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This thesis evaluates two variants of Volumeof fluid method, namely Piecewise Linear Interface Construction (PLIC) and Multidimensional Tangent of Hyperbola for Interface Capturing (MTHINC) used in two-fluid simulations for interface tracking.Simulations of a single rising bubble in different conditions are performed aimed to assess the accuracy of the methods, and to check their convergence with grid size. The results show that both methods demonstrate convergence with mesh refinement, while PLIC captures the transient part of rising process of bubble more accurately than MTHINC in 2D case. / Denna avhandling utvärderar två varianter av metoden Volume of fluid för flerfas strömningar, nämligen Piecewise Linear Interface Construction (PLIC) och Multidimensional Tangent of Hyperbola for Interface Capturing (MTHINC) som används i tvåvätskesimuleringar för gränssnittsspårning.Simuleringar av en enda stigande bubbla under olika förhållanden utförs för att bedöma metodernas noggrannhet och för att kontrollera deras konvergens med gridsstorlek. Resultaten visar att båda metoderna visar konvergens med grid förfining, medan PLIC fångar den övergående delen av stigande bubbelprocess mer exakt än MTHINC i 2D-fall.

This effort explores novel sub-resolution particle center estimation algorithms for Digital Particle Tracking Velocimetry (DPIV). The errors of these new methods were classified through Monte-Carlo simulations. These schemes provide direct measurements of the apparent particle image diameter and the subpixel position. The new methods significantly reduce the bias error due to pixel discretization, thus reducing the total error in the position and sizing measurement compared to the classic three point and least squares Gaussian estimators. In addition, the accuracy of the least-squares fits were essentially independent of the true particle diameter and significantly reduced the particle position error compared with current estimation schemes. The results of the Monte Carlo simulations were validated in a high pressure spray atomization experiment. / Master of Science

Dense fluid-particulate systems are widely encountered in the pharmaceutical, energy, environmental and chemical processing industries. Prediction of the heat transfer characteristics of these systems is challenging. Use of a high fidelity Discrete Element Method (DEM) for particle scale simulations coupled to Computational Fluid Dynamics (CFD) requires large simulation times and limits application to small particulate systems.  The overall goal of this research is to develop and implement parallelization techniques which can be applied to large systems with O(105- 106) particles to investigate particle scale heat transfer in rotary kiln and fluidized bed environments. The strongly coupled CFD and DEM calculations are parallelized using the OpenMP paradigm which provides the flexibility needed for the multimodal parallelism encountered in fluid-particulate systems. The fluid calculation is parallelized using domain decomposition, whereas N-body decomposition is used for DEM. It is shown that OpenMP-CFD with the first touch policy, appropriate thread affinity and careful tuning scales as well as MPI up to 256 processors on a shared memory SGI Altix. To implement DEM in the OpenMP framework, ghost particle transfers between grid blocks, which consume a substantial amount of time in DEM, are eliminated by a suitable global mapping of the multi-block data structure. The global mapping together with enforcing perfect particle load balance across OpenMP threads results in computational times between 2-5 times faster than an equivalent MPI implementation. Heat transfer studies are conducted in a rotary kiln as well as in a fluidized bed equipped with a single horizontal tube heat exchanger. Two cases, one with mono-disperse 2 mm particles rotating at 20 RPM and another with a poly-disperse distribution ranging from 1-2.8 mm and rotating at 1 RPM are investigated. It is shown that heat transfer to the mono-disperse 2 mm particles is dominated by convective heat transfer from the thermal boundary layer that forms on the heated surface of the kiln. In the second case, during the first 24 seconds, the heat transfer to the particles is dominated by conduction to the larger particles that settle at the bottom of the kiln. The results compare reasonably well with experiments. In the fluidized bed, the highly energetic transitional flow and thermal field in the vicinity of the tube surface and the limits placed on the grid size by the volume-averaged nature of the governing equations result in gross under prediction of the heat transfer coefficient at the tube surface. It is shown that the inclusion of a subgrid stress model and the application of a LES wall function (WMLES) at the tube surface improves the prediction to within ± 20% of the experimental measurements. / Ph. D.

Code verification is the process of ensuring, to the degree possible, that there are no algorithm deficiencies and coding mistakes (bugs) in a scientific computing simulation. In this work, techniques are presented for performing code verification of boundary conditions commonly used in compressible and incompressible Computational Fluid Dynamics (CFD) codes. Using a compressible CFD code, this study assesses the subsonic inflow (isentropic and fixed-mass), subsonic outflow, supersonic outflow, no-slip wall (adiabatic and isothermal), and inviscid slip-wall. The use of simplified curved surfaces is proposed for easier generation of manufactured solutions during the verification of certain boundary conditions involving many constraints. To perform rigorous code verification, general grids with mixed cell types at the verified boundary are used. A novel approach is introduced to determine manufactured solutions for boundary condition verification when the velocity-field is constrained to be divergence-free during the simulation in an incompressible CFD code. Order of accuracy testing using the Method of Manufactured Solutions (MMS) is employed here for code verification of the major components of an open-source, multiphase flow code - MFIX. The presence of two-phase governing equations and a modified SIMPLE-based algorithm requiring divergence-free flows makes the selection of manufactured solutions more involved than for single-phase, compressible flows. Code verification is performed here on 2D and 3D, uniform and stretched meshes for incompressible, steady and unsteady, single-phase and two-phase flows using the two-fluid model of MFIX. In a CFD simulation, truncation error (TE) is the difference between the continuous governing equation and its discrete approximation. Since TE can be shown to be the local source term for the discretization error, TE is proposed as the criterion for determining which regions of the computational mesh should be refined/coarsened. For mesh modification, an error equidistribution strategy to perform r-refinement (i.e., mesh node relocation) is employed. This technique is applied to 1D and 2D inviscid flow problems where the exact (i.e., analytic) solution is available. For mesh adaptation based upon TE, about an order of magnitude improvement in discretization error levels is observed when compared with the uniform mesh. / Ph. D.

O principal objetivo deste trabalho é contribuir para o desenvolvimento de uma nova técnica de reconstrução numérica do problema de tomografia por impedância elétrica. A abordagem adotada baseia-se na minimização de um funcional de erro convenientemente definido, cujo ponto de mínimo global está relacionado com a imagem do escoamento sensoriado. Nesta formulação, o mau condicionamento se manifesta através de características topológicas dos funcionais de erro (patologia) que prejudicam o desempenho dos métodos de otimização na obtenção do mínimo. Esta abordagem tem vantagens significativas em relação às abordagens tradicionais, normalmente baseadas em hipóteses restritivas e pouco realistas como, por exemplo, considerar o campo de sensoriamento bidimensional e paralelo, além de independente do escoamento. Testes numéricos permitiram realizar estudos preliminares sobre as características topológicas do funcional de erro, necessários para a seleção de métodos de otimização passíveis de serem especializados para a solução do problema tratado neste trabalho. Nestes testes identificou-se a patologia característica do problema tratado: presença de uma região plana (inclinação virtualmente nula) circundando o mínimo global procurado. Dentre os diferentes métodos de otimização considerados, optou-se pelo desenvolvimento de uma estratégia baseada em algoritmos genéticos, devido às suas características serem melhor adaptáveis à patologia do problema em questão. O desempenho do método de otimização desenvolvido foi testado extensivamente em dois problemas básicos: a) posicionar corretamente uma inclusão de forma e contraste conhecidos e b) determinar os valores do contraste em uma sub-região do domínio de sensoriamento, no interior do qual sabe-se que existe uma inclusão. No primeiro caso, os resultados mostraram que, de fato, o algoritmo genético superou a patologia do problema e convergiu para a solução correta. No segundo caso, de dimensionalidade maior, a convergência em um tempo aceitável só pode ser alcançada com a introdução de informações à priori, seja na forma de restrições sobre o espaço de busca, seja na forma de penalidades aplicadas ao funcional de erro. / The main objective of this work is to contribute to the development of a new two-phase flow tomographic reconstruction method suited for electrical impedance tomography. The adopted approach consists in minimizing an error functional, defined so that is global minimum is related with the sensed flow image. In this formulation, the ill conditioning appears through topological features of the error functionals (pathologies) which compromises the performance of the optimization algorithms employed to determine the minimum. This approach has several important advantages over the classical ones, generally based on restrictive and unrealistic hypothesis such as the sensing field being two-dimensional, parallel and independent of the flow. Numerical simulations permitted to conduct preliminary studies about the topological features of the error functional, necessary to select possible optimization methods to be specialized to reach the solution of the problem treated in this work. The characteristic pathology of the problem was identified in these tests: the presence of a flat region (virtually null inclination) around the sought global minimum. Among the different considered methods, genetic algorithms were adopted because of their characteristics of being best adaptive to the pathologies of the current problem. The performance of the developed optimization method was tested through extensive numerical tests in two basic problems: a) to correctly place aninclusion with known shape and contrast and b) to determine the values of the contrast inside a sub-region of the sensed domain, which is known that contains the inclusion. In the first case, results show that the genetic algorithm overcame the pathologies of the problem and converged to the correct solution. In the second case, with higher dimensionality, convergence was achieved in an acceptable time only after the introduction of a priori information, either in the form of restrictions on the search space or in the form of penalties applied to the error functional.

O principal objetivo deste trabalho é contribuir para o desenvolvimento de uma nova técnica de reconstrução numérica do problema de tomografia por impedância elétrica. A abordagem adotada baseia-se na minimização de um funcional de erro convenientemente definido, cujo ponto de mínimo global está relacionado com a imagem do escoamento sensoriado. Nesta formulação, o mau condicionamento se manifesta através de características topológicas dos funcionais de erro (patologia) que prejudicam o desempenho dos métodos de otimização na obtenção do mínimo. Esta abordagem tem vantagens significativas em relação às abordagens tradicionais, normalmente baseadas em hipóteses restritivas e pouco realistas como, por exemplo, considerar o campo de sensoriamento bidimensional e paralelo, além de independente do escoamento. Testes numéricos permitiram realizar estudos preliminares sobre as características topológicas do funcional de erro, necessários para a seleção de métodos de otimização passíveis de serem especializados para a solução do problema tratado neste trabalho. Nestes testes identificou-se a patologia característica do problema tratado: presença de uma região plana (inclinação virtualmente nula) circundando o mínimo global procurado. Dentre os diferentes métodos de otimização considerados, optou-se pelo desenvolvimento de uma estratégia baseada em algoritmos genéticos, devido às suas características serem melhor adaptáveis à patologia do problema em questão. O desempenho do método de otimização desenvolvido foi testado extensivamente em dois problemas básicos: a) posicionar corretamente uma inclusão de forma e contraste conhecidos e b) determinar os valores do contraste em uma sub-região do domínio de sensoriamento, no interior do qual sabe-se que existe uma inclusão. No primeiro caso, os resultados mostraram que, de fato, o algoritmo genético superou a patologia do problema e convergiu para a solução correta. No segundo caso, de dimensionalidade maior, a convergência em um tempo aceitável só pode ser alcançada com a introdução de informações à priori, seja na forma de restrições sobre o espaço de busca, seja na forma de penalidades aplicadas ao funcional de erro. / The main objective of this work is to contribute to the development of a new two-phase flow tomographic reconstruction method suited for electrical impedance tomography. The adopted approach consists in minimizing an error functional, defined so that is global minimum is related with the sensed flow image. In this formulation, the ill conditioning appears through topological features of the error functionals (pathologies) which compromises the performance of the optimization algorithms employed to determine the minimum. This approach has several important advantages over the classical ones, generally based on restrictive and unrealistic hypothesis such as the sensing field being two-dimensional, parallel and independent of the flow. Numerical simulations permitted to conduct preliminary studies about the topological features of the error functional, necessary to select possible optimization methods to be specialized to reach the solution of the problem treated in this work. The characteristic pathology of the problem was identified in these tests: the presence of a flat region (virtually null inclination) around the sought global minimum. Among the different considered methods, genetic algorithms were adopted because of their characteristics of being best adaptive to the pathologies of the current problem. The performance of the developed optimization method was tested through extensive numerical tests in two basic problems: a) to correctly place aninclusion with known shape and contrast and b) to determine the values of the contrast inside a sub-region of the sensed domain, which is known that contains the inclusion. In the first case, results show that the genetic algorithm overcame the pathologies of the problem and converged to the correct solution. In the second case, with higher dimensionality, convergence was achieved in an acceptable time only after the introduction of a priori information, either in the form of restrictions on the search space or in the form of penalties applied to the error functional.

La compréhension des écoulements à bulles dans les centrales nucléaires demeure encore un élément limitant dans l’analyse des opérations et de la sûreté des installations. Pour ne citer qu’un exemple, l’amélioration de la durée de vie etde la performance des générateurs de vapeur nécessite d’appréhender les régimes d’écoulement au sein des tubes qui sont responsables de leur vibration. Cependant, pour simuler avec précision ces écoulements, les codes de simulation numérique doivent relever de nombreux défis parmi lesquels la capacité à simuler des inclusions ayant des tailles très variées. Dans cette thèse, une nouvelle approche, appelée approche multi-champ, est implémentée dans le code NEPTUNE_CFD, basé sur un modèle bi-fluide. Cette approche inclut une méthode de suivi d’interface pour les grandes structures déformables et prend en compte les effets liés à la turbulence et aux changements de phase.Pour simuler de tels écoulements complexes en limitant le coût CPU, l’approche multi-champ considère séparément les petites inclusions sphériques des grandes inclusions déformables. Ainsi, les petites structures sphériques sont définies via un champ eulérien dispersé évoluant au sein d’un champ continu porteur, comme c’est habituellement le cas avec le modèle bi-fluide. Les grosses bulles déformables sont considérées comme des interfaces entre deux champs continus, un champ liquide et un champ gaz. Si on prend l’exemple d’un écoulement diphasique avec de l’eau et des bulles d’air de différentes tailles, trois champs sont alors définis pour cet écoulement: un champ continu liquide, un champ continu gaz et un champ dispersé gaz contenant les petites bulles sphériques. Cependant, simuler avec précision des interfaces entre deux champscontinus avec le modèle bi-fluide nécessite le développement de traitements spécifiques afin de coupler les deux champs à l’interface et de limiter la diffusion de cette interface.Après avoir amélioré la simulation des interfaces dans des écoulements laminaires, les effets liés à la turbulence sont étudiés. Une étude a priori de simulations aux grandes échelles est proposée pour identifier les termes sous-mailles et comparer différents modèles de turbulence disponibles dans la littérature. L’implémentation et la validation du modèle de turbulence retenu suite à l’étude sont détaillées. Les changements de phase sont ensuite explorés via le développement d’un modèle spécifique pour le terme de transfert de masse. Pour finir, des simulations trois champs sont présentées. De nouveauxcritères sont définis pour modéliser la fragmentation des grandes inclusions déformables en petites bulles sphériques ainsi que la coalescence de ces dernières pour former de grandes bulles déformables.A chaque étape de l’implémentation des différents modèles évoqués, des validations basées sur des données analytiques et issues d’expériences sont présentées afin de s’assurer que les phénomènes physiques sont bien prédits. Des cas tests dans des configurations industrielles sont également détaillés pour montrer la capacité de l’approche développée à simuler des écoulements complexes / Bubbly flows occurring in nuclear power plants remain a major limiting phenomenon for the analysis of operation and safety. As an example, the improvement of steam generator lifetime and performance relies on the comprehension of flow regimes inside the tubes responsible for tube vibrations. However, to ensure an accurate simulation of these flows, theComputational Multi-Fluid Dynamics (CMFD) codes have to take up many challenges, among others the ability of dealing with a variety of inclusion sizes. The classical two-fluid model allows simulating small spherical inclusions but is not able to compute large deformable inclusions. Thus, in this thesis, a new approach, called the multifield approach, is implementedin the CMFD code NEPTUNE_CFD, based on a two-fluid model. This approach includes an interface tracking method for large and deformable structures and takes into account turbulence and phase change effects.To simulate such complex flows with reasonable computational costs, the multifield approach considers separately the small spherical inclusions and the large deformable ones. Thus, the small spherical structures are defined as a dispersed field evolving in a continuous carrier field, as usually done in the two-fluid model. The large deformable bubbles are considered as interfaces between two continuous phases treated as two different fields in the two-fluid model. In the example of a two-phase flow with water and air bubbles of different sizes, three fields are defined: a continuous liquid field, a continuous gas field and a dispersed gas field containing the small spherical bubbles. However, the accurate simulation of interfaces between the two continuous fields within the two-fluid model requires specific treatments to couple the two fields at the interface and to limit the interface smearing.After improving the interface simulation in laminar flows, turbulence effects are investigated. An a priori Large Eddy Simulation (LES) study is performed to identify the predominant subgrid terms and to compare different availableturbulence models. The implementation and validation of the most suitable model is proposed. Phase change interfaces are then explored with the development of a specific model for the mass transfer term. Finally, three fields simulations are performed. New criteria are defined for the breakup of the large deformable inclusions into small spherical bubbles and for the coalescence of the latter forming large deformable bubbles.Validation at each step of the models implementations are presented using analytical and experimental data to ensure that the physical phenomena are well predicted. Test cases in industrial configurations are finally performed to show the ability of the developed approach to deal with complex flows

Magnetic induction tomography (MIT) is a non-invasive, soft field imaging modality that has the potential to map the electrical conductivity (σ) distribution inside an object under investigation. In MIT, a number of exciter and receiver coils are distributed around the periphery of the object. A primary magnetic field is emitted by each exciter, and interacts with the object. This induces eddy currents in the object, which in turn create a secondary field. This latter is coupled to the receiver coils and voltages are induced. An image reconstruction algorithm is then used to infer the conductivity map of the object. In this thesis, the application of MIT for volumetric imaging of objects with low conductivity materials (< 5 Sm-1) and dimensions < 1 m is investigated. In particular, two low conductivity applications are approached: imaging cerebral stroke and imaging the saline water in multiphase flows. In low conductivity applications, the measured signals are small and the spatial sensitivity is critically compromised making the associated inverse problem severely non-linear and ill-posed.The main contribution from this study is to investigate three non-linear optimisation techniques for solving the MIT inverse problem. The first two methods, namely regularised Levenberg Marquardt method and trust region Powell's Dog Leg method, employ damping and trust region strategies respectively. The third method is a modification of the Gauss Newton method and utilises a damping regularisation technique. An optimisation in the convergence and stability of the inverse solution was observed with these methods compared to standard Gauss Newton method. For such non linear treatment, re-evaluation of the forward problem is also required. The forward problem is solved numerically using the impedance method and a weakly coupled field approximation is employed to reduce the computation time and memory requirements. For treating the ill-posedness, different regularisation methods are investigated. Results show that the subspace regularisation technique is suitable for absolute imaging of the stroke in a real head model with synthetic data. Tikhonov based smoothing and edge preserving regularisation methods also produced successful results from simulations of oil/water. However, in a practical setup, still large geometrical and positioning noise causes a major problem and only difference imaging was viable to achieve a reasonable reconstruction.

Fluidized beds have widespread industrial applications ranging from chemical industries to power plants. The flow inside a fluidized bed system consists of two main phases, a particle phase and the fluid phase. The two phases are strongly coupled to each other through various forces like drag and pressure. Capturing this multiphase phenomenon requires modeling strategies that possess good fidelity over a range of scales. Discrete Element Modeling (DEM) coupled with Computational Fluid Dynamics (CFD) provides a good platform to analyze the complex coupled multiphase hydrodynamics inside fluidized bed systems. Conventional DEM-CFD framework suffers from contradictory spatial resolution requirements for the particle and fluid phases, respectively. This prevents the conventional DEM-CFD method to be applied to geometries that have features comparable to the particle diameter of the solid phase. The novelty of this work lies in the development and validation of a two-grid formulation that removes the resolution restrictions of the conventional DEM-CFD framework. The results obtained from this new framework agree reasonably well with the experiments showing the capability of the new scheme to simulate conditions not possible with conventional DEM-CFD framework. In addition, this research also focuses on performing both 2D and 3D jetting fluidized bed simulations having millions of particles; validate/compare results with experiments and to perform heat transfer studies in a jetting fluidized bed system. The results suggest convective and diffusive mixing for a single jet at higher superficial velocity to be better than the mixing obtained in a multiple jet framework. The comparison with experimental results obtained in a multiple jetting setup shows that a 2D simulation captures the essential jet characteristics near the distributor plate reasonably well while a 3D simulation is needed to capture proper bubble dynamics near the freeboard of the bed. These results give insight into the detailed dynamics of fluidized bed systems and provide a foundation for a better design of these systems. / Ph. D.