An accurate discretization for an inhomogeneous transport equation with arbitrary coefficients and source

A new way of obtaining the algebraic relation between the nodal values in a general one-dimensional transport equation is presented. The equation can contain an arbitrary source and both the convective flux and the diffusion coefficient may vary arbitrarily. Contrary to the usual approach of approximating the derivatives involved, the algebraic relation is based on the exact solution written in integral terms. The required integrals can be speedily evaluated by approximating the integrand with Hermite splines or applying Gauss quadrature rules. The startling point about the whole procedure is that a very high accuracy can be obtained with few nodes, and more surprisingly, it can be increased almost up to machine accuracy by augmenting the number of quadrature points or the Hermite spline degree with little extra cost

An Accurate and Robust Numerical Scheme for Transport Equations

En esta tesis se presenta una nueva técnica de discretización para ecuaciones de transporte en problemas de convección-difusión para el rango completo de números de Péclet. La discretización emplea el flujo exacto de una ecuación de transporte unidimensional en estado estacionario para deducir una ecuación discreta de tres puntos en problemas unidimensionales y cinco puntos en problemas bidimensionales. Con "flujo exacto" se entiende que se puede obtener la solución exacta en función de integrales de algunos parámetros del fluido y flujo, incluso si estos parámetros son vari- ables en un volumen de control. Las cuadraturas de alto orden se utilizan para lograr resultados numéricos cercanos a la precisión de la máquina, incluso con mallas bastas.Como la discretización es esencialmente unidimensional, no está garantizada una solución con precisión de máquina para problemas multidimensionales, incluso en los casos en que las integrales a lo largo de cada coordenada cartesiana tienen una primitiva. En este sentido, la contribución principal de esta tesis consiste en una forma simple y elegante de obtener soluciones en problemas multidimensionales sin dejar de utilizar la formulación unidimensional. Además, si el problema es tal que la solución tiene precisión de máquina en el problema unidimensional a lo largo de las líneas coordenadas, también la tendrá para el dominio multidimensional.In this thesis, we present a novel discretization technique for transport equations in convection-diffusion problems across the whole range of Péclet numbers. The discretization employs the exact flux of a steady-state one-dimensional transport equation to derive a discrete equation with a three-point stencil in one-dimensional problems and a five-point stencil in two-dimensional ones. With "exact flux" it is meant that the exact solution can be obtained as a function of integrals of some fluid and flow parameters, even if these parameters are variable across a control volume. High-order quadratures are used to achieve numerical results close to machine- accuracy even with coarse grids. As the discretization is essentially one-dimensional, getting the machine- accurate solution of multidimensional problems is not guaranteed even in cases where the integrals along each Cartesian coordinate have a primitive. In this regard, the main contribution of this thesis consists in a simple and elegant way of getting solutions in multidimensional problems while still using the one-dimensional formulation. Moreover, if the problem is such that the solution is machine-accurate in the one-dimensional problem along coordinate lines, it will also be for the multidimensional domain.<br /

Estimation and Control of Contaminant Transport in Water Reservoirs

Ph.DDOCTOR OF PHILOSOPH

The Sixth Copper Mountain Conference on Multigrid Methods, part 2

The Sixth Copper Mountain Conference on Multigrid Methods was held on April 4-9, 1993, at Copper Mountain, Colorado. This book is a collection of many of the papers presented at the conference and so represents the conference proceedings. NASA Langley graciously provided printing of this document so that all of the papers could be presented in a single forum. Each paper was reviewed by a member of the conference organizing committee under the coordination of the editors. The multigrid discipline continues to expand and mature, as is evident from these proceedings. The vibrancy in this field is amply expressed in these important papers, and the collection clearly shows its rapid trend to further diversity and depth

Numerical, Analytical, and Experimental Studies of Reciprocating Mechanism Driven Heat Loops for High Heat Flux Cooling

The Reciprocating Mechanism Driven Heat Loop (RMDHL) is a novel heat transfer device that utilizes reciprocating flow, either single-phase or two-phase flow, to enhance the thermal management in high tech inventions. The device attains a high heat transfer rate through a reciprocating flow of the working fluid inside the heat transfer device. Although the concept of the device has been tested and validated experimentally, analytical or numerical studies have not been undertaken to understand its working mechanism and provide guidance for the device design. The objectives of this study are to understand the underlying physical mechanisms of heat transfer in internal reciprocating flow, formulate corresponding heat transfer correlations, conduct an experimental study for the heat transfer coefficient, and numerically model the single-phase and two-phase operations of the RMDHL to predict its performance under different working conditions. The two-phase flow boiling model was developed from the Rensselaer Polytechnic Institute (RPI) model, and a virtual loop written in C programming language was used to eliminate the need for fluid structure interaction (FSI) modelling. The accuracy of several turbulence formulations, including the Standard, RNG, and Realizable k-ɛ Models, Standard and SST k-ω Models, Transition k - - ω Model, and Transition SST Model, have been tested in conjunction with a CFD solver to select the most suitable turbulence modelling techniques. The numerical results obtained from the single-phase and two-phase models are compared with relevant experimental data with good agreement. Three-dimensional numerical results indicate that the RMDHL can meaningfully reduce the peak temperature of an electronic device and result in significantly more uniform temperature across the device. In addition to the numerical study, experimental studies in conjunction with analytical studies are undertaken. Experimental data and related heat transfer coefficient as well as practically useful semi-empirical correlations have been produced, all of which provide archival information for the design of heat transfer devices involving a reciprocating flow. In particular, this research will lead to the development of more powerful RMDHLs, achieve a heat flux goal of 600 W/cm2, and significantly advance the thermal management at various levels. Considering the other advantages of coolant leakage free and the absence of cavitation problems, the RMDHL could also be employed for aerospace and battery cooling applications

Turbine Engine Hot Section Technology, 1985

The Turbine Engine Section Technology (HOST) Project Office of the Lewis Research Center sponsored a workshop to discuss current research pertinent to turbine engine hot section durability problems. Presentations were made concerning hot section environment and the behavior of combustion liners, turbine blades, and turbine vanes

Development of Gradient Smoothing Operations and Application to Biological Systems

Ph.DDOCTOR OF PHILOSOPH

Gas turbine advanced performance simulation

Current commercial 'state of the art' engine simulation software is of a low fidelity. Individual component performance characteristics are typically represented via nondimensional maps with empirical adjustments for off-design effects. Component nondimensional characteristics are usually obtained through the averaging of experimental readings from rig test analyses carried out under nominal operating conditions. In those cases where actual component characteristics are not available and default maps are used instead, conventional simulation tools can offer a good prediction of the performance of the whole engine close to design point, but can deviate substantially at of design and transient conditions. On the other hand, even when real component characteristics are available, zero-dimensional engine cycle simulation tools can not predict the performance of the engine at other than nominal conditions satisfactorily. Low-fidelity simulation tools are generally incapable of analyzing the performance of individual engine components in detail, or capturing complex physical phenomena such as inlet flow distortion. Although the available computational power has increased exponentially over the last two decades, a detailed, three-dimensional analysis of an entire propulsion system still seems to be so complex and computationally intensive as to remain cost-prohibitive. For this reason, alternative methods of integrating different types and levels of analysis are necessary. The integration of simulation codes that model at different levels of fidelity into a single simulation provides the opportunity to reduce the overall computing resource needed, while retaining the desired level of analysis in specific engine components. The objective of this work was to investigate different simulation strategies for communicating the performance characteristics of an isolated gas turbine engine component, resolved from a detailed, high-fidelity analysis, to an engine system analysis carried out at a lower level of resolution. This would allow component-level, complex physical processes to be captured and analyzed in the context of the whole engine performance, at an affordable computing resource and time. More specifically, this work identified and thoroughly investigated several advanced simulation strategies in terms of their actual implementation and potential, by looking into relative changes in engine performance after integrating into the basic, nondimensional cycle analysis, the performance characteristics of i) two-dimensional Streamline Curvature (SLC) and ii) three-dimensional Computational Fluid Dynamics (CFD), engine component models. In the context of this work, several case studies were carried out, utilising different two-dimensional and three-dimensional component geometries, under different operating conditions, such as different types and extents of compressor inlet pressure distortion and turbine inlet temperature distortion. More importantly, this research effort established the necessary methodology and technology required for a full, twodimensional engine cycle analysis at an affordable computational resource.EThOS - Electronic Theses Online ServiceGBUnited Kingdo