Fundação de Amparo a Pesquisa do Estado de Minas Gerais / This work presents the developing of analytical solutions based on Green's function to be applied in inverse problems techniques. Special attention is given to the problems that deals to unknown heat ux input such as the heat generation due to the friction in orthogonal machining processes or to the thermal properties measurement using optimization techniques. The great advantage of using Green's function is the ability of obtaining solutions of complex heat conduction problem that involves transient heat source or non homogenous boundary conditions as heat ux input or prescribed temperature varying with time and space. In this work, analytical solutions of one, two and three-dimensional transient heat conduction problems are presented. A practical application of using analytical solution in optimization problem is also presented. Any inverse or optimization technique has a basic and common characteristic: both of them need to solve the direct solution several times. This characteristic is the cause of the large time consumed. In heat conduction problem, the time consumed is, usually, due to the use of numerical solutions of multidimensional models with rened mesh. In this case, if analytical solutions are available the computational time can be reduced drastically. This study presents the development and application of a 3D-transient analytical solution based on Green's function to obtain thermal properties of solids materials. / Este trabalho dedica-se à obtenção e aplicação de soluções analíticas baseadas em funções de Green (FG) em técnicas de problemas inversos. Especialmente, o estudo é voltado a problemas decorrentes de fonte de calor desconhecidas como a geração de calor devido ao atrito presentes em processos de usinagem ortogonal e, principalmente, à medição de propriedade térmicas usando técnicas de otimização e estimativas de parâmetros. A grande força do uso das FG está na possibilidade de obtenção de soluções de problemas de condução de calor dos tipos mais variados e complexos, como por exemplo, problemas tridimensionais transientes, com termos de geração de calor transientes e não uniformes e que possam ainda estar sujeitos as condições de contorno não homogêneas variando com o tempo e o espaço. Apresentam-se neste trabalho a solução analítica de vários problemas de condução de calor unidimensionais, bidimensionais e tridimensionais transientes. Além do desenvolvimento destas soluções, apresentam-se também resultados em forma de grácos permitindo um melhor entendimento físico das soluções e a sua vericação. Dois problemas de otimização são abordados através da aplicação de soluções analíticas. Um dos problemas trata da estimativa de propriedades térmicas enquanto o outro se refere ao desenvolvimento do método de observadores dinâmicos usando funções de Green. O uso das FG na estimativa de parâmetros reduziu drasticamente o tempo computacional gasto enquanto no método dos observadores introduziu maior conança e estabilidade à técnica. / Mestre em Engenharia Mecânica

Descreve-se neste trabalho um estudo experimental da Emissão Eletrociclotrônica (EEC) no tokamak TCABR. Um radiômetro de EEC foi instalado, calibrado e utilizado para o estudo do plasma em descargas térmicas. O radiômetro é do tipo heteródino de varredura operando na faixa de 50-85 GHz, no modo extraordinário e na segunda harmônica. Determinou-se a temperatura de ruído do radiômetro e também sua estabilidade em amplitude e freqüência. Foi medida a largura de banda em freqüência do radiômetro (resolução espacial horizontal). A antena utilizada é do tipo gaussiana sendo que o raio da cintura do feixe gaussiano e a posição do foco foram experimentalmente determinados (W0 ~ 1 cm e d ~ 37 cm, respectivamente). A posição da cintura da antena foi posicionada próxima do centro geométrico do vaso. Foi feita a calibração absoluta do equipamento considerando-se os efeitos das janelas de diagnóstico (reflexão e absorção). O sistema pode operar em modo varredura, para a obtenção de perfis radiais de Te ou modo freqüência única onde se tem alta resolução temporal. As medidas da radiação EC foram feitas, na sua maioria, em descargas com densidade eletrônica média entre 1.10+19 m-3 e 1,5.1019 m-3 de forma a se ter acessibilidade da radiação EC e também minimizar-se a presença de elétrons fugitivos. Para ne > 1,5.1019 m-3 (com B0 = 1,14 T) verifica-se o corte parcial da radiação EC. Nesta condição, o corte na EEC foi utilizado na determinação do perfil radial da densidade eletrônica e aplicado em três diferentes situações: descargas com injeção adicional de gás, com a aplicação do eletrodo de polarização e em descargas com injeção de ondas de radiofreqüência na região das ondas de Alfvén para o TCABR. Usando um perfil parabólico típico para a densidade eletrônica, observou-se que, para descargas com injeção adicional de gás ou em descargas com a aplicação de ondas de radiofreqüência tem-se 0,85 < alfa < 1, e para descargas com aplicação do eletrodo de polarização obteve-se alfa ~ 0,6. Foram feitas observações simultâneas da temperatura eletrônica, a partir do sinal da EEC, e das oscilações de Mirnov (freqüência ~ 11,7 kHz) em descargas térmicas com q(r=0) > 1. Os resultados indicam a presença de um modo de ruptura dominante em rs ~ 9,5 cm com a largura da ilha magnética de W ~ 2,0-2,5 cm. Estes resultados experimentais obtidos estão em acordo com os resultados indicados por teorias de transporte na região das ilhas magnéticas. Observou-se também que a localização da ilha magnética coincide com uma região onde o perfil radial da temperatura de plasma é aproximadamente plano. Num outro cenário, com q(r=0) < 1, observaram-se oscilações dente de serra com período de ~ 0,44 ms, tempo de queda de ~ 0,12 ms, e raio de inversão em r ~ 4 cm. Neste tipo de descargas observou-se que, no perfil radial da amplitude das oscilações da Te, |DeltaTe|, devido à propagação dos pulsos dente de serra, apresentavam posições de mínimos e que estes coincidiam com as posições onde ocorrem patamares no perfil radial da temperatura eletrônica. Partindo destes resultados, juntamente com o perfil de q(r), dão-nos os modos racionais (m/n), posições (r) e larguras(W) para as ilhas magnéticas, presentes nestas descargas, a saber: m/n = 4/3 (r ~ 9 cm, W4/3 ~ 0,9 cm), m/n = 3/2 (r ~ 11,8 cm, W3/2 ~ 0,9 cm) e m/n = 2/1 (r ~ 13,7 cm, W2/1 ~ 1,4 cm). Este novo método, aqui proposto, permite a determinação direta da posição e da largura das ilhas magnéticas, em descargas onde a instabilidade dente de serra encontra-se presente.¶ / In this work, an experimental study of the Electron Cyclotron Emission (ECE) in the TCABR Tokamak, is described. An ECE sweeping heterodyne radiometer, operating in the 50-85 GHz frequency range, was installed, calibrated and used to detect ECE radiation in the second harmonic extraordinary mode from thermal plasma discharges. The noise temperature, amplitude and frequency stability of the radiometer were determined. The frequency bandwidth (horizontal space resolution) was measured. A Gaussian Antenna is used and the gaussian beam waist radius (W0 ~ 1 cm) and the focus position (d ~ 37 cm) were experimentally determined. The focus of the antenna was positioned close to the center of the vacuum vessel. The absolute calibration of the equipment was done and the effect of the diagnostic window was considered (reflections and absorptions). The system can operate in sweeping mode, in order to obtain the radial electron temperature profiles, and also in the single frequency mode to obtain temporal electron temperature profiles with high time resolution. Due to the TCABR accessibility conditions and also to avoid runaway electrons, most of the ECE measurements were obtained in discharges with line electron density between 1.0x10+19 m-3 and 1.5x1019 m-3. For ne > 1.5x1019 m-3 (with B0 = 1.14 T) the cutoff in the ECE radiation was observed. The ECE cutoff was used to determine the radial profile of the electron density and applied to three different situations: discharges with additional gas puffing, with the application of a biasing electrode and in discharges with radio-frequency wave injection. Using a parabolic profile it was observed that, 0.85 < alfa < 1.0 for discharges with additional gas injection or with RF injection, and alfa ~ 0.6 for the electrode biasing experiments. The electron temperature profiles and Mirnov oscillations (f ~ 11.7 kHz) were simultaneously measured in discharges with q (r=0) > 1. The position and the width of the magnetic island were therefore calculated. The results indicate the presence of a dominant tearing mode in rs ~ 9.5 cm and the magnetic island width W ~ 2.0-2.5 cm. These experimental results are in agreement with the theoretical results foreseen by models of heat transport in the presence of magnetic islands. It was also observed that, the position of the magnetic island coincided with the region where the temperature radial profile is approximately flat. In another plasma scenario, with q(r=0) < 1, sawteeth oscillations with a period ~ 0.44 ms, crash time ~ 0.12 ms, inversion radius r ~ 4 cm, were measured. Peculiarities in the Te radial profile associated with the amplitude of Te oscillations, |DeltaTe|, due to the sawtooth instability, were observed. It was verified that the minimum values of the |DeltaTe| profile coincided with the region where the temperature radial profile was approximately flat. These results together with the q(r) profile yielded the following mode numbers (m/n), positions (r) and widths (W) of the magnetic islands: m/n = 4/3 (r ~ 9 cm, W4/3 ~ 0.9 cm), m/n = 3/2 (r ~ 11.8 cm, W3/2 ~ 0.9 cm) and m/n = 2/1 (r ~ 13.7 cm, W2/1; ~ 1.4 cm). A novel method to determine the position and width of the magnetic islands, in discharges with the presence of sawtooth instability, is presented here.

A têmpera dos aços envolve a austenitização de uma peça seguida por um resfriamento rápido para promover a formação de microestrutura martensítica. É necessário avaliar os meios de têmpera para manter o processo de têmpera sob controle. Os parâmetros mais importantes no processo de resfriamento são o coeficiente de transferência de calor e/ou o fluxo de calor entre o meio de têmpera e a peça a ser resfriada. Um dos métodos de se avaliar os meios de têmpera (meios de resfriamento) e saber o que está acontecendo dentro da peça durante o resfriamento do ponto de vista térmico é o problema inverso de condução de calor. O problema inverso de condução de calor consiste na determinação de parâmetros como fluxo de calor, taxa de resfriamento e temperatura em qualquer posição através da peça, assim como o coeficiente de transferência de calor. Esses parâmetros são obtidos a partir de medições de temperatura em um ou mais pontos dentro da peça. O escopo deste trabalho foi desenvolver um software baseado no problema inverso condução de calor para avaliar meios de resfriamento para têmpera. A validação deste código foi feita usando água, óleo de soja, óleo mineral e solução aquosa de NaNO3. / Steels quenching involves part austenitization followed by a fast cooling to promote martensitic microstructure formation. It is necessary to evaluate quenchants in order to keep the quenching process under control. The most important cooling process parameters are the heat transfer coefficient and/or the heat flux between the quenchant and the part to be cooled. One of the methods to evaluate quenchants (cooling media) and to know what is happening inside the part during the cooling in the thermal point of view is the inverse heat conduction problem. The inverse heat conduction problem consists in the determination of parameters like heat flux, cooling rate and temperature in any position across the part, as well as the heat transfer coefficient. These parameters are obtained from temperature measurements in one or more points inside the part. The scope of this work was to develop a software based in the inverse heat conduction problem in order to evaluate quenchants for quenching. The validation of this code was made using water, soybean oil, mineral oil and NaNO3 aqueous solution.

Em decorrência ao grande crescimento e evolução dos processos de usinagem e a demanda para adequação ambiental, novos fluidos de corte tem sido aplicados. Uma comprovação de sua eficiência em refrigerar a peça, e a ferramenta melhorando a produtividade do processo ainda é necessária. O presente trabalho propõe o estudo e o desenvolvimento de um sistema para avaliar a eficácia de fluidos de corte em operações de usinagem. Inicia-se com uma abordagem matemática da modelagem do processo de dissipação de calor em operações de usinagem. Em seguida prossegue-se com uma investigação de diferentes maneiras de solução do modelo proposto. Experimentos práticos foram realizados no laboratório de Otimização de Processos de Fabricação - OPF. A partir dos dados obtidos foi realizada uma análise assintótica das equações diferencias parciais que governam o modelo. Finalizando, o modelo selecionado foi aplicado no fresamento do aço AISI 4340 endurecido usinado sob alta velocidade. / Due to the rapid growth and development of machining processes there has been a demand for environmental sustainability and news cutting fluids have been applied. A reliable assessment of their efficiency in cooling the workpiece, tools and improving productivity is still a requirement. The present thesis presents a theoretical study and a proposal of a system to assess the effectiveness of cutting fluids applied to machining operation. It begins using a mathematical approach to model the heat propagation during machining operations. Then, it continues with an investigation into different ways to solve the proposed theorical model. Machining experiments using realistic cutting operations were also conducted at the Laboratory for Optimization of Manufacturing Processes - OPF. From the experimental data, was carried out an asymptotic analysis of partial differential equations, which govern the mathematical model. Finally, the selected model will be applied to a milling operation using High Speed Machining (HSM) technique on hardened steel AISI 4340.

Abstract This thesis considers two related problems where heat conduction is accompanied by phase transformation during the cooling of carbon steels – phenomena which are fundamental to modern thermomechanical treatment processes. In the first problem, a non-linear heat equation formulation is described which includes linkage between irreversible diffusive and diffusionless phase transformation processes and thermophysical properties. A family of numerical schemes using finite difference methods with diagonally implicit Runge-Kutta method integrators for solving this formulation is present. Sample calculations using these schemes are presented for a mild steel cooled under range of industrially relevant heat transfer conditions. These calculations illustrate the need for careful scheme design and solver selection when coupled heat conduction and microstructure evolution equations become non-linear and stiff. The second section of the thesis extends this heat conduction formulation into the realm of inverse analysis. The problem of temperature reconstruction and boundary condition estimation using temperature measurements obtained thermocouples embedded into laboratory samples undergoing phase transformation is considered. A solution method based on iterative regularization is described for solving the resulting ill-posed problem. An analysis of extremely high rate cooling experiments made on a pilot-plant descaling unit using the inverse method is presented. This analysis highlights some of the practical issues associated with embedded thermocouple temperature measurements made in this fashion. / Tiivistelmä Väitöstyössä tutkitaan kahta ongelmaa liittyen hiiliteräksen termomekaanisen käsittelyn numeeriseen mallintamiseen. Työssä tarkastellaan teräksessä tapahtuvaa lämmönsiirtoa ja faasimuutoksia jäähdytyksen aikana, eli ensisijaisen tärkeitä ilmiöitä kehittynyttä teräksen valmistusta ja prosessointia ajatellen. Ensimmäisenä ongelmana tutkitaan epälineaarisen energiayhtälön muodostaminen huomioiden teräksen termofysikaaliset materiaaliominaisuudet, diffuusion kontrolloimat ja diffuusiosta riippumattomat irreversiibelit faasimuutokset. Lisäksi huomioidaan näiden väliset kytkennät. Yhtälöt ratkaistaan numeerisesti ja käytetyt menetelmät esitellään differenssimenetelmien ja diagonaalisesti implisiittisten Runge-Kutta-menetelmien osalta. Väitöstyössä näiden käyttöä havainnollistetaan simuloimalla niukkahiilisen teräksen käyttäytymistä teollisia olosuhteita vastaavan jäähdytyksen aikana. Laskentatulokset osoittavat ratkaisumenetelmän suunnittelun ja valinnan tärkeyden erityisesti silloin, kun lämmönjohtuminen, mikrorakenteen kehittyminen ja termofysikaaliset materiaaliominaisuudet muuttavat ratkaistavan ongelman epälineaariseksi ja jäykäksi. Toisena ongelmana tutkitaan edellä esitetyn lämmönsiirtomallin käyttöä osanainversioanalyysiä. Laboratoriokokeiden, termopareilla suoritettujen lämpötilamittausten, työssä kehitetyn lämmönsiirtomallin ja suoritetun inversioanalyysin avulla rekonstruoidaan teräskappaleiden lämpötila- ja faasimuutoskäyttäytymistä sekä estimoidaan mallin reunaehtoja. Näin luotu inversio-ongelma on kuitenkin matemaattisesti tarkasteltuna ns. huonosti asetettu ongelma, ja sen ratkaisemiseksi käytetään iteratiiviseen säännöllistämiseen perustuvaa menetelmää. Väitöstyön inversioanalyysiä havainnollistetaan pilot-mittakaavan kokeiden avulla, joissa hilsepesuria käyttäen koekappaleen jäähtymisnopeus saadaan erittäin korkeaksi. Tulokset nostavat esille inversio-analyysiin liittyviä ongelmia ja rajoitteita nopeaan jäähtymiseen sekä lämpötilamittauksiin liittyen.

Gypsum board assemblies are now widely used in buildings, as fire resistant walls or ceilings, to provide passive fire protection. The fire resistance of such systems is fundamentally due to the desirable thermal properties of gypsum. Yet there is wide variability in reported values of thermal properties of gypsum at high temperatures and a lack of understanding of its integrity in fire. To evaluate the fire protection performance of gypsum board assemblies, it is essential to quantify its thermal properties and obtain information on its mechanical properties at high temperatures. Gypsum boards shrink and crack at high temperatures, and this leads to collapse of parts of the gypsum boards in fire. Fall-off of gypsum in fire affects the fire resistance of the assembly considerably, and cannot be overlooked when evaluating the fire resistance of gypsum board assemblies. The current research proposes a model to define the temperature-dependent thermal properties of gypsum boards at high temperatures. Thermal conductivity of gypsum is considered as the most influential parameter in conduction of heat through gypsum, and a hybrid numerical-experimental method is presented for extracting thermal conductivity of various gypsum board products at elevated temperatures. This method incorporates a validated one-dimensional Finite Difference heat conduction program and high temperature test results on small samples of gypsum boards. Moreover, high temperature mechanical tests have been performed on different gypsum board products; thermal shrinkage, strength and stress-strain relationships of gypsum products at elevated temperatures are extracted for use in numerical mechanical analysis. To simulate the structural performance of gypsum boards in fire, a two-dimensional Finite Element model has been developed in ABAQUS. This model successfully predicts the complete opening of a through-thickness crack in gypsum, and is validated against medium-scale fire tests designed and conducted as part of this research. Gypsum fall-off in fire is a complex phenomenon; however, it is believed that delaying the formation of through-thickness cracking will delay falling off of gypsum in fire, and hence improve the fire resistance of gypsum board assemblies. Finally, a study has been performed on the effects of various detailing parameters in gypsum board wall assemblies, and recommendations are offered for improving the fire resistance of such systems.

<p>The study of Surface Air Cooled Oil Coolers (SACOC) is motivated by the need for new cooling concepts for compact machinery designs with high thermal load. Installing finned heat exchangers in the bypass duct of a turbofan engine provides an additional cooling source having transonic flow as a heat sink. The characterization of the heat transfer and the aerodynamics of the design are essential to minimize the impact on the overall efficiency of the engine. In the present study, the SACOC is studied numerically and experimentally. Two geometries are tested in a high-speed linear wind tunnel where measurements are taken with multiple sensors and optical techniques. For the heat transfer characterization, an Inverse Heat Conduction Methodology (IHCM) based on a Levenberg-Marquardt Algorithm is developed. The experimental results are matched to numerical simulations using a Reynolds Averaged Navier-Stokes (RANS) solver. Finally, a multi-objective optimization algorithm is coupled <a>with the RANS solver</a> to explore new geometries that maximize the heat transfer and minimize the pressure drop across the studied domain. The 400 profiles generated allow for the identification of the features that have a higher influence on the performance of the fins and six profiles that present large improvements are chosen for further analysis.</p>

The master's thesis deals with possible ways of accelerating numerical computations, which are present in problems related to heat conduction in solids. The thesis summarizes basic characteristics of heat transfer phenomena with emphasis on heat conduction. Theoretical principles of control volume method are utilized to convert a direct heat conduction problem into a sparse linear system. Relevant fundamentals from the field of inverse heat conduction problems are presented with reference to intensive computations of direct problems of such kind. Numerical methods which are well-suited to find a solution of direct heat conduction problems are described. Remarks on practical implementation of time-efficient computations are made in relation with a two-dimensional heat conduction model. The results are compared and discussed with respect to obtained computational time for several tested methods.

Nowadays numerical simulations are used to optimize manufacturing process. These numerical simulations need a large amount of input parameters and some of these parameters have not been sufficiently described. One of this parameter is thermal contact resistance, which is not sufficiently described for high temperatures and high contact pressure. This work describes experimental measuring of thermal contact resistance and how to determine thermal contact conductance which can be used as a boundary condition for numerical simulations. An Experimental device was built in Heat Transfer and Fluid Flow Laboratory, part of Brno University of Technology, and can be used for measuring thermal contact conductance in various conditions, such as contact pressure, initial temperatures of bodies in contact, type of material, surface roughness, presence of scales on the contact surface. Bodies in contact are marked as a sensor and a sample, both are embedded with thermocouples. The temperature history of bodies during an experiment is measured by thermocouples and then used to estimate time dependent values of thermal contact conductance by an inverse heat conduction calculation. Results are summarized and the dependence of thermal contact conductance in various conditions is described.

Basierend auf dem Reaktordynamikcode DYN3D für LWR, wurde die Codeversion DYN3D-HTR für das Blockkonzept eines graphit-moderierten, helium-gekühlten Hochtemperaturreaktors entwickelt. Diese Entwicklung umfasst die: • methodische Weiterentwicklung der 3D stationären Neutronenflussberechnung für hexagonale Geometrie (HTR-Brennelement-Blöcke), • Generierung von Wirkungsquerschnittsdaten unter Berücksichtigung der doppelten Heterogenität, • Modellierung der Wärmeleitung und des Wärmetransports in der Graphitmatrix. Die nodale SP3-Neutronentransport-Methode in DYN3D wurde auf hexagonale Brennelementgeometrie erweitert. Es wird eine Unterteilung der Hexagone in Dreiecke vorgenommen, so dass die Verfeinerung hexagonaler Strukturen untersucht werden kann. Die Verifikation erfolgte durch Vergleiche mit Monte-Carlo-Referenzlösungen. Für die Behandlung der doppelten Heterogenität der Brennelementstruktur bei Homogenisierung der Wirkungsquerschnitte wurden neue Methoden entwickelt. Zum einen wurde ein zweistufiges Homogenisierungsverfahren basierend auf der Methode der sog. Reactivity Equivalent Transformation (RPT) weiterentwickelt. Zum anderen ermöglichte die Verfügbarkeit des neuen Monte-Carlo-Codes SERPENT die Anwendung eines einstufigen Verfahrens, wobei die 3D heterogenen Strukturen in einem Rechenschritt konsistent erfasst werden können. Weiterhin wur-de in DYN3D ein 3D Wärmeleitungsmodell implementiert, das den radialen und axialen Wärmetransport in der Graphitmatrix beschreiben kann. DYN3D-HTR wurde schließlich anhand der Testfälle für Reaktivitätstransienten erprobt. Die Verifikation erfolgte durch Vergleich zwischen 3D und 1D Berechnung der Wärmeleitung. Schließlich wurde DYN3D mit dem CFD-Code ANSYS-CFX gekoppelt, um auch dreidimensionale Strömungen in Reaktorkernen berechnen zu können. Der Kern wird als poröser Körper modelliert. Die Kopplung wurde an anhand von 2 Testbeispielen, dem Auswurf eines Steuerstabes und einer lokalen Strömungsblockade in einem Brennelement, erprobt.