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.

According to the World Health Organization, urban air pollution is a high public health priority due its linkage to cardio-pulmonary disease and association with increased mortality and morbidity (1, 2). Additionally, air pollution impacts climate change, visibility, and ecosystem health. The development of effective strategies for improving air quality requires accurate estimates of air pollutant emissions. In response to the need for new approaches to measuring emissions, we have designed a mobile Flux Lab for the Atmospheric Measurement of Emissions (FLAME) that applies a proven, science-based method known as eddy covariance for the direct quantification of anthropogenic emissions to the atmosphere. The mobile flux lab is a tool with novel, multifaceted abilities to assess air quality and improve the fidelity of emission inventories. Measurements of air pollutant concentrations in multiple locations at the neighborhood scale can provide much greater spatial resolution for population exposure assessments. The lab's mobility allows it to target specific sources, and plumes from these can be analyzed to determine emission factors. Through eddy covariance, the lab provides the new ability to directly measure emissions of a suite of air pollutants. We have deployed the FLAME to three different settings: a rural Appalachian town where coal transport is the dominant industry; schools in the medium-sized city of Roanoke, Virginia; and the large urban areas around Norfolk, Virginia, to measure neighborhood-scale emissions of air pollution. These areas routinely experience high ozone and particulate matter concentrations and include a diverse array of residential neighborhoods and industries. The FLAME is able to capture emissions from all ground-based sources, such as motor vehicles, rail and barge traffic, refuse fires and refueling stations, for which no direct measurement method has been available previously. Experiments focus on carbon dioxide (CO₂), the principal greenhouse gas responsible for climate change; nitrogen oxides (NOx), a key ingredient in ground-level ozone and acid rain; volatile organic compounds (VOCs), a second key ingredient in ozone and many of which are air toxics; and fine particulate matter (PM2.5), a cause of mortality, decreased visibility, and climate change. This research provides some of the first measurements of neighborhood-scale anthropogenic emissions of CO₂, NOx, VOCs and PM2.5 and as a result, the first opportunity to validate official emission inventories directly. The results indicate that a mobile eddy covariance system can be used successfully to measure fluxes of multiple pollutants in a variety of urban settings. With certain pollutants in certain locations, flux measurements confirmed inventories, but in others, they disagreed by factors of up to five, suggesting that parts of the inventory may be severely over- or underestimated. Over the scale of a few kilometers within a city, emissions were highly heterogeneous in both space and time. FLAME-based measurements also confirmed published emission factors from coal barges and showed that idling vehicles are the dominant source of emissions of air toxics around seven schools in southwest Virginia. Measurements from this study corroborate existing emission inventories of CO₂ and NOx and suggest that inventories of PM2.5 may be overestimated. Despite the tremendous spatial and temporal variability in emissions found in dense urban areas, CO₂ fluxes on average are very similar across the areas in this study and other urban areas in the developed world. Nevertheless, the high level of variability in spatial and temporal patterns of emissions presents a challenge to air quality modelers. The finding that emissions from idling vehicles at schools are likely responsible for creating hot spots of air toxics adds to the urgency of implementing no-idling and other rules to reduce the exposure of children to such pollutants. Ultimately, the results of this study can be used in combination with knowledge from existing emission inventories to improve the science and policies surrounding air pollution. / Ph. D.

Large Eddy Simulation (LES) is a relatively more accurate and reliable alternative to solution of Reynolds Averaged Navier Stokes (RANS) equations in simulating complex turbulent flows at a lesser computational cost than a direct numerical simulation (DNS). However, LES of wall-bounded flows still requires a very high grid resolution in the inner wall layer making its widespread use difficult. Different attempts have been made in the past time to overcome this problem by modeling the near wall turbulence instead of resolving it. One such approach is a two-layer wall model that solves for a reduced one-dimensional equation in the inner wall layer, while solving for the filtered Navier-Stokes equations in the outer layer. The use of such a model allows for a coarser grid resolution than a wall resolved LES. This work validates the performance of a two-layer wall model developed for an arbitrary body fitted non-orthogonal grid in the flow over a wall mounted hump at Reynolds number 9.36x105. The wall modeled large eddy simulation (WMLES) relaxes the grid requirement compared to a wall resolved LES (WRLES) by allowing the first off-wall grid point to be placed at a y+ of approximately 20-40. It is found that the WMLES results are general good agreement with WRLES and experiments. Surface pressure coefficient, skin friction, mean velocity profiles, and the reattachment location compare very well with experiment. The WMLES and WRLES exhibit some under prediction of the peak values in the turbulent quantities close to the reattachment location, with better agreement with the experiment in the separated region. In contrast, a simulation that did not employ the wall model on the grid used for WMLES failed to predict flow separation and showed large discrepancies with the experimental data. In addition to the relaxation of the grid requirement in the wall normal direction, it was also observed that the wall model allowed a reduction in the number of computational cells in the span-wise direction by half. However an LES calculation on a grid with reduced number of cells in span-wise direction turned unstable almost immediately, thereby highlighting the effectiveness of the wall model. Besides reducing the number of grid points in the spatial domain, the relaxed grid resolution for the WMLES also permitted the use of a larger time step. This resulted in an order of magnitude reduction in the total CPU time relative to WRLES. / Master of Science

A região oceânica adjacente ao Embaiamento de Tubarão (ET) e ao Banco de Abrolhos (BAb) talvez seja uma das menos investigadas da margem continental brasileira. Estudos acerca da circulação nesta porção da costa atualmente restringem-se a trabalhos realizados na década de 80 e 90. Recentemente, estudos focando a atividade de mesoescala e a variabilidade sazonal da circulação ao largo da costa leste brasileira, tem relatado padrões de escoamento complexos e despertado o interesse da comunidade científica na compreensão da dinâmica local. Buscando compreender o padrão de escoamento na região e dispondo de dados sinóticos dos anos de 2004 e 2005 provenientes do Projeto Abrolhos, este trabalho se propôs a estudar as principais feições encontradas na área em questão através de modelagem numérica. Com este intuito, o campo inicial foi construído através de dados hidrográficos sinóticos, interpolados objetivamente com campos climatológicos mensais do World Ocean Atlas 01. Para tal, os perfis dos dados sinóticos e climatológicos foram adimensionalizados e redimensionalizados, com imagens termais de satélite e campo sintético de salinidade. Após a construção do campo inicial, foi realizada simulação numérica com o Regional Ocean Modeling System - ROMS, para os cenários de inverno (2004) e verão (2005). No cenário de inverno foi identificado um anticiclone dentro do Embaiamento de Tubarão, aqui denominado Vórtice de Tubarão, entretanto o Vórtice de Vitória (VV) e o Vórtice de Abrolhos (VA) só foram encontrados no cenário de verão, estando o o VV associado a um anticiclone simétrico ao eixo da Corrente do Brasil. Os resultados refutam a hipótese de que os anticiclones ao largo do Banco de Abrolhos apresentariam a mesma estrutura dinâmica dos ciclones presentes no Embaiamento de Tubarão. Além disso, pode-se também, atestar a natureza não perene do VV. / The region adjacent to the Tubarão Embayment and Abrolhos Bank is maybe one of the less investigated of the Brazillian continental margin. Studies about the cirulation in this area are currently restricted to studies carried out during the 80\'s and 90\'s. Recently, studies focusing the mesoscale activity and the seazonal variability of the circulation off the Brazillian eastern coast have reported complex flow patterns and raised attention of the scientific community to the lack of knowledge of the local dynamics. In order to comprehend the flow pattern in the region, having synoptic data for 2004 and 2005 from the Abrolhos Project, this work aims to study the main features identified in the study area through numerical modelling. With this intent, the initial field was built through hydrographic synoptic data objectively interpolated with monthly climatological fields of the World Ocean Atlas 01. For that, the profiles of the synoptic and climatological data were non-dimensionalyzed and re-dimensionalyzed with thermal satellite images and synthetic salinity field. After the initial field was built, a numerical simulation with the Regional Ocean Modeling System - ROMS was carried out, for the winter (2004) and summer (2005) scenarios. In the winter scenario an anticyclone, here named Tubarão Eddy, was identified inside the Tubarão Embayment, while the Vitória Eddy (VE) and the Abrolhos Eddy (AE) were only identified in the summer scenario, being the VE associated with an anticyclone symetric to the Brazil Current axis. The results deny the hypothesis that the anticyclones offshore the Abrolhos Bank present the same dynamical structure as the cyclones present in the Tubarão Embayment. Besides, we state the non-permanent nature of the VE.

A região oceânica adjacente ao Embaiamento de Tubarão (ET) e ao Banco de Abrolhos (BAb) talvez seja uma das menos investigadas da margem continental brasileira. Estudos acerca da circulação nesta porção da costa atualmente restringem-se a trabalhos realizados na década de 80 e 90. Recentemente, estudos focando a atividade de mesoescala e a variabilidade sazonal da circulação ao largo da costa leste brasileira, tem relatado padrões de escoamento complexos e despertado o interesse da comunidade científica na compreensão da dinâmica local. Buscando compreender o padrão de escoamento na região e dispondo de dados sinóticos dos anos de 2004 e 2005 provenientes do Projeto Abrolhos, este trabalho se propôs a estudar as principais feições encontradas na área em questão através de modelagem numérica. Com este intuito, o campo inicial foi construído através de dados hidrográficos sinóticos, interpolados objetivamente com campos climatológicos mensais do World Ocean Atlas 01. Para tal, os perfis dos dados sinóticos e climatológicos foram adimensionalizados e redimensionalizados, com imagens termais de satélite e campo sintético de salinidade. Após a construção do campo inicial, foi realizada simulação numérica com o Regional Ocean Modeling System - ROMS, para os cenários de inverno (2004) e verão (2005). No cenário de inverno foi identificado um anticiclone dentro do Embaiamento de Tubarão, aqui denominado Vórtice de Tubarão, entretanto o Vórtice de Vitória (VV) e o Vórtice de Abrolhos (VA) só foram encontrados no cenário de verão, estando o o VV associado a um anticiclone simétrico ao eixo da Corrente do Brasil. Os resultados refutam a hipótese de que os anticiclones ao largo do Banco de Abrolhos apresentariam a mesma estrutura dinâmica dos ciclones presentes no Embaiamento de Tubarão. Além disso, pode-se também, atestar a natureza não perene do VV. / The region adjacent to the Tubarão Embayment and Abrolhos Bank is maybe one of the less investigated of the Brazillian continental margin. Studies about the cirulation in this area are currently restricted to studies carried out during the 80\'s and 90\'s. Recently, studies focusing the mesoscale activity and the seazonal variability of the circulation off the Brazillian eastern coast have reported complex flow patterns and raised attention of the scientific community to the lack of knowledge of the local dynamics. In order to comprehend the flow pattern in the region, having synoptic data for 2004 and 2005 from the Abrolhos Project, this work aims to study the main features identified in the study area through numerical modelling. With this intent, the initial field was built through hydrographic synoptic data objectively interpolated with monthly climatological fields of the World Ocean Atlas 01. For that, the profiles of the synoptic and climatological data were non-dimensionalyzed and re-dimensionalyzed with thermal satellite images and synthetic salinity field. After the initial field was built, a numerical simulation with the Regional Ocean Modeling System - ROMS was carried out, for the winter (2004) and summer (2005) scenarios. In the winter scenario an anticyclone, here named Tubarão Eddy, was identified inside the Tubarão Embayment, while the Vitória Eddy (VE) and the Abrolhos Eddy (AE) were only identified in the summer scenario, being the VE associated with an anticyclone symetric to the Brazil Current axis. The results deny the hypothesis that the anticyclones offshore the Abrolhos Bank present the same dynamical structure as the cyclones present in the Tubarão Embayment. Besides, we state the non-permanent nature of the VE.

Multiphase flows are a common phenomenon. Rains, sediment transport in rivers, snow and dust storms, mud slides and avalanches are examples of multiphase flows occurring in nature. Blood flow is an example of multiphase flow in the human body, which is of vital importance for survival. Multiphase flows occur widely in industrial applications from hydrocarbon extrac-tion to fuel combustion in engines, from spray painting to spray drying, evaporators, pumps and pneumatic conveying. Predicting multiphase flows is of vital importance to understand natural phenomenon and to design and improve industrial processes. Separated flows and dispersed flows are two types of multiphase flows, which occur together in many industrial applications. Physical features of these two classes are different and the transition from one to another involves complex flow physics. Experimental studies of multiphase flows are not easy, as most real world phenomenon cannot be scaled down to laboratory models. Even for those phenomenon that can be demonstrated at lab-oratory scale, rescaling to real world applications requires mathematical models. There are many challenges in experimental measurements of multiphase flows as well. Measurement techniques well suited for single phase flows have constraints when measuring multiphase phenomenon. Un-certainty in experimental measurements poses considerable difficulties in validating numerical models developed for predicting these flows. Owing to the computational effort required, direct simulation of multiphase flows, even for small scale real world applications is out of present scope. Numerical methods have been developed for dealing with each class of flow separately, that in-volves use of models for phenomenon that is computationally demanding. Reynolds Averaged Navier-Stokes (RANS) methods for predicting multiphase flows place strong requirements on turbulence models, as information about fluctuating quantities in the field, that have significant effects on dispersed phase, is not available. Large Eddy Simulation (LES) gives better predictions than RANS as the instantaneous field data is available and large scale unsteadiness that effects the dispersed phase can be captured. Recent LES studies of multiphase flows showed that the sub-grid-scale (SGS) model used for the continuous phase has an effect on the evolution of the dispersed phase. In this work, LES of multiphase flows is performed using Explicit Filtering Large Eddy Sim-ulation method. In this method, spatial derivatives are computed using higher order compact schemes that have spectral-like resolution. SGS modeling is provided by the use of a filter with smoothly falling transfer function. This method is mathematically consistent and converges to a DNS as the grid is refined. It has been successfully applied to combustion and aero-acoustics and this work is the first application of the method to multiphase flows. Study of dispersed multiphase flows was carried out in this work. Modeling of the dispersed phase is kept simple since the in-tention was to evaluate the capability of explicit filtering LES method in predicting multiphase flows. Continuous phase is solved using a compressible formulation with explicit filtering method. Spatial derivatives are computed using fourth and sixth order compact schemes that use derivative splitting method proposed by Hixon & Turkel (2000a) and second order Runge-Kutta (RK2) time stepping. The grid is stretched as needed. Non-reflecting boundary conditions due to Poinsot & Lele (1992) are used to avoid acoustic reflections from boundaries. Buffer zones (Bogey & Bailly (2002)) are employed at outflow and lateral boundaries to damp vortical structures. The code developed for continuous phase is evaluated by studying round jets at Re =36,000 and comparing with experimental measurements of Hussein et al. (1994) and Panchapakesan & Lumley (1993). Simulations showed excellent agreement with experimental results. Rate of decay of axial velocity and the evolution of turbulence intensities on the centerline matched very well with measurements. Radial profiles of mean and fluctuating components of velocities exhibit self-similarity. A set of studies were then performed using this code to assess the effect of numerical scheme, grid refinement & stretching and simulation times on the predictions. Results from these simulations showed good agreements with experiments and established the code for use in multiphase flows under various simulation conditions. To assess the prediction of multiphase flows using this LES method, an evaporating spray ex-periment by Chen et al. (2006) was simulated. The experiment uses a nebuliser for generating a finely atomized spray of acetone, which avoids complex breakdown phenomenon associated with air blast atomizers and provides well defined boundary conditions for model evaluation. The neb-uliser sits upstream in a pipe carrying air and droplets travel along with air for a distance of 10 diameters before exiting into a wind tunnel with co-flowing air. Droplet breakdown, if any, takes place inside the pipe and the spray is finely atomized by the time it reaches pipe exit. One of the experimental cases at Re =31,600, with a mass loading of 1.1% and a jet velocity of 56 m/s is simulated. Particle size has a χsquared distribution with a Sauter mean diameter of 18µm. In the self-similar region, decay of centerline velocity and turbulence intensities matched well with ex-perimental results. Continuous phase exhibits self-similar behavior. A series of simulations were then performed to match the initial region of the spray by altering the inflow conditions in the sim-ulation. Simulation that matched the breakdown location of the experiment revealed the presence of a relaxation zone with a higher initial spreading rate, followed by a lower asymptotic spreading rate. Studies were performed to understand the effect of various phenomenon like evaporation and droplet size on this behavior. A study of breakdown region of particle-laden jets was performed to understand the presence of relaxation zone post breakdown. Flow conditions were similar to evaporating spray experiment except that particles do not evaporate, mass loading is 2% and jet Reynolds number Re =2000. A series of grid refinements were performed and on the largest grid, gird spacing Δy =7.5η, where ηis an estimate of the Kolmogorov length scale based on flow conditions. Decay of axial velocity on the centerline showed variations with grid refinement, tending to the experimentally measured value as the grid is refined. Variation of turbulence intensities along the centerline revealed a jump in axial velocity fluctuations at the breakdown location, while radial and azimuthal velocities showed a smooth increase to their asymptotic value. This jump was resolved on grid refinement and on fine grids axial velocity fluctuations followed the other two quantities closely in their rise to asymptotic state. Comparison of these quantities with a jet without particles revealed that the flow features are same for a jet with and without particles, and at the mass loading studied, particles have negligible effect on jet breakdown. Another study performed at a higher Reynolds number of Re =11,000, under similar flow conditions showed similar behavior. To assess the ability of predicting dispersed phase, simulations of particle-laden flows at low Stokes number were performed and compared against an experiment by Lau & Nathan (2014). The experiment studies variation of velocity and particle concentration along the centerline, and half widths of a jet velocity and concentration. Particles are injected into a pipe along with air, and the two phase flow is fully developed by the time it exits the pipe into a wind tunnel along with a co-flow. Particles are mono-disperse with a density of 1200 kg/m3. Mass loading is 40% so that particles have a significant effect on the continuous phase. Two cases at particle Stokes number of 1.4, one with Re =10,000, bulk velocity of 12 m/s and particle diameter of 20µm and another with Re =22,500, bulk velocity of 36 m/s and particle diameter of 10µm were simulated. Simulations of both the cases showed good match with experimental measurements of centerline decay for the continuous phase. For the dispersed case, simulations with larger particles showed good match with experimental results, while smaller particles showed differences. This was understood to be the effect of lateral migration which is prominent in case of smaller particles, the models for which have not been used in the present simulation study.

In dieser Dissertation wird das kompressible, nicht-hydrostatische und dreidimensionale Modell All Scale Atmospheric Model (ASAM) für Grobstruktur- bzw. Large-Eddy-Simulationen (LES) angewendet, um lokale Inseleffekte in der karibischen Passatwindzone zu untersuchen. Da das Modell bis dato noch keine Anwendung im Bereich von LES feuchter atmosphärischer Grenzschichten und heterogener Oberflächen fand, wurden einige Bestandteile zum Modellcode hinzugefügt oder überarbeitet. Ein Hauptaugenmerk liegt dabei auf das Einbeziehen orographischer Strukturen mittels angeschnittener Zellen (engl. cut cells). Sowohl die räumliche und zeitliche Diskretisierung der Modellgleichungen als auch die nötigen physikalischen Parameterisierungen werden in einer umfassenden Modellbeschreibung zusammengefasst. Die Robustheit und Stabilität der Modellformulierung wird durch eine Reihe von Simulationen idealisierter Testfälle bestätigt. Large-Eddy-Simulationen werden für das Gebiet der Karibikinsel Barbados zur Untersuchung von Inseleffekten bezüglich Grenzschichtmodifikation, Wolkenbildung und vertikaler Durchmischung von Aerosolen durchgeführt. Durch das Vorhandensein einer topographisch strukturierten Inseloberfläche in der Mitte des Modellgebietes muss das Modellsetup offene seitliche Randbedingungen beinhalten. Damit das einströmende Windfeld konsistent mit der Dynamik einer turbulenten, marinen Grenzschicht ist, wird eine neue Methode implementiert und angewendet, welche auf Störungen des potentiellen Temperaturfeldes mittels finiter Amplituden basiert. Beobachtungen aus der SALTRACE-Messkampagne werden benutzt, um die Modellläufe anzutreiben. Die Ergebnisse einiger Sensitivitätstests zeigen Probleme der Modellierung im Bereich der \"Terra incognita\" auf. Dabei handelt es sich um die Modellierung auf räumlichen Skalen, welche zwischen denen von LES und wolkenauflösenden Modellen liegen. Außerdem werden Auswirkungen von entweder turbulent oder laminar anströmenden Windfeldern auf die Simulationsergebnisse untersucht. Besonders die Wolkeneigenschaften im Lee von Barbados werden in diesen Simulationen merklich beeinflusst. Ergebnisse einer weiteren Simulation mit einer sehr starken Passatinversion bringt deren Einfluss auf die Dicke und Höhe der simulierten Wolkenschichten zum Vorschein. Die Veränderung von Saharastaubschichten, welche Barbados über weiträumigen Transport über den Atlantik erreichen, wird analysiert. Die Auswirkungen beinhalten sowohl eine Ausdünnung und ein Absinken dieser Schichten als auch turbulenter Transport in Richtung Erdoberfläche. Die genaue Position der beeinflussten Schichten und die Stärke des turbulenten Mischens werden hauptsächlich von der atmosphärischen Schichtung, der Inversionsstärke und Windscherung gesteuert. Vergleiche zwischen den LES-Modellergebnissen und Daten aus Doppler-Windlidarmessungen zeigen gute Übereinstimmungen in der Formierung der konvektiven Strukturen tagsüber und des Vertikalwindfeldes. / In this thesis, the fully compressible, three-dimensional, nonhydrostatic atmospheric model called All Scale Atmospheric Model (ASAM) is utilized for large eddy simulations (LES) to investigate local island effects at the Caribbean. Since the model has not been applied to LES for moist boundary layers and heterogeneous surfaces so far, several parts are added to the model code or reworked. A special focus lies on the inclusion of orographical structures via the cut cell method. Spatial and temporal discretization as well as necessary physical parameterizations are summarized in a thorough model description. The robustness of the model formulation is confirmed by a set of idealized test case simulations. Large eddy simulations are performed for the area of the Caribbean island Barbados to investigate island effects on boundary layer modification, cloud generation and vertical mixing of aerosols. Due to the presence of a topographically structured island surface in the domain center, the model setup has to be designed with open lateral boundaries. In order to generate inflow turbulence consistent with the upstream marine boundary layer forcing, the newly developed cell perturbation method based on finite amplitude perturbations is applied. Observations from the SALTRACE field campaign are used to initialize the model runs. Several numerical sensitivity tests are carried out to demonstrate the problems related to \"gray zone modeling\" beyond LES scales or when the turbulent marine boundary layer flow is replaced by laminar winds. Especially cloud properties west of Barbados (downwind) are markedly affected in these simulations. Results of an additional simulation with a strong trade-wind inversion reveal its effect on cloud layer depth and height. The modification of Saharan dust layers reaching Barbados via long-range transport over the North Atlantic is analyzed. Effects of layer thinning, subsidence and turbulent downward transport near the layer bottom become apparent. The position of these layers and strength of downward mixing is found to be mainly controlled atmospheric stability, inversion strength and wind shear. Comparisons of LES model output with wind lidar data show similarities in the formation of the daytime convective plume and the vertical wind structure.

Current climate models often predict fractional cloud cover on the basis of a diagnostic probability density function (PDF) describing the subgrid-scale variability of the total water specific humidity, qt, favouring schemes with limited complexity. Standard shapes are uniform or triangular PDFs the width of which is assumed to scale with the gridbox mean qt or the grid-box mean saturation specific humidity, qs. In this study, the qt variability is analysed from large-eddy simulations for two stratocumulus, two shallow cumulus, and one deep convective cases. We find that in most cases, triangles are a better approximation to the simulated PDFs than uniform distributions. In two of the 24 slices examined, the actual distributions were so strongly skewed that the simple symmetric shapes could not capture the PDF at all. The distribution width for either shape scales acceptably well with both the mean value of qt and qs, the former being a slightly better choice. The qt variance is underestimated by the fitted PDFs, but overestimated by the existing parameterisations. While the cloud fraction is in general relatively well diagnosed from fitted or parameterised uniform or triangular PDFs, it fails to capture cases with small partial cloudiness, and in 10 – 30% of the cases misdiagnoses clouds in clear skies or vice-versa. The results suggest choosing a parameterisation with a triangular shape, where the distribution width would scale with the grid-box mean qt using a scaling factor of 0.076. This, however, is subject to the caveat that the reference simulations examined here were partly for rather small domains and driven by idealised boundary conditions.

Turbulent flow and transition are some of the most important phenomena of fluid mechanics and aerodynamics and represent a challenging engineering problem for aircraft manufacturers looking to improve aerodynamic efficiency. Laminar flow technology has the potential to provide a significant reduction to aircraft drag by manipulating the instabilities within the laminar boundary layer to achieve a delay in transition to turbulence. Currently prediction and simulation of laminar-turbulent transition is con- ducted using either a low-fidelity approach involving the stability equations or via a full Direct Numerical Simulation (DNS). The work in this thesis uses an alternative high-fidelity simulation method that aims to bridge the gap between the two simulation streams. The methodology uses an LES approach with a low-computational cost sub-grid scale model (WALE) that has inherent ability to reduce its turbulent viscosity contribution to zero in laminar regions. With careful grid spacing the laminar regions can be explicitly modelled as an unsteady Navier-Stokes simulation while the turbulent and transitional regions are simulated using LES. The methodology has been labelled as an unsteady Navier-Stokes/Large Eddy Simulation (UNS/LES) approach. Two test cases were developed to test the applicability of the method to simulate and control the crossflow instability. The first test case replicated the setup from an experiment that ran at a chord-based Reynolds number of 390, 000. Two methods were used to generate the initial disturbance for the crossflow vortices, firstly using a continuous suction hole and secondly an isolated roughness element. The results for this test case showed that the approach was capable of modelling the full transition process, from explicitly modelling the growth of the initial amplitude of the disturbances to final breakdown to turbulence. Results matched well with the available experimental data. The second test case replicated an experimental setup using a custom- designed aerofoil run at a chord-based Reynolds number of 2.4 million. The test case used Distributed Roughness Elements (DRE) to induce crossflow vortices at both a critical and a control wavelength. By forcing the crossflow vortices at a stable (control) wavelength a delay in laminar-turbulent transition can be achieved. The results showed that the UNS/LES approach was capable of capturing the initial disturbance amplitudes due to the roughness elements and their growth rates matched well with experimental data. Finally, downstream a transitional region was assessed with low-freestream turbulence provided using a modified Synthetic Eddy Method (SEM). The full laminar-turbulent transition pro- cess was simulated and results showed significant promise. In conclusion, the method employed in this thesis showed promising results and demonstrated a possible route to high-fidelity transition simulation run at more realistic flow conditions and geometries than DNS. Further work and validation is required to test the secondary instability region and the final breakdown to turbulence.

A metodologia LES (Large Eddy Simulation) é uma alternativa viável para a solução numérica de escoamentos de interesse prático em virtude da limitação computacional imposta pela resolução direta de todas as escalas presentes em escoamentos turbulentos. Entretanto, a compreensão detalhada do fenômeno da turbulência é ainda uma tarefa desafiadora em consequência do seu comportamento não linear e alta sensibilidade às condições iniciais e de contorno. Dessa forma, o sucesso de simulações LES está associado à utilização de um código computacional eficiente, com modelagem submalha que represente corretamente a dinâmica do escoamento, juntamente com a especificação de condições iniciais turbulentas fisicamente consistentes. Nesse contexto, o presente trabalho tem como objetivo o desenvolvimento de um código LES de alta ordem aliado a um método de geração de perturbações para o estudo de escoamentos turbulentos em camada limite sobre superfície plana. Foi adotada a formulação vorticidadevelocidade. A metodologia numérica baseia-se no método de diferenças finitas em malhas colocalizadas, onde as derivadas nas direções longitudinal e normal ao escoamento são aproximadas usando diferenças compactas de alta ordem. Esse estudo assume periodicidade na direção transversal do escoamento e então um método espectral é adotado nessa direção. A integração temporal é feita através do método Runge-Kutta de 4a ordem e a solução da equação de Poisson se dá por meio de um método multigrid. Para a modelagem submalha é adotado o modelo WALE (Wall-Adapting Local Eddy-viscosity). O método RFG (Random Flow Generation) foi responsável pela geração das flutuações de velocidade. Os resultados obtidos mostraram-se em boa concordância com os dados DNS (Direct Numerical Simulation) e LES presentes na literatura. / LES methodology is a viable alternative for the numerical solution of practical interest flows due to the computational limitations imposed by the direct resolution of all scales presented in turbulent flow. However, the detailed understanding of the turbulence phenomenon is still a challenging task as a result of its non-linear behavior and high sensitivity to initial and boundary conditions. Thus, the success of LES simulations is associated with the use of an efficient computational code, wherein the subgrid scale modeling accurately represents the flow dynamics, together with the specification of realistic inicial boundary conditions. In this context, this study aims to develop a high-order LES code combined with a method for generating velocity fluctuations to compute turbulent boundary layer flows over a flat plate. The vorticity-velocity formulation was adopted. The numerical scheme is based on the finite difference method in collocated grid, where the derivatives in the streamwise and wall-normal are approximated using high order compact finite difference schemes. We also assume periodicity in spanwise direction therefore it is adopted a spectral method in this direction. The method chosen for the temporal evolution is the 4th order Runge-Kutta method and the solution of Poisson equation solution is accessed via a multigrid algorithm. For subgrid modelling it is adopted the Wall-Adapting Local Eddy-viscosity (WALE) model. The RFG (Random Flow Generation) method was responsible for the generation of unsteady turbulent velocity signal. The results obtained were in good agreement with DNS (Direct Numerical Simulation) and LES from the literature.