-infinite programming problems is a class of optimization problems in finite dimensional variables which are subject to infinitely many inequality constraints. If the infinite index of inequality constraints depends on the decision variable, then the problem is called generalized semi-infinite programming problem (GSIP). If the infinite index set is fixed, then the problem is called standard semi-infinite programming problem (SIP). In this thesis, convergence of a semismooth Newton method for generalized semi-infinite programming problems with convex lower level problems is investigated. In this method, using nonlinear complementarity problem functions the upper and lower level Karush-Kuhn-Tucker conditions of the optimization problem are reformulated as a semismooth system of equations. A possible violation of strict complementary slackness causes nonsmoothness. In this study, we show that the standard regularity condition for convergence of the semismooth Newton method is satisfied under natural assumptions for semi-infinite programs. In fact, under the Reduction Ansatz in the lower level problem and strong stability in the reduced upper level problem this regularity condition is satisfied. In particular, we do not have to assume strict complementary slackness in the upper level. Furthermore, in this thesis we neither assume strict complementary slackness in the upper nor in the lower level. In the case of violation of strict complementary slackness in the lower level, the auxiliary functions of the locally reduced problem are not necessarily twice continuously differentiable. But still, we can show that a standard regularity condition for quadratic convergence of the semismooth Newton method holds under a natural assumption for semi-infinite programs. Numerical examples from, among others, design centering and robust optimization illustrate the performance of the method.