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As the performance required of high pressure turbines continues to increase, there is a need to investigate many details of the flow which occur in a gas turbine stage that were previously overlooked. These include the effects of rotation and three-dimensional flow as well as unsteady effects due to the relative motion of the blade rows. In order to obtain a better understanding of the turbine flowfield a new transient facility has been commissioned in which aerodynamic and heat transfer measurements can be undertaken in a full stage turbine at engine representative conditions. The previously used technique of measuring the heat transfer rate by mounting thin film gauges on models manufactured from machineable glass ceramic was not suitable for use on the rotor blade because of the high stress levels involved. An alternative technique has been developed in which a metal turbine blade is coated with an insulating layer of enamel and thin film gauges painted on top. The developments in signal processing and calibrations which were necessary for the use of this type of thin film gauge are discussed in detail. Signal conditioning electronics have been developed which permit amplification of the thin film gauge output to a higher level within the rotating frame before transmission through a slipring. Extensive tests have been undertaken, in a purpose built spinning rig, to establish the effects of rotation on the performance and mechanical integrity of the instrumentation and associated electronics. The heat transfer measurements recorded in the rotor facility to date are presented and compared with data from a previous two-dimensional simulation of wake passing flow on the mid-height section of the same blade.

This thesis presents a Lagrangian formulation of the Euler equations for subsonic flows. A special coordinate transformation is used to define the Lagrangian coordinates, namely the stream function and the Lagrangian distance, in function of the Cartesian coordinates. This Lagrangian formulation introduces two new geometry state variables, and a Lagrangian behavior parameter defining a pseudo-Lagrangian time used during the iteration procedure to obtain the solution for subsonic flows. / The eigenstructure and characteristics analysis for the new system of equations is based on a linear Jacobian matrix-mapping procedure, which starts from the well-known eigenstructure and characteristics in the Eulerian plane and uses the coordinate transformation to find their counterparts in the Lagrangian plane. This analysis studies the basic properties of the Euler equations in the Lagrangian formulation, such as hyperbolicity, homogeneity and rotational invariance. The Riemann problem in the Lagrangian plane is also studied. Those elements are used to construct the numerical scheme for solving the Euler equations in the Lagrangian formulation. / The numerical scheme is constructed using first and second-order dimensional-splitting with hybrid flux operators, based on flux vector splitting and Godunov methods, which include a 2-D Riemann solver in the Lagrangian plane. The numerical method is validated by comparing the present solutions with the results obtained with an Eulerian formulation for several internal flows. / This numerical method based on a Lagrangian formulation has also been extended for the solution of unsteady subsonic flows by using a dual time approach. The method validation in this case has been done by comparison with the Eulerian formulation solutions for several internal subsonic flows with oscillating boundaries.

In the present study,transint flow analyses of a long oil pipeline are performed.

[Abstract]This thesis reports the development of new meshless schemes for solving timedependent partial differential equations (PDEs) and for the numerical simulation of some typical unsteady incompressible viscous flows.The new numerical schemes are based on the Idirect/Integrated Radial Basis Function Network (IRBFN) method which is fully meshless as no element-typemesh is required. The IRBFN method has been successfully applied to solve time-independent elliptic PDEs, some steady fluid flows and recently unsteady Navier-Stokes equations in streamfunction-vorticiy formulation using simple time integration methods (e.g. first-order backward Euler method). The main objective of the present research is to devise and implement meshless numerical schemes for unsteady problems in computational fluid dynamics where notonly the accuracy but also the efficiency and stability of the numerical schemes are of primary concerns. In addition, the effects of different parameters of theIRBFN method on the accuracy, stability and efficiency of the proposed numerical schemes are extensively studied in this research.As the first step in extending the IRBFN method to various types of timedependent PDEs, two numerical schemes combining the IRBFN method with high-order time stepping algorithms are developed for solving parabolic, hyperbolic,and advection-diffusion equations. Sensitivity analysis of the method to point density, time-step size and shape parameter are extensively performed to study the influence of these parameters to the overall accuracy of the method.A further extension of the IRBFN method for incompressible fluid flows with moving interfaces, especially for passive transport problems is accomplished in this research with a novel meshless approach in which the level set methodis coupled with the the IRBFN method for capturing moving interfaces in an ambient fluid flow without any explicit computation of the actual front location.Another contribution of this research is the development of two new meshless schemes based on the IRBFN method for the numerical simulation of unsteady incompressible viscous flows governed by the Navier-Stokes equations. In the new schemes, the splitting approach is used to deal with the momentum equation and the incompressibility constraint in a segregated manner. Numerical experiments on the new schemes in terms of accuracy and stability are performed for verification purposes.Finally, a novel meshless hybrid scheme is developed in this research to numerically simulate interfacial flows in which the motion and deformation of the interface between the two immiscible fluids are fully captured. Unlike the passive transport problems mentioned above where the influence of the moving interface on the surrounding fluid is ignored, the interfacial flows are studied here with the surface tension taken into account. As a result, a two-way interaction between the moving interface and the ambient flow is fully investigated.All numerical schemes developed in this research are verified through a wide range of transient problems including different kinds of time-dependent PDEs,typical passive transport problems and interfacial flows as well as unsteady incompressible viscous flows governed by Navier-Stokes equations.

Thesis (Ph. D.)--Duke University, 2008. / Includes bibliographical references.