La turbulence axisymétrique est un écoulement bidimensionnel trois-composantes. L’étude de ce type de turbulence est motivée par le fait que celle-ci représente la limite asymptotique des écoulements anisotropes, et qu’elle a été le sujet des investigations théoriques dans le passé. Dans ce manuscrit, la turbulence axisymétrique a étudié en géométrie fermée en utilisant des simulations numériques spectrales et pseudo-spectrales.Études antérieures concernant la génération des structures cohérentes, obtenues dans les écoulements en déclin libre, sont considérées ici dans le contexte des écoulements statistiquement stationnaires, où l’énergie est injectée soit par un forçage spectralement localisé ou par une rotation des disques en haut et en bas du cylindre. On montre que les structures observées sont conformes aux prédictions théoriques.Lorsqu’un protocole de forçage anisotrope est utilisé, une bifurcation est observée entre un état non-tourbillonnant (bidimensionnel deux-composantes, 2D2C) et un écoulement tourbillonnant turbulent (bidimensionnel trois-composante, 2D3C). Cette transition est modélisée à travers un système de deux équations différentielles ordinaires (ODE), et on montre que ce modèle retient la physique essentielle de cette transition. La transition de l’écoulement axisymétrique à un écoulement tridimensionnel (3D3C) est ensuite étudiée à l’aide d’une dimension non-entière, en introduisant de façon continue la variation azimutale dans le système. On montre que la limite 2D2C est singulière et qu’une petite variation azimutale permet une redistribution d’énergie sur les différentes composante énergétiques. Le modèle ODE est adapté pour ce système et on montre que pour l’écoulement considéré la corrélation pression-déformation est responsable d'un niveau approximativement proportionnel à la dimension non-entière. Des Simulations des Grandes Echelles sont réalisées pour évaluer la robustesse des observations à grands nombres de Reynolds. / Axisymmetric turbulence is a two-dimensional three-component flow. The investigation of this type of turbulence is motivated by the fact that it represents the asymptotic limit of anisotropic flows and since it has been the subject of theoretical investigations in the past. In the present manuscript such a flow is investigated in wall-bounded cylindrical geometry using spectral and pseudo-spectral numerical simulations.Previous results on the generation of coherent structures, obtained for freely decaying flow, are here assessed in the context of statistically steady flow, where the energy is supplied by either a spectrally localized forcing, or by moving top and bottom plates of the cylinder. It is shown that the observed structures are consistent with theoretical predictions.When an anisotropic forcing protocol is used, a bifurcation is observed from a non-swirling (two-dimensional two-component, 2D2C) flow to a swirling (two-dimensional three-component 2D3C) turbulent flow. This transition is modelled by a system of two ordinary differential equations (ODE), and it is shown that this model retains the essential physics of the transition.The transition of the axisymmetric flow to three-dimensional (3D3C) flow is then studied using non-integer dimension, by smoothly introducing azimuthal variation into the system. It is shown that the 2D2C limit is singular and that small azimuthal variation allows a redistribution of energy over the different energy components. The ODE model is adapted for this system and it is shown that for the considered flow the pressure-strain correlation is responsible for a swirl-level approximately proportional to the non-integer dimension. Large-Eddy Simulations are carried out to assess the robustness of the observations at higher Reynolds number.

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The goal of this work is to investigate the capabilities of two different commercial codes, OpenFOAM and ANSYS CFX, to predict forced convection heat transfer in low Prandtl number fluids and investigate the sensitivity of these predictions to the type of code and to several input parameters.The goal of the work is accomplished by predicting forced convection heat transfer in two different experimental setups with the codes OpenFOAM and ANSYS CFX using three different turbulence models and varying the input parameters in an extensive sensitivity analysis. The computational results are compared two the experimental data and analyzed for qualitative and quantitative parameters, such as shape of velocity and temperature profiles, thickness of the boundary layers and wall temperatures.The results show that predictions of the temperature and velocity field are generally sufficient to good, however, the sensitivity especially to the turbulent Prandtl number has to be taken into account when computing forced convection heat transfer in low Prandtl number fluids. The results also show that methods applied to OpenFOAM cannot directly be applied to ANSYS CFX. / <p>QC 20130531</p> / GENIUS

Development of a novel high-order flux correction method on strand grids is presented. The method uses a combination of flux correction in the unstructured plane and summation-by-parts operators in the strand direction to achieve high-fidelity solutions. Low-order truncation errors are cancelled with accurate flux and solution gradients in the flux correction method, thereby achieving a formal order of accuracy of 3, although higher orders are often obtained, especially for highly viscous flows. In this work, the scheme is extended to high-Reynolds number computations in both two and three dimensions. Turbulence closure is achieved with a robust version of the Spalart-Allmaras turbulence model that accommodates negative values of the turbulence working variable, and the Menter SST turbulence model, which blends the k-ε and k-ω turbulence models for better accuracy. A major advantage of this high-order formulation is the ability to implement traditional finite volume-like limiters to cleanly capture shocked and discontinuous flow. In this work, this approach is explored via a symmetric limited positive (SLIP) limiter. Extensive verification and validation is conducted in two and three dimensions to determine the accuracy and fidelity of the scheme for a number of different cases. Verification studies show that the scheme achieves better than third order accuracy for low and high-Reynolds number flow. Cost studies show that in three-dimensions, the third-order flux correction scheme requires only 30% more walltime than a traditional second-order scheme on strand grids to achieve the same level of convergence. In order to overcome meshing issues at sharp corners and other small-scale features, a unique approach to traditional geometry, coined "asymptotic geometry," is explored. Asymptotic geometry is achieved by filtering out small-scale features in a level set domain through min/max flow. This approach is combined with a curvature based strand shortening strategy in order to qualitatively improve strand grid mesh quality.

Standard eddy-viscosity models lack curvature and system rotation sensitized terms in their formulation. Hence they fail to capture the effects of curvature and system rotation on turbulence anisotropy. As part of this effort, an algebraic expression for a characteristic rotation term is developed and tuned with the help of rotating homogeneous shear flow. This formulation is primarily based upon the rotation and curvature sensitized eddy-viscosity coefficient developed by York et al. (2009). A new scalar transport equation loosely based on Durbin’s wall normal turbulent velocity scale (Durbin, 1991) is introduced to account for the modification in turbulence structure due to system rotation and curvature effects. The added transport equation also introduces history effects and stability in the solution with small increase in computational cost. The eddy-viscosity is redefined based on new turbulent velocity scale and hence the effects of rotation and streamline curvature are introduced into the mean momentum equation. A number of canonical test cases with significant curvature and rotation effects along with a cyclone flow, a representative of complex industrial flows, are considered for model validation. Hybrid modeling framework combines the strength of RANS in boundary layers and LES in separated shear layers to alleviate the weaknesses of RANS and limitations of LES model in some complex flows. A recently proposed hybrid RANS-LES modeling framework uses a weighing parameter that dynamically determines the RANS and LES regions based on solution statistics. The hybrid modeling methodology is implemented on a normal jet in crossflow, and a film cooling case for the purpose of model validation and evaluation. The final goal of the proposed effort is to combine advanced RANS modeling capability with LES using the new hybrid modeling framework. Specifically, the curvature and rotation sensitive RANS model developed here is coupled with commonly used LES models to produce a novel model for complex turbulent flows with the potential to improve accuracy of CFD predictions (versus existing RANS models) as well as significantly reduce the computational expense (versus existing LES models). Performance of the model form hence developed is evaluated on a cyclone flow case.

Modeling of complex flows involving the combined effects of flow transition and streamline curvature using two advanced turbulence models, one in the Reynolds-averaged Navier-Stokes (RANS) category and the other in the hybrid RANS-Large eddy simulation (LES) category is considered in this research effort. In the first part of the research, a new scalar eddy-viscosity model (EVM) is proposed, designed to exhibit physically correct responses to flow transition, streamline curvature, and system rotation effects. The four equation model developed herein is a curvature-sensitized version of a commercially available three-equation transition-sensitive model. The physical effects of rotation and curvature (RC) enter the model through the added transport equation, analogous to a transverse turbulent velocity scale. The eddy-viscosity has been redefined such that the proposed model is constrained to reduce to the original transition-sensitive model definition in nonrotating flows or in regions with negligible RC effects. In the second part of the research, the developed four-equation model is combined with a LES technique using a new hybrid modeling framework, dynamic hybrid RANS-LES. The new framework is highly generalized, allowing coupling of any desired LES model with any given RANS model and addresses several deficiencies inherent in most current hybrid models. In the present research effort, the DHRL model comprises of the proposed four-equation model for RANS component and the MILES scheme for LES component. Both the models were implemented into a commercial computational fluid dynamics (CFD) solver and tested on a number of engineering and generic flow problems. Results from both the RANS and hybrid models show successful resolution of the combined effects of transition and curvature with reasonable engineering accuracy, and for only a small increase in computational cost. In addition, results from the hybrid model indicate significant levels of turbulent fluctuations in the flowfield, improved accuracy compared to RANS models predictions, and are obtained at a significant reduction of computational cost compared to full LES models. The results suggest that the advanced turbulence modeling techniques presented in this research effort have potential as practical tools for solving low/high Re flows over blunt/curved bodies for the prediction of transition and RC effects.

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There is increasing interest in design methods and performance prediction for turbine engines operating at low Reynolds numbers. In this regime, boundary layer separation may be more likely to occur in the turbine flow passages. For accurate CFD predictions of the flow, correct modeling of laminar-turbulent boundary layer transition is essential to capture the details of the flow. To investigate possible improvements in model fidelity, both two-dimensional and three-dimensional CFD models were created for the flow over several low pressure turbine blade designs. A new three-equation eddy-viscosity type turbulent transitional flow model originally developed by Walters and Leylek was employed for the current RANS CFD calculations. Flows over three low pressure turbine blade airfoils with different aerodynamic characteristics were simulated over a Reynolds number range of 15,000-100,000, and predictions were compared to experiments. The turbulent transitional flow model sensitivity to inlet turbulent flow parameters showed a dependence on free-stream turbulence intensity and turbulent length scale. Using the total pressure loss coefficient as a measurement of aerodynamic performance, the Walters and Leylek transitional flow model produced adequate prediction of the Reynolds number performance in the Lightly Loaded blade. Furthermore, the correct qualitative flow response to separated shear layers was observed for the Highly Loaded blade. The vortex shedding produced by the separated flow was largely two-dimensional with small spanwise variations in the separation region. The blade loading and separation location was sufficiently predicted for the Aft-Loaded L1A blade flowfield. Investigations of the unsteady flowfield of the Aft-Loaded L1A blade showed the shear layer produced a large separation region on the suction surface. This separation region was located more downstream and significantly reduced in size when impinged upon by the upstream wakes, thus improving the aerodynamic performance consistent with experiments. For all cases investigated, the Walters and Leylek transitional flow model was judged to be sufficient for understanding the separation and transition characteristics, and superior to other widely-used turbulence models in accuracy of describing the details of the transitional and separated flow. This research characterized and assessed a new model for low Reynolds number turbine aerodynamic flow prediction and design improvement. / Ph. D.

In this work, a three-dimensional turbulent boundary layer experiment was set up with alternating stream-wise and span-wise pressure gradients. The pressure gradients are generated as a result of the test section wavy side wall shape. Each side had six sine waves with a trough to peak magnitude to wavelength ratio of 0.25. Boundary layer control was used so that the flow over the side walls remains attached. The mean flow velocity components, static and total pressures were measured at six plane along the stream-wise direction. The alternating mean span-wise and stream-wise pressure gradients created alternating stream-wise and span-wise vorticity fluxes, respectively, along the test section. As the flow developed downstream the vorticity created at the tunnel floor and ceiling diffused away from the wall. The vorticity components in the stream-wise and span-wise directions are strengthened due to stretching and tilting terms in the vorticity transport equations. The positive-z half of the test section contains large areas that generate positive vorticity flux in the trough region and smaller areas generating negative vorticity around the wave peak. The opposite is true for the negative-z half of the test-section. This results in a large positive stream-wise vorticity in the positive-z half and negative stream-wise vorticity in the negative-z half of the test-section. The smaller regions of opposite sign vorticity in each half tend to mix the flow such that as they diffuse away from the wall, the turbulent stresses are more uniform. Turbulent fluctuating velocity components were measured using Laser Doppler Velocimetery. Mean velocities as well as Reynolds stresses and triple velocity component correlations were measured at thirty stations along the last wave in the test section. Profiles at the center of the test section showed three dimensionality, but exhibited high turbulence intensities in the outer layer. Profiles off the test section centerline are highly three dimensional with multiple peaks in the normal stress profiles. The flow also reaches a state where all the normal stresses have equal magnitudes while the shear stresses are non-zero. Flow angles, flow gradient angles and shear stress angles show very large differences between wall values and outer layer vlaues. The shear stress angle lagged the flow gradient angle indicating non-equilibrium. A turbulent kinetic energy transport budget is performed for all profiles and the turbulence kinetic energy dissipation rate is estimated. Spectral measurements were also made and an independent estimate of the kinetic energy dissipation rate is made. These estimates agree very well with those estimates made by balancing the turbulence kinetic energy transport equation. Multiple turbulent diffusion models are compared to measured quantities. The models varied in agreement with experimental data. However, fair agreement with turbulence kinetic energy turbulent diffusion is observed. A model for the dissipation rate tensor anisotropy is used to extract estimates of the pressure-strain tensor from the Reynolds stress transport equations. The pressure-strain estimates are compared with some of the models in the literature. The comparison showed poor agreement with estimated pressure-strain values extracted from experimental data. A tentative model for the turbulent Reynolds shear stress angle is developed that captures the shear stress angle near wall behavior to a very good extent. The model contains one constant that is related to mean flow variables. However, the developed expression needs modification so that the prediction is improved along the entire boundary layer thickness. / Ph. D.

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