In this work the predictive capability of a number of Reynolds stress transport(RST) models was first tested in a range of non-equilibrium homogeneous flows, comparisons being drawn with existing direct numerical simulation (DNS) results and physical measurements. The cases considered include both shear and normally strained flows, in some cases with a constant applied strain rate, and in others where this varied with time. Models were generally found to perform well in homogeneous shear at low shear rates, but their performance increasingly deteriorated at higher shear rates. This was attributed mainly to weaknesses in the pressure-strain rate models, leading to over-prediction of the shear stress component of the stress anisotropy tensor at high shear rates. Performance in irrotational homogeneous strains was generally good, and was more consistent over a much wider range of strain rates. In the experimental plane strain and axisymmetric contraction cases, with time-varying strain rates, there was evidence of an accelerated dissipation rate generation. Significant improvement was achieved through the use of an alternative dissipation rate generation term, Pε , in these cases, suggesting a possible route for future modelling investigation. Subsequently, the models were also tested in the inhomogeneous case of pulsating channel flow over a wide range of frequencies, the reference for these cases being the LES of Scotti and Piomelli (2001). A particularly challenging feature in this problem set was the partial laminarisation and re-transition that occurred cyclically at low and, to a lesser extent, intermediate frequencies. None of the models tested were able to reproduce correctly all of the observed flow features, and none returned consistently superior results in all the cases examined. Finally, models were tested in the case of a plane jet interacting with a rectangular dead-end enclosure. Two geometric configurations are examined, corresponding a steady regime, and an intrinsically unsteady regime in which periodic flow oscillations are experimentally observed (Mataoui et al., 2003). In the steady case generally similar flow patterns were returned by the models tested, with some differences arising in the degree of downward deflection of the impinging jet, which in turn affected the level of turbulence energy developing in the lower part of the cavity. In the unsteady case, only two of the models tested, a two-equation k-ε model and an advanced RST model, correctly returned purely periodic solutions. The other two RST models, based on linear pressure-strain rate terms, returned unsteady flow patterns that exhibited complex oscillations with significant cycle-to-cycle variations. Unfortunately, the limited availability of reliable experimental data did not allow a detailed quantitative examination of model performance.

This thesis considers the advantages of incorporating laminar kinetic energy modelling into turbulence modelling, in order to predict laminar-turbulent transition. The final aim is to implement an improved transition model into the industrial Finite-Volume code, Code Saturne. The literature review suggests that in order for a RANS-based model to predict transition accurately, modelling of complex, anisotropic phenomena is necessary. The Walters-Cokljat model is shown to compare very well to other transition modelling methods, including correlation-based modelling. The Walters-Cokljat model is a single-point RANS-based model that solves an additional transport equation for laminar kinetic energy. This transition model is especially desirable from an industrial stand-point, due to its single-point RANS basis, with only 3 transport equations. Although this method shows great promise as an industrial tool for transition prediction, results presented here show that there are aspects of the model that require modification. The definition of effective length-scale and the method of accounting for the effects of shear sheltering are the two main areas for consideration. The current definition of effective length-scale is found to be inappropriate for flows with large free-stream length-scales, which are common-place in turbomachinery applications. Another phenomenon commonly found in turbomachinery is separation-induced transition; however, the current function for shear sheltering effects inhibits transition when turbulence intensity is not the forcing factor. Additionally, when reviewed analytically, the definition and placement of the shear sheltering function does not match the observations of Jacobs and Durbin. Alternatives for the definitions of the effective length-scale and the shear sheltering function are proposed. The individual proposals are tested, and steps towards a full working implementation are documented.

This thesis describes the development and validation of a modified eddy viscosity model to take into account the misalignment between stress a_{ij} and strain S_{ij} fields for reacting flow. The stress-strain misalignment is quantified by introducing a C_{as}=-a_{ij}S_{ij} /\sqrt{2S_{ij}S_{ij}} parameter. A new transport equation for C_{as} was derived from a full Reynolds stress model (RSM). The C_{as} transport equation was coupled to a standard EVM model (e.g. k-\omega SST) to form three equations model. This model is a new version of the SST-C_{as} model introduced by Revell (Revell2006), to incorporate buoyancy and combustion effects for buoyant reacting flow (e.g. fire). The performance of the proposed model was initially investigated via non-reacting buoyant plumes with different level of unsteadiness. The buoyant plumes were also simulated using different turbulence models and the results were compared to proposed model and experimental data. The model shows significant improvements for velocity and scalar profiles in region closed to plume centreline compared to the original SST model. The SST-C_{as} model was then applied for a real fire test case (Steckler room), and the results were compared to experimental data and results of RSM models. The SST-C_{as} model generally yields better than classical EVM models and reduces the gap between the RSM and EVM prediction with 25-30\% additional computational expenses. This work is still under development and validation for reacting flows, further work is going on to include the turbulence combustion interaction and validate it with DNS data.

Three-dimensional turbulent flow in a cylindrical hydrocyclone is considered and studied by means of computational fluid dynamics using software packages CFX and Fluent. The aim has been to identify the methods that can be used for accurate simulation of the flow in three-dimensional configurations in hydrocyclones at high swirl numbers. As a starting point, swirling pipe flows created by tangential inlets, where detailed experimental data were available in literature, were considered. It was found that the velocity profiles for the flow with a swirl number of 2.67 could be predicted accurately using a Reynolds stress model and an accurate numerical discretization on a fine-enough mesh. At a higher swirl number, 7.84, under-prediction in the tangential velocity profiles was observed; however the prediction of the axial velocity profiles was satisfactory. The validated methods were then used to simulate the flow in a cylindrical hydrocyclone at a swirl number as large as 21. The calculated tangential velocity profiles were compared against experimental data measured with a pitometer. Acceptable agreements were recorded except near the geometric axis of the cyclone. Due to the lack of the aircore in the numerical model, disagreements near the axis of the cyclone could be expected to some extent. Numerical experiments performed in the present work indicated that the RNG k-ε model is not likely to be capable to predict highly swirling flows accurately and a Reynolds stress model is required. For three-dimensional models, where the computing capacity and the available memory set strong restrictions on the computational mesh, optimizing the maximum mesh resolution available play an important role on the accuracy and stability of the solution procedure. The most stable results in the present study were found using the Reynolds stress model proposed by Launder et al. on an as regular and structured mesh as possible using a higher order discretization scheme in Fluent. Therefore, the meshing capabilities of the pre-processor, the available turbulence models and the accuracy of the numerical methods must be considered in parallel. Acceptable results were also generated using the Baseline Reynolds stress model implemented in CFX, however, only with a transient procedure which was likely to be more time-consuming. Present simulations present a complex flow structure in the cylindrical cyclone with a double axial flow reversal. The effect of such a flow pattern on the fractionation of the fibres with small differences in density needs to be investigated in future studies. / QC 20101207

This thesis studies the implementation of an Explicit Algebraic Reynolds-Stress Model(EARSM) for Atmospheric Boundary Layer (ABL) in an open source ComputationalFluid Dynamics (CFD) software, OpenFOAM, following the guidance provided by thewind company ENERCON that aims to make use of this novel model to improvesites’ wind-field predictions. After carefully implementing the model in OpenFOAM,the EARSM implementation is verified and validated by testing it with a stratifiedCouette flow case. The former was done by feeding mean flow properties, takenfrom OpenFOAM, in a python tool containing the full EARSM system of equationsand constants, and comparing the resulting flux profiles with the ones extracted bythe OpenFOAM simulations. Subsequently, the latter was done by comparing theprofiles of the two universal functions used by Monin-Obukhov Similarity Theory(MOST) for mean velocity and temperature to the results obtained by Želi et al. intheir study of the EARSM applied to a single column ABL, in “Modelling of stably-stratified, convective and transitional atmospheric boundary layers using the explicitalgebraic Reynolds-stress model” (2021). The verification of the model showed minordifferences between the flux profiles from the python tool and OpenFOAM thus, themodel’s implementation was deemed verified, while the validation step showed nodifference in the unstable and neutral stratification cases, but a significant discrepancyfor stably stratified flow. Nonetheless, the reason behind the inconsistency is believedto be related to the choice of boundary conditions thus, the model’s implementationitself is considered validated. Finally, the comparison between the EARSM and the k − ε model showed thatthe former is able to capture the physics of the flow properties where the latter failsto. In particular, the diagonal momentum fluxes resulting from the EARSM reflectthe observed behaviour of being different from each other, becoming isotropic withaltitude in the case of unstable stratification, and having magnitude u′u′ > v′v′ > w′w′ for stably stratified flows. On the other hand, the eddy viscosity assumption used bythe k − ε model computes the diagonal momentum fluxes as being equal to each other.Moreover, the EARSM captures more than one non-zero heat flux component in theCouette flow case, which has been observed to be the case in literature, while the eddydiffusivity assumption used by the k − ε model only accounts for one non-zero heat fluxcomponent.

Kinematic simulation (KS) is a means of generating a turbulent-like velocity field, in a manner that enforces an input Eulerian energy spectrum. Such models have also been applied in particle-laden flows, due to their ability to enforce spatial organization of the fluid velocity field when simulating the trajectories of individual particles. A critical evaluation of KS is presented; in particular, its ability to reproduce single-particle Lagrangian statistics is examined. Also the ability of KS to reproduce the preferential concentration of inertial particles is explored. Some numerical results are presented, in which fluid tracers and inertial particles are transported alternatively by (1) simulated turbulence generated by direct numerical simulation (DNS) of the incompressible Navier-Stokes equations, and (2) KS. The effect of unsteadiness formulation in particular is examined. It is found that even steady KS qualitatively reproduces the continuity effect, clustering of inertial particles, elevated dispersion of inertial particles and the intermittent turbulence velocity signal. A novel method is then motivated and formulated, in which, for input RANS parameters, a simulated spectrum is used to generate a KS field which enforces a target Lagrangian timescale. This method is then tested against an existing experimental benchmark, and good agreement is obtained. / Thesis / Doctor of Philosophy (PhD) / Turbulence arises in an immense variety of industrial and scientific applications; from weather to automotive design; from medicine to nuclear engineering. Because turbulence is chaotic, it is difficult to make accurate predictions of how a turbulent flow will behave in a given scenario. The objective of my research is to find easier ways of accurately modelling turbulence in a certain class of particle-laden flows.

Cavitation is characterized by the formation of vapor bubbles when the pressure in a working fluid drops sharply below the vapor pressure. These bubbles, upon exiting the low-pressure region burst emanating tremendous amounts of energy. Unsteady cavitating flows have been influential in several aspects from being responsible for erosion damage and vibrations in hydraulic engineering devices to being used for non-invasive medical surgeries and drilling for geothermal energy. While the phenomenon has been investigated using both experimental and numerical methods, it continues to pose a challenge for numerical modelling techniques due to its flow unsteadiness and the cavitation-turbulence interaction. One of the principal aspects to modelling cavitation requires the coupling of a cavitation and a turbulence model. While, scale-resolving turbulence modelling techniques like Direct Numerical Simulations (DNS) and Large Eddy Simulations (LES) upto a certain extent may seem an intuitive solution, the physical complexities involved with cavitation result in extremely high computational costs. Thus, Unsteady Reynolds-Averaged Navier-Stokes (URANS) models have been widely utilized as a workhorse for cavitating simulations. However, URANS models are unable to reproduce the periodic vapor shedding observed in experiments and thus, are often corrected by empirical correction. Recently, some models termed as hybrid RANS-LES models that behave as RANS or LES depending on location of flow have been introduced and employed to model cavitating flows. In addition, there has also been a rise in defining some frameworks that use data from high-fidelity simulations or experiments to drive numerical algorithms and aid standard turbulence modelling procedures for accurately simulating turbulent flows. This dissertation is aimed at (1) evaluating the abilities of these corrections, traditional URANS and hybrid RANS-LES models to model cavitation and (2) optimizing the URANS modelling strategy by designing a methodology driven by experimental data to augment the turbulence modelling to simulate cavitating flow in a converging-diverging nozzle. / Doctor of Philosophy / The famous painting Arion on the Dolphin by the French artist François Boucher shows a dolphin rescuing the poet Arion from the choppy seas after being thrown overboard. Today, seeing silhouettes of dolphins swimming near the shore as the Sun sets is a calming sight. However, as these creatures splash their fins in the water, these fins create a drastic pressure difference resulting in the formation of ribbons of vapor bubbles. As the bubbles exit the low-pressure zones, they collapse and release tremendous amounts of energy. This energy manifests in the form of shockwaves rendering this pleasant sight to the human eye, extremely painful for dolphins. These shocks also impact the metal blades in hydraulic machinery like pumps and ship propellers. This dissertation aims to investigate the physics driving this phenomenon using accurate numerical simulations. We first conduct two-dimensional simulations and observe that standard numerical techniques to model the turbulence are unable to simulate cavitation accurately. The investigation is then extended to three-dimensional simulations using hybrid RANS-LES models that aim to strike a delicate balance between accuracy and efficiency. It is observed that these models are able to reproduce the flow dynamics as observed in experiments but are extremely expensive in terms of computational costs due to the three-dimensional nature of the calculations. The investigation then switches to a data-driven approach where a machine learning algorithm driven by experimental data informs the standard turbulence models and is able to simulate cavitating flows accurately and efficiently.

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.

The separating turbulent flow in a plane asymmetric diffuser with 8.5 degrees opening angle is investigated experimentally and computationally. The considered flow case is suitable for fundamental studies of separation, separation control and turbulence modelling. The flow case has been studied in a specially designed wind-tunnel under well controlled conditions. The average velocity and fluctuation fields have been mapped out with stereoscopic particle image velocimetry (PIV). Knowledge of all velocity components allows the study of several quantities of interest in turbulence modelling such as the turbulence kinetic energy, the turbulence anisotropy tensor and the turbulence production rate tensor. Pressures are measured through the diffuser. The measured data will form a reference database which can be used for evaluation of turbulence models and other computational investigations. Time-resolved stereoscopic PIV is used in an investigation of turbulence structures in the flow and their temporal evolution. A comparative study is made where the measured turbulence data are used to evaluate an explicit algebraic Reynolds stress turbulence model (EARSM). A discussion regarding the underlying reasons for the discrepancies found between the experimental and the model results is made. A model for investigations of separation suppression by means of vortex generating devices is presented together with results from the model in the plane asymmetric diffuser geometry. A short article on the importance of negative production-rates of turbulent kinetic energy for the reverse flow region in separated flows is presented. A detailed description of the experimental setup and PIV measurement procedures is given in a technical report. / QC 20100923

This thesis aims to explore the potential for using large eddy simulation (LES) as a predictive tool for gas-turbine compressor flows. Compressors present a significant challenge for the Reynolds Averaged Navier-Stokes (RANS) based CFD methods commonly used in industry. RANS models require extensive calibration to experimental data, and thus cannot be used predictively. This thesis explores how LES can offer a more predictive alternative, by exploring the sensitivity of LES to sources of uncertainty. Specifically, the importance of the numerical scheme, the Sub-Grid Scale (SGS) model, and the correct specification of inflow turbulence is examined. The sensitivity of LES to the numerical scheme is explored using the Taylor-Green vortex test case. The numerical smoothing, controlled by a user defined smoothing constant, is found to be important. To avoid tuning the numerical scheme, a locally adaptive smoothing (LAS) scheme is implemented. But, this is found to perform poorly in a forced isotropic turbulence test case, due to the intermittency of the dispersive error. A novel scheme, the LAS with windowing (LASW) scheme, is thus introduced. The LASW scheme is shown to be more suitable for predictive LES, as it does not require tuning to a known solution. The LASW scheme is used to perform LES on a compressor cascade, and results are found to be in close agreement with direct numerical simulations. Complex transition mechanisms, combining characteristics of both natural and bypass modes, are observed on the pressure surface. These mechanisms are found to be sensitive to numerical smoothing, emphasising the importance of the LASW scheme, which returns only the minimum smoothing required to prevent dispersion. On the suction surface, separation induced transition occurs. The flow here is seen to be relatively insensitive to numerical smoothing and the choice of SGS model, as long as the Smagorinsky-Lilly SGS model is not used. These findings are encouraging, as they show that, with the LASW scheme and a suitable SGS model, LES can be used predictively in compressor flows. In order to be predictive, the accurate specification of inflow conditions was shown to be just as important as the numerics. RANS models are shown to over-predict the extent of the three dimensional separation in the endwall - suction surface corner. LES is used to examine the challenges for RANS in this region. The LES shows that it is important to accurately capture the suction surface transition location, with early transition leading to a larger endwall separation. Large scale aperiodic unsteadiness is also observed in the endwall region. Additionally, turbulent anisotropy in the endwall - suction surface corner is found to be important. Adding a non-linear term to the RANS model leads to turbulent stresses that are in better agreement with the LES. This results in a stronger corner vortex which is thought to delay the corner separation. The addition of a corner fillet reduces the importance of anisotropy, thereby reducing the uncertainty in the RANS prediction.