This thesis presents the numerical algorithms to carry out the face transformation. The main efforts are denoted to the finite volume method (FVM) with the Delaunay triangulation to solve the Laplace equations in the harmonic transformation undergone in face images. The advantages of the FVM with the Delaunay triangulation are: (1) Easy to formulate the linear algebraic equations, (2) Good to retain the geometric and physical properties, (3) less CPU time needed. The numerical and graphical experiments are reported for the face transformations from a female to a male, and vice versa. The computed sequential and absolute errors are and , where N is division number of a pixel into subpixels. Such computed errors coincide with the analysis on the splitting-shooting method (SSM) with piecewise constant interpolation in [Li and Bui, 1998c].

In this study, the non-equilibrium Johnson and King Turbulence Model (JK model) is implemented in a three-dimensional, Navier-Stokes flow solver. The main program is a structured Euler/Navier-Stokes flow solver in which spatial discretization is accomplished by a finite volume formulation and a multigrid technique is used as a convergence accelerator. The aim is the validation of this in-house developed CFD (Computational Fluid Dynamics) tool with this enhanced enlarged capability in order to obtain a reliable flow solver that can solve flows over swept wings accurately. Various test cases were evaluated against reference solutions in order to demonstrate the accuracy of the newly implemented JK turbulence model. The selected test cases are NACA 0012 airfoil, ONERA M6 wing, DLR-F4 wing and two wings taken from the 3rd Drag Prediction Workshop. The solutions were analyzed and discussed in detail. The results show appreciably good agreement with the experimental data including force coefficients and surface pressure distributions.

There is a strong need in forging industry to reduce waste of material, improve quality, and reduce cost of forgings. About 30% of the material is wasted during conventional closed-die forging. Therefore, in order to reduce the cost of forged products and to obtain near-net or net shape parts, new forging methods should be applied. Precision forging concept is a cost-effective way to produce net-shape or near-net shape components. In recent years, there has been an increased interest in the production of gears by the net-shape forging technique. This has specific advantages over the traditional manufacturing processes of cutting gears such as hobbing, turning, and grinding including savings on cost and raw material, increased productivity, and gears with higher dynamic properties than conventionally cut ones. In this study, precision forging of a particular spur gear has been investigated. The precision forging die set has been conceptually designed and modeled in a computer aided design environment. The forging process of particular spur gear has been simulated by using a commercially available finite volume program. After the successful simulation results, the prototype die set and the tube-shaped billets were manufactured. The real-life experiments have been realized by using 1000 tons mechanical forging press available in METUBILTIR Research and Application Center Forging Laboratory. The results have been compared with the computer simulations. After the real-life experiments, it has been observed that the conceptual die design is appropriate and near-net shape spur gears are successfully obtained by the proposed precision forging die set.

The main purpose of this research is to develop a Computational Fluid Dynamics (CFD) software to be used as an educational tool in teaching introductory level fluid mechanics and CFD courses. The software developed for this purpose is called Virtual Flow Lab. It has a graphical user interface (GUI) that enables basic pre-processing, solver parameter and boundary condition setting and post-processing steps of a typical CFD simulation. The pressure-based solver is capable of solving incompressible, laminar, steady or time-dependent problems on two-dimensional Cartesian grids using the SIMPLE algorithm and its variants. Blocked-cell technique is implemented to extend the types of the problems that can be studied on a Cartesian grid. A parametric study is conducted using a number of benchmark problems in order to test the accuracy and efficiency of the solver and successful results are achieved.

Most materials used in many industries such as plastic, food, pharmaceuticals, electronics, dye, etc. exhibit viscoelastic properties under their processing or flow conditions. Due to the elasticity of such materials, deformation-stress in addition to their hydrodynamic behavior differ from simple Newtonian fluids in many important respects. Rod climbing, siphoning, secondary flows are all common examples to how a viscoelastic fluid can exhibit quite distinctive flow behavior than a Newtonian fluid would do under similar flow conditions. In industrial processes involving flow of viscoelastic materials, understanding complexities associated with the viscoelasticity can lead to both design and development of hydrodynamically efficient processes and to improved quality of the final products. In the present study, the main objective is to develop two dimensional finite volume based convergent numerical algorithm for the simulation of viscoelastic flows using nonlinear differential constitutive equations. The constitutive models adopted are Oldroyd-B, Phan-Thien Tanner (PTT) and White-Metzner models. The semi-implicit method for the pressure-linked equation (SIMPLE) and SIMPLE consistent (SIMPLEC) are used to solve the coupled continuity, momentum and constitutive equations. Extra stress terms in momentum equations are solved by decoupled strategy. The schemes to approximate the convection terms in the momentum equations adopted are first order upwind, hybrid, power-law second order central differences and finally third order quadratic upstream interpolation for convective kinematics QUICK schemes. Upwind and QUICK schemes are used in the constitutive equations for the stresses. Non-uniform collocated grid system is employed to discretize flow geometries. As test cases, three problems are considered: flow in entrance of planar channel, stick-slip and lid driven cavity flow. Detailed investigation of the flow field is carried out in terms of velocity and stress fields. It is found that range of convergence of numerical solutions is very sensitive to the type of rheological model, Reynolds number and polymer contribution of viscosity as well as mesh refinement. Use of White-Metzner constitutive differential model gives smooth, non oscillatory solutions to much higher Weissenberg number than Oldroyd-B and PTT models. Differences between the behavior of Newtonian and viscoelastic fluids for lid-driven cavity, such as the normal stress effects and secondary eddy formations, are highlighted. In addition to the viscoelastic flow simulations, steady incompressible Newtonian flow of lid-driven cavity flow at high Reynolds numbers is also solved by finite volume approach. Effect of the solution procedure of pressure correction equation cycles, which is called inner loop, on the solution is discussesed in detail and results are compared with the available data in literature.

Combination of high strength with light weight which is the prominent property of aluminum alloy forgings has led aluminum forgings used in rapidly expanding range of applications. In this study, to produce a particular 7075 aluminum alloy part, the forging process has been designed and analyzed. The forging process sequence has been designed by using Finite Volume Method. Then, the designed process has been analyzed by using Finite Element Method and the stress, strain and temperature distributions within the dies have been determined. Five different initial temperatures of the billet / 438, 400, 350, 300 and 250 degree Celsius have been considered in the thermo-mechanically coupled simulations. The initial temperatures of the dies have been taken as 200 degree Celsius for all these analyses. Finite volume analysis and finite element analysis results of the preform and finish part have been compared for the initial billet temperature of 400 oC. Close results have been observed by these analyses. The experimental study has been carried out for the range of the initial billet temperatures of 251&amp / #8211 / 442 degree Celsius in METU-BILTIR Center Forging Research and Application Laboratory. It has been observed that the numerical and the experimental results are in good agreement and a successful forging process design has been achieved. For the initial die temperature of 200 degree Celsius, to avoid the plastic deformation of the dies and the incipient melting of the workpiece, 350 degree Celsius is determined to be the appropriate initial billet temperature for the forging of the particular part.

Aluminum forging products has been increasingly used in automotive and aerospace industry due to their lightness and strength. In this study, aluminum forging processes of a particular industrial part for the two different alloys (Al 7075 and Al 6061) have been analyzed. The forging part, forging process and the required dies have been designed according to the aluminum forging design parameters. The proposed process has been simulated by using the Finite Volume Method. In the simulations, analysis of the part during forging process has been performed / and the required forging force, the temperature distribution and the effective stress distribution in the parts have been obtained. The forging dies were produced in the METU-BILTIR Center CAD/CAM Laboratory. The experimental study has been performed in the METU-BILTIR Center Forging Research and Application Laboratory. The parts were produced without any defects as obtained in the finite volume simulations. The results of the experiment and finite volume simulation are compared and it has been observed good agreement.

Thesis (M.S.)--Mississippi State University. Department of Mechanical Engineering. / Title from title screen. Includes bibliographical references.

Thesis (Ph. D.)--University of Washington, 2001. / Vita. Includes bibliographical references (leaves 160-166).

The two-dimensional depth-averaged shallow water equations have attracted considerable attentions as a practical way to solve flows with free surface. Compared to three-dimensional Navier-Stokes equations, the shallow water equations give essentially the same results at much lower cost. Solving the shallow water equations by the Godunov-type finite volume method is a newly emerging area. The Godunov-type finite volume method is good at capturing the discontinuous fronts in numerical solutions. This makes the method suitable for solving the system of shallow water equations. In this dissertation, both the shallow water equations and the Godunov-type finite volume method are described in detail. A new surface flow routing method is proposed in the dissertation. The method does not limit the shallow water equations to open channels but extends the shallow water equations to the whole domain. Results show that the new routing method is a promising method for prediction of watershed runoff. The method is also applied to turbulence modeling of free surface flow. The κ - ε turbulence model is incorporated into the system of shallow water equations. The outcomes prove that the turbulence modeling is necessary for calculation of free surface flow. At last part of the dissertation, a total load sediment transport model is described and the model is tested against 1D and 2D laboratory experiments. In summary, the proposed numerical method shows good potential in solving free surface flow problems. And future development will be focusing on river meandering simulation, non-equilibrium sediment transport and surface flow - subsurface flow interaction.