The aim of this study is to develop a code that is capable of solving three-dimensional compressible flows which are viscous and turbulent, and parallelization of this code. Purpose of parallelization is to obtain a computational efficiency in time respect which enables the solution of complex flow problems in reasonable computational times. In the first part of the study, which is the development of a three-dimensional Navier-Stokes solver for turbulent flows, first step is to develop a two-dimensional Euler code using Roe flux difference splitting method. This is followed by addition of sub programs involving calculation of viscous fluxes. Third step involves implementation of Baldwin-Lomax turbulence model to the code. Finally, the Euler code is generalized to three-dimensions. At every step, code validation is done by comparing numerical results with theoretical, experimental or other numerical results, and adequate consistency between these results is obtained. In the second part, which is the parallelization of the developed code, two-dimensional code is parallelized by using Message Passing Interface (MPI), and important improvements in computational times are obtained.

En vue d’applications aux turbines éoliennes, cette thèse vise à étendre l’utilisation des méthodes de type domaines fictifs et en particulier la méthode de pénalisation pour la simulation de l’écoulement turbulent instationnaire autour d’obstacles de géométrie complexe.La modélisation de la turbulence instationnaire à nombres de Reynolds élevés a été abordée par des approches hybrides RANS/LES telles que la (DES) et la (DDES). Afin d’améliorer la prédiction, un modèle de paroi de type TBLE a été introduit.Après une brève présentation des méthodes et des outils mis en oeuvre, des simulations2D/3D sur la configuration de cylindre et du canal sont ensuite présentées, analysées et comparées aux résultats numériques et expérimentaux.Les résultats de simulation montrent la faisabilité et l’efficacité des modèles et de la méthode de couplage (DDES/TBLE). La dernière étude se concentre sur la simulation de l’écoulement d’air autour d’un profil de pale. Les réussites et les échecs des simulations numériques sont soulignés et étudiés.En conclusion, l’étude établit les fondements pour une future application dans le cas de l’écoulement autour d’un rotor éolien en mouvement. / In the perspective of application to wind turbine design, this thesis aims to extend theuse of fictitious domain methods and in particular the method of penalization for the simulation of unsteady turbulent flows around obstacles of complex geometry. The unsteady turbulence modeling at high Reynolds numbers was studied by hybrid approaches(RANS / LES) such as (DES) and (DDES). In order to improve the prediction, a wall model based on simplified Thin Boundary Layer Equations (TBLE) was introduced.After a brief presentation of the tools and methods implemented, full 2D / 3D computations on cylinder and channel configuration are then presented, analyzed and compared to numerical and experimental results.The simulation results show the feasibility and effectiveness of the proposed models and the coupling method (DDES / TBLE).The latest investigation focuses on the simulation of the flow around the airfoil of a wind turbine. The success and fails of the computations are highlighted and explained.

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In gas stirred steelmaking ladles, entrainment of slag into metal and vice versa takes place. The slag entrainment has been shown to abruptly increase the mass transfer rates of refining reactions through high temperature and water modeling studies of the past. However such an effect has not been correlated with the degree of entrainment, since the latter has not been quantified in terms of operating parameters like gas injection rate and fluid properties. Much of the past works are limited to finding the critical conditions for onset of entrainment. The difficulty lies in measuring the degree of entrainment in industrial ladles or even in a water model. Mathematical modeling is also challenging due to the complexity of the multiphase phenomena. So in this thesis, a modular mathematical modeling approach is presented wherein the phenomena of slag entrainment into metal is resolved into four aspects, models developed for each and finally integrated to study its role. The individual models are (1) multiphase large eddy simulations to simulate slag entrainment in a narrow domain that receives its boundary conditions from (2) single phase RANS simulation of a full ladle, (3) a Lagrangian particle tracking method to compute the residence times of slag droplets in metal phase and (4) a kinetic model that integrates the above three models to compute mass transfer rate as a function of degree of entrainment. Mass transfer rate predictions comparable to a literature correlation were obtained. This supports the modeling approach and also the assessment of role of various system parameters on entrainment characteristics. In essence, the present work shows a systematic approach to model and study the complex multiphase phenomena. / Thesis / Doctor of Philosophy (PhD) / The entrainment of liquid slag into liquid steel in gas stirred-steelmaking ladles is known to increase the rate of refining drastically. However, there is lack of correlation between degree of entrainment and ladle operating conditions, which this thesis addresses through mathematical modeling.

Yes / A problem with 1-D water hammer modelling is in the application of accurate unsteady friction. Moreover, investigating the time response of fluid dynamics and unsteady turbulence structures during the water hammer is not possible with a 1-D model. This review article provides a summary of 1-D modelling using the recent finite volume approach and the discussion extends to a quasi-2-D model and historical developments as well as recent advancements in 3-D CFD simulations of water hammer. The eddy viscosity model is excellent in capturing pressure profiles but it is computationally intensive and requires more computational time. This article reviews 3-D CFD simulations with sliding mesh, an immersed solid approach, and dynamic mesh approaches for modelling valve closures. Despite prediction accuracy, a huge computational time and high computer resources are required to execute 3-D flow simulations with advanced valve modelling techniques. Experimental validation shows that a 3-D CFD simulation with a flow rate reduction curve as a boundary condition predicted accurate pressure variation results. Finally, a brief overview of the transient flow turbulence structures for a rapidly accelerated and decelerated pipe flow using DNS (Direct numerical simulation) data sets is presented. Overall, this paper summarises past developments and future scope in the field of water hammer modelling using CFD.

Thesis (MEng)--University of Stellenbosch, 2000. / ENGLISH ABSTRACT: This study investigates the implementation of the finite volume numerical method applicable to non-orthogonal control volumes and the application of the method to calculate the thermo-flow field within the collector area of a solar chimney power generating plant. The discretisation of the governing equations for the transient, Newtonian, incompressible and turbulent fluid flow, including heat transfer, is presented for a non-orthogonal coordinate frame. The standard k - E turbulence model, modified to include rough surfaces, is included and evaluated in the method. An implicit solution procedure (SIP-semi implicit procedure) as an alternative to a direct solution procedure for the calculation of the flow field on nonstaggered grids is investigated, presented and evaluated in this study. The Rhie and Chow interpolation practice was employed with the pressurecorrection equation to eliminate the presence of pressure oscillations on nonstaggered grids. The computer code for the solution of the three-dimensional thermo-flow fields is developed in FORTRAN 77. The code is evaluated against simple test cases for which analytical and experimental results exist. It is also applied to the analysis of the thermo-flow field of the air flow through a radial solar collector. KEYWORDS: NUMERICAL METHOD, FINITE VOLUME, NON-ORTHOGONAL, k+-e TURBULENCE MODEL, SIP / AFRIKAANSE OPSOMMING: Die studie ondersoek die implementering van 'n eindige volume numeriese metode van toepassing op nie-ortogonale kontrole volumes asook die toepassing van die metode om die termo-vloei veld binne die kollekteerder area van 'n sonskoorsteen krag aanleg te bereken. Die diskretisering van die behoudsvergelykings vir die tyd-afhanlike, Newtonse, onsamedrukbare en turbulente vloei, insluitende hitteoordrag, word beskryf vir 'n nie-ortogonale koordinaatstelsel. Die standaard k - E turbulensiemodel, aangepas om growwe oppervlakrandvoorwaardes te hanteer, is ingesluit en geevalueer in die studie. 'n Implisiete oplossings metode (SIP-semi implisiete prosedure) as alternatief vir 'n direkte oplossingsmetode is ondersoek en geimplimenteer vir die berekening van die vloeiveld met nie-verspringde roosters. 'n Rhie en Chow interpolasie metode is gebruik tesame met die drukkorreksie-vergelyking ten einde ossilasies in die drukveld in die nie-verspringde roosters te vermy. Die rekenaarkode vir die oplossing van die drie dimensionele termo-vloeiveld is ontwikkel in FORTRAN 77. Die kode is geevalueer teen eenvoudige toetsprobleme waarvoor analitiese en eksperimentele resultate bestaan. Die kode IS ook gebruik om die termo-vloeiveld binne 'n radiale son kollekteerder te analiseer. SLEUTELWOORDE: NUMERIESE METODE, EINDIGE VOLUME, NIE-ORTOGONAAL, k - E TURBULENSIE MODEL, SIP

This study addressed the numerical modelling of flow and diffusion in packed beds of mono-sized spheres. Comprehensive research was conducted in order to implement various numerical approaches in explicit1 and implicit2 simulations of flow through packed beds of uniform spheres. It was noted from literature that the characterization of a packed bed using porosity as the only geometrical parameter is inadequate (Van Antwerpen, 2009) and is still under much deliberation due to the lack of understanding of different flow phenomena through packed beds. Explicit simulations are not only able to give insight into this lack of understanding in fluid mechanics, but can also be used to develop different flow correlations that can be implemented in implicit type simulations. The investigation into the modelling approach using STAR-CCM+®, presented a sound modelling methodology, capable of producing accurate numerical results. A new contact treatment was developed in this study that is able to model all the aspects of the contact geometry without compromising the computational resources. This study also showed, for the first time, that the LES (large eddy simulation) turbulence model was the only model capable of accurately predicting the pressure drop for low Reynolds numbers in the transition regime. The adopted modelling approach was partly validated in an extensive mesh independency test that showed an excellent agreement between the simulation and the KTA (1981) and Eisfeld and Schnitzlein (2001) correlations' predicted pressure drop values, deviating by between 0.54% and 3.45% respectively. This study also showed that explicit simulations are able to accurately model enhanced diffusion due to turbulent mixing, through packed beds. In the tortuosity study it was found that the tortuosity calculations were independent of the Reynolds number, and that the newly developed tortuosity tests were in good agreement with techniques used by Kim en Chen (2006), deviating by between 2.65% and 0.64%. The results from the TMD (thermal mixing degree) tests showed that there appears to be no explicit link between the porosity and mixing abilities of the packed beds tested, but this could be attributed to relatively small bed sizes used and the positioning and size of the warm inlet. A multi-velocity test showed that the TMD criterion is also independent of the Reynolds number. It was concluded that the results from the TMD tests indicated that more elaborate packed beds were needed to derive applicable conclusions from these type of mixing tests. The explicit BETS (braiding effect test section) simulation results confirmed the seemingly irregular temperature trends that were observed in the experimental data, deviating by between 5.44% and 2.29%. From the detail computational fluid dynamics (CFD) results it was possible to attribute these irregularities to the positioning of the thermocouples in high temperature gradient areas. The validation results obtained in the effective thermal conductivity study were in good agreement with the results of Kgame (2011) when the same fitting techniques were used, deviating by 5.1%. The results also showed that this fitting technique is highly sensitive for values of the square of the Pearson product moment correlation coefficient (RSQ) parameter and that the exclusion of the symmetry planes improved the RSQ results. It was concluded that the introduction of the new combined coefficient (CC) parameter is more suited for this type of fitting technique than using only the RSQ parameter. / Thesis (M.Ing. (Mechanical Engineering))--North-West University, Potchefstroom Campus, 2012

Pour améliorer la conception des turbomachines, les industriels doivent appréhender des phénomènes aéroélastiques complexes présents dans les compresseurs comme les cycles limites d’interaction fluide-structure des fans. La compréhension et la modélisation de ces phénomènes impliquent de développer des modèles numériques complexes intégrant des phénomènes multi-physique et de valider ces modèles à l’aide de bancs d’essais. Le banc d’essai du compresseur CREATE est instrumenté pour étudier des instabilités aérodynamiques couplées à des vibrations, notamment sur le rotor du premier étage, et permet de valider des modèles numériques. La modélisation de l’écoulement en amont du premier étage du compresseur à l’aide du logiciel Turb’Flow, développé pour l’étude des écoulements dans les compresseurs aéronautiques, a permis de mettre en évidence l’importance des conditions limites d’entrée pour l’obtention de résultats précis. En particulier, il a été possible de modéliser correctement l’ingestion d’une alimentation non-homogène en entrée de la roue directrice d’entrée. Ce phénomène peut se produire en amont des fans et interagir avec un mode de la structure. Une stratégie de couplage partitionné fort explicite dans le domaine temporel a été introduite dans le logiciel Turb’Flow. Comme cette méthode présente un risque de décalage temporel à l’interface fluide-structure, une attention particulière a été portée à la modélisation de la conservation de l’énergie à cette interface. La conservation de l’énergie à l’interface est cruciale quand les déplacements sont importants et quand un comportement non-linéaire fort apparaît entre le fluide et la structure (onde de choc et amortissement structurel nonlinéaire). Parallèlement au développement du module aéroélastique, le schéma implicite de Runge- Kutta d’ordre 3 en temps (RKI-3) a été développé et évalué sur un cas de dynamique (vibration d’une aube de turbine transsonique) et sur un cas de propagation d’onde de choc. L’utilisation du schéma RKI-3 permet d’augmenter, à iso-précision, d’un ordre le pas de temps par rapport aux schémas de Gear et de Newmark. S’il apporte un gain en temps CPU pour l’étude de la dynamique des structures, il est pénalisant dans le cadre de simulation URANS. Cependant, le schéma RKI-3 est utilisable dans le cadre de simulations couplées fluide-structure. / To increase turbomachinery design, manufacturers have to comprehend complex aeroelastic phenomena involving compressors like fluid-structure interaction limit cycles of fans. The understanding and the modeling of these phenomena involve developing complex solvers coupling techniques and validating these techniques with bench tests. The bench test of the CREATE compressor is instrumented to study the coupling between aerodynamic instabilities and structure vibration, in particular on the first stage rotor, and allows to validate numerical techniques. The flow modeling upstream to the first stage with the Turb’Flow flow solver (targeting turbomachinery applications) shows that, to have accurate results, inlet limit conditions must take into account. The ingestion of non-homogeneous flow upstream to the inlet guide vane is accurately modeled. This phenomenon can appear upstream to fans and interact with structure Eigen-modes. Explicit partitioned strong coupling considered in time domain was implemented in a Turb’Flow flow solver. As there is a risk of time shift at the fluid-structure interface, careful attention should be paid to energy conservation at the interface. This conservation is crucial when displacements are large and when strong non-linear behaviors occur in both fluid and structure domains, namely shock waves, flow separations and non-linear structural damping. In parallel with coupling technique development, the three-order implicit Runge-Kutta scheme (RKI-3) was implemented and validated on a structure dynamic case (transonic turbine blade vibration) and on a case of shock waves propagation. The RKI-3 scheme allows increasing the time step of one order of magnitude with the same accuracy. There is a CPU time gain for structure dynamics simulations, but no for URANS simulations. However, the RKI-3 scheme can be to use for fluid-structure coupling simulations. The coupling technique was validated on a test case involving tube in which the shock wave impinges on a cross flow flexible panel, initially at rest. This case allows modeling an interaction between sonic flow and a panel movement with a tip clearance. Some numerical simulations were carried out with different temporal schemes. The RKI-3 scheme has no influence on results (compared with Gear and/or Newmark scheme) on the energy conservation at the fluid-structure interface. Compared to experimental results, pressure is in fairly good ix Liste des publications agreement. The analysis of numerical results highlighted that a vertical shock tube with up and down waves creates pressure fluctuation. Frequency is under predicted and amplitude is not in fairly good agreement. The panel root modeling might be questionable.

[pt] Neste trabalho três métodos foram utilizados para estudar o escoamento turbulento em regiões de florestas. No primeiro método, a influência da vegetação no escoamento foi modelada através da adição de termos fontes nas equações de quantidade de movimento, energia cinética turbulenta e sua taxa de dissipação. No segundo, a vegetação foi considerada um meio poroso homogêneo. Finalmente, a camada do dossel foi representada por modelos 3-D de árvores, consideradas como obstáculos individuais. As equações foram resolvidas através do modelo de turbulência k −E padrão com o programa comercial FLUENT 6.2.16. As previsões dos perfis verticais da velocidade do vento médio, da intensidade da turbulência e dos tensores de Reynolds, foram comparadas com dados de experimentos de túnel de vento. Os resultados preditos dos perfis verticais da velocidade média e intensidade da turbulência, na primeira e na segunda metodologias, apresentaram boa concordância com os valores experimentais, porém, foram observadas discrepâncias nos perfis modelados do tensor de Reynolds. Entretanto, qualitativamente, a modelagem consegue capturar o comportamento físico do tensor de Reynolds no interior de florestas. Uma possível explicação para este fato, é que o modelo considera a isotropia para a viscosidade turbulenta, implicando na incapacidade de prever qualquer forte anisotropia do campo turbulento. Na terceira metodologia, as previsões dos perfis verticais de velocidade média e intensidade da turbulência apresentaram discrepâncias em relação às medições. Porém, os perfis verticais do tensor de Reynolds apresentaram boa concordância. Todos os perfis verticais da velocidade média apresentaram um ponto de inflexão na interface vegetação-atmosfera, característico de uma camada de mistura. Nas duas primeiras metodologias, este padrão foi confirmado nos perfis de tangente hiperbólica de uma camada de mistura. / [en] This work investigates different procedures in order to study the turbulent flow over the scale model of a forest region. Initially, the canopy flow was modeled by using source terms in the momentum, turbulent kinetic energy and its dissipation rate equations. After that, the forest canopy was considered a homogeneous porous medium. In the last step, the canopy boundary layer was modeled by artificial 3-D tree models. This was done by using the standard k−E turbulence model with the FLUENT commercial program. The modeled profiles of mean velocity, turbulence intensity and Reynolds stress were compared against data from wind tunnel experiments. In the two first methodologies, the model predictions of the vertical profiles of the wind speed and turbulence intensity showed good agreement with the experimental data. It was found that predictions of the Reynolds tensor were sensitive to the parameterization scheme of the standard k −E model. However, qualitatively, the model was capable of predicting the physical behavior of the Reynolds stress tensor in the canopy flow. A possible explanation for this behavior is the omission of any anisotropic eddy-viscosity effects within the k - E modelling approach. When it was considered the tree array, the model predictions for the wind speed and turbulence intensity were less satisfactory. However, it was found that the predicted results of the Reynolds stress tensor agreed well with the measured data. All the vertical profiles of the mean velocity contained an inflection point, something which is a necessary criterion for the mixing layer flow. In the tree array, the modeled results failed to the capture this behavior of the canopy flow. In the 2-D numerical simulations, it was found the characteristic hyperbolic tangent profile of a mixing layer.

Orientador: Alcides Padilha / Banca: Ivan De Domenico Valarelli / Banca: Kamal Abdel Radi Ismail / Resumo: Neste trabalho apresenta-se uma análise teórica e experimental dos resultados comparativos entre as curvas características de um ventilador axial utilizado em um sistema de pulverização agrícola para um ângulo de ataque da pá em 32 graus nas rotações de 1500, 1750, 2600 e 3000 rpm e resultados numéricos da influência da variação do ângulo de ataque da pá em 28, 32 e 36 graus e da otimização do sistema de pulverização ambos para uma rotaç]ao de 2600 rpm. O campo médio turbulento foi obtido com a aplicação da média temporal sendo que o modelo de turbulência exigido para o fechamento do conjunto de equações foi o modelo k-ε de duas equações. A resolução de todos os fenômenos acoplados foi alcançada com o auxílio do código de fluidodinâmica computacional CFX que utiliza a técnica dos volumes finitos como método numérico. Para validação da análise teórica, realizaram-se experimentos em um túnel de vento horizontal de seção circular com diâmetro de 622 mm, usando um tubo de Pitot para as tomadas de pressão de acordo com a norma para ensaios em laboratório. Apresentam-se resultados qualitativos na forma de vetores e mapas de gradiente de velocidade e, quantitativos na forma de tabelas e gráficos para as curvas características. / Abstract: This paper presents a theoretical and experimental analysis of comparative results the characteristic curves of an axial fan used in an agricultural spraying system for a blade attack angle of 32 degrees at rotations of 1500, 1750, 2600 and 3000 rpm and numerical results for the influence of blade attack angle variation at 28, 32 and 36 degrees and optimization of the spraying system, both for a rotation of 2600 rpm. The average turbulent field was obtained from the application of time average where the turbulence model required for closing the set of equations was the k-ε model for two equations. Resolution of all connected phenomena was achieved with the help of the fluid dynamics computacional, CFX, which uses the finite volumes technique as a numerical method. In order to validate the theoretical analysis, an experiment was conducted in a circular section of a horizontal wind tunnel, 622 mm in diameter and 6220 mm in length, using a Pitot tube for pressure readings according to the norm for laboratory assays. Qualitative results are shown as vectors and gradient maps for speed and quantitative results are shown in tables and graphics for characteristic curves. / Mestre