In this thesis study, implementation, numerical stability and convergence rate issues of turbulence modeling are explored. For this purpose, a one equation turbulence model, Spalart-Allmaras, and a two-equation turbulence model, SST k-w, are adapted to an explicit, cell centered, finite volume method based, structured / hybrid multi grid flow solver, SENSE2D, developed at TUBITAK-SAGE. Governing equations for both the flow and the turbulence are solved in a loosely coupled manner, however, each set of equations are solved using a coupled, semi-implicit solution algorithm. In multigrid solutions, the semi-implicit solution algorithm and the turbulence model equations are employed only in the finest level grid. As a result, stable and convergent numerical solutions are obtained. In order to validate the turbulence models and the semi-implicit solution algorithm implemented, turbulent flow solutions over a flat plate, RAE2822 airfoil and NLR7301 multi element airfoil are performed. The results are compared with the experimental data and the numerical results of the commercial CFD package FLUENT. It is shown that the numerical results obtained by SENSE2D are in good agreement with the experimental data and the FLUENT results. In addition to the turbulence modeling studies, convergence rate studies are also performed by multigrid and semi-implicit solution methods. It is shown that, the convergence rates of the semi-implicit solutions are increased about 5 times for single grid and 35% for multigrid solutions in comparison to the explicit solutions.

In order to handle turbulent flow problems, one equation turbulence models are implemented in to a previously developed explicit, Reynolds averaged Navier-Stokes solver. Discretization of Navier-Stokes solver is based on cell-vertex finite volume formulation combined with single step Lax-Wendroff numerical method which is second order accurate in space. Turbulent viscosity is calculated by using one equation Spalart-Allmaras and Baldwin-Barth turbulence transport equations. For the discretization of Spalart-Allmaras and Baldwin-Barth equations, both finite volume scheme which is used for Navier-Stokes equation in this work and explicit finite difference discretization method are used. In order to increase the convergence rate of the solver, local time stepping technique is applied. Stabilization of non-physical oscillations resulting from the numerical scheme is maintained by adding second and fourth order artificial smoothing terms. Three test cases are considered. In order to validate the accuracy of the Navier-Stokes solver, solver is tested over a laminar flat plate. The results are compared with analytical solutions. Later, in order to check the performance of the turbulence models, turbulent flow over flat plate and turbulent transonic flow over NACA-0012 airfoil are handled. For turbulent flow over flat plate obtained results are compared with analytical and empirical solutions, whereas for transonic turbulent flow obtained results are compared with numerical and experimental solutions.

Com os grandes avanços ocorridos na disponibilização de computadores, existe uma tendência contínua para a utilização de técnicas computacionais auxiliando no projeto de equipamentos de engenharia. Cada vez mais estão se obtendo resultados bastante próximos às condições reais, incluindo a simulação de motores de combustão interna. Neste sentido o presente trabalho tem o objetivo de analisar o escoamento turbulento no processo de admissão de ar em um motor operando em ciclo Diesel. A investigação é focada na determinação da influência do passo de tempo no cálculo do coeficiente de descarga e razão de swirl. Adicionalmente, o campo de velocidades, pressão, energia cinética turbulenta e outros parâmetros são apresentados e analisados, com o objetivo de auxiliar no entendimento da dinâmica envolvida. Essencialmente, dois modelos de turbulência são empregados, juntamente com dois tratamentos de parede. Seus resultados também são confrontados e discutidos. A geometria considerada é de um motor Fiat 1.9 L quatro tempos com duas válvulas. A análise é concentrada em um único cilindro. O pacote computacional utilizado é o Star-cd, e seu aplicativo es-ice. A independência de malha foi obtida, chegando a 1.672.056 volumes. Os resultados são apresentados de duas formas. A primeira delas refere-se a resultados de simulações em regime permanente, realizadas em boa parte por outros autores, com ênfase na determinação do coeficiente de descarga e razão de swirl, estes confrontados com valores experimentais, visando à validação da metodologia. Fica evidente a importância da escolha do modelo de turbulência na simulação de motores de combustão interna, assim como das funções de interpolação utilizadas. Na segunda parte os resultados referem-se a uma análise transiente, considerando o movimento do pistão e válvulas, a 1500 RPM. Observa-se a grande exigência quanto ao passo de tempo requerido no transiente real, ficando demonstrado que para esta velocidade o menor passo de tempo utilizado, 0,05° (5.5555E-6 s), ainda é insuficiente para alguns momentos do ciclo. É possível notar maior influência no coeficiente de descarga do que na razão de swirl, em relação aos passos de tempo utilizados. A forte dependência do modelo de turbulência nos resultados obtidos é mais uma vez confirmada, conforme o esperado, já que as hipóteses sobre a física do fenômeno são diferentes em cada modelo. Os resultados quanto ao tratamento na parede não apresentaram significantes diferenças, quando aplicados junto ao modelo de turbulência k-ω SST. / Considering the increase in the availability of computers, there is a continuing trend toward the use of computational simulation aiding in the design of engineering equipments. Reasonable results, close to the real conditions, are obtained, including the simulation of internal combustion engines. In this way, the present work has the objective of analyzing the turbulent flow in the air intake process of an engine operating in Diesel cycle. The investigation focuses on the determination of the time step in the calculation of the air discharge coefficient and swirl ratio. Additionally, the turbulent kinetic energy, pressure and velocity fields, besides other parameters, are presented and analyzed, with the objective of aiding in the understanding of the involved dynamics. Essentially, two turbulence models are employed, together with two wall treatments. Their results are also confronted and discussed. The considered geometry is a four-stroke, 1.9-L FIAT engine, with two valves. The analysis is concentrated on a single cylinder. The software package used is the Star-cd, and its application es-ice. The mesh independence is carried out, arriving in 1.672.056 volumes. The results are presented in two ways. The first one refers to simulation results of the steady state, also accomplished by other authors, with emphasis in the determination of the discharge coefficient and swirl ratio. These data are confronted with experimental values, aiming to validate the applied methodology. The importance of the choice of the turbulent model becomes evident in the simulation of internal combustion engines, as well as the interpolation functions used. In the second part the results refer to a transient analysis, considering the valves and piston movement, at 1500 rpm. It is observed the great demand on time step required is observed for the real transient, demonstrating that, for this speed, the smallest time step used, 0.05º (5.5555E-6 s), is still insufficient for some moments of the cycle. Also regarding the time step, it is possible to notice a greater influence in the discharge coefficient than in the swirl ratio. The strong dependence of the turbulence model on the results is once again confirmed, as expected, since the hypotheses about the physics of the phenomenon are different in each model. The results, regarding the wall treatment, presented no significant differences, when applied together with the SST k-ω turbulence model.

CoordenaÃÃo de AperfeiÃoamento de Pessoal de NÃvel Superior / No presente trabalho foi realizada a investigaÃÃo numÃrica e experimental do desempenho aerodinÃmico de dois aerogeradores tripà de pequeno porte com 3 m de diÃmetro. Os perfis aerodinÃmicos utilizados, NACA 0012 (simÃtrico) e NACA 4412 (cambado), foram projetados para aplicaÃÃes em baixas velocidades, como à o caso de turbinas eÃlicas de eixo horizontal. Os aerogeradores foram construÃdos e testados no LaboratÃrio de Energia Solar e GÃs Natural - UFC. Isto permitiu a determinaÃÃo das curvas de desempenho dos mesmos, possibilitando a comparaÃÃo posterior com os resultados da anÃlise numÃrica. A fim de calibrar o modelo de turbulÃncia k-ω SST para aplicaÃÃo em turbinas eÃlicas de pequeno porte, foram realizadas simulaÃÃes numÃricas utilizando o pacote de CFD OpenFOAM, versÃo 1.7.1. Os resultados numÃricos e experimentais foram comparados, de tal forma que, a partir da variaÃÃo de parÃmetros como intensidade de turbulÃncia, comprimento caracterÃstico turbulento e β* (constante de calibraÃÃo do modelo), pode-se concluir que os resultados numÃricos foram pouco sensÃveis aos dois primeiros parÃmetros, enquanto a variaÃÃo de β* impactou de forma significativa os resultados numÃricos. A mudanÃa do aerofÃlio nÃo alterou o valor de β* que melhor ajustou o resultado. Isto, alÃm do sucesso do processo de calibraÃÃo, indica que a cambagem nÃo influenciou na calibraÃÃo do modelo de turbulÃncia, o que à muito positivo, pois permite uma avaliaÃÃo de cenÃrios diferentes, tal como pÃs projetadas com outros perfis aerodinÃmicos. / In this work it was performed a numerical and experimental investigation of the aerodynamic performance of two small three-bladed wind turbines with diameter of 3m. The airfoils used, NACA 0012 (symmetrical) e NACA 4412 (unsymmetrical), were designed for low speed applications, such as the horizontal axis wind turbines. The wind turbines were built and tested at the Solar Energy and Natural Gas Laboratory âUFC. This allowed the attainment of the performance curves, enabling the comparison between the results of the numerical analysis. In order to calibrate the turbulence model k-ω SST to applications in small wind turbines, it was performed numerical simulations using the open source package for CFD solutions OpenFOAM, version 1.7.1. The numerical and experimental results were compared, in a way that, from the variation of parameters such as turbulence intensity, characteristic length and β* (calibration constant), it can be concluded that the numerical results were little sensitive to the first two parameters, while the variation of β* impacted significantly the numerical results. The change of airfoil did not modify the value of β* that best adjusted the result. This, beyond the success of the calibration process, indicates that the camber did not affect the calibration of the turbulence model, which is very positive because it allows an evaluation of different scenarios, such as blades designed with other airfoils.

Conventional one-point turbulence closures have beenextended with an additional transported scalar for modeling ofmagnetohydrodynamic (MHD) turbulence. The new scalar, α ,captures the length scale anisotropy and tendency towardstwo-dimensionality, which is characteristic feature of MHDturbulence, and allows accurate modeling of the Jouledissipation of turbulence. The concept has been used for both afull Reynolds stress closure, and a three-equationK-ε -αmodel. An exact transport equation forαwas derived from the governing equations. All terms inthe equation require modeling, however. The proposed modeltransport equation for α includes terms for magneticdissipation, nonlinear energy transfer, and effects of meanshear and strain. Modeling of the magnetic and strain-relatedterms was based on rapid distortion analysis of the linearizedequations, while modeling of nonlinear effects isphenomenological in nature. For homogeneous turbulence, themodel was compared with linear theory, direct numericalsimulations and experiments. For turbulence subjected to astrong magnetic field, the model reproduces the energy andlength scale evolution predicted by linear theory. Whennonlinear effects are of importance, it predicts energy decayand length scale evolution in agreement with experiments. Theeddy viscosity and Reynolds stress versions of the modelcoincide with the respective conventional models in the absenceof a magnetic field. The objective of this project has been todevelop efficient MHD turbulence models for engineeringapplications, especially for modeling of continuous steelcasting. The novel MHD turbulence models appear to benumerically robust, and they have been implemented in acommercial flow solver, together with electromagnetic equationsfor the Lorentz forces in the mean momentum equations. <b>Keywords:</b>Turbulence model, magnetohydrodynamics, MHD,magnetohydrodynamic turbulence, computational fluid dynamics,continuous casting, dimensionality, Reynolds stresses, eddyviscosity

Turbulent gas-solid flows are readily encountered in many industrial and environmental processes. The development of a generic modeling technique for gas-solid turbulent flows remains a significant challenge in the field of mechanical engineering. Eulerian models are typically used to model large systems of particles. In this dissertation, a numerical analysis was carried out to assess a current state-of-the-art Eulerian two-fluid model for fully-developed turbulent gas-solid upward flow in a vertical pipe. The two-fluid formulation of Bolio et al. (1995) was adopted for the current study and the drag force was considered as the dominant interfacial force between the solids and fluid phase. In the first part of the thesis, a two-equation low Reynolds number k-ε model was used to predict the fluctuating velocities of the gas-phase which uses an eddy viscosity model. The stresses developed in the solids-phase were modeled using kinetic theory and the concept of granular temperature was used for the prediction of the solids velocity fluctuation. The fluctuating drag, i.e., turbulence modulation term in the transport equation of the turbulence kinetic energy and granular temperature was used to capture the effect of the presence of the dispersed solid particles on the gas-phase turbulence. The current study documents the performance of two popular turbulence modulation models of Crowe (2000) and Rao et al. (2011). Both models were capable of predicting the mean velocities of both the phases which were generally in good agreement with the experimental data. However, the phenomena that small particles cause turbulence suppression and large particles cause turbulence enhancement was better captured by the model of Rao et al. (2011); conversely, the model of Crowe (2000) produced turbulence enhancement in all cases. Rao et al. (2011) used a modified wake model originally proposed by Lun (2000) which is activated when the particle Reynolds number reaches 150. This enables the overall model to produce turbulence suppression and augmentation that follows the experimental trend. The granular temperature predictions of both models show good agreement with the limited experimental data of Jones (2001). The model of Rao et al. (2011) was also able to capture the effect of gas-phase turbulence on the solids velocity fluctuation for three-way coupled systems. However, the prediction of the solids volume fraction which depends on the value of the granular temperature shows noticeable deviations with the experimental data of Sheen et al. (1993) in the near-wall region. Both turbulence modulation models predict a flat profile for the solids volume fraction whereas the measurements of Sheen et al. (1993) show a significant decrease near the wall and even a particle-free region for flows with large particles. The two-fluid model typically uses a low Reynolds number k-ε model to capture the near-wall behavior of a turbulent gas-solid flow. An alternative near-wall turbulence model, i.e., the two-layer model of Durbin et al. (2001) was also implemented and its performance was assessed. The two-layer model is especially attractive because of its ability to include the effect of surface roughness. The current study compares the predictions of the two-layer model for both clear gas and gas-solid flows to the results of a conventional low Reynolds number model. The effects of surface roughness on the turbulence kinetic energy and granular temperature were also documented for gas-particle flows in both smooth and rough pipes.

Experiments and simulations were performed to examine the complex processes that occur in Rayleigh�Taylor driven mixing. A water channel facility was used to examine a buoyancy-driven Rayleigh�Taylor mixing layer. Measurements of �uctuating den- sity statistics and the molecular mixing parameter were made for Pr = 7 (hot/cold water) and Sc 103 (salt/fresh water) cases. For the hot/cold water case, a high- resolution thermocouple was used to measure instantaneous temperature values that were related to the density �eld via an equation of state. For the Sc 103 case, the degree of molecular mixing was measured by monitoring a di�usion-limited chemical reaction between the two �uid streams. The degree of molecular mixing was quanti- �ed by developing a new mathematical relationship between the amount of chemical product formed and the density variance 02. Comparisons between the Sc = 7 and Sc 103 cases are used to elucidate the dependence of on the Schmidt number. To further examine the turbulent mixing processes, a direct numerical simu- lation (DNS) model of the Sc = 7 water channel experiment was constructed to provide statistics that could not be experimentally measured. To determine the key physical mechanisms that in�uence the growth of turbulent Rayleigh�Taylor mixing layers, the budgets of the exact mean mass fraction em1, turbulent kinetic energy fE00, turbulent kinetic energy dissipation rate e 00, mass fraction variance gm002 1 , and mass fraction variance dissipation rate f 00 equations were examined. The budgets of the unclosed turbulent transport equations were used to quantitatively assess the relative magnitudes of di�erent production, dissipation, transport, and mixing processes. Finally, three-equation (fE00-e 00-gm002 1 ) and four-equation (fE00-e 00-gm002 1 -f 00) turbulent mixing models were developed and calibrated to predict the degree of molecular mix- ing within a Rayleigh�Taylor mixing layer. The DNS data sets were used to assess the validity of and calibrate the turbulent viscosity, gradient-di�usion, and scale- similarity closures a priori. The modeled transport equations were implemented in a one-dimensional numerical simulation code and were shown to accurately reproduce the experimental and DNS results a posteriori. The calibrated model parameters from the Sc = 7 case were used as the starting point for determining the appropri- ate model constants for the mass fraction variance gm002 1 transport equation for the Sc 103 case.

Finite volume method was employed for analyzing the three-dimensional turbulent flow structures, species distributions, and mixing behaviors of combustion flows in a rotary kiln under various operation conditions. The modified £e-£`turbulence model together with wall functions was adopted. Devolatilization of solid wastes were simulated by gaseous methane (CH4) non-uniformly distributed along the kiln bed. Combustion process was considered as a two-step reaction when primary air entered and mixed with methane gas in the first combustion chamber. Mixing-controlled eddy-dissipation model was employed for predicting the reaction rates of CH4, O2, CO2, CO and H2O. Effects of inleakage air, kiln rotation speed and methane distribution along the kiln bed were also examined. Results show that 128% excess air will get the best combustion efficiency, above which the combustion efficiency will decrease. The temperature and species are not uniformly distributed and are vertically stratified on cross-sectional plane. The combustion efficiency will also be lowered if there is inleakage airflow. Results also show rotation speed and methane distributions have little effect on combustion efficiency.

<p>Conventional one-point turbulence closures have beenextended with an additional transported scalar for modeling ofmagnetohydrodynamic (MHD) turbulence. The new scalar, α ,captures the length scale anisotropy and tendency towardstwo-dimensionality, which is characteristic feature of MHDturbulence, and allows accurate modeling of the Jouledissipation of turbulence. The concept has been used for both afull Reynolds stress closure, and a three-equation<i>K-ε -α</i>model. An exact transport equation forαwas derived from the governing equations. All terms inthe equation require modeling, however. The proposed modeltransport equation for α includes terms for magneticdissipation, nonlinear energy transfer, and effects of meanshear and strain. Modeling of the magnetic and strain-relatedterms was based on rapid distortion analysis of the linearizedequations, while modeling of nonlinear effects isphenomenological in nature. For homogeneous turbulence, themodel was compared with linear theory, direct numericalsimulations and experiments. For turbulence subjected to astrong magnetic field, the model reproduces the energy andlength scale evolution predicted by linear theory. Whennonlinear effects are of importance, it predicts energy decayand length scale evolution in agreement with experiments. Theeddy viscosity and Reynolds stress versions of the modelcoincide with the respective conventional models in the absenceof a magnetic field. The objective of this project has been todevelop efficient MHD turbulence models for engineeringapplications, especially for modeling of continuous steelcasting. The novel MHD turbulence models appear to benumerically robust, and they have been implemented in acommercial flow solver, together with electromagnetic equationsfor the Lorentz forces in the mean momentum equations.</p><p><b>Keywords:</b>Turbulence model, magnetohydrodynamics, MHD,magnetohydrodynamic turbulence, computational fluid dynamics,continuous casting, dimensionality, Reynolds stresses, eddyviscosity</p>

This dissertation examined individual and joint storytelling as a communicative process to explore relational turbulence about stressful events. Response to change in romantic relationships inherently involves a degree of instability as individuals alter their thoughts and actions. The instability and chaos that results when transitions impact interpersonal relationships is relational turbulence (e.g., Knobloch & Solomon, 2004). The theoretical focus is the relational turbulence model (RTM) that serves to illustrate the ambiguity and complexity embedded in relationship experiences and the negotiation of behavior. Examination of stories showcased the representational relational state (i.e., uncertainty) and cognitive activities (i.e., partner interdependence) present in the relationship. First, the dissertation further positioned the influence turbulence has on individual and relational communication to negotiate discomfort, negative emotions, and difficulties that ensued during transitions. Second, this study examined expressions individuals chose to highlight, through storytelling, that apply to relational turbulence mechanisms: relational uncertainty and interdependence. Third, this dissertation examined identity development and/or fluctuation as a byproduct of turbulence exhibited through stories exploring another potential relational turbulence mechanism. A review of literature discussed the theoretical framework for the relational turbulence model and storytelling content and structure. The exploration of stories and storytelling was reviewed as a means for investigating RTM, followed by analysis procedures outlining individual and relational storytelling processes. Results revealed 14 transitional events categories and 23 subcategories. Additionally, qualitative themes and subthemes that emerged for relational uncertainty, partner interdependence, individual and relational identity. Results for relational uncertainty triangulated previous scholarship while also identified two new themes. Partner interdependence results indicated more specificity in forms of partner interference and facilitation. Identity emerged as a third mechanism and preliminary investigation found static and dynamic forms. Quantitative results analyzed significant correlations and comparisons between narrative completeness in individuals' and relational partners' storytelling experiences. The dissertation highlighted how relational turbulence influenced the storytelling content and structure of individual and joint stories. / text