Artificial neural networks (ANNs) are commonly considered as "black boxes": they can approximate any function without giving any interpretation. Novel research has observed that the laws of physics, which govern everything around us, can supplement the implementation of a neural network. For this purpose, we have physics-informed neural networks (PINNs): they are networks trained to consider the physics outlined in nonlinear partial differential equations (PDEs).  This thesis focuses on the thermal modelling of power transformers applying PINNs constrained to the heat diffusion equation. The aim is to estimate the top-oil temperature and the thermal distribution of a transformer. A solution of the equation will be provided by the Finite Volume Method (FVM), which will constitute a benchmark for the PINNs predictions. Differently from other works on PINNs, an additional challenge in this problem is the availability of field measurements. The results obtained show good accuracy in estimating the distribution and the top-oil temperature with PINN almost mimicking exactly FVM. Further improvements could be attained by rearranging the equation using more specific parameters to model the thermal behaviour of transformers and scaling the equation to dimensionless form. / Artificiella neurala nätverk (ANN) betraktas vanligtvis som "svarta lådor": de kan approximera vilken funktion som helst utan att tillhandahålla någon tolkning. Inom ny forskning har man sett att fysikens lagar, som styr allt runt omkring oss, kan komplettera implementeringen av ett neuralt nätverk. För detta ändamål har formulerats fysikinformerade neurala nätverk (PINN): de är nätverk som har tränats att ta hänsyn till den fysik som beskrivs i ickelinjära partiella differentialekvationer (PDE). Denna avhandling fokuserar på termisk modellering av transformatorer med tillämpning av PINN begränsat till värmeledningsekvationen. Syftet är att uppskatta en toppoljetemperatur och en transformators värmefördelning. Lösningen till ekvationen erhålls med finita volymmetoden (FVM), som används som en referenslösning för att utvärdera förutsägelserna från PINN. Implementeringen av PINN-algoritmen medförde en extra utmaning eftersom källtermen innefattade uppmätta värden. En metod att kringgå denna svårighet genom att approximera värdena på mätningarna i det neurala nätverket genom träning på motsvarande data presenteras. De erhållna resultaten visar god noggrannhet vid uppskattning av fördelningen och toppoljetemperaturen med PINN i jämförelse med FVM-lösningen. Ytterligare förbättringar kan uppnås genom att arrangera om ekvationen med mer specifika parametrar för att modellera transformatorernas termiska beteende och skalning av ekvationen till dimensionslös form.

No description available.

Heat transfer is key to understanding many processes in engineering. At a steel mill heat transfer is absolutely crucial to understanding most of the processes. One such a process is the pre-heating of a freshly relined ladle. The goal of this project was to develop code which could solve the diffusion equation, in an arbitrary three-dimensional geometry, subject to Dirichlet, Robin, Neumann, and certain kinds of non-linear boundary conditions. In order to approximate the solution the code uses a cell centred finite volume methodology. In order to verify the computational correctness of the code it was used on three simple cases where analytic solutions are known, a rarity for three-dimensional boundary value problems. A mathematical model for the heat conduction inside a ladle at Ovako’s site in Hofors was developed. The model was evaluated based on measurements on the outside of the ladle as well as from a temperature probe inside the bottom of the ladle. The model was found to adequately agree with the measured temperature. The code can thus be used to find a more optimal heating regiment of the ladle, possibly reducing emissions. / Värmeöverföring är nyckeln till att förstå många processer inom teknik. På ett stålverk är värmeöverföring helt avgörande för att förstå de flesta av processerna. En sådan process är förvärmning av en nymurad skänk. Målet med detta projekt var att utveckla en kod som kunde lösa diffusionsekvationen i en godtycklig tredimensionell geometri under Dirichlet-, Robin-, Neumann- och vissa typer av icke-linjära randvillkor. För att approximera lösningen använder koden en cellcentrerad finita volymmetodik. För att verifiera kodens beräkningsmässiga korrekthet användes den i tre enkla fall där analytiska lösningar är kända, vilket är en sällsynthet för tredimensionella randvärdesproblem. En matematisk modell för värmeledningen i en skänk vid Ovakos anläggning i Hofors utvecklades. Modellen utvärderades utifrån mätningar på utsidan av skänken samt från ett termoelement inuti botten av skänken. Modellen visade sig stämma väl överens med den uppmätta temperaturen. Koden kan därför användas för att hitta ett mer optimalt uppvärmningsschema för skänken, vilket eventuellt kan minska utsläppen från processen.

A finite volume, shock-capturing scheme is used to solve the shallow water equations on unstructured triangular meshes. The conditions are characterised by: slow flow velocities (up to 1m/s), long time scale (around 10 days), and large domains (50-100km across). Systematic verification is carried out by comparing numerical with analytical results, and by comparing parameter variation in the numerical scheme with perturbation analysis, and good agreement is found. It is the first time a shock-capturing scheme has been applied to slow flows in Moreton Bay. The scheme is used to simulate transport of a pollutant in Moreton Bay, to the east of the city of Brisbane, Australia. Tidal effects are simulated using a sinusoidal time-dependent boundary condition. An advection equation is solved to model the path of a contaminant that is released in the bay, and the effect of tide and wind on the contaminant is studied. Calibration is done by comparing numerical results with measurements made at a study site in Moreton Bay. It is found that variation in the wind speed and bed friction coefficients changes the solution in the way predicted by the asymptotics. These results vary according to the shape of the bathymetry of the domain: in shallower areas, flow is more subject to shear and hence changes in wind speed or bed friction had a greater effect in adding energy to the system. The results also show that the time-dependent boundary condition reproduces the tidal effects that are found on the Queensland coast, i.e. semi-diurnal with amplitude of about 1 metre, to a reasonable degree. It is also found that the simulated path of a pollutant agrees with field measurements. The computer model means different wind speeds and directions can be tested which allows management decisions to be made about which conditions have the least damaging effect on the area.

There is a growing interest in tidal energy, owing to its predictable nature in comparison to other renewable sources. In the case of the UK, its importance also lies on the availability of exploitable areas as well as their total capacity, which is estimated to cover more than 20% of the country demand. However, the level of development of this kind of technology is still far behind other types of renewable energy. However, several studies focused on a variety of individual devices, followed by more recent research on the deployment of large arrays or tidal farms. Potential sites for energy extraction can be found in narrows between islands and the coast or estuaries. The latter present some advantages for the installation and the connection to the grid but estuaries are often prone to flood risk from tides and surges. Therefore, the objective of this thesis is to evaluate the effect that very large groups of turbines could have on peak water levels during flooding events in the case of being deployed in estuarine areas. For that purpose, a new methodology has been developed, which implies the use of a numerical model (MIKE 21 by DHI), and it has been demonstrated against a real case study in the UK: the Solway Firth estuary. Another objective has consisted of integrating in this thesis the results from detailed CFD modelling and optimisation techniques involved in the project. A literature review has been carried out in order to identify the current state of the art for the different subjects considered in the thesis. Different aspects of the numerical model used for this study (MIKE 21) have been presented and the modelling of the turbines within the code has been validated against experimental and CFD data. The procedure to include large numbers of turbines in the code is also developed. An analysis has been done of the different estuaries existing in the UK suitable for tidal energy extraction, identifying their main geometrical features. Based on this, idealised models of estuaries have been used to assess the influence that the channel geometry could have on the impact of tidal farms under extreme water levels. The effect has been measured by comparing the results of the numerical model between the case with and without turbines under different flooding scenarios. Finally, the same methodology has been applied to a real case study selected from the previous group of estuaries namely the Solway Firth. An initial model has been created, according to the available data at the start of the research, which contained some errors related to the water depth at the intertidal areas in the upper estuary. Therefore, when a more realistic dataset became available, an improved model was created. The improved model has been used to assess the effects of tidal farms in the estuary under a coastal flooding event. It is concluded that there is significant influence of the channel geometry over the locations where the maximum changes in water levels due to the tidal farms will happen. Nevertheless, the effects seem to be more relevant in terms of the decrease rather than the increase of peak water levels for all geometries and the maximum changes seem to be in the order of dm. This is in agreement with the results of the Solway Firth models and can be summarised as a positive net effect over flood risk. On the other hand, a concern has been raised about the impact on intertidal areas, which could be the subject of future research.

Much of the planned installation of wind turbines in Sweden will be located in the northern region, characterized by a lower population density so that problems related to sound pollution and visual acceptance are of lower concern. This area is generally distinguished by complex topography and the presence of forest, that significantly affects the wind characteristics, complicating their modelling and simulation. There are concerns about how good an industrial code can simulate a forest, a question of paramount importance in the planning of new onshore farms. As a first step, a sensitivity analysis was initially carried out to investigate the impact on the ow of different boundary conditions and cell discretization inside the forest for a 2D domain with a homogeneous forest. Subsequently, a comparative analysis between the industrial code WindSim and Large Eddy Simulation (LES) data from Segalini. et al. (2016) was performed with the same domain. Lastly, simulations for a real Swedish forest, Ryningsnäs, was conducted to compare a roughness map approach versus modelling the forest as a momentum sink and a turbulence source. All simulations were conducted for neutral stability conditions with the same domain size and refinement. The main conclusions from each part can be summarized as follows. (i) The results from the sensitivity analysis showed that discretization of cells in the vertical direction inside the forest displayed a correlation between an increasing number of cells and a decreased streamwise wind speed above the canopy. (ii) The validation with the LES data displayed good agreement in terms of both horizontal mean wind speed and turbulence intensity. (iii) In terms of horizontal wind speed for Ryningsnäs, forest modelling was prevailing for all wind directions, where the most accurate simulation was found by employing a constant forest force resistive constant (C2) equal to 0.05. All forest models overestimated the turbulence intensity, whereas the roughness map approaches underestimated it. Based solely on the simulations for Ryningsnäas, a correlation between lower streamwise wind speed and higher turbulence intensity can be deduced.

The subject of this study is the determination of the resistance of an inland vessel engaged in cargo transport in the lower course of the Magdalena River, considering that the hydrodynamic effects in shallow water navigation are very different compared to the effects in deep water navigation. The hydrodynamic analysis is realized numerically using Computational Fluid Dynamics (CFD). The Reynolds-Averaging Navier-Stokes equation (RANS) solver is applied to simulate viscous and pressure effects around a tank and a hull in confined tank considering the wall bottom and side effects in shallow water navigation. For turbulence effects, realizable k-? model is used. The motion of the vessel causes elevations of the free surface, in which, is captured using the Volume of Fluid method (VOF). For discretization of flow domain, the Finite Volume Method (FVM) is applied. The motion of the fluids is updated for each time step that allows the calculation of the resistance acting on the hull. The numerical simulation results are compared with experimental data obtained by the Technological Research Institute of the State of São Paulo (IPT, acronym in Portuguese) together with the existing empirical methods for this type of cases. / É apresentado um estudo para determinar a resistência de uma barcaça empregada no transporte de carga que poderia operar no setor baixo do rio Magdalena. Os efeitos hidrodinâmicos de um navio em águas rasas são muito diferentes, comparados a esses efeitos em águas com profundidade infinita. A análise hidrodinâmica é realizada numericamente usando a Dinâmica dos Fluidos Computacional (CFD, acrônimo em inglês). A solução das equações de Navier-Stokes (NS) junto com a decomposição do Reynolds (RANS, acrônimo em inglês) é aplicada para simular os efeitos viscosos e de pressão em torno de um tanque e de uma embarcação em um tanque confinado que é caracterizado pelos efeitos do fundo e das paredes. Para efeitos de turbulência, o modelo realizado k-? é usado. O movimento da embarcação do rio provoca elevações da superfície livre que são capturadas usando o método do Volume de Fluido (VOF, acrônimo em inglês). Para a discretização do domínio de fluxo, o Método dos Volumes Finitos (FVM, acrônimo em inglês) é utilizado. O movimento dos fluidos é atualizado para cada intervalo de tempo o que permite o cálculo da resistência atuando no casco. Os resultados da simulação numérica são comparados com dados experimentais obtidos pelo Instituto de Pesquisas Tecnológicas do Estado de São Paulo (IPT), juntamente com os métodos empíricos existentes para esse tipo de casos.

L'utilisation croissante des sources d'énergie renouvelable avec une grande volatilité de production, comme l'énergie éolienne et solaire, conduit à des fluctuations dans le réseau électrique qui doivent être compensées. Pour cette raison les machines hydrauliques, turbines et pompes, sont plus souvent opérées dans les régimes de fonctionnement hors fonctionnement nominal et la fréquence des phases de démarrage et arrêt augmente. Ce type de fonctionnement peut avoir des conséquences importantes sur le cycle de vie des machines. Il est donc essentiel de prendre en compte l'écoulement dans les phases transitoires lors de la conception de la machine et la simulation numérique des écoulements est un outil adapté pour cela. La présente étude a pour objectif de développer une méthode de couplage flexible qui combine la méthode à maillage volumes finis (VF) et la méthode sans maillage Smoothed Particle Hydrodynamics - Arbitrary Lagrange Euler (SPH-ALE). Cette méthode couplée peut être utilisée comme outil pour l'investigation des phénomènes transitoires dans les machines hydrauliques. SPH-ALE est particulièrement bien adapté aux simulations des écoulements fortement dynamiques avec des géométries mobiles mais elle a des difficultés pour calculer des forts gradients de pression et vitesse. Un raffinement de particules est difficile à implémenter, surtout si les particules doivent être raffinées de manière anisotrope. Les méthodes volumes finis (VF) sont établies pour les simulations numériques d'écoulements grâce à leur stabilité et précision. Par contre, elles peuvent être lourdes pour les simulations avec des géométries mobiles et demandent souvent une interface entre des parties mobiles et statiques du maillage ce qui génère des erreurs supplémentaires. Pour combiner les deux approches complémentaires, une méthode de couplage a été développée qui décompose le domaine de calcul en zones où la vitesse et la pression sont calculées par la méthode VF, en zones où elles sont obtenues par SPH-ALE et en zones de recouvrement où les informations sont transférées de la zone VF à la zone SPH et inversement. Dans les zones de recouvrement les points de calcul VF sont utilisés comme voisins pour l'intégration en espace des particules SPH. Aux limites du maillage VF la vitesse et la pression sont interpolées des particules SPH, similairement aux méthodes Chimére des maillages recouvrants. Un logiciel SPH-ALE existant du groupe ANDRITZ est utilisé pour cette étude. Un solveur VF faiblement compressible est implémenté dans ce logiciel. Le solveur discrétise la même forme des équations de Navier-Stokes que le solveur SPH-ALE. Des solveurs de Riemann avec des états reconstruits par la méthode MUSCL sont employés. En outre, le solveur SPH-ALE est amélioré et adapté aux écoulements internes. Pour cette raison des conditions à l'entrée et à la sortie du type subsonique sont implémentées. Du plus, une méthode de correction du gradient de la fonction kernel est présentée qui améliore la précision du champ de pression, notamment si les particules ne sont pas distribuées régulièrement. La méthode couplée est validée à l'aide des cas test académiques en unidimensionnel et en bidimensionnel, comme le cas de tube à choc, les tourbillons de Taylor-Green et l'écoulement autour d'une aube symétrique du type NACA avec des particules en description eulérienne. En outre, le couplage offre la possibilité d'imposer des conditions à la sortie aux particules lagrangiennes. La méthode est appliquée aux simulations d'écoulement transitoire en 2D avec des particules qui se déplacent en suivant les géométries mobiles. / The increased use of intermittent forms of renewable energy like wind and solar energy produces fluctuations in the electric grid that have to be compensated. For this reason, hydraulic machines like turbines and pumps are more often operated under non-conventional operating conditions and are submitted to frequent starts and stops. This type of operating conditions has important consequences on the life cycle of the machines. It is thus of paramount importance that transient flows at off-design conditions are properly taken into account in the design phase and numerical simulation is an appropriate way to do so. The present study aims at developing a flexible coupling method of the meshbased Finite Volume Method (FVM) and the meshless Smoothed Particle Hydrodynamics - Arbitrary Lagrange Euler (SPH-ALE) method, which can be used as a tool for the investigation of transient phenomena in hydraulic machines. SPH-ALE is very well adapted for the simulation of highly dynamic flows with moving geometries but has difficulties to correctly represent rapidly changing gradients of the field variables. Particle refinement is difficult to implement, especially if particles are refined in an anisotropic way. FV methods are well established in CFD because of their accuracy and stability. However, they can be tedious for simulations with moving geometries and often necessitate an interface between moving and static parts of the mesh which introduces additional errors. To overcome the shortcomings of both methods, a coupling method is developed that uses a decomposition of the computational domain into regions where the physical field variables are computed by the FV method, regions where they are computed by SPH-ALE and overlapping regions where the information is transferred from the FV domain to the SPH domain and vice versa. In the overlapping regions FV calculation points are used as neighbors for the SPH integration in space. At the boundaries of the FV mesh, velocity and pressure are interpolated from the SPH particles by means of scattered data interpolation techniques, similarly to Chimera methods for overlapping grids. For this study, an existing SPH-ALE software of the ANDRITZ Group is used. A weakly compressible FV solver is implemented into this software that discretizes the same form of the Navier-Stokes equations than the SPH-ALE solver. Similar to the present SPH-ALE method, Riemann solvers with reconstructed states, obtained by a MUSCL scheme, are employed. Moreover, adaptations and improvements of the SPH-ALE solver itself are made, which are important for the coupling and for the simulation of internal flows in general. Thus, subsonic inlet and outlet conditions are implemented. Furthermore, a correction method of the kernel gradient is presented that ensures zeroth order consistency of the SPH-ALE approximation of the divergence of the convective fluxes. The correction improves greatly the SPH pressure field on non-uniform particle distributions. The implemented coupled method is successfully validated by means of inviscid academic one-dimensional and two-dimensional testcases like a shock tube case, Taylor-Green vortices and the flow around a symmetric NACA airfoil with particles in Eulerian description. Furthermore, the coupling provides a possibility to implement outlet boundary conditions to Lagrangian moving SPH particles. It is then applied to the simulation of transient flows in rotor stator systems in 2D with moving particles.

Fair Value Accounting is becoming increasingly more prominent, and auditing such measurements is at times difficult as a great deal of estimates and judgments are involved. This makes auditors jobs more challenging. Research has found that there is a need for understanding how auditing standards affect the audit process. Furthermore, some studies have shown that there is a gap between auditors and inspectors view of what constitutes sufficient and appropriate audit evidence regarding fair value measurements, the “FVM gap”. The aim of this study is to provide new insight on how auditing standards and inspectors affect the judgment of auditors in regards to fair value measurements. This study contributes to audit standard setters by illuminating how current auditing standards affect auditor judgment when auditing fair value measurements. It also contributes knowledge on how inspections affect judgment in the auditing process. Finally, it provides insight to practitioners on how box-checking and similar tools affect auditor judgment. We performed semi-structured interviews with respondents who have considerable experience of fair value measurements. The empirical data was thematically analysed and related to theories on judgment and decision-making as well as structure versus judgment research. A number of interesting findings were made; auditing standards seem to be well adjusted to auditors’ needs, documentation is one of the major issues when dealing with fair value measurements and the toughness of inspections between countries seem to differ. Some potential topics for future research were identified: whether or not a gap of interpretations exists between auditors and the lawyers of inspecting entities, and what effects such a gap could have; if the documentation of both audit clients and auditors needs to be improved upon. More potential areas for future research can be found in the Conclusion.

O princípio operacional do dispositivo de galgamento consiste de uma estrutura que utiliza uma rampa para direcionar as ondas incidentes para o reservatório. A água armazenada retorna para o oceano após a passagem por uma turbina que está acoplada a um gerador de energia elétrica. O presente trabalho propõe dois estudos numéricos a respeito de um conversor de energia das ondas do mar do tipo galgamento. Para ambos os casos, o objetivo do estudo é a aplicação do método Design Construtal na definição da melhor forma para a rampa de modo a maximizar a massa de água que entra no reservatório, conduzindo a uma maior geração de energia elétrica. O grau de liberdade b/B, isto é, a razão entre a base superior e a base inferior da rampa trapezoidal, foi otimizado, mantendo-se fixos a área total do tanque de ondas, a área da rampa e as características da onda. Para a análise numérica do princípio de funcionamento deste dispositivo foi empregado um domínio computacional tridimensional (3D), gerado através do software GAMBIT, onde o conversor é acoplado a um tanque de ondas regulares. A solução das equações de conservação e a equação do transporte da fração volumétrica foi realizada com o código comercial de Dinâmica dos Fluidos Computacional FLUENT, que é baseado no Método de Volumes Finitos (MVF). Aplica-se o modelo multifásico Volume of Fluid (VOF) no tratamento da interação água-ar. Para o primeiro estudo, as características da onda regular empregada estavam em escala de laboratório. Os resultados mostraram que houve uma razão ótima (b/B)o = 0.43, que maximiza a quantidade de água que entra no reservatório para o caso estudado. Para ambos os casos, a razão ótima foi encontrada para o extremo inferior do grau de liberdade, além dos resultados apontarem um aumento significativo na massa admitida no reservatório e, por consequente, um maior aproveitamento das ondas incidentes. / The operational principle of an overtopping device consists of a structure which utilizes a ramp to direct incident waves to the reservoir. The stored water returns to the ocean after passing through a turbine that is coupled to an electric generator. This work proposes two numerical studies of a WEC of sea waves of the type overtopping. In both cases, the objective of the study is the application of Constructal Design method to define the best geometry of the ramp which maximizes the mass of water entering the reservoir, leading to increase the generation of electricity. The degree of freedom b/B, that is, the ratio between the upper base and the lower base of the trapezoidal ramp, has been optimized, keeping fixed the total area of the wave tank, the area of the ramp and the wave characteristics. For the numerical analysis of the working principle of this device it was used a three-dimensional computational domain (3D) generated by GAMBIT software where the device is inserted to a tank of regular waves. The solution of conservation equations and equation of transport of the volumetric fraction was carried out with the Commercial Code of Computational Fluid Dynamics FLUENT, which is based on Finite Volume Method (FVM). It was applied the multiphase model Volume of Fluid (VOF) in the treatment of the interaction water-air. For the first study, the characteristics of the employed regular wave were on a laboratory scale. The results showed that there were an optimal ratio (b/B)o = 0.43, which maximizes the amount of water entering the reservoir for the case study. For the second study, the characteristics of the regular wave were employed at actual scale and the results showed that there was an optimum ratio (b/B)o = 0.38, which maximizes the amount of water entering the reservoir for the case study. In both cases, the optimum ratio is found for the extreme lower of freedom of degree and the results showed a significant increase in the mass allowed in the reservoir and, consequently, larger use of the incident waves.