Finite element analysis of heat transfer and mineralization in layered hydrothermal systems with upward throughflow

We use the finite element method to solve the coupled problem between convective pore-fluid flow, heat transfer and mineralization in layered hydrothermal systems with upward throughflow. In particular, we present the improved rock alteration index (IRAI) concept for predicting the most probable precipitation and dissolution regions of gold (Au) minerals in the systems. To validate the numerical method used in the computation, analytical solutions to a benchmark problem have been derived. After the numerical method is validated, it is used to investigate the pattern of pore-fluid Aom, the distribution of temperature and the mineralization pattern of gold minerals in a layered hydrothermal system with upward throughflow. The related numerical results have demonstrated that the present concept of IRAI is useful and applicable for predicting the most probable precipitation and dissolution regions of gold (Au) minerals in hydrothermal systems. (C) 2000 Elsevier Science S.A. All rights reserved.

Finite element modelling of heat transfer through permeable cracks in hydrothermal systems with upward throughflow

We use the finite element method to model the heat transfer phenomenon through permeable cracks in hydrothermal systems with upward throughflow. Since the finite element method is an approximate numerical method, the method must be validated before it is used to soh,e any new, kind of problem. However, the analytical solution, which can be used to validate the finite element method and other numerical methods, is rather limited in the literature, especially, for the problem considered here. Keeping this in mind, we have derived analytical solutions for the temperature distribution along the vertical axis of a crack in a fluid-saturated porous layer. After the finite element method is validated by comparing the numerical solution with the analytical solution for the same benchmark problem, it is used to investigate the pore-fluid flow and heat transfer in layered hydrothermal systems with vertical permeable cracks. The related analytical and numerical results have demonstrated that vertical cracks are effective and efficient members to transfer heat energy from the bottom section to the top section in hydrothermal systems with upward throughflow.

Computer simulations of coupled problems in geological and geochemical systems

The finite element method is used to simulate coupled problems, which describe the related physical and chemical processes of ore body formation and mineralization, in geological and geochemical systems. The main purpose of this paper is to illustrate some simulation results for different types of modelling problems in pore-fluid saturated rock masses. The aims of the simulation results presented in this paper are: (1) getting a better understanding of the processes and mechanisms of ore body formation and mineralization in the upper crust of the Earth; (2) demonstrating the usefulness and applicability of the finite element method in dealing with a wide range of coupled problems in geological and geochemical systems; (3) qualitatively establishing a set of showcase problems, against which any numerical method and computer package can be reasonably validated. (C) 2002 Published by Elsevier Science B.V.

Periodic electric field enhanced transport through membranes

We examine the mean flux across a homogeneous membrane of a charged tracer subject to an alternating, symmetric voltage waveform. The analysis is based on the Nernst-Planck flux equation, with electric field subject to time dependence only. For low frequency electric fields the quasi steady-state flux can be approximated using the Goldman model, which has exact analytical solutions for tracer concentration and flux. No such closed form solutions can be found for arbitrary frequencies, however we find approximations for high frequency. An approximation formula for the average flux at all frequencies is also obtained from the two limiting approximations. Numerical integration of the governing equation is accomplished by use of the numerical method of lines and is performed for four different voltage waveforms. For the different voltage profiles, comparisons are made with the approximate analytical solutions which demonstrates their applicability. (c) 2005 Elsevier B.V. All rights reserved.

Calculating current densities and fields produced by shielded magnetic resonance imaging probes

A method is presented for computing the fields produced by radio frequency probes of the type used in magnetic resonance imaging. The effects of surrounding the probe with a shielding coil, intended to eliminate stray fields produced outside the probe, are included. An essential feature of these devices is the fact that the conducting rungs of the probe are of finite width relative to the coil radius, and it is therefore necessary to find the distribution of current within the conductors as part of the solution process. This is done here using a numerical method based on the inverse finite Hilbert transform, applied iteratively to the entire structure including its shielding coils. It is observed that the fields are influenced substantially by the width of the conducting rungs of the probe, since induced eddy currents within the rungs become more pronounced as their width is increased. The shield is also shown to have a significant effect on both the primary current density and the resultant fields. Quality factors are computed for these probes and compared with values measured experimentally.

Predicting cave initiation and propagation

The most widely used method for predicting the onset of continuous caving is Laubscher's caving chart. A detailed examination of this method was undertaken which concluded that it had limitations which may impact on results, particularly when dealing with stronger rock masses that are outside current experience. These limitations relate to inadequate guidelines for adjustment factors to rock mass rating (RMR), concerns about the position on the chart of critical case history data, undocumented changes to the method and an inadequate number of data points to be confident of stability boundaries. A review was undertaken on the application and reliability of a numerical method of assessing cavability. The review highlighted a number of issues, which at this stage, make numerical continuum methods problematic for predicting cavability. This is in particular reference to sensitivity to input parameters that are difficult to determine accurately and mesh dependency. An extended version of the Mathews method for open stope design was developed as an alternative method of predicting the onset of continuous caving. A number of caving case histories were collected and analyzed and a caving boundary delineated statistically on the Mathews stability graph. The definition of the caving boundary was aided by the existence of a large and wide-ranging stability database from non-caving mines. A caving rate model was extrapolated from the extended Mathews stability graph but could only be partially validated due to a lack of reliable data.

Simulação numérica do comportamento dinâmico de uma laje

Nesta dissertação pretende-se simular o comportamento dinâmico de uma laje de betão armado aplicando o Método de Elementos Finitos através da sua implementação no programa FreeFEM++. Este programa permite-nos a análise do modelo matemático tridimensional da Teoria da Elasticidade Linear, englobando a Equação de Equilíbrio, Equação de Compatibilidade e Relações Constitutivas. Tratando-se de um problema dinâmico é necessário recorrer a métodos numéricos de Integração Directa de modo a obter a resposta em termos de deslocamento ao longo do tempo. Para este trabalho escolhemos o Método de Newmark e o Método de Euler para a discretização temporal, um pela sua popularidade e o outro pela sua simplicidade de implementação. Os resultados obtidos pelo FreeFEM++ são validados através da comparação com resultados adquiridos a partir do SAP2000 e de Soluções Teóricas, quando possível.

Desenvolvimento de módulos para planeamento e controlo de execução de missões de veículos aéreos não tripulados

Com a evolução da tecnologia, os UAVs (unmanned aerial vehicles) são cada vez mais utilizados, não só em missões de risco para o ser Humano, mas também noutro tipo de missões, como é o caso de missões de inspeção, vigilância, busca e salvamento. Isto devese ao baixo custo das plataformas assim como à sua enorme fiabilidade e facilidade de operação. Esta dissertação surge da necessidade de aumentar a autonomia dos UAVs do projeto PITVANT (Projeto de Investigação e Tecnologia em Veículos Aéreos Não Tripulados), projeto de investigação colaborativa entre a AFA (Academia da Força Aérea) e a FEUP (Faculdade de Engenharia da Universidade do Porto), relativamente ao planeamento de trajetórias entre dois pontos no espaço, evitando os obstáculos que intersetem o caminho. Para executar o planeamento da trajetória mais curta entre dois pontos, foi implementado o algoritmo de pesquisa A*, por ser um algoritmo de pesquisa de soluções ótimas. A área de pesquisa é decomposta em células regulares e o centro das células são os nós de pesquisa do A*. O tamanho de cada célula é dependente da dinâmica de cada aeronave. Para que as aeronaves não colidam com os obstáculos, foi desenvolvido um método numérico baseado em relações trigonométricas para criar uma margem de segurança em torno de cada obstáculo. Estas margens de segurança são configuráveis, sendo o seu valor por defeito igual ao raio mínimo de curvatura da aeronave à velocidade de cruzeiro. De forma a avaliar a sua escalabilidade, o algoritmo foi avaliado com diferentes números de obstáculos. As métricas utilizadas para avaliação do algoritmo foram o tempo de computação do mesmo e o comprimento do trajeto obtido. Foi ainda comparado o desempenho do algoritmo desenvolvido com um algoritmo já implementado, do tipo fast marching.

Estudo de reparações adesivas pela técnica de remendo embebido com reforços exteriores para aumento da resistência

As ligações adesivas têm sido utilizadas em áreas como a indústria aeroespacial, aeronáutica, de defesa, automóvel, da construção civil e das madeiras. As juntas adesivas têm vindo a substituir métodos como a soldadura, e ligações parafusadas e rebitadas, devido à facilidade de fabricação, maiores cadências de produção, menores custos, facilidade em unir materiais diferentes, melhor resistência à fadiga, entre outras razões. Como tal, também se utilizam reparações adesivas para restituição da resistência de estruturas danificadas, cujas técnicas mais comuns são a sobreposição simples, sobreposição dupla e remendo embebido. As reparações por remendo embebido, que são as mais eficientes, consistem na realização de um furo cónico na zona danificada e colagem de um remendo com a forma complementar do furo, de tal forma que não é alterada a forma inicial do componente. Neste trabalho pretende-se estudar experimental e numericamente reparações adesivas por remendo embebido, nomeadamente o efeito da utilização de reforços exteriores (em um ou nos dois lados da estrutura), para diferentes ângulos de inclinação. Foi considerado um adesivo dúctil (Araldite® 2015) e outro frágil (Araldite® AV138), o que permitiu abranger processos de rotura bastante distintos. O estudo experimental é acompanhado por outro numérico no software ABAQUS®, usando modelos coesivos para a previsão numérica da resistência das reparações. O trabalho numérico permitiu o estudo das distribuições de tensões, o que possibilitou a análise detalhada dos resultados obtidos. Foi também realizado um estudo numérico de otimização das reparações por alteração da espessura dos reforços e utilização de chanfro nas extremidades dos mesmos. Nos resultados obtidos, constatou-se a adequabilidade do método numérico na previsão fiável da resistência, e também que a utilização dos reforços aumenta consideravelmente o rendimento das reparações (até 530 % e 340 % para os adesivos Araldite® 2015 e AV138, respetivamente), o que poderá justificar a sua utilização em aplicações industriais em que a perturbação aerodinâmica causada por esta alteração não seja relevante.

Dynamic stiffness of the piled foundation of a onshore wind turbine

One of today's biggest concerns is the increase of energetic needs, especially in the developed countries. Among various clean energies, wind energy is one of the technologies that assume greater importance on the sustainable development of humanity. Despite wind turbines had been developed and studied over the years, there are phenomena that haven't been yet fully understood. This work studies the soil-structure interaction that occurs on a wind turbine's foundation composed by a group of piles that is under dynamic loads caused by wind. This problem assumes special importance when the foundation is implemented on locations where safety criteria are very demanding, like the case of a foundation mounted on a dike. To the phenomenon of interaction between two piles and the soil between them it's given the name of pile-soil-pile interaction. It is known that such behavior is frequency dependent, and therefore, on this work evaluation of relevant frequencies for the intended analysis is held. During the development of this thesis, two methods were selected in order to assess pile-soil-pile interaction, being one of analytical nature and the other of numerical origin. The analytical solution was recently developed and its called Generalized pile-soil-pile theory, while for the numerical method the commercial nite element software PLAXIS 3D was used. A study of applicability of the numerical method is also done comparing the given solution by the nite element methods with a rigorous solution widely accepted by the majority of the authors.

Fractional bioheat equation

In this work we develop a new mathematical model for the Pennes’ bioheat equation assuming a fractional time derivative of single order. A numerical method for the solu- tion of such equations is proposed, and, the suitability of the new model for modelling real physical problems is studied and discussed

Mortar-Techniken zur Behandlung von Grenzschichtproblemen

Elliptic differential equations, finite element method, mortar element method, streamline diffusion FEM, upwind method, numerical method, error estimate, interpolation operator, grid generation, adaptive refinement

Generating vortex rings in Bose-Einstein condensates in the line-source approximation

We present a numerical method for generating vortex rings in Bose-Einstein condensates confined in axially symmetric traps. The vortex ring is generated using the line-source approximation for the vorticity, i.e., the curl of the superfluid velocity field is different from zero only on a circumference of a given radius located on a plane perpendicular to the symmetry axis and coaxial with it. The particle density is obtained by solving a modified Gross-Pitaevskii equation that incorporates the effect of the velocity field. We discuss the appearance of density profiles, the vortex core structure, and the vortex nucleation energy, i.e., the energy difference between vortical and ground-state configurations. This is used to present a qualitative description of the vortex dynamics.

Pore-scale modeling of two-phase flow instabilities in porous media

Les problèmes d'écoulements multiphasiques en média poreux sont d'un grand intérêt pour de nombreuses applications scientifiques et techniques ; comme la séquestration de C02, l'extraction de pétrole et la dépollution des aquifères. La complexité intrinsèque des systèmes multiphasiques et l'hétérogénéité des formations géologiques sur des échelles multiples représentent un challenge majeur pour comprendre et modéliser les déplacements immiscibles dans les milieux poreux. Les descriptions à l'échelle supérieure basées sur la généralisation de l'équation de Darcy sont largement utilisées, mais ces méthodes sont sujettes à limitations pour les écoulements présentant de l'hystérèse. Les avancées récentes en terme de performances computationnelles et le développement de méthodes précises pour caractériser l'espace interstitiel ainsi que la distribution des phases ont favorisé l'utilisation de modèles qui permettent une résolution fine à l'échelle du pore. Ces modèles offrent un aperçu des caractéristiques de l'écoulement qui ne peuvent pas être facilement observées en laboratoire et peuvent être utilisé pour expliquer la différence entre les processus physiques et les modèles à l'échelle macroscopique existants. L'objet premier de la thèse se porte sur la simulation numérique directe : les équations de Navier-Stokes sont résolues dans l'espace interstitiel et la méthode du volume de fluide (VOF) est employée pour suivre l'évolution de l'interface. Dans VOF, la distribution des phases est décrite par une fonction fluide pour l'ensemble du domaine et des conditions aux bords particulières permettent la prise en compte des propriétés de mouillage du milieu poreux. Dans la première partie de la thèse, nous simulons le drainage dans une cellule Hele-Shaw 2D avec des obstacles cylindriques. Nous montrons que l'approche proposée est applicable même pour des ratios de densité et de viscosité très importants et permet de modéliser la transition entre déplacement stable et digitation visqueuse. Nous intéressons ensuite à l'interprétation de la pression capillaire à l'échelle macroscopique. Nous montrons que les techniques basées sur la moyenne spatiale de la pression présentent plusieurs limitations et sont imprécises en présence d'effets visqueux et de piégeage. Au contraire, une définition basée sur l'énergie permet de séparer les contributions capillaires des effets visqueux. La seconde partie de la thèse est consacrée à l'investigation des effets d'inertie associés aux reconfigurations irréversibles du ménisque causé par l'interface des instabilités. Comme prototype pour ces phénomènes, nous étudions d'abord la dynamique d'un ménisque dans un pore angulaire. Nous montrons que, dans un réseau de pores cubiques, les sauts et reconfigurations sont si fréquents que les effets d'inertie mènent à différentes configurations des fluides. A cause de la non-linéarité du problème, la distribution des fluides influence le travail des forces de pression, qui, à son tour, provoque une chute de pression dans la loi de Darcy. Cela suggère que ces phénomènes devraient être pris en compte lorsque que l'on décrit l'écoulement multiphasique en média poreux à l'échelle macroscopique. La dernière partie de la thèse s'attache à démontrer la validité de notre approche par une comparaison avec des expériences en laboratoire : un drainage instable dans un milieu poreux quasi 2D (une cellule Hele-Shaw avec des obstacles cylindriques). Plusieurs simulations sont tournées sous différentes conditions aux bords et en utilisant différents modèles (modèle intégré 2D et modèle 3D) afin de comparer certaines quantités macroscopiques avec les observations au laboratoire correspondantes. Malgré le challenge de modéliser des déplacements instables, où, par définition, de petites perturbations peuvent grandir sans fin, notre approche numérique apporte de résultats satisfaisants pour tous les cas étudiés. - Problems involving multiphase flow in porous media are of great interest in many scientific and engineering applications including Carbon Capture and Storage, oil recovery and groundwater remediation. The intrinsic complexity of multiphase systems and the multi scale heterogeneity of geological formations represent the major challenges to understand and model immiscible displacement in porous media. Upscaled descriptions based on generalization of Darcy's law are widely used, but they are subject to several limitations for flow that exhibit hysteric and history- dependent behaviors. Recent advances in high performance computing and the development of accurate methods to characterize pore space and phase distribution have fostered the use of models that allow sub-pore resolution. These models provide an insight on flow characteristics that cannot be easily achieved by laboratory experiments and can be used to explain the gap between physical processes and existing macro-scale models. We focus on direct numerical simulations: we solve the Navier-Stokes equations for mass and momentum conservation in the pore space and employ the Volume Of Fluid (VOF) method to track the evolution of the interface. In the VOF the distribution of the phases is described by a fluid function (whole-domain formulation) and special boundary conditions account for the wetting properties of the porous medium. In the first part of this thesis we simulate drainage in a 2-D Hele-Shaw cell filled with cylindrical obstacles. We show that the proposed approach can handle very large density and viscosity ratios and it is able to model the transition from stable displacement to viscous fingering. We then focus on the interpretation of the macroscopic capillary pressure showing that pressure average techniques are subject to several limitations and they are not accurate in presence of viscous effects and trapping. On the contrary an energy-based definition allows separating viscous and capillary contributions. In the second part of the thesis we investigate inertia effects associated with abrupt and irreversible reconfigurations of the menisci caused by interface instabilities. As a prototype of these phenomena we first consider the dynamics of a meniscus in an angular pore. We show that in a network of cubic pores, jumps and reconfigurations are so frequent that inertia effects lead to different fluid configurations. Due to the non-linearity of the problem, the distribution of the fluids influences the work done by pressure forces, which is in turn related to the pressure drop in Darcy's law. This suggests that these phenomena should be taken into account when upscaling multiphase flow in porous media. The last part of the thesis is devoted to proving the accuracy of the numerical approach by validation with experiments of unstable primary drainage in a quasi-2D porous medium (i.e., Hele-Shaw cell filled with cylindrical obstacles). We perform simulations under different boundary conditions and using different models (2-D integrated and full 3-D) and we compare several macroscopic quantities with the corresponding experiment. Despite the intrinsic challenges of modeling unstable displacement, where by definition small perturbations can grow without bounds, the numerical method gives satisfactory results for all the cases studied.

Kromaattisuuserojen laskentamalli

Työssä esitellään Lappeenrannan teknillisen yliopiston Tietotekniikan osastolla kehitettyä kromaattisuuserojen laskentamallia. Työn keskeisimpinä tavoitteina on luoda tiivis katsaus jo olemassa oleviin värierojen laskentamenetelmien tekniikoihin ja käydä läpi värien havaitsemiseen liittyviä yksityiskohtia. Työn käytännön osuudessa tutkitaan kehitettyä mallia ja esitetään ideoita kehittäen mallia täsmällisemmäksi. Kromaattisuuserojen laskentamalli perustuu MacAdamin määrittelemien ellipsien hyödyntämiseen CIE-1931 kromaattisuusdiagrammissa. Ideana on projisoida ellipsit iso- ja pikkuakseleidensa suhteen vakiosäteisiksi ympyröiksi kolmiulotteiselle pinnalle. Kromaattisuuserot lasketaan pinnalta käyttämällä numeerista menetelmää. Tuloksena todetaan mallin täyttävän osittain sille asetetut vaatimukset ja parantavan CIE-1931 kromaattisuusdiagrammin yhtenäisyyttä erityisesti diagrammin vihreän ja sinisen värin alueilla.