A systematic approach of testing and validating transition models is developed and employed in testing of a recently developed transition model. The testing methodology uses efficient computational tools and a wide range of test cases. The computational tools include a boundary layer code, single zone Navier Stokes solver, and a multi-block Navier Stokes solver which uses MPI and is capable of handling complex geometries and moving grids. Test cases include simple flat plate experiments, cascade experiments, and unsteady wake/blade interaction experiments. The test cases are used to test the predicting capabilities of the transition model under various effects such as free stream turbulence intensity, Reynolds number variations, pressure gradient, flow separation, and unsteady wake/blade interaction. Using the above test cases and computational tools a method is developed to validate transition models. The transition model is first implemented in boundary layer code and tested for simple flat plate cases. Then the transition model is implemented in single zone Navier Stokes solver and tested for hysteresis effects for flat plate cases. Finally the transition model is implemented in multi zone Navier Stokes solver and tested for compressor and turbine cascade cases followed by unsteady wake/blade interaction experiments. Using the method developed a new correlation based transition model (Menter et al. 2004) which uses local variables is tested and validated. The new model predicted good results for high free stream turbulence and high Reynolds number cases. For low free stream turbulence and low Reynolds number cases, the results were satisfactory.

This thesis investigates how magnetographic data may be used to study the longterm behaviour of the magnetic field distribution across the surface of the sun.

No description available.

[ES] La forma más exacta de conocer el desplazamiento de los neutrones a través de un medio material se consigue resolviendo la Ecuación del Transporte Neutrónico. Tres diferentes aproximaciones de esta ecuación se han investigado en esta tesis: Ecuación del transporte neutrónico resuelta por el método de Ordenadas Discretas, Ecuación de la Difusión y Ecuación de Armónicos Esféricos Simplificados. Para resolver estás ecuaciones se estudian diferentes esquemas del Método de Diferencias Finitas. La solución a estas ecuaciones describe la población de neutrones y las reacciones ocasionadas dentro de un reactor nuclear. A su vez, estas variables están relacionadas con el flujo y la potencia, parámetros fundamentales para el Análisis de Seguridad Nuclear. La tesis introduce la definición de las ecuaciones mencionadas y en particular se detallan para el estado estacionario. Se plantea el Método Modal como solución a los problemas de autovalores definidos por dichas ecuaciones. Primero se desarrollan varios algoritmos para la resolución del estado estacionario de la Ecuación del Transporte de Neutrones con el Método de Ordenadas Discretas para la discretización angular y el Método de Diferencias Finitas para la discretización espacial. Se ha implementado una formulación capaz de resolver el problema de autovalores para cualquier número de grupos energéticos con upscattering y anisotropía. Varias cuadraturas utilizadas por este método en su resolución angular han sido estudiadas e implementadas para cualquier orden de aproximación de Ordenadas Discretas. Además, otra formulación se desarrolla para la solución del problema fuente de la ecuación del transporte neutrónico. A continuación, se lleva a cabo un algoritmo que permite resolver la Ecuación de la Difusión de Neutrones con dos variantes del método de diferencias Finitas, una centrada en celda y otra en vértice o nodo. Se utiliza también el Método Modal calculando cualquier número de autovalores para varios grupos de energía y con upscattering. También se implementan los dos esquemas del Método de Diferencias Finitas anteriormente mencionados en el desarrollo de diferentes algoritmos para resolver las Ecuaciones de Armónicos Esféricos Simplificados. Además, se ha realizado un análisis de diferentes aproximaciones de las condiciones de contorno. Finalmente, se han realizado cálculos de la constante de multiplicación, los modos subcríticos, el flujo neutrónico y la potencia para diferentes tipos de reactores nucleares. Estas variables resultan esenciales en Análisis de Seguridad Nuclear. Además, se han realizado diferentes estudios de sensibilidad de parámetros como tamaño de malla, orden utilizado en cuadraturas o tipo de cuadraturas. / [CA] La forma més exacta de conèixer el desplaçament dels neutrons a través d'un mitjà material s'aconsegueix resolent l'Equació del Transport Neutrònic. Tres diferents aproximacions d'esta equació s'han investigat en aquesta tesi: Equació del Transport Neutrònic resolta pel mètode d'Ordenades Discretes, Equació de la Difusió i Equació d'Ármonics Esfèrics Simplificats. Per a resoldre estes equacions s'estudien diferents esquemes del Mètode de Diferències Finites. La solució a estes equacions descriu la població de neutrons i les reaccions ocasionades dins d'un reactor nuclear. Al seu torn, estes variables estan relacionades amb el flux i la potència, paràmetres fonamentals per a l'Anàlisi de Seguretat Nuclear. La tesi introduïx la definició de les equacions mencionades i en particular es detallen per a l'estat estacionari. Es planteja el Mètode Modal com a solució als problemes d'autovalors definits per les dites equacions. Primer es desenvolupen diversos algoritmes per a la resolució de l'estat estacionari de l'Equació del Transport de Neutrons amb el Mètode d'Ordenades Discretes per a la discretiztació angular i el Mètode de Diferències Finites per a la discretització espacial. S'ha implementat una formulació capaç de resoldre el problema d'autovalors per a qualsevol nombre de grups energètics amb upscattering i anisotropia. Diverses quadratures utilitzades per este mètode en la seua resolució angular han sigut estudiades i implementades per a qualsevol orde d'aproximació d'Ordenades Discretes. A més, una altra formulació es desenvolupa per a la solució del problema font de l'Equació del Transport Neutrònic. A continuació, es du a terme un algoritme que permet resoldre l'Equació de la Difusió de Neutrons amb dos variants del mètode de Diferències Finites, una centrada en cel·la i una altra en vèrtex o node. S'utilitza també el Mètode Modal calculant qualsevol nombre d'autovalors per a diversos grups d'energia i amb upscattering. També s'implementen els dos esquemes del Mètode de Diferències Finites anteriorment mencionats en el desenvolupament de diferents algoritmes per a resoldre les Equacions d'Harmònics Esfèrics Simplificats. A més, s'ha realitzat una anàlisi de diferents aproximacions de les condicions de contorn. Finalment, s'han realitzat càlculs de la constant de multiplicació, els modes subcrítics, el flux neutrònic i la potència per a diferents tipus de reactors nuclears. Estes variables resulten essencials en Anàlisi de Seguretat Nuclear. A més, s'han realitzat diferents estudis de sensibilitat de paràmetres com la grandària de malla, orde utilitzat en quadratures o tipus de quadratures. / [EN] The most accurate way to know the movement of the neutrons through matter is achieved by solving the Neutron Transport Equation. Three different approaches to solve this equation have been investigated in this thesis: Discrete Ordinates Neutron Transport Equation, Neutron Diffusion Equation and Simplified Spherical Harmonics Equations. In order to solve the equations, different schemes of the Finite Differences Method were studied. The solution of these equations describes the population of neutrons and the occurred reactions inside a nuclear system. These variables are related with the flux and power, fundamental parameters for the Nuclear Safety Analysis. The thesis introduces the definition of the mentioned equations. In particular, they are detailed for the steady state case. The Modal Method is proposed as a solution to the eigenvalue problems determined by the equations. First, several algorithms for the solution of the steady state of the Neutron Transport Equation with the Discrete Ordinates Method for the angular discretization and Finite Difference Method for spatial discretization are developed. A formulation able to solve eigenvalue problems for any number of energy groups, with scattering and anisotropy has been developed. Several quadratures used by this method for the angular discretization have been studied and implemented for any order of approach of the discrete ordinates. Furthermore, an adapted formulation has been developed as a solution of the source problem for the Neutron Transport Equation. Next, an algorithm is carried out that allows to solve the Neutron Diffusion Equation with two variants of the Finite Difference Method, one with cell centered scheme and another edge entered. The Modal method is also used for calculating any number of eigenvalues for several energy groups and upscattering. Both Finite Difference schemes mentioned before are also implemented to solve the Simplified Spherical Harmonics Equations. Moreover, an analysis of different approaches of the boundary conditions is performed. Finally, calculations of the multiplication factor, subcritical modes, neutron flux and the power for different nuclear reactors were carried out. These variables result essential in Nuclear Safety Analysis. In addition, several sensitivity studies of parameters like mesh size, quadrature order or quadrature type were performed. / Me gustaría dar las gracias al Ministerio de Economía, Industria y Competitividad y a la Agencia Estatal de Investigación de España por la concesión de mi contrato predoctoral de formación de personal investigador con referencia BES-2016-076782. La ayuda económica proporcionada por este contrato fue esencial para el desarrollo de esta tesis, así como para el financiamiento de una estancia. / Morato Rafet, S. (2020). Contributions to solve the Multi-group Neutron Transport equation with different Angular Approaches [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/159271 / TESIS

This work presents the development and application of analytical, numerical, and experimental methods for the study of thermal and electrical transport in nanoscale systems, with special emphasis on those materials and phenomena which can be important in thermoelectric and semiconductor device applications. Analytical solutions to the Boltzmann transport equation (BTE) using the relaxation time approximation (RTA) are presented and used to study the thermal and electrical transport properties of indium antimonide (InSb), indium arsenide (InAs), bismuth telluride (Bi₂Te₃), and chromium disilicide (CrSi₂) nanowires. Experimental results for the thermal conductivity of single layer graphene supported by SiO₂ were analyzed using an RTA-based model and compared to a full quantum mechanical numerical BTE solution which does not rely on the RTA. The ability of these models to explain the measurement results as well as differences between the two approaches are discussed. Alternatively, numerical solutions to the BTE may be obtained statistically through Monte Carlo simulation for complex geometries which may prove intractable for analytical methods. Following this approach, phonon transport in silicon (Si) sawtooth nanowires was studied, revealing that thermal conductivity suppression below the diffuse surface limit is possible. The experimental investigation of energy transport in nanostructures typically involved the use of microfabricated devices or non-contact optical methods. In this work, two such approaches were analyzed to ascertain their thermal behavior and overall accuracy as well as areas for possible improvement. A Raman spectroscopy-based measurement design for investigating the thermal properties of suspended and supported graphene was examined analytically. The resulting analysis provided a means of determining from measurement results the thermal interface conductance, thermal contact resistance, and thermal conductivity of the suspended and supported graphene regions. Previously, microfabricated devices of several different designs have been used to experimentally measure the thermal transport characteristics of nanostructures such as carbon nanotubes, nanowires, and thin films. To ascertain the accuracy and limitations of various microdevice designs and their associated conduction analyses, finite element models were constructed using ANSYS and measurements of samples of known thermal conductance were simulated. It was found that designs with the sample suspended were generally more accurate than those for which the sample is supported on a bridge whose conductance is measured separately. The effects of radiation loss to the environment of certain device designs were also studied, demonstrating the need for radiation shielding to be at temperatures close to that of the device substrate in order to accurately calibrate the resistance thermometers. Using a suspended microdevice like those analyzed using finite element analysis, the thermal conductivities of individual bismuth (Bi) nanowires were measured. The results were correlated with the crystal structure and growth direction obtained by transmission electron microscopy on the same nanowires. Compared to bulk Bi in the same crystal direction, the thermal conductivity of a single-crystal Bi nanowires of 232 nm diameter was found to be 3 - 6 times smaller than bulk between 100 K and 300 K. For polycrystalline Bi nanowires of 74 nm to 255 nm diameter the thermal conductivity was reduced by a factor of 18 - 78 over the same temperature range. Comparable thermal conductivity values were measured for polycrystalline nanowires of varying diameters, suggesting a grain boundary scattering mean free path for all heat carriers in the range of 15 - 40 nm which is smaller than the nanowire diameters. An RTA-based transport model for both charge carriers and phonons was developed which explains the thermal conductivity suppression in the single-crystal nanowire by considering diffuse phonon-surface scattering, partially diffuse surface scattering of electrons and holes, and scattering of phonons and charge carriers by ionized impurities such as oxygen and carbon of a concentration on the order of 10¹⁹ cm⁻³. Using a similar experimental setup, the thermoelectric properties (Seebeck coefficient, electrical conductivity, and thermal conductivity) of higher manganese silicide (HMS) nanostructures were investigated. Bulk HMS is a passable high temperature thermoelectric material which possesses a complex crystal structure that could lead to very interesting and useful nanoscale transport properties. The thermal conductivities of HMS nanowires and nanoribbons were found to be reduced by 50 - 60 % compared to bulk values in the same crystal direction for both nanoribbons and nanowires. The measured Seebeck coefficient data was comparable or below that of bulk, suggesting unintentional doping of the samples either during growth or sample preparation. Difficulty in determining the amorphous oxide layer thickness for nanoribbons samples necessitated using the total, oxide-included cross section in the thermal and electrical conductivity calculation. This in turn led to the determined electrical conductivity values representing the lower bound on the actual electrical conductivity of the HMS core. From this approach, the measured electrical conductivity values were comparable or slightly below the lower end of bulk electrical conductivity values. This oxide thickness issue affects the determination of the HMS nanostructure thermoelectric figure of merit ZT as well, though the lower bound values obtained here were found to still be comparable to or slightly smaller than the expected bulk values in the same crystal direction. Analytical modeling also indicates higher doping than in bulk. Overall, HMS nanostructures appear to have the potential to demonstrate measurable size-induced ZT enhancement, especially if optimal doping and control over the crystallographic growth direction can be achieved. However, experimental methods to achieve reliable electrical contact to quality four-probe samples needs to be improved in order to fully investigate the thermoelectric potential of HMS nanostructures. / text

Heat transport by phonons and magnons in crystals due to a local perturbation in temperature is described by the Boltzmann transport equation. In this project a one phonon one magnon system was studied in a one dimensional rod with reflective boundaries. Using the splitting algorithm the problem was reduced to a transport and collision term. The resulting stabilization time for a initial phonon and magnon distribution and the respective temperatures at equilibrium was calculated. This study shows how energy propagates in crysials and gives further understanding of how the coupling of phonons and magnons affect heat transport.

Estudamos neste trabalho as contribuições de 1-loop da eletrodinâmica quântica não-comutativa a altas temperaturas. Obtivemos as amplitudes de n-pontos por meio do método de diagramas de Feynman e mostramos que os mesmos resultados podem ser obtidos pelo método das equações de transporte de Boltzmann. Em paralelo estudamos as massas de blindagem que seguem do setor não-comutativo da teoria no limite estático, assim como a ação efetiva em 1-loop que gera todas as funções de n-pontos com índices espaciais. Também estudamos a quantização do campo de gauge no espaço não-comutativo pelo método do campo de fundo, obtendo uma generalização da base de ondas planas que se transforma covariantemente. / In this work we study the 1-loop contributions for noncommutative electrodynamics at high temperature. We calculate the n-point amplitudes by the Feynman diagrams method and we show that the same results can be obtained by the method of Boltzmann transport equations. We also study the screening mass derived from the noncommutative sector in the static limit case and the effective generating functional that determine all the amplitudes at one loop with spatial indices only. We quantize noncommutative QED by the background field gauge method and obtain a generalization of plane waves that transforms covariantly.

Herein we present the development of a fluorescence-enhanced, frequency-domain radiative transport reconstruction system designed for small animal optical tomography. The system includes a time-dependent data acquisition instrument, a radiative transport based forward model for prediction of time-dependent propagation of photons in small, non-diffuse volumes, and an algorithm which utilizes the forward model to reconstruct fluorescent yields from air/tissue boundary measurements. The major components of the instrumentation include a charge coupled device camera, an image intensifier, signal generators, and an optical switch. Time-dependent data were obtained in the frequency-domain using homodyne techniques on phantoms with 0.2% to 3% intralipid solutions. Through collaboration with Transpire, Inc., a fluorescence-enhanced, frequency-domain, radiative transport equation (RTE) solver was developed. This solver incorporates the discrete ordinates, source iteration with diffusion synthetic acceleration, and linear discontinuous finite element differencing schemes, to predict accurately the fluence of excitation and emission photons in diffuse and transport limited systems. Additional techniques such as the first scattered distributed source method and integral transport theory are used to model the numerical apertures of fiber optic sources and detectors. The accuracy of the RTE solver was validated against diffusion and Monte Carlo predictions and experimental data. The comparisons were favorable in both the diffusion and transport limits, with average errors of the RTE predictions, as compared to experimental data, typically being less than 8% in amplitude and 7% in phase. These average errors are similar to those of the Monte Carlo and diffusion predictions. Synthetic data from a virtual mouse were used to demonstrate the feasibility of using the RTE solver for reconstructing fluorescent heterogeneities in small, non-diffuse volumes. The current version of the RTE solver limits the reconstruction to one iteration and the reconstruction of marginally diffuse, frequency-domain experimental data using RTE was not successful. Multiple iterations using a diffusion solver successfully reconstructed the fluorescent heterogeneities, indicating that, when available, multiple iterations of the RTE based solver should also reconstruct the heterogeneities.

Temperature rise due to Joule heating of on-chip interconnects can severely affect performance and reliability of next generation microprocessors. Thermal predictions become difficult due to large number of features, and the impact of electron size effects on electrical and thermal transport. It is thus necessary to develop efficient numerical approaches, and accurate metal and dielectric thermal characterization techniques. In this research, analytical, numerical, and experimental techniques were developed to enable accurate and efficient predictions of interconnect temperature rise. A finite element based compact thermal model was developed to obtain temperature rise with fewer elements and acceptable accuracy. Temperature drop across the interconnect cross-section was ignored. The compact model performed better than standard finite element model in two and three-dimensional case studies, and the predictions for a real world structure agreed closely with experimentally measured temperature rise. A numerical solution was developed for electron transport based on the Boltzmann Transport Equation (BTE). This deterministic technique, based on the path integral solution of BTE within the relaxation time approximation, free electron model, and linear response, was applied to a constriction in a finite size thin metallic film. A correlation for effective conductance was obtained for different constriction sizes. The Atomic Force Microscope (AFM) based Scanning Joule Expansion Microscopy (SJEM) was used to develop a new technique to measure thermal conductivity of thin metallic films in the size effect regime. This technique does not require suspended metal structures, and thus preserves the original electron interface scattering characteristics. The thermal conductivities of 43 nm and 131 nm gold films were extracted to be 82 W/mK and 162 W/mK respectively. These measurements were close to Wiedemann-Franz Law predictions and are significantly smaller than the bulk value of 318 W/mK due to electron size effects. The technique can potentially be applied to interconnects in the sub-100 nm regime. A semi-analytical solution for the 3-omega method was derived to account for thermal conduction within the metallic heater. It is shown that significant errors can result when the previous solution is applied for anisotropic thermal conductivity measurements.

Herein we present the development of a fluorescence-enhanced, frequency-domain radiative transport reconstruction system designed for small animal optical tomography. The system includes a time-dependent data acquisition instrument, a radiative transport based forward model for prediction of time-dependent propagation of photons in small, non-diffuse volumes, and an algorithm which utilizes the forward model to reconstruct fluorescent yields from air/tissue boundary measurements. The major components of the instrumentation include a charge coupled device camera, an image intensifier, signal generators, and an optical switch. Time-dependent data were obtained in the frequency-domain using homodyne techniques on phantoms with 0.2% to 3% intralipid solutions. Through collaboration with Transpire, Inc., a fluorescence-enhanced, frequency-domain, radiative transport equation (RTE) solver was developed. This solver incorporates the discrete ordinates, source iteration with diffusion synthetic acceleration, and linear discontinuous finite element differencing schemes, to predict accurately the fluence of excitation and emission photons in diffuse and transport limited systems. Additional techniques such as the first scattered distributed source method and integral transport theory are used to model the numerical apertures of fiber optic sources and detectors. The accuracy of the RTE solver was validated against diffusion and Monte Carlo predictions and experimental data. The comparisons were favorable in both the diffusion and transport limits, with average errors of the RTE predictions, as compared to experimental data, typically being less than 8% in amplitude and 7% in phase. These average errors are similar to those of the Monte Carlo and diffusion predictions. Synthetic data from a virtual mouse were used to demonstrate the feasibility of using the RTE solver for reconstructing fluorescent heterogeneities in small, non-diffuse volumes. The current version of the RTE solver limits the reconstruction to one iteration and the reconstruction of marginally diffuse, frequency-domain experimental data using RTE was not successful. Multiple iterations using a diffusion solver successfully reconstructed the fluorescent heterogeneities, indicating that, when available, multiple iterations of the RTE based solver should also reconstruct the heterogeneities.