An expansion method for the stationary Schrodinger equation of a particle moving freely in an arbitrary axisymmeric three dimensional region defined by an analytic function is introduced. The region is transformed into the unit ball by means of coordinate substitution. As a result the Schrodinger equation is considerably changed. The wavefunction is expanded into a series of spherical harmonics, thus, reducing the transformed partial differential equation to an infinite system of coupled ordinary differential equations. A Fourier-Bessel expansion of the solution vector in terms of Bessel functions with real orders is employed, resulting in a generalized matrix eigenvalue problem. The method is applied to two particular examples. The first example is a prolate spheroidal billiard which is also treated by using an alternative method. The numerical results obtained by using both the methods are compared. The second exampleis a billiard family depending on a parameter. Numerical results concerning the second example include the statistical analysis of the eigenvalues.

In this thesis, fatigue life of a stationary component of F110-GE-100 jet engine is assessed. Three-dimensional finite element model of the component itself and the neighboring components are modeled by using a finite element package program, ANSYS, in order to perform thermal, stress and fracture mechanics analyses. Coupled-field (thermal-stress) analysis is performed to identify fracture-critical locations and to describe the stress histories of the components. After determining the critical location, fracture mechanics calculations are performed by modeling a crack of various lengths at the critical locations with FRANC3D in order to calculate mode I and II stress intensity factors and geometry factors beta. Combining the outputs of coupled-field and fracture mechanics analyses, fatigue lives and creep rupture times are calculated with a crack growth life prediction program, AFGROW. A linear damage summation method is used to assess the fatigue life of the component of interest.

This thesis analyzes the probable outcome of the fictitious failure of a dam under a set of pre-defined scenarios, within the framework of a case study, the case subject being the Cinarcik Dam located within Bursa Province of Turkey. The failure of the dam is not analyzed neither structural nor hydraulic-wise but is assumed to be triggered when certain critical criteria are exceeded. Hence, the analyses focus on the aftermath of the failure and strive to anticipate the level of inundation downstream of the dam itself. For the purpose of the analyses, the FLDWAV software developed by the National Weather Service of USA is used to spatially and temporally predict the flow profiles, water surface elevations and discharges occurring downstream of the &Ccedil / inarcik Dam under the defined set of scenarios. Based on these analyses, indicative inundation maps and settlements under risk will be identified, and the thesis study will further address some available pre-event measures that may be taken in advance.

In this thesis, Finite Volume Weighted Essentially Non-Oscillatory (FV-WENO) codes for one and two-dimensional discretised Euler equations are developed. The construction and application of the FV-WENO scheme and codes will be described. Also the effects of the grid coefficients as well as the effect of the Gaussian Quadrature on the solution have been tested and discussed. WENO schemes are high order accurate schemes designed for problems with piecewise smooth solutions containing discontinuities. The key idea lies at the high approximation level, where a convex combination of all the candidate stencils is used with certain weights. Those weights are used to eliminate the stencils, which contain discontinuity. WENO schemes have been quite successful in applications, especially for problems containing both shocks and complicated smooth solution structures. The applications tested in this thesis are the Diverging Nozzle, Shock Vortex Interaction, Supersonic Channel Flow, Flow over Bump, and supersonic Staggered Wedge Cascade. The numerical solutions for the diverging nozzle and the supersonic channel flow are compared with the analytical solutions. The results for the shock vortex interaction are compared with the Roe scheme results. The results for the bump flow and the supersonic staggered cascade are compared with results from literature.

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.