The handling of gradient calculations on non-orthogonal meshes in the Finite Volume Method (FVM) is important in the modelling of complex geometries, since different implementation methods have an influence on the accuracy and the stability of the solution. The application in the current study is the numerical solution of heat conduction in a complex geometry. It finds relevance in many engineering applications such as the Micro-Channel Heat Exchanger (MCHE) that acts as a recuperator in a High Temperature Reactor (HTR) power generation cycle. A program based on the FVM was developed in Excel for the solution of the diffusion equation on a non-orthogonal mesh. A test case of heat conduction in a rectangular block, meshed with a tetrahedral mesh, was solved with the Excel code. The same test case was solved with OpenFOAM. The results of the two codes were compared. Small differences were found and their origins were traced to slightly different implementation methods. Knowledge of the differences in implementation between the two codes resulted in a better understanding of the aspects that influenced accuracy and stability. Computations on meshes with the presence of mesh skewness and non-orthogonal mesh lines at boundaries were performed and an accompanying decrease in accuracy was observed. The results showed that the standard FVM as implemented in the Excel code and in OpenFOAM will need advanced methods to compensate for mesh skewness and non-orthogonality found at boundaries. During the study, a deeper knowledge and understanding was gained of the challenge of obtaining accurate solutions of heat conduction on non-orthogonal meshes. This knowledge may lead to the overall improvement of the simulation of heat transfer models in general and for the MCHE specifically. / Thesis (MIng (Nuclear Engineering))--North-West University, Potchefstroom Campus, 2013.

The handling of gradient calculations on non-orthogonal meshes in the Finite Volume Method (FVM) is important in the modelling of complex geometries, since different implementation methods have an influence on the accuracy and the stability of the solution. The application in the current study is the numerical solution of heat conduction in a complex geometry. It finds relevance in many engineering applications such as the Micro-Channel Heat Exchanger (MCHE) that acts as a recuperator in a High Temperature Reactor (HTR) power generation cycle. A program based on the FVM was developed in Excel for the solution of the diffusion equation on a non-orthogonal mesh. A test case of heat conduction in a rectangular block, meshed with a tetrahedral mesh, was solved with the Excel code. The same test case was solved with OpenFOAM. The results of the two codes were compared. Small differences were found and their origins were traced to slightly different implementation methods. Knowledge of the differences in implementation between the two codes resulted in a better understanding of the aspects that influenced accuracy and stability. Computations on meshes with the presence of mesh skewness and non-orthogonal mesh lines at boundaries were performed and an accompanying decrease in accuracy was observed. The results showed that the standard FVM as implemented in the Excel code and in OpenFOAM will need advanced methods to compensate for mesh skewness and non-orthogonality found at boundaries. During the study, a deeper knowledge and understanding was gained of the challenge of obtaining accurate solutions of heat conduction on non-orthogonal meshes. This knowledge may lead to the overall improvement of the simulation of heat transfer models in general and for the MCHE specifically. / Thesis (MIng (Nuclear Engineering))--North-West University, Potchefstroom Campus, 2013.

Le travail de cette thèse a pour but de fournir et valider des outils permettant d'étudier et de comprendre les phénomènes mis en jeu lors de l'injection d'un carburant dans un moteur à combustion interne, principalement axé sur l'écoulement intra-injecteur. Ces outils sont numériques et permettent de simuler la formation d'un spray. Une première partie est axée sur la modélisation 0D. Les modèles permettant de prédire des caractéristiques de spray comme son angle, sa pénétration ou encore la longueur du corps liquide, sont comparés à des données expérimentales. Les conclusions sont que la modélisation 0D permet d'obtenir de bons résultats. Par contre une meilleure connaissance de l'influence de la cavitation sur le spray, qui passe par la compréhension de l'écoulement intra-injecteur, pourrait être bénéfique pour la prédiction de ces modèles. Une seconde étude sur l'écoulement intra-injecteur est alors menée en utilisant un modèle à équation barotrope. Une validation de celui-ci est effectuée de façon à vérifier qu'il est capable de prédire correctement l'écoulement dans un injecteur. Le modèle offre de bons résultats et peut être utilisé pour l'étude suivante. Enfin, dans la dernière partie, le modèle de cavitation qui a été validé est utilisé. Une géométrie d'injecteur mono-trou est utilisée avec des pressions comparables à celles utilisées actuellement en automobile. L'étude consiste à étudier l'influence de plusieurs paramètres géométriques sur l'apparition de la cavitation. Le mouvement de l'aiguille est aussi étudié et est comparé, après avoir offert au code la possibilité de maillage mobile, à des résultats in-stationnaires pour plusieurs levées d'aiguille.

O processo de moldagem por injeção de peças de paredes finas apresenta diferenças significativas em relação a processos convencionais de moldagem por injeção de termoplásticos. Processos de paredes finas são caracterizados pelo preenchimento de cavidades com espessuras inferiores a 1 mm utilizando velocidades de preenchimento elevadas. Estes dois fatores afetam o desenvolvimento de tensões induzidas pelo escoamento durante o preenchimento da cavidade, sendo que não foram encontrados na literatura estudos de determinação de tensões induzidas pelo escoamento em cavidades de paredes finas. Neste trabalho são apresentados resultados de determinação de tensões induzidas pelo escoamento em cavidades de paredes finas em comparação com resultados de simulação com cavidades características de processos convencionais. Para o cálculo das tensões induzidas pelo escoamento foi utilizado o modelo incompressível de Leonov. Para isso foi desenvolvida uma metodologia numérica para tratar problemas não isotérmicos utilizando o pacote CFD OpenFOAM. Foi utilizada a abordagem não acoplada, ou seja, o comportamento viscoelástico não é considerado na obtenção dos campos de velocidade, pressão e temperatura. Esta metodologia foi utilizada na simulação do preenchimento de cavidades bidimensionais. Os resultados indicaram que as tensões são influenciadas fortemente pela espessura da cavidade enquanto a velocidade de escoamento causou pequena variação das tensões induzidas pelo escoamento. Este trabalho mostrou que as tensões induzidas pelo escoamento não podem ser desconsideradas na produção de peças moldadas por injeção pelo processo de paredes finas. / Thin wall injection molding process of thermoplastics has significant differences compared to conventional injection molding process. Thin wall processes are characterized by cavities thinner than 1 mm and very high injection velocities. Although these two factors are expected to increase the flow induced stresses development during cavities filling, no previous study on this subject has been found in literature. In the present work, flow induced stresses under thin wall injection molding conditions are calculated using a viscoelastic model and compared to the results obtained under conventional injection conditions. In order to do this, a numerical methodology, based on the solver viscoelasticInterFoam, was developed in the OpenFOAM package to deal with the non-isothermal flow occurring during the mold filling stage. A non-coupled approach was used to calculate the stress field, i.e., the viscoelastic behavior was not considered in the determination of velocity, pressure and temperature fields. This methodology was used in the analysis of the filling stage of two-dimensional cavities. The results indicated that the cavity thickness has more influence on the flow induced stresses than the injection velocity. The obtained results also indicate that the flow induced stresses cannot be neglected in thin wall injection molding processes.

This thesis presents the development of a novel numerical model capable of evaluating suspended sediment dynamics under breaking waves, and is based in the open source Computational Fluid Dynamics software, OpenFOAM®. The hydrodynamics were determined by solving the incompressible, Reynolds-Averaged Navier-Stokes equations for a two-phase fluid using the Finite Volume method, along with a Volume of Fluid scheme that modelled the interface between the air and water phases. A new library of five turbulence models was developed to include weakly compressible effects through the introduction of density variations in the conservation equations. This library was thoroughly evaluated against existing physical data for surf zone dynamics. A skill score was applied, based on the MSE, to rank the models, with the nonlinear k−ε performing best overall, and the k−ω predicting turbulent kinetic energy most accurately. Furthermore, the numerical model was shown to predict the near-bed hydrodynamics well, through comparison with new in-house physical data obtained in the COAST laboratory. Suspended sediment concentrations were determined using an advection-diffusion methodology, with near-bed processes modelled using a flux based approach that balances entrainment and deposition. The model was validated against existing experimental data for steady state flow conditions, as well as for regular and breaking waves. The agreement was generally good, with the results indicating that the model is capable of capturing complicated processes such as sediment plumes under plunging breakers. The validated model was applied to investigate the properties of the sediment diffusivity, which is a vital parameter in suspended sediment dynamics. In physical experiments, sediment diffusivity is commonly estimated implicitly, based on the vertical concentration profile. In this work, this approach was applied to the numerical concentration predictions, and compared with the value directly determined within the model. The estimated value was generally acceptable providing that large horizontal concentration gradients were not present, and diffusion dominated flow advection. However, near the breaking point of waves, large errors were observed at mid-depth of the water column, which strongly correlates with a region of large flow advection relative to diffusion. Therefore, when using this estimation, caution is recommended since this approach can potentially lead to substantial discrepancies.

O processo de moldagem por injeção de peças de paredes finas apresenta diferenças significativas em relação a processos convencionais de moldagem por injeção de termoplásticos. Processos de paredes finas são caracterizados pelo preenchimento de cavidades com espessuras inferiores a 1 mm utilizando velocidades de preenchimento elevadas. Estes dois fatores afetam o desenvolvimento de tensões induzidas pelo escoamento durante o preenchimento da cavidade, sendo que não foram encontrados na literatura estudos de determinação de tensões induzidas pelo escoamento em cavidades de paredes finas. Neste trabalho são apresentados resultados de determinação de tensões induzidas pelo escoamento em cavidades de paredes finas em comparação com resultados de simulação com cavidades características de processos convencionais. Para o cálculo das tensões induzidas pelo escoamento foi utilizado o modelo incompressível de Leonov. Para isso foi desenvolvida uma metodologia numérica para tratar problemas não isotérmicos utilizando o pacote CFD OpenFOAM. Foi utilizada a abordagem não acoplada, ou seja, o comportamento viscoelástico não é considerado na obtenção dos campos de velocidade, pressão e temperatura. Esta metodologia foi utilizada na simulação do preenchimento de cavidades bidimensionais. Os resultados indicaram que as tensões são influenciadas fortemente pela espessura da cavidade enquanto a velocidade de escoamento causou pequena variação das tensões induzidas pelo escoamento. Este trabalho mostrou que as tensões induzidas pelo escoamento não podem ser desconsideradas na produção de peças moldadas por injeção pelo processo de paredes finas. / Thin wall injection molding process of thermoplastics has significant differences compared to conventional injection molding process. Thin wall processes are characterized by cavities thinner than 1 mm and very high injection velocities. Although these two factors are expected to increase the flow induced stresses development during cavities filling, no previous study on this subject has been found in literature. In the present work, flow induced stresses under thin wall injection molding conditions are calculated using a viscoelastic model and compared to the results obtained under conventional injection conditions. In order to do this, a numerical methodology, based on the solver viscoelasticInterFoam, was developed in the OpenFOAM package to deal with the non-isothermal flow occurring during the mold filling stage. A non-coupled approach was used to calculate the stress field, i.e., the viscoelastic behavior was not considered in the determination of velocity, pressure and temperature fields. This methodology was used in the analysis of the filling stage of two-dimensional cavities. The results indicated that the cavity thickness has more influence on the flow induced stresses than the injection velocity. The obtained results also indicate that the flow induced stresses cannot be neglected in thin wall injection molding processes.

La modélisation mathématique des systèmes électrochimiques, et en général la modélisa- tion des systèmes fluidiques réactifs en présence de champs électriques, est un problème d’une complexité telle que des solutions analytiques n’existent que dans des cas très simpli- fiés et la solution numérique est, malgré toute la puissance de calcul moderne, encore très difficile. À ce jour, les avancées dans la modélisation au niveau des modèles d’écoulement sont majeures, mais la modélisation couplée de l’écoulement, avec le champ électrique en présence de solutions concentrées demeure encore un défi de taille. Le couplage des diffé- rents champs décrits par les modèles mathématiques devient critique dans les régions où ont lieu les réactions hétérogènes aux interfaces chargées modélisées par l’équation non linéaire de Butler-Volmer. Les logiciels commerciaux modernes commencent à permettre de coupler les modules d’électrochimie avec la mécanique des fluides numérique (CFD), mais l’ impossibilité d’ac- céder au code source ne permet pas au chercheur de modifier à volonté la formulation des modèles. Par conséquent, le projet de recherche actuel vise le développement d’une plate-forme logicielle ouverte (open-source) comme OpenFOAM, qui peut garantir une complète accessibilité au code-source, la liberté des utilisateurs à faire des modifications, la transparence des détails des modèles, et tous les autres développements qui sont requis pour chaque problème rencontré par les chercheurs. Le développement de modèles reposant sur des lois physiques établies permettra la modéli- sation des systèmes électrochimiques complexes, et la compréhension des phénomènes qui s’y déroulent. Il vise la modélisation du transfert de masse d’une cellule où l’écoulement de la solution concentrée (molten salt) est turbulent, biphasique et incompressible, et les réactions électrochimiques de surface sont calculées en utilisant une distribution tertiaire de densité de courant. Le principal enjeu sur le plan scientifique, dans le cadre de ce projet, demeure donc de développer un modèle qui soit bien calé sur le problème technologique visé afin qu’il puisse reproduire de façon réaliste les systèmes électrochimiques. Il vise éga- lement à amener la modélisation à un point où l’outil pourra être utilisé comme instrument de prédiction et de validation de nouveaux concepts des systèmes électrochimiques. / Abstract: The modeling of electrochemical systems, and in general the modeling of reacting flows ex- posed to electric field, is a complex problem to the point that analytic solutions exist only for simplified cases despite the increasing computer power. The state of art shows major improvements in the fluid-dynamics of electrochemical reactors; but the full coupling of the flow with the electric field in presence of concentrated electrolytic solutions still needs to be properly investigated. The coupling gets even more critical along the charged in- terfaces where heterogeneous reactions are modeled through the non-linear Butler-Volmer equation. Commercial software are slowly try to connect electrochemical modules to the well val- idated CFDs, but most of the time costly licenses, and poor accessibility to the source code, do not allow a deep integration between the two. Instead, this research study pro- poses an open-source code implemented in OpenFOAM, that guarantees full accessibility to the source code, user’s modifications, full transparency of the model’s details, and any possible further developments required by the specificity of the problem. The final code implements the mass transfer of a cell where the concentrated solution (molten salt) is a two-phase turbulent incompressible flow and the electrochemical surface reactions consider tertiary current distributions. The aim of this work is to create an open source platform to predict and analyze industrial reactor’s performances. The advanced modeling can be later exploited and used as a validation instrument for new electrochemical concepts.

O processo de moldagem por injeção de peças de paredes finas apresenta diferenças significativas em relação a processos convencionais de moldagem por injeção de termoplásticos. Processos de paredes finas são caracterizados pelo preenchimento de cavidades com espessuras inferiores a 1 mm utilizando velocidades de preenchimento elevadas. Estes dois fatores afetam o desenvolvimento de tensões induzidas pelo escoamento durante o preenchimento da cavidade, sendo que não foram encontrados na literatura estudos de determinação de tensões induzidas pelo escoamento em cavidades de paredes finas. Neste trabalho são apresentados resultados de determinação de tensões induzidas pelo escoamento em cavidades de paredes finas em comparação com resultados de simulação com cavidades características de processos convencionais. Para o cálculo das tensões induzidas pelo escoamento foi utilizado o modelo incompressível de Leonov. Para isso foi desenvolvida uma metodologia numérica para tratar problemas não isotérmicos utilizando o pacote CFD OpenFOAM. Foi utilizada a abordagem não acoplada, ou seja, o comportamento viscoelástico não é considerado na obtenção dos campos de velocidade, pressão e temperatura. Esta metodologia foi utilizada na simulação do preenchimento de cavidades bidimensionais. Os resultados indicaram que as tensões são influenciadas fortemente pela espessura da cavidade enquanto a velocidade de escoamento causou pequena variação das tensões induzidas pelo escoamento. Este trabalho mostrou que as tensões induzidas pelo escoamento não podem ser desconsideradas na produção de peças moldadas por injeção pelo processo de paredes finas. / Thin wall injection molding process of thermoplastics has significant differences compared to conventional injection molding process. Thin wall processes are characterized by cavities thinner than 1 mm and very high injection velocities. Although these two factors are expected to increase the flow induced stresses development during cavities filling, no previous study on this subject has been found in literature. In the present work, flow induced stresses under thin wall injection molding conditions are calculated using a viscoelastic model and compared to the results obtained under conventional injection conditions. In order to do this, a numerical methodology, based on the solver viscoelasticInterFoam, was developed in the OpenFOAM package to deal with the non-isothermal flow occurring during the mold filling stage. A non-coupled approach was used to calculate the stress field, i.e., the viscoelastic behavior was not considered in the determination of velocity, pressure and temperature fields. This methodology was used in the analysis of the filling stage of two-dimensional cavities. The results indicated that the cavity thickness has more influence on the flow induced stresses than the injection velocity. The obtained results also indicate that the flow induced stresses cannot be neglected in thin wall injection molding processes.

Nanoparticles represent a very exciting new area of research. Their small size, ranging from several nanometers to tens of nanometers, is responsible for many changes in the structural, thermal, electromagnetic, optical and mechanical properties in comparison with the bulk solid of the same materials. However, promoting the use of such material requires well-controlled synthesis techniques to be developed. Inductively coupled thermal plasma (ICTP) reactors have been shown to offer unique advantages over other synthesis methods. The purpose of this thesis is to develop a numerical model to assist the design of an ICTP reactor for the efficient and controlled production of nanoparticles at industrial scale. The complete model describes the evaporation of the micron-sized precursor particles in the plasma flow and the subsequent formation of the nanoparticles in the quenching reactor. The plasma flow is described by a coupled system of the fluid mechanics equations of continuity, momentum, and energy with the vector potential formulation of Maxwell's equations. The solid particles precursors are treated following a Lagrangian approach, taking into account the vapor production field in the plasma flow. An Eulerian model based on the method of moments with interpolative closure is used to describe the formation of nanoparticles by simultaneous nucleation and growth by condensation and coagulation. The coupled plasma torch, particle evaporation and nanoparticle formation models are implemented in 2D and 3D configurations, using the OpenFoam source code. The results show that the effects of the particle evaporation on the temperature field are substantial, even for low particle mass loading. The associated vapor concentration which enters in the reactor has then a direct influence on the formation of nanoparticles. The effects of the plasma torch parameters and the quenching configuration (quench type, position, injection angle and cooling rate) on the contribution of the different formation mechanisms and on the generated particle's size and distribution are studied in both 2D axi-symmetric and 3D geometries. The quench mechanism strongly affects the temperature and the vapor concentration in the reactor, and consequently has an impact on the final particle size distribution. It is shown that the size of the nanoparticles obtained for different quenching conditions is not only a consequence of the cooling rate but also of the trajectories of the vapor and the generated particles imposed by quenching gas. The results have also demonstrated that the predicted particle are smaller and more sensitive to the modifications of the quenching condition when quenching at high temperature. The sensitivity of the complete model to the physical properties of the vapor (vapor pressure and surface tension) is also investigated, in order to identify their effect on the final particle size. The results obtained provide an insight into the phenomena involved during the production of nanoparticles and enable the improvement of ICTP rectors design and nanoparticles synthesis process. / Doctorat en Sciences de l'ingénieur et technologie / info:eu-repo/semantics/nonPublished

Le travail de cette thèse a pour but de fournir et valider des outils permettant d'étudier et de comprendre les phénomènes mis en jeu lors de l'injection d'un carburant dans un moteur à combustion interne, principalement axé sur l'écoulement intra-injecteur. Ces outils sont numériques et permettent de simuler la formation d'un spray. Une première partie est axée sur la modélisation 0D. Les modèles permettant de prédire des caractéristiques de spray comme son angle, sa pénétration ou encore la longueur du corps liquide, sont comparés à des données expérimentales. Les conclusions sont que la modélisation 0D permet d'obtenir de bons résultats. Par contre une meilleure connaissance de l'influence de la cavitation sur le spray, qui passe par la compréhension de l'écoulement intra-injecteur, pourrait être bénéfique pour la prédiction de ces modèles. Une seconde étude sur l'écoulement intra-injecteur est alors menée en utilisant un modèle à équation barotrope. Une validation de celui-ci est effectuée de façon à vérifier qu'il est capable de prédire correctement l'écoulement dans un injecteur. Le modèle offre de bons résultats et peut être utilisé pour l'étude suivante. Enfin, dans la dernière partie, le modèle de cavitation qui a été validé est utilisé. Une géométrie d'injecteur mono-trou est utilisée avec des pressions comparables à celles utilisées actuellement en automobile. L'étude consiste à étudier l'influence de plusieurs paramètres géométriques sur l'apparition de la cavitation. Le mouvement de l'aiguille est aussi étudié et est comparé, après avoir offert au code la possibilité de maillage mobile, à des résultats in-stationnaires pour plusieurs levées d'aiguille. / The work of this thesis aims to provide and validate tools useful to study and understand the phenomena involved in the injection of fuel, mainly focused on intra-flow injector. These tools are numeric and simulate the formation of a spray. A first part focuses on zero-dimensional modelling. Models which predict these following characteristics of spray like the spray angle, the spray penetration or the liquid length are compared with experimental data. The conclusions are that zero-dimensional modelling provides good results very quickly in some cases. Although, a better understanding of the influence of cavitation on the spray, which requires an understanding of the intra-flow injector, could be beneficial for the prediction of these models. A second study is carried out to select a model of multi-dimensional cavitation. The chosen model is a barotropic equation model. A validation of this model is then performed to ensure that it is able to predict the cavitating flow inside a nozzle. The model provides good results and can be used for the next step. Finally, in the third part, the cavitation model previously validated is used. Single-hole nozzle geometry is used with an injection pressure comparable to that used in internal combustion engines with direct injection system. The study is done to investigate the influence of several geometrical parameters on the onset of cavitation. The movement of the needle is also studied and compared, after offering to the code the possibility of moving mesh, to the results of several stationary needle lifts.