For the past several years there has been great effort in the analysis of internal duct cooling. The steady increase in power output and thermal efficiency requirements for gas turbine engines has called for significant advancement in turbine blade internal duct cooling technology. Numerical analysis of turbulent duct flow has been largely limited to Reynolds Averaged Navier-Stokes (RANS) simulations. This is because of the low computational requirements of such calculations relative to Large Eddy Simulation (LES) and Direct Numerical Simulation (DNS). However, the tides have started to turn in favor of LES, partly because of the exponential increase in computer hardware performance in recent years. Three conference papers make up the contents of this thesis. LES is performed for fully developed flow and heat transfer in a staggered 45º ribbed duct in the first paper. The rib pitch-toheight ratio P / e is 10 and a rib height to hydraulic diameter ratio h e / D is 0.1. The Reynolds numberbased on the bulk flow rate and hydraulic diameter is 47,300. The overall heat transfer enhancement obtained was a factor of 2.3, which matched experimental data within 2%. The surfaces of highest heat transfer enhancement were the ribbed walls and the outer wall. Results from LES of an orthogonally rotating 90º ribbed duct are presented in the second paper for rotation numbers: Ro = 0.18, 0.35 and 0.67. The Reynolds number is 20,000. The P / e and h e / D were the same as in the first paper. Turbulence and heat transfer are augmented on the trailing surface and reduced at the leading surface. Secondary flows induced by Coriolis forces, increase heat transfer augmentation on the smooth walls. Finally, the third paper studies the same flow conditions of the second paper and goes further by including effects of centrifugal buoyancy forces using LES. Two buoyancy numbers are studied: Bo = 0.12 and 0.29. Centrifugal buoyancy does not have a large effect on leading side augmentation ratios for all rotation numbers, but increases heat transfer significantly on the trailing side. In all papers, mean flow and heat transfer results compare well with experimental data. / Master of Science

This thesis proposes a large eddy simulation reduced order model (LES-ROM) framework for the numerical simulation of realistic flows. In this LES-ROM framework, the proper orthogonal decomposition (POD) is used to define the ROM basis and a POD differential filter is used to define the large ROM structures. An approximate deconvolution (AD) approach is used to solve the ROM closure problem and develop a new AD-ROM. This AD-ROM is tested in the numerical simulation of the one-dimensional Burgers equation with a small diffusion coefficient ( ν= 10⁻³). / Master of Science

According to the United Nations, 55% of the world's population currently lives in urban areas and which is projected to increase to 67% by 2050. Thus, it is imperative that effective strategies are developed to mitigate urban pollution. Complementing field experiments, computational fluid dynamics (CFD) analyses are becoming an effective strategy for identifying critical factors that influence urban pollution and its mitigation. This thesis focuses on two scales of the urban micro-climate environment: (i) evaluation of LES simulations with a simplified grid for modeling pollution dispersion in a street canyon and (ii) investigation of the effects of leaf surface micro-characteristics, wind speed, and particle sizes on the dry deposition of fine particulate matter (PM2.5). The first of these studies focuses on reproducing the pollution dispersion in a street canyon measured in a wind tunnel at Karlsruhe Institute of Technology (KIT), Germany. A simplified grid with the Large Eddy Simulations (LES) approach for canyon ratio W/H = 1 is proposed with the goal to reduce the computational cost by eliminating the need to model the entire canyon while striving to preserve the mixing induced by individual jets used to model vehicle emission in the experiment. LES is also capable of providing transient flow field and pollution concentration data not available with widely-used steady approaches such as RANS. The time-dependent information is crucial for pollution mitigation since pedestrians are usually exposed to pollution on a short-time basis. The predictions are in satisfactory agreement with the experiment for W/H = 1, yielding the Pearson correlation coefficient R = 0.81, with better performance near the leeward wall. Due to the small span modeled, three-dimensional instabilities fail to develop which could probably explain the overprediction of pollution concentration near ground level. However, other LES investigations where the full canyon was modeled also observed over-predictions. The use of a discrete emission source was not observed to provide benefits. The current model could be further improved by using a larger spanwise domain with a continuous line source to allow large wavelength instabilities to develop and increase turbulent diffusion. The second part of this thesis investigates the impact of trichome morphology and wind speed on the deposition of 0.3 μm and 1.0 μm particles on leaves. Using the one-way coupling approach to predict the fluid-particle interactions with the assumption that all particles that impact the leaf or trichome surface deposit, trichomes of 5 μm and 20 μm in diameter are modeled as equally spaced and uniform cylinders on an infinitely large plane. The results show that trichome diameter, density, and wind speed have a favorable impact on deposition velocity. Comparing to the smooth leaf, the presence of the thicker 20 μm hairs increases the deposition velocity by 1.5 – 4 times, whereas, the presence of short 5um trichomes reduces the deposition by 15 - 45%. Increasing trichome height from H/D = 20 to 30 shows benefits for the thinner trichomes but lowers the deposition for the densely packed thicker trichomes. Less aerosol deposition is also observed when the particle diameter increases from 0.3 μm to 1.0 μm. Due to the non-uniform contributions of these various traits, a non-dimensional ratio Rhp is proposed to model the aerosol deposition on leaf surface at wind speed of 1 m/s which yields a satisfactory linear correlation coefficient of 0.89 for 0 < R_hp < 0.3. Comparing to other published field and wind tunnel experiments conducted on a much larger scale, the deposition velocities predicted are at the lower end (U_dep^* = 0.002 to 0.012 cm/s) because of the idealized conditions. Nonetheless, the results still offer valuable insight into the effects of trichome morphology on pollutant deposition in isolation from other macro-factors. / Master of Science / According to the United Nations, 55% of the world’s population currently lives in urban areas and which is projected to increase to 67% by 2050. Thus, it is imperative that effective strategies are developed to mitigate urban pollution. Complementing field experiments, computational fluid dynamics (CFD) analyses are becoming an effective strategy for identifying critical factors that influence urban pollution and its mitigation. This thesis focuses on two scales of the urban micro-climate environment: (i) evaluation of Large Eddy Simulation (LES) with a simplified method for modeling pollution dispersion in a street canyon and (ii) investigation of the effects of leaf surface micro-characteristics, wind speed, and particle sizes on the dry deposition of fine particulate matter (PM2.5). The first of these studies focuses on reproducing the pollution dispersion in a street canyon measured in a wind tunnel at Karlsruhe Institute of Technology (KIT), Germany. A simplified grid with the LES approach for canyon ratio W/H = 1 is proposed. The goal of this study is to reduce the computational cost by modelling the canyon with a very thin span instead of the entire canyon while providing time-dependent information which is crucial for pollution mitigation since pedestrians are usually exposed to pollution on a short-time basis. The predictions are in satisfactory agreement with the experiment for W/H = 1 with better performance near the leeward wall (i.e. the left wall) and overprediction of pollution concentration near ground level – as observed by other LES investigations. The current model could be further improved by using a larger spanwise domain with a continuous line source to allow instabilities to develop, thus improve prediction accuracy. The second part of this thesis investigates the impact of trichome (i.e. a hair or an outgrowth from leaf surface) morphology and wind speed on the deposition of 0.3 mm and 1.0 mm particles on leaves. The results show that trichome diameter, density, and wind speed have a favorable impact on deposition velocity. Less aerosol deposition is also observed when the particle diameter increases from 0.3 mm to 1.0 mm. No clear effects is observed by altering the trichome height. Due to the non-uniform contributions of these various traits, a non-dimensional ratio D∗ �D∗ �2 Rhp = hair hair is proposed to model the aerosol deposition on leaf surface at wind speed of D∗ H∗ S∗ p hair hair 1 m/s which yields a satisfactory linear correlation coefficient of 0.89 for 0 < Rhp < 0.3. This ratio includes trichome diameter (D∗ ), height (H∗ ), spacing (S∗ ) as well as the ratio of hair hair hair trichome diameter to particle diameter (D∗ /D∗ ). The results offer valuable insight into the hair p effects of trichome morphology on pollutant deposition in isolation from other macro-factors.

The work presented in this thesis attempts to provide an understanding of the physics behind the dynamic stall process by simulating the flow past pitching NACA-0012 airfoil at 100,000 and 1 million Reynolds number based on the chord length of the airfoil and at different reduced frequencies of 0.188 and 0.25 respectively in a three dimensional flow field. The mean angles of attack are 12 deg. and 15 deg. and the amplitudes of pitching are 6 deg. and 10 deg. respectively. The turbulence in the flow field is resolved using large eddy simulations with dynamic Smagorinsky model at the sub grid scale. The lift hysteresis plots of this simulation for both the configurations are compared with the corresponding experiments. The development of dynamic stall vortex, vortex shedding and reattachment as predicted by the present study are discussed in detail. There is a fairly good match between the predicted and experimentally measured lift coefficient during the upstroke for both cases. The net lift coefficient for the Re = 100,000 case during downstroke matches with the corresponding experimental data, the present study under-predicts the lift coefficient as compared to the experimental values at the start of downstroke and over-estimates for the remaining part of the downstroke. The trend of the lift coefficient hysteresis plot with the experimental data for the Re = 1 million case is also similar. This present simulations have shown that the downstroke phase of the pitching motion is strongly three dimensional and is highly complex, whereas the flow is practically two dimensional during the upstroke. / Master of Science

This thesis presents a computational framework that models the coupled behavior between sand deposits and their surrounding fluid. Particle deposits that form in gas turbine engines and industrial burners, can change flow dynamics and heat transfer, leading to performance degradation and impacting durability. The proposed coupled framework allows insight into the coupled behavior of sand deposits at high temperatures with the flow, which has not been available previously. The coupling is done by using a CFD-DEM framework in which a physics based collision model is used to predict the post-collision state-of-the-sand-particle. The collision model is sensitive to temperature dependent material properties of sand. Particle deposition is determined by the particle's softening temperature and the calculated coefficient of restitution of the collision. The multiphase treatment facilitates conduction through the porous deposit and the coupling between the deposit and the fluid field. The coupled framework was first used to model the behavior of softened sand particles in a laminar impinging jet flow field. The temperature of the jet and the impact surface were varied(T^* = 1000 – 1600 K), to observe particle behavior under different temperature conditions. The Reynolds number(Rejet = 20, 75, 100) and particle Stokes numbers (Stp = 0.53, 0.85, 2.66, 3.19) were also varied to observe any effects the particles' responsiveness had on deposition and the flow field. The coupled framework was found to increase or decrease capture efficiency, when compared to an uncoupled simulation, by as much as 10% depending on the temperature field. Deposits that formed on the impact surface, using the coupled framework, altered the velocity field by as much as 130% but had a limited effect on the temperature field. Simulations were also done that looked at the formation of an equilibrium deposit when a cold jet impinged on a relatively hotter surface, under continuous particle injection. An equilibrium deposit was found to form as deposited particles created a heat barrier on the high temperature surface, limiting more particle deposition. However, due to the transient nature of the system, the deposit temperature increased once deposition was halted. Further particle injection was not performed, but it can be predicted that the formed deposit would begin to grow again. Additionally, a Large-Eddy Simulation (LES) simulation, with the inclusion of the Smagorinsky subgrid model, was performed to observe particle deposition in a turbulent flow field. Deposition of sand particles was observed as a turbulent jet (Re jet=23000,T_jet^*= 1200 K) impinged on a hotter surface(T_surf^*= 1600 K). Differences between the simulated flow field and relevant experiments were attributed to differing jet exit conditions and impact surface thermal conditions. The deposit was not substantive enough to have a significant effect on the flow field. With no difference in the flow field, no difference was found in the capture efficiency between the coupled and decoupled frameworks. / Master of Science

Large-Eddy Simulations (LES or wall-resolved LES, WRLES) has been used extensively in capturing the physics of anisotropic turbulent flows. However, near wall turbulent scales in the inner layer in wall bounded flows makes it unfeasible for large Reynolds numbers due to grid requirements. This study evaluates the use of a wall model for LES (WMLES) on a channel with rotation at ã Reã _b = 34,000 from ã Roã _b = 0 to 0.38, non-staggered 90° ribbed duct with rotation at ã Reã _b = 20,000 from ã Roã _b = 0 to 0.70, stationary 45° staggered ribbed duct at ã Reã _b = 49,000, and two-pass smooth duct with a U-bend at ã Reã _b = 25,000 for ã Roã _b = 0 to 0.238 against WRLES and experimental data. In addition, for the two-pass smooth duct with a U-bend simulations, the synthetic eddy method (SEM) is used to artificially generate eddies at the inlet based on given flow characteristics. It is presented that WMLES captures the effects of Coriolis forces and predicts mean heat transfer augmentation ratios reasonably well for all simulations. The alleviated grid resolution for these simulations indicates significant reductions in resources, specifically, by a factor of 10-20 in non-staggered 90° ribbed duct simulations. The combined effects of density ratio, Coriolis forces, with SEM for the inlet turbulence, capture the general trends in heat transfer in and after the bend. / Master of Science

Gas turbines for military applications, when operating in harsh environments like deserts often encounter unexpected operation faults. Such performance deterioration of the gas turbine decreases the mission readiness of the Air Force and simultaneously increases the maintenance costs. Some of the major factors responsible for the reduced performance are ingestion of debris during take off and landing, distorted intake flows during low altitude maneuvers, and hot gas ingestion during artillery firing. The focus of this thesis is to study ingestion of debris; specifically sand. The region of interest being the internal cooling ribbed duct of the turbine blade. The presence of serpentine passages and strong localized cross flow components makes this region prone to deposition, erosion, and corrosion (DEC) by sand particles. A Lagrangian particle tracking technique was implemented in a generalized coordinate multi-block Navier-Stokes solver in a distributed parallel framework. The developed algorithm was validated by comparing the computed particle statistics for 28 microns lycopodium, 50 microns glass, and 70 microns copper with available data [2] for a turbulent channel flow at Ret=180. Computations were performed for a particle-laden turbulent flow through a stationary ribbed square duct (rib pitch / rib height = 10, rib height / hydraulic diameter = 0.1) using an Eulerian-Lagrangian framework. Particle sizes of 10, 50, and 100 microns with response times (normalized by friction velocity and hydraulic diameter) of 0.06875, 1.71875, and 6.875 respectively are considered. The calculations are performed for a nominal bulk Reynolds number of 20,000 under fully developed conditions. The carrier phase was solved using Large Eddy Simulation (LES) with Dynamic Smagorinsky Model [1]. Due to low volume fraction of the particles, one-way fluid-particle coupling was assumed. It is found that at any given instant in time about 40% of the total number of 10 micron particles are concentrated in the vicinity (within 0.05 Dh) of the duct surfaces, compared to 26% of the 50 and 100 micron particles. The 10 micron particles are more sensitive to the flow features and are prone to preferential concentration more so than the larger particles. At the side walls of the duct, the 10 micron particles exhibit a high potential to erode the region in the vicinity of the rib due to secondary flow impingement. The larger particles are more prone to eroding the area between the ribs and towards the center of the duct. At the ribbed walls, while the 10 micron particles exhibit a fairly uniform propensity for erosion, the 100 micron particles show a much higher tendency to erode the surface in the vicinity of the reattachment region. The rib face facing the flow is by far the most susceptible to erosion and deposition for all particle sizes. While the top of the rib does not exhibit a large propensity to be eroded, the back of the rib is as susceptible as the other duct surfaces because of particles which are entrained into the recirculation zone behind the rib. / Master of Science

La modélisation par simulation des grandes échelles (Large-Eddy Simulation - LES) des processus physiques régissant la couche limite atmosphérique (CLA) demeure complexe de part la difficulté des modèles à capter l'évolution de la turbulence entre différentes conditions de stratification. De ce fait, l'étude LES du cycle diurne complet de la CLA comprenant des situations convectives la journée et des conditions stables la nuit est très peu documenté. La simulation de la couche limite stable où la turbulence est faible, intermittente et qui est caractérisée par des structures turbulentes de petite taille est tout particulièrement compliquée. En conséquence, la capacité de la LES à bien reproduire les conditions météorologiques de la CLA, notamment en situation stable, est étudiée à l'aide du code de mécanique des fluides développé par EDF R&D, Code_Saturne. Dans une première étude, le modèle LES est validé sur un cas de couche limite convective quasi stationnaire sur terrain homogène. L'influence des modèles sous-maille de Smagorinsky, Germano-Lilly, Wong-Lilly et WALE (Wall-Adapting Local Eddy-viscosity) ainsi que la sensibilité aux méthodes de paramétrisation sur les champs moyens, les flux et les variances est discutées. Dans une seconde étude le cycle diurne complet de la CLA pendant la campagne de mesure Wangara est modélisé. L'écart aux mesures étant faible le jour, ce travail se concentre sur les difficultés rencontrées la nuit à bien modéliser la couche limite stable. L'impact de différents modèles sous-maille ainsi que la sensibilité au coefficient de Smagorinsky ont été analysés. Par l'intermédiaire d'un couplage radiatif réalisé en LES, les répercussions du rayonnement infrarouge et solaire sur le jet de basse couche nocturne et le gradient thermique près de la surface sont exposées. De plus l'adaptation de la résolution du domaine à l'intensité de la turbulence et la forte stabilité atmosphérique durant l'expérience Wangara sont commentées. Enfin un examen des oscillations numériques inhérentes à Code_Saturne est réalisé afin d'en limiter les effets / Large-eddy simulation (LES) of the physical processes in the atmospheric boundary layer (ABL) remains a complex subject. LES models have difficulties to capture the evolution of the turbulence in different conditions of stratification. Consequently, LES of the whole diurnal cycle of the ABL including convetive situations in daytime and stable situations in the night time is seldom documented. The simulation of the stable atmospheric boundary layer which is characterized by small eddies and by weak and sporadic turbulence is espacialy difficult. Therefore The LES ability to well reproduce real meteorological conditions, particularly in stable situations, is studied with the CFD code developed by EDF R&D, Code_Saturne. The first study consist in validate LES on a quasi-steady state convective case with homogeneous terrain. The influence of the subgrid-scale models (Smagorinsky model, Germano-Lilly model, Wong-Lilly model and Wall-Adapting Local Eddy-viscosity model) and the sensitivity to the parametrization method on the mean fields, flux and variances are discussed.In a second study, the diurnal cycle of the ABL during Wangara experiment is simulated. The deviation from the measurement is weak during the day, so this work is focused on the difficulties met during the night to simulate the stable atmospheric boundary layer. The impact of the different subgrid-scale models and the sensitivity to the Smagorinsky constant are been analysed. By coupling radiative forcing with LES, the consequences of infra-red and solar radiation on the nocturnal low level jet and on thermal gradient, close to the surface, are exposed. More, enhancement of the domain resolution to the turbulence intensity and the strong atmospheric stability during the Wangara experiment are analysed. Finally, a study of the numerical oscillations inherent to Code_Saturne is realized in order to decrease their effects

Les orages tropicaux jouent un rôle incertain dans le transport de l'air troposphérique dans la stratosphère limitant notre capacité à prévoir le climat futur. Le transport par les orages pourrait en effet être sous-estimé dans les modèles de climat aux résolutions trop grossières. L'efficacité de ce transport est analysée à partir de simulations numériques de l'orage Hector the Convector jusqu'à une résolution de 100 m, la plus fine jamais utilisée pour un cas de convection très profonde. Les percées nuageuses, qui avaient été observées à son sommet à 18 km d'altitude, sont reproduites et l'hydratation nette de la stratosphère est quantifiée. La contribution des orages tropicaux au flux d'eau de la troposphère à la stratosphère est ainsi estimée à près de 20 %. La quasi-convergence aux résolutions de 200 m et 100 m suggère que de telles résolutions sont nécessaires pour représenter correctement les ascendances. L'analyse individuelle des ascendances indique que les deux plus grandes contribuent à plus de 90 % du flux de masse vers la basse stratosphère. Elles sont plus larges, plus puissantes et contiennent plus d'eau que les plus grandes ascendances une heure avant et une heure après, et leur cœur convectif apparaît très peu dilué. L'alimentation en surface par des lignes de convergence intensifiées par des poches froides et la faible dilution des deux plus grandes ascendances sont déterminantes dans l'apparition de la convection très profonde. L'analyse isentropique de la circulation générale dans Hector confirme le flux de masse calculé par l'analyse des ascendances. Elle le corrige dans les basses couches en prenant en compte les flux turbulents, et en haute troposphère en filtrant les ondes de gravité. Elle met en évidence l'importance du dégagement de chaleur latente dû à la congélation dans les plus grandes ascendances pendant la phase de percée en stratosphère. / The tropical thunderstorms play an uncertain role in the transport of tropospheric air into the stratosphere, limiting our capability to predict the future climate. The transport by the thunderstorms may be underestimated by the climate models, due to their coarse resolutions. The efficiency of this transport is analysed using numerical simulations of the thunderstorm Hector the Convector with resolutions down to 100 m, the finest ever used for a case of very deep convection. The overshoots, that were observed at its top at 18 km altitude, are captured and the net hydration of the stratosphere is quantified. The contribution of the tropical thunderstorms to the water flux from the troposphere to the stratosphere is then estimated to about 20 %. The almost convergence at 200 m and 100 m suggests that such resolutions are necessary to correctly represent the updafts. The individual analysis of the updrafts indicates that the two tallest contribute beyond 90 % of the mass flux into the stratosphere. They are larger, more vigorous and contain more water than the tallest updrafts one hour before and one hour after, and their convective core was weakly diluted. The supply from the surface by the convergence lines, intensified by the cold pools, and the weak dilution of the two tallest updrafts are determinant for the development of very deep convection. The isentropic analysis of the overturning inside Hector confirms the mass flux computed with the updrafts analysis. It corrects the estimate in the lower troposphere by taking into account the turbulent flux, and in the upper troposphere by filtering out the gravity waves. It highlights the importance of the latent heating due to freezing in the two tallest updrafts during the phase of overshoot in the stratosphere.

Turbulence is an open and challenging problem for mathematical approaches, physical modeling and numerical simulations. Numerical solutions contribute significantly to the understand of the nature and effects of turbulence. The focus of this thesis is the development of appropriate numerical methods for the computer simulation of turbulent flows. Many of the existing approaches to turbulence utilize analogies from kinetic theory. Degond & Lemou (J. Math. Fluid Mech., 4, 257-284, 2002) derived a k-✏ type turbulence model completely from kinetic theoretic framework. In the first part of this thesis, a numerical method is developed for the computer simulation based on this model. The Boltzmann equation used in the model has an isotropic, relaxation collision operator. The relaxation time in the collision operator depends on the microscopic turbulent energy, making it difficult to construct an efficient numerical scheme. In order to achieve the desired numerical efficiency, an appropriate change of frame is applied. This introduces a stiff relaxation source term in the equations and the concept of asymptotic preserving schemes is then applied to tackle the stiffness. Some simple numerical tests are introduced to validate the new scheme. In the second part of this thesis, alternative approaches are sought for more efficient numerical techniques. The Lattice Boltzmann Relaxation Scheme (LBRS) is a novel method developed recently by Rohan Deshmukh and S.V. Raghuram Rao for simulating compressible flows. Two different approaches for the construction of implicit sub grid scale -like models as Implicit Large Eddy Simulation (ILES) methods, based on LBRS, are proposed and are tested for Burgers turbulence, or Burgulence. The test cases are solved over a largely varying Reynolds number, demonstrating the efficiency of this new ILES-LBRS approach. In the third part of the thesis, as an approach towards the extension of ILES-LBRS to incompressible flows, an artificial compressibility model of LBRS is proposed. The modified framework, LBRS-ACM is then tested for standard viscous incompressible flow test cases.