The research was motivated by the desire to use Large Eddy Simulations (LES) to calculate liner heat transfer in industrial scale gas turbine combustors, which operate at high Reynolds numbers and high Swirl numbers. LES has several challenges which need to be surmounted for general application to complex high Reynolds number turbulent flows. The primary challenge in wall bounded flows is the need for very fine grids in the vicinity of walls, which makes LES impractical at high Reynolds numbers. An additional challenge is the accurate representation of inlet turbulent conditions for developing flows such that the computational domain size is limited to the immediate region of interest. The generalization of solutions to surmount these issues in complex geometries and grids is yet another challenge. To meet these challenges, a novel formulation, implementation, and validation of a two layer velocity and temperature zonal wall model along with the implementation of the synthetic eddy method in a generalized coordinate system LES framework is presented in this thesis. The wall model greatly alleviates the grid requirements, whereas the synthetic eddy method provides accurate turbulent inlet boundary conditions. The methods are validated in turbulent channel flow up to a Reynolds number of 2x106, a backward facing step at Re=40,000, before application to a model swirl combustor at Re=20,000 with a Swirl number of 0.43 and flow and heat transfer in an industrial scale can combustor at Re=80,000 and Swirl number of 0.7. The integrated zonal near wall approach for velocity and temperature is then successfully used to investigate flow and heat transfer in a statistically three-dimensional flow of a ribbed duct passage used for the internal cooling of turbine blades. The zonal wall model is further modified to take in to account the effects of surface roughness and successfully used to investigate flow in a rod roughened channel at high Reynolds numbers up to 60,000. In all cases it is shown that the zonal wall model used with the synthetic eddy method for inlet turbulence generation can result in large savings in computational cost without any significant loss in accuracy when compared to wall resolved LES and experiments. In a turbulent channel flow at Re=45,000, computational complexity was reduced by a factor of 285 using wall modeled LES, whereas in a statistically three-dimensional flow and heat transfer in a ribbed duct, at Re=20,000, the computational complexity was reduced by a factor between 60 and 140. In a swirl dominated can combustor at Re=20,000, the reduction was more modest at a factor of 9. / Ph. D.

This thesis investigates the impact of upstream duct convolution on the plume development for high speed jets. In particular, investigations are carried out into an unconventional aero-engine exhaust systems comprised of a modified convergent-divergent rectangular nozzle where the converging section of the nozzle includes an S-bend in the duct. The motivation for this work comes from both the military and civilian sectors of the aerospace industry. The growing interest into highly efficient engines in the civilian sector and increasing complexities involved in stealth technologies for military applications has led to new design constraints on aero-engine exhaust systems that require further research into flows through more complex duct geometries. Due to a lack of experimental data into this area in the open literature validation studies are undertaken into flows through an S-bend duct and exhaust plume development from a rectangular convergent-divergent nozzle. The validation work is simulated using RANS CFD with common industrial turbulence models as well as LES with artificial inlet conditions. Subsequently, a CFD investigation into three unconventional aero-engine exhaust systems, with over-expanded conditions, with differing angles of curvature across the converging S-bend is undertaken using both RANS and LES methodologies governed by the validation work. As the curvature of the S-bend was increased it was found that the thrust and effective NPR both decrease. Whilst these changes were within acceptable levels (with some optimisation) for a circumferential extent of up to 53.1 the losses became prohibitive large at extents. For the ducts with a greater circumferential extents separation was seen to occur at the throat of the nozzle; this changes the design parameters of the nozzle leading to a higher Mach number and could potentially be harnessed to improve performance of the engine creating a `variable throat' nozzle. The impact of using different numerical solvers to simulate the flow through an unconventional aero-engine exhaust system has also been considered. The use of LES has shown that the octagonal, hexahedral and trapezoidal shapes initially observed in the development of the plumes of the RANS cases are likely to be an artifact caused by the RANS solver, as would the transverse total pressure gradients observed in the RANS cases at the nozzle exit as they are both absent from all of the LES results. Likewise the implementation of realistic inlet conditions has a significant impact on the development of the plume, particularly in the length of the potential core and the number of shock cells.

La simulation numérique d'écoulements turbulents dans les systèmes de refroi- dissement de joints de pompes hydrauliques demande à considérer des domaines de calcul très étendus et des temps d'intégration très longs. La modélisation hybride RANS/LES zo- nale pourrait permettre de reproduire, dans un temps de calcul acceptable industriellement, l'ensemble des phénomènes thermiques et dynamiques en présence. L'approche consiste à faire interagir une simulation des grandes échelles (LES), représentant finement les phé- nomènes instationnaires de la turbulence dans certaines régions critiques de l'écoulement, avec l'approche statistique (RANS), moins coûteuse numériquement et dont la mise en oeuvre dans le reste du domaine permet de rendre compte des variations globales imposées à l'écoulement (injection d'eau froide dans de l'eau chaude, rotation de l'arbre et de la roue, etc...). Dans cette optique, une étude détaillée des modélisations adaptées aux écoulements en rotation est réalisée, suivant les deux approches RANS et LES. De nombreux modèles de turbulence sont comparés sur un cas test de canal en rotation. Le couplage zonal aux faces de bord par la méthode des structures turbulentes synthétiques (SEM) est étudié et une méthode innovante de couplage volumique par force de rappel (Forçage Linéaire Ani- sotrope) sur une zone de recouvrement RANS/LES est proposée. Ces deux méthodes sont étendues pour la première fois à la thermique. Les simulations hybrides RANS/LES zonales présentées, sur des cas test de canal fixe, en rotation ou en convection forcée, montrent la faisabilité de telles modélisations pour des applications industrielles.

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.

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.