Orientadores: José Roberto Nunhez, Everton Moraes Matos / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Química / Made available in DSpace on 2018-08-21T22:56:39Z (GMT). No. of bitstreams: 1 Fontoura_DienerVolpinRibeiro_D.pdf: 11658919 bytes, checksum: 6a2be1fd48301240f5f4b18c84757db1 (MD5) Previous issue date: 2013 / Resumo: O escoamento de fluidos é, sem dúvida, de grande importância na indústria, especialmente no transporte de fluidos entre as unidades de operação. Sistemas multifásicos são bastante comuns, e em muitos casos, também ocorrem processos de transferência de massa e energia, como é o caso dos fornos de pré-aquecimento na indústria petroquímica. O escoamento gás-líquido nessas linhas é muitas vezes complexos, pois durante a vaporização da carga ocorre também o craqueamento térmico do petróleo. É comum nestas operações a formação de coque no interior do tubo, o que é muito indesejável. Para entender as condições nas quais esta formação de coque é minimizada, ou aumentada, foi proposto um modelo uidodinâmico computacional para simular o escoamento bifásico gás - liquido do petróleo no interior desses tubos. O modelo foi implementado na plataforma OpenFOAM, ao qual foram acrescidas novas rotinas para a estimativa das temperaturas e concentrações através das equações de conservação de massa e energia. O modelo k - epsilon foi utilizado para descrever a turbulência e dois modelos de vaporização foram utilizado para caracterizar a mudança de fase. Uma formulação não conservativa foi adotada na escrita das equações do modelo para maior estabilidade numérica em altas frações volumétricas. Foi também implementada uma rede cinética dependente da temperatura para descrever o craqueamento térmico. Através do modelo foi possível simular o escoamento tridimensional de petróleo no interior de um tubo com as dimensões da planta obtendo como resultado os perfis de velocidades, temperaturas e concentrações das fases líquida e gasosa / Abstract: Fluid flow is of great importance in the industry, especially for its transport between the operating units. Multiphase systems are very frequent. In many cases, mass and energy transfer processes, such as the case of preheating furnaces in petrochemical industry, are also observed. The gas-liquid flow in these lines is often complex, because during the vaporization of the charge it also occurs the petroleum thermal cracking. It is common in these operations the very undesirable formation of coke inside the tube. With the aim of understanding under which conditions the formation of coke is minimized or increased it was proposed a computational fluid dynamic model for simulating the petroleum gas-liquid two-phase flow inside of these tubes. The model was implemented on the OpenFOAM software, to which new routines for the calculation of temperatures and concentrations using the equations of conservation of mass and energy were added. The model k - epsilon was used to describe the turbulence and two vaporization models were used to characterize the phase change. A non-conservative formulation was adopted for describing the equations of the model in order to obtain numerical stability at high volumetric fractions. It was also implemented a temperature dependent kinetic net to describe the thermal cracking. With this model it was possible to simulate the three-dimensional flow of petroleum inside a tube with real industrial dimensions as a result of the gas and liquid phase's profiles of velocities, temperatures and concentrations / Doutorado / Desenvolvimento de Processos Químicos / Doutor em Engenharia Química

Orientadores: Sérgio Tonini Button, José Divo Bressan / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica / Made available in DSpace on 2018-08-21T04:08:51Z (GMT). No. of bitstreams: 1 Martins_MarceloMatos_D.pdf: 11233728 bytes, checksum: 163e9bff5c80ef1c025e8c1083bed472 (MD5) Previous issue date: 2012 / Resumo: A simulação numérica computacional é nos dia de hoje frequentemente aplicada na elaboração de projetos ou análise dos processos de conformação plástica dos metais. A extrusão de metais é um dos principais processos de conformação plástica e largamente aplicado na fabricação de produtos e peças na indústria metal-mecânica. Tradicionalmente, essas análises são feitas utilizando o Método dos Elementos Finitos. Entretanto, há um aumento no interesse dos pesquisadores na utilização do Método dos Volumes Finitos para este fim. A literatura sugere que o escoamento na extrusão de metais pode ser analisado pela formulação do escoamento plástico (flow Formulation). No qual, pode-se assumir como o escoamento de um fluido incompressível e viscoso. Essa hipótese pode ser assumida já que o processo de extrusão é um processo isocórico. O método MacCormack é geralmente aplicado para simular os escoamentos de fluidos compressíveis pelo Método do Volumes Finitos. No escoamento de um fluido incompressível ou no escoamento de metal não existe uma equação para a evolução da variável pressão, sendo necessário a utilização de um método de acoplamento entre a pressão e a velocidade. Este trabalho trata da apresentação de um novo esquema numérico para a determinação de informações sobre o escoamento de um fluido incompressível e viscoso e sobre o escoamento de metal em um processo de extrusão direta, ambos em regime permanente. As equações governantes foram discretizadas pelo Método dos Volume Finitos através do Método de MacCormack explícito para uma malha estruturada e co-localizada. O acoplamento entre a pressão e a velocidade foi feita pelo método SIMPLE. O novo esquema numérico foi aplicado em escoamentos incompressíveis e viscosos para a glicerina e em escoamento de metais em processos de extrusão direta para o chumbo e uma liga de alumínio. O escoamento da glicerina foi avaliado para o caso entre placas paralelas e em dutos circulares sob condição axissimétrica e obtiveram boa concordância em relação ao resultados analíticos. Os campos de velocidades obtidos para a extrusão de metal alcançaram rápida convergência, em torno de 20000 iterações, essa quantidade de iterações foi inferior a quantidade que a glicerina necessitou. Para todos os materiais analisados os resultados numéricos tiveram boa concordância em comparação com resultados analíticos e experimentais obtidas da literatura. O método MacCormack produziu resultados coerentes para o escoamento da glicerina e dos metais sem a necessidade da adição de viscosidade artificial, como sugere a sua definição. Portanto, os resultados numéricos sugerem que o método MacCormack com o SIMPLE pode ser aplicado na resolução de escoamentos de fluidos incompressíveis e na conformação de metais além da sua tradicional aplicação na resolução de escoamentos compressíveis / Abstract: Computational numerical simulation is nowadays largely applied in the design and analysis of metal forming process. Extrusion of metals is one main forming process largely applied in the manufacturing of metallic products or parts. Historically, the Finite Element Method has been applied for decades in extrusion analysis. However, recently in the academy, there is a trend to use Finite Volume Method: literature suggests that metal flow by extrusion can be analysed by the flow formulation. Thus, metal flow can be modelled such us an incompressible viscous fluid. This hypothesis can be assumed because extrusion process is an isochoric process. The MacCormack Method is commonly used to simulate compressible fluid flow by the finite volume method. However, metal extrusion and incompressible fluid flow do not present state equations for the evolution of pressure, and therefore, a velocity-pressure coupling method is necessary to obtain a consistent velocity and pressure fields. Present work proposes a new numerical scheme to obtain information about both incompressible viscous fluid flow and metal flow in the extrusion process, in steady state. The governing equations were discretized by Finite Volume Method, using the Explicit MacCormack Method to structured and collocated mesh. The SIMPLE Method was applied to attain pressure-velocity coupling. These new numerical scheme was applied to incompressible viscous fluid flow of glycerine and forward extrusion process of lead and an aluminium alloy. The numerical results for glicerine fluid flow for parallel plates and axisymmetric flow in circular tube cases had quite good agreement in relation to the analytical solutions. The incompressible metal extrusion velocity fields achieved faster convergence than for liquid glycerine after 20.000 iterations and a good agreement with analytical and experimental results obtained from literature. The MacCormack Method applied for both glycerine and metals produced consistent results without the need of artificial viscosity as employed by the compressible flow simulation approaches. Hence, the present numerical results also suggest that MacCormack Method and SIMPLE can be applied in the solution of incompressible fluid flow and metal forming processes in adition to the traditional application for compressible fluid flow / Doutorado / Materiais e Processos de Fabricação / Doutor em Engenharia Mecânica

Le schéma Marker-And-Cell (MAC) est un schéma de discrétisation des équations aux dérivées partielles sur maillages cartésiens, très connu en mécanique des fluides. Nous nous intéressons ici à son analyse mathématique dans le cadre des écoulements incompressibles sur des maillages cartésiens non-uniformes en dimension 2 ou 3. Dans un premier temps nous discrétisons les équations de Navier-Stokes pour un écoulement incompressible stationnaire; nous établissons des estimations a priori sur les suites de vitesses et pressions approchées qui permettent d’une part d'établir l’existence d’une solution au schéma, et d’obtenir la compacité de ces suites lorsque le pas d’espace tend vers 0. Nous montrons alors la convergence de ces suites (à une sous-suite près) vers une solution faible du problème continu, ce qui nécessite une analyse fine du terme de convection non linéaire. Nous nous intéressons ensuite aux équations de Navier-Stokes en régime instationnaire avec une discrétisation en temps implicite. Nous démontrons que le schéma préserve les propriétés de stabilité du problème continu et obtenons ainsi l’existence d’une solution au schéma. Puis, grâce à des techniques de compacité et en passant à la limite dans le schéma, nous démontrons qu’une suite de vitesses approchées converge. Si l’on se restreint au problème de Stokes, et en supposant de plus que la condition initiale de la vitesse est dans H 1 , nous obtenons une estimation sur la pression qui permet de montrer la convergence forte des pressions approchées. Enfin nous étendons l’analyse aux écoulements incompressibles à masse volumique variable. On montre la convergence du schéma. / The Marker-And-Cell (MAC) scheme is a discretization scheme for partial derivative equations on Cartesian meshes, which is very well known in fluid mechanics. Here we are concerned with its mathematical analysis in the case of incompressible flows on two or three dimensional non-uniform Cartesian grids. We first discretize the steady-state incompressible Navier-Stokes equations. We show somea priori estimates that allow to show the existence of a solution to the scheme and some compactness and consistency results. By a passage to the limit on the scheme, we show that the approximate solutions obtained with the MAC scheme converge (up to a subsequence) to a weak solution of the Navier-Stokes equations, thanks to a careful analysis of the nonlinear convection term. Then, we analyze the convergence of the unsteady-case Navier-Stokes equations. The algorithm is implicit in time. We first show that the scheme preserves the stability properties of the continuous problem, which yields, the existence of a solution. Then, invoking compactness arguments and passing to the limit in the scheme, we prove that any sequence of solutions (obtained with a sequence of discretizations the space and time step of which tend to zero) converges up to the extraction of a subsequence to a weak solution of the continuous problem. If we restrict ourselves to the Stokes equations and assume that the initial velocity belongs to H 1, then we obtain estimates on the pressure and prove the convergence of the sequences of approximate pressures. Finally, we extend the analysis of the scheme to incompressible variable density flows. we show the convergence of the scheme.

Ce travail traite de la modélisation des plasmas de fusion qui est ici abordée à l'aide d'un modèle Euler bi-températures et du modèle de la magnétohydrodynamique (MHD) idéale et résistive. Ces modèles sont tout d'abord établis à partir des équations de la MHD bi-fluide et nous montrons qu'ils correspondent à des régimes asymptotiques différents pour des plasmas faiblement ou fortement magnétisés. Nous décrivons ensuite les méthodes de volumes finis pour des maillages structurés et non-structurés qui ont été utilisées pour approcher les solutions de ces modèles. Pour les trois modèles mathématiques étudiés dans cette thèse, les méthodes numériques reposent sur des schémas de relaxation. Afin d'appliquer ces méthodes aux problèmes de fusion par confinement magnétique, nous décrivons comment modifier les méthodes de volumes finis pour les appliquer à des problèmes formulés en coordonnées cylindriques tout en gardant une formulation conservative forte des équations. Enfin nous étudions une stratégie pour maintenir la contrainte de divergence nulle du champ magnétique qui apparait dans les modèles MHD. Une série de cas tests numériques pour les trois modèles est présentée pour différentes géométries afin de valider les méthodes numériques proposées. / This work deals with the modeling of fusion plasma which is discussed by using a bi-temperature Euler model and the ideal and resistive magnetohydrodynamic (MHD) ones. First, these models are established from the bi-fluid MHD equations and we show that they correspond to different asymptotic regimes for lowly or highly magnetized plasma. Next, we describe the finite volume methods for structured and non-structured meshes which have been used to approximate the solution of these models. For the three mathematical models studied in this thesis, the numerical methods are based on relaxation schemes. In order to apply those methods to magnetic confinement fusion problems, we explain how to modify the finite volume methods to apply it to problem given in cylindrical coordinates while keeping a strong conservative formulation. Finally, a strategy dealing with the divergence-free constraint of the magnetic field is studied. A set of numerical tests for the three models is presented for different geometries to validate the proposed numerical methods.

This thesis deals with the development of a new adaptive algorithm for three-dimensional fluid flows based on a residual error estimator. The residual, known as the R –parameter has been successfully extended to three dimensions using a novel approach for arbitrary grid topologies. The computation of the residual error estimator in three dimensions is based on a least-squares based reconstruction and the order of accuracy of the latter is critical in obtaining a consistent estimate of the error. The R –parameter can become inconsistent on three–dimensional meshes depending on the grid quality. A Zero Mean Polynomial(ZMP) which is k–exact, and which preserves the mean has been used in this thesis to overcome the problem. It is demonstrated that the ZMP approach leads to a more accurate estimation of solution derivatives as opposed to the conventional polynomial based least-squares method. The ZMP approach is employed to compute the R –parameter which is the n used to derive the criteria for refinement and derefinement. Studies on three different complex test problems involving inviscid, laminar and turbulent flows demonstrate that the new adaptive algorithm is capable of detecting the sources of error efficiently and lead to accurate results independent of the grid topology.

This Ph.D. thesis aims to develop numerical models for two-dimensional and three-dimensional shallow water systems over mobile beds. In order to accomplish the goal of this dissertation, the following sub-projects are defined and completed. 1: The first sub-project consists in developing a robust two-dimensional coupled numerical model based on an unstructured mesh, which can simulate rapidly varying flows over an erodible bed involving wet–dry fronts that is a complex yet practically important problem. In this task, the central-upwind scheme is extended to simulation of bed erosion and sediment transport, a modified shallow water system is adopted to improve the model, a wetting and drying scheme is proposed for tracking wet-dry interfaces and stably predict the bed erosion near wet-dry area. The shallow water, sediment transport and bed evolution equations are coupled in the governing system. The proposed model can efficiently track wetting and drying interfaces while preserving stability in simulating the bed erosion near the wet-dry fronts. The additional terms in shallow water equations can improve the accuracy of the simulation when intense sediment-exchange exists; the central-upwind method adopted in the current study shows great accuracy and efficiency compared with other popular solvers; the developed model is robust, efficient and accurate in dealing with various challenging cases. 2: The second sub-project consists in developing a novel numerical scheme for a coupled two-dimensional hyperbolic system consisting of the shallow water equations with friction terms coupled with the equations modeling the sediment transport and bed evolution. The resulting 5*5 hyperbolic system of balance laws is numerically solved using a Godunov-type central-upwind scheme on a triangular grid. A spatially second-order and temporally third-order central-upwind scheme has been derived to discretize the conservative hyperbolic sub-system. However, such schemes need a correct evaluation of local wave speeds to avoid instabilities. To address such an issue, a mathematical result by the Lagrange theorem is used in the proposed scheme. Consequently, a computationally expensive process of finding all of the eigenvalues of the Jacobian matrices is avoided: The upper/lower bounds on the largest/smallest local speeds of propagation are estimated using the Lagrange theorem. In addition, a special discretization of the bed-slope term is proposed to guarantee the well-balanced property of the designed scheme. 3: The third sub-project consists in designing a novel scheme to estimate bed-load fluxes which can produce more accurate results than the previously reported coupled model. Using a pair of local wave speeds different from those used for the flow, a novel wave estimator in conjunction with the central upwind method is proposed and successfully applied to the coupled water-sediment system involving a rapid bed-erosion process. It was demonstrated that, in comparison with the decoupled model, applying the proposed novel scheme to approximate the bed-load fluxes can successfully avoid the numerical oscillations caused by simple and less stable schemes, e.g. simple upwind methods; in comparison with the coupled model using same flux-estimator for both hydrodynamic and morphological systems, the proposed numerical scheme successfully prevents excessive numerical diffusion for prediction of bed evolution. Consequently, the proposed scheme has advantages in terms of accuracy which are shown in several numerical tests. In addition, analytical expressions have been provided for calculating the eigenvalues of the coupled shallow-water-Exner system, which greatly enhances the efficiency of the proposed method. 4: The fourth sub-project consists in developing a three-dimensional numerical model for the simulation of unsteady non-hydrostatic shallow water flows on unstructured grids using the finite volume method. The free surface variations are modeled by a characteristics-based scheme which simulates sub- and super-critical flows. Three-dimensional velocity components are considered in a collocated arrangement with a sigma coordinate system. A special treatment of the pressure term is developed to avoid the water surface oscillations. Convective and diffusive terms are approximated explicitly, and an implicit discretization is used for the pressure term. The unstructured grid in the horizontal direction and the sigma coordinate in the vertical direction facilitate the use of the model in complicated geometries. 5: The fifth sub-project consists in developing a well-balanced three-dimensional shallow water model which is able to simulate shock waves over dry bed. Due to the hydrostatic simplification of the vertical momentum equation, the governing system of equations is not hyperbolic and can not be solved using standard hyperbolic solvers. That is, one can not use a high-order Godunov-type scheme to compute all fluxes through cell-interfaces. This may cause the model to fail in simulations of some unsteady-flows with discontinuities, e.g., dam-break flows and floods. To overcome this difficulty, a novel numerical scheme for the three-dimensional shallow water equations is proposed using a relaxation approach in order to convert the system to a hyperbolic one. Thus, a high-order Godunov-type central-upwind scheme based on the finite volume method can be applied to approximate the numerical fluxes. The proposed model can also preserve the ``lake at rest'' state and positivity of water depth over irregular bottom topographies based on special reconstruction of the corresponding parameters. 6: The sixth sub-project consists in extending the result of the fifth sub-project to development of a three-dimensional numerical model for shallow water flows over mobile beds, which is able to simulate morphological evolutions under shock waves, e.g. dam-break flows. The hydrodynamic model solves the three-dimensional shallow water equations using a finite volume method on prismatic cells in sigma coordinates based on the scheme prposed in sub-project 5. The morphodynamic model solves an Exner equation consisting of bed-load sediment transportation. The performance of the proposed model has been demonstrated by several laboratory experiments of dam-break flows over mobile beds.

Submitted by Fabio Sobreira Campos da Costa (fabio.sobreira@ufpe.br) on 2017-07-14T12:28:59Z No. of bitstreams: 2 license_rdf: 811 bytes, checksum: e39d27027a6cc9cb039ad269a5db8e34 (MD5) Dissertacao Bautista Nilson.pdf: 11338318 bytes, checksum: ae22c70eb1719f066a5eeb3de436c953 (MD5) / Made available in DSpace on 2017-07-14T12:28:59Z (GMT). No. of bitstreams: 2 license_rdf: 811 bytes, checksum: e39d27027a6cc9cb039ad269a5db8e34 (MD5) Dissertacao Bautista Nilson.pdf: 11338318 bytes, checksum: ae22c70eb1719f066a5eeb3de436c953 (MD5) Previous issue date: 2016-01-26 / CNPQ / A modelagem e a simulação numérica do transporte de solutos, como por exemplo traçadores, em meios porosos heterogêneos e anisotrópicos, tais como aquíferos e reservatórios de petróleo constituem-se num grande desafio de natureza matemática e numérica. A modelagem de falhas selantes, canais, poços inclinados, pinchouts e outras características complexas demanda o uso de malhas não-estruturadas e não-ortogonais, capazes de se adaptar naturalmente ao domínio em estudo. Os pacotes computacionais utilizados comumente na indústria do petróleo, na sua grande maioria, se baseiam no Método das Diferenças Finitas com Aproximação de Fluxo por Dois Pontos (Two-Point Flux Approximation - TPFA) e no Método de Ponderação à Montante de Primeira Ordem (First Order Upwind Method - FOU), devido a sua facilidade de implementação e sua eficiência computacional. Infelizmente, os métodos TPFA são incapazes de produzir soluções convergentes em malhas não-ortogonais ou para tensores de dispersão ou permeabilidades completos e os métodos FOU produzem soluções com difusão numérica excessiva, exigindo malhas demasiadamente refinadas para obtermos soluções confiáveis. Uma alternativa ao TPFA, e que permite o uso de tensores completos e malhas não-ortogonais, é o Método dos Elementos Finitos de Galerkin (MEF), porém este método não produz soluções localmente conservativas, o que pode ser um problema sério para a modelagem de problemas envolvendo leis de conservação, como no escoamento em meios porosos. Outra alternativa são os Métodos de Volumes Finitos (MVF). Nas suas variantes mais robustas, estes métodos são capazes de lidar com malhas poligonais quaisquer e tensores de dispersão e permeabilidades completos e com razão de anisotropia arbitrária, além de produzir aproximações discretas de alta ordem e localmente conservativas. Neste contexto, no presente trabalho, apresentamos uma formulação MVF centrado na célula para a modelagem do transporte de um traçador não-reativo num escoamento monofásico em meios porosos heterogêneos e anisotrópicos. Para a discretização dos termos elípticos, tanto da equação de pressão quanto da equação de Advecção-Dispersão-Reação (ADRE), utilizou-se um MVF com aproximação de fluxo por múltiplos pontos que faz uso do estêncil diamante (MPFA-D) e para a discretização dos termos hiperbólicos, usamos o método FOU e um MVF do tipo MUSCL (Monotone Upstream Centered Scheme for Conservation Laws). A fim de testar nossa formulação, resolvemos alguns problemas benchmark encontrados na literatura. / Modeling and numerical simulation of solutes (e.g. Tracers) in heterogeneous and anisotropic porous media such as aquifers and oil reservoirs, constitute a bigger challenge of mathematics and numerical nature. Modeling sealants faults, channels, inclined wells, pinch outs and other complex features of these geological formations demand the use of unstructured and not orthogonal meshes, able to adapt naturally to the domain under study. The computational packages used commonly in the oil industry, mostly, are based on the Finite Difference Method with Two Point Flow Approximation (TPFA) and the Amount First Order Upwind method (FOU), due to its ease of implementation and its computational efficiency. Unfortunately, TPFA methods are unable to produce conver-gent solutions in non-orthogonal meshes or in permeability or dispersion full Tensor and FOU methods produce solutions with excessive numerical diffusion, requiring excessively refined mesh to obtain reliable solutions. An interesting alternative to TPFA, which allows the use of full tensor and not orthogonal meshes, is the Galerkin Finite Element Method (FEM), but this method does not produce solutions locally conservative, which can be a serious problem for modeling problems involving conservation laws as the flow in porous media. An interesting alternative is the Finite Volume Methods (MVF). In its most robust embodiments, these methods are able to cope with any polygonal mesh and full permeability or dispersion tensors and with an arbitrary anisotropy ratio, beyond producing discrete approximations of high order and locally conservative. In this context, the present study, we present one MVF formulation cell centered to modeling the transport of a non-reactive tracer in single-phase flow in heterogeneous and anisotropic porous media. For the elliptical discretization terms, both, the pressure equation as the equation advection-dispersion-reaction (ADRE), we used The FVMF multipoint flow approximation that uses the diamond stencil (MPPA-D) and for the discretization of hyperbolic terms, we use the FOU method and an MVF type MUSCL (Monotone Upstream Centered Scheme for Conservation Laws). In order to test our formulation, we solve some benchmark problems in the literature.

O bulbo molhado formado na irrigação por gotejamento pode ser modelado a partir informações das propriedades físico-hídricas do solo. Mas apesar do grande progresso na modelagem, a aplicação de modelos na irrigação e drenagem ainda não foi implementada em nenhum nível de maneira substancial. Assim, o objetivo do presente trabalho foi desenvolver um modelo numérico utilizando a técnica dos volumes finitos para estimar a forma e as dimensões do volume de solo molhado sob irrigação por gotejamento, e verificar a validade do modelo através da comparação com dados recolhidos em condições experimentais. O ensaio foi conduzido na área experimental do Departamento de Engenharia de Biossistemas da Escola Superior de Agricultura Luiz de Queiroz-ESALQ/USP. As sondas de TDR foram confeccionadas segundo procedimentos descritos por Souza et al. (2006). O perfil do bulbo molhado formado no solo abaixo de um emissor do tipo gotejador foi determinado para 3 tipos de material: areia, solo arenoso e solo argiloso e para 3 vazões nominais do emissor: 2, 4 e 6 L/h. Cada uma das combinações entre tipo de solo e vazão foi repetida três vezes em caixas (1000 L) diferentes, totalizando 27 medições. Um modelo numérico foi desenvolvido para simular a distribuição da água no perfil do solo abaixo de uma fonte pontual. A solução da equação diferencial para o movimento da água em solo não saturado foi realizada pela discretização do espaço-tempo utilizando a técnica dos volumes finitos. Um algoritmo em linguagem Visual Basic foi escrito para implementar o conjunto de equações e simular a evolução do bulbo molhado no tempo. Foi simulada a formação do bulbo molhado nas mesmas condições do experimento, e gráficos de isolinhas de umidade foram traçados no software Surfer. O modelo numérico proposto foi capaz de simular a formação do bulbo molhado em diferentes condições de tipo de solo e vazão do emissor. / The soil water patterns in drip irrigation can be modeled from physical and hydraulic properties of soil. But despite the great progress in modeling, the models have not been implemented at any level in irrigation and drainage. The objective of this study was to develop a numerical model using finite volume technique to estimate the shape and dimensions of the wetted soil volume under drip irrigation and verify the validity of the model by comparing data collected under experimental conditions. The trial was conducted at the experimental site of the Department of Biosystems Engineering, Escola Superior de Agricultura Luiz de Queiroz- ESALQ/USP. The TDR probes were manufactured according Souza et al. (2006). The soil water patterns under a drip emitter type was determined for three types of material: sand, sandy soil and clay soil and three nominal flows of the emitters: 2, 4 and 6 L/h. Each of the combinations of soil type and flow rate was repeated three times in boxes (1000 L), totaling 27 measurements. A numerical model was developed to simulate the distribution of water in the soil profile below a point source. The solution of the differential equation for the movement of water in unsaturated soil was carried out by the discretization of space-time using the technique of finite volume. An algorithm in Visual Basic language was written to implement the set of equations and simulate the evolution of wetted soil volume in time. Contour plots of soil water content were drawn in Surfer software. The proposed numerical model was able to simulate wetted soil volume under different conditions of soil type and flow of the emitter.

The theses is focused on efficient use of numerical methods in development of low-voltage switching devices, namely to create a physically correct and reliable numerical model of the temperature field to find an application in the design of the current path of a device for various operating conditions. The creation of this numerical model requires not only correct inclusion of all modes of heat transfer - conduction, convection and radiation, but also correct solution of problematic transient resistance - both electrical and thermal in electrical contacts at different stages of usage. Therefore an essential part of the theses forms a thorough experimental analysis of the necessary material properties and dependencies which forms input data for the numerical model that is based on the finite volume method. The last part of the theses deals with debugging and verification of numerical model to correspond with experimentally obtained data. The result of the theses is the numerical model which is able to solve correctly both steady and various transient states of swiching devices.

This master`s thesis analyzes the pressure distribution on the premises of scintillation detector secondary electron in the variant with three aperture. The aim of this study is analyzing the fluid flow depending on the application of the third aperture in the entrance of the detector, thus creating more self-pumped chamber, which is responsible for ensuring a better distribution of pressure in the premises of the detector. The result of the analysis would be determining how to change parameters within the detector. If it is found that application of the third aperture has a positive effect on water flow in the premises of the detector, this arrangement may be used for improvement of the detector. Master`s thesis is divided into several chapters. First describes the basic principles of electron microscopy, including sample preparation, conditions for the proper functioning of microscopes and sharing different types of electron microscopes. The next chapters describe briefly the physical descriptions of gases flow in low pressures and small apertures, the mathematical models and simulation software used in this analysis. The analysis is done in SolidWorks with the module called Cosmos FloSimulation. The conclusion summarizes the results of the analysis, including graphical representations of simulation.