A dynamic hybrid Reynolds-averaged Navier-Stokes (RANS)-Large Eddy Simulation (LES) modeling framework has been investigated and further developed to improve the Computational Fluid Dynamics (CFD) prediction of turbulent flow features along with laminar-to-turbulent transitional phenomena. In recent years, the use of hybrid RANS/LES (HRL) models has become more common in CFD simulations, since HRL models offer more accuracy than RANS in regions of flow separation at a reduced cost relative to LES in attached boundary layers. The first part of this research includes evaluation and validation of a dynamic HRL (DHRL) model that aims to address issues regarding the RANS-to-LES zonal transition and explicit grid dependence, both of which are inherent to most current HRL models. Simulations of two test cases—flow over a backward facing step and flow over a wing with leading-edge ice accretion—were performed to assess the potential of the DHRL model for predicting turbulent features involved in mainly unsteady separated flow. The DHRL simulation results are compared with experimental data, along with the computational results for other HRL and RANS models. In summary, these comparisons demonstrate that the DHRL framework does address many of the weaknesses inherent in most current HRL models. Although HRL models are widely used in turbulent flow simulations, they have limitations for transitional flow predictions. Most HRL models include a fully turbulent RANS component for attached boundary layer regions. The small number of HRL models that do include transition-sensitive RANS models have issues related to the RANS model itself and to the zonal transition between RANS and LES. In order to address those issues, a new transition-sensitive HRL modeling methodology has been developed that includes the DHRL methodology and a physics-based transition-sensitive RANS model. The feasibility of the transition-sensitive dynamic HRL (TDHRL) model has been investigated by performing numerical simulations of the flows over a circular cylinder and a PAK-B airfoil. Comparisons with experimental data along with computational results from other HRL and RANS models illustrate the potential of TDHRL model for accurately capturing the physics of complex transitional flow phenomena.

Wind energy industry thrived in the last three decades, environmental concerns and government regulations stimulate studies on wind farm location selection and wind turbine design. Full-scale experiments and high-fidelity simulations are restrictive due to the prohibitively high cost, while the model-scale experiments and low-fidelity calculations miss key flow physics of unsteady high Reynolds number flows. A hybrid RANS/LES turbulence model integrated with transition formulation is developed and tested by a surrogate model problem through joint experimental and computational fluid dynamics approaches. The model problem consists of a circular cylinder for generating coherent unsteadiness and a downstream airfoil in the cylinder wake. The cylinder flow is subcritical, with a Reynolds number of 64,000 based upon the cylinder diameter. The quantitative dynamics of vortex shedding and Reynolds stresses in the cylinder near wake were well captured, owing to the turbulence-resolving large eddy simulation method that was invoked in the wake. The power spectrum density of velocity components showed that the flow fluctuations were well-maintained in cylinder wake towards airfoil and the hybrid model switched between RANS/LES mode outside boundary layer as expected. According to the experimental and simulation results, the airfoil encountered local flow angle variations up to ±50 degrees, and the turbulent airfoil boundary layer remained attached. Inspecting the boundary layer profiles over one shedding cycle, the oscillation about mean profile resembled the Stokes layer with zero mean. Further processing the data through phase-averaging technique found phase lags along the chordwise locations and both the phase-averaged and mean profiles collapsed into the Law of Wall in the range of 0 < y+ < 50. The features of high blade loading fluctuations due to unsteadiness and transitional boundary layers are of interest in the aerodynamic studies of full-scale wind turbine blades, making the model problem a comprehensive benchmark case for future model development and validation. / Ph. D. / Wind energy industry thrived in the last three decades, environmental concerns and government regulations stimulate studies on wind farm location selection and wind turbine design. Full-scale experiments and high-fidelity simulations are restrictive due to the prohibitively high cost, while the model-scale experiments and low-fidelity calculations miss key flow physics of of the full-scale models. The current study adopted a joint experimental and computational fluid dynamic approach to design a surrogate problem that features the unsteady flow physics presented in the full-scale wind turbine blades. A new hybrid turbulence model was implemented and validated against the complementary experimental results. The new model improves the accuracy of the current industry-standard turbulence models without excessive computational cost, making it a viable solution to the high-fidelity full-scale simulations in the future.

The aerodynamics of modern rotorcraft is highly complex and has proven to be an arduous challenge for computational fluid dynamics (CFD). Flow features such as massively separated boundary layers or transition to turbulence are common in engineering applications and need to be accurately captured in order to predict the vehicle performance. The recent advances in numerical methods and turbulence modeling have resolved each of these issues independent of the other. First, state-of-the-art hybrid RANS-LES turbulence closures have shown great promise in capturing the unsteady flow details and integrated performance quantities for stalled flows. Similarly, the correlation-based transition model of Langtry and Menter has been successfully applied to a wide range of applications involving attached or mildly separated flows. However, there still lacks a unified approach that can tackle massively separated flows in the transitional flow region. In this effort, the two approaches have been combined and expended to yield a methodology capable of accurately predicting the features in these highly complex unsteady turbulent flows at a reasonable computational cost. Comparisons are evaluated on several cases, including a transitional flat plate, circular cylinder in crossflow and NACA 63-415 wing. Cost and accuracy correlations with URANS and prior hybrid URANS-LES approaches with and without transition modeling indicate that this new method can capture both separation and transition more accurately and cost effectively. This new turbulence approach has been applied to the study of wings in the reverse flow regime. The flight envelope of modern helicopters has increased significantly over the last few decades, with design concepts now reaching advance ratios up to μ = 1. In these extreme conditions, the freestream velocity exceeds the rotational speed of the blades, and a large region of the retreating side of the rotor disk experiences reverse flow. For a conventional airfoil with a sharp trailing edge, the reverse flow regime is generally characterized by massive boundary layer separation and bluff body vortex shedding. This complex aerodynamic environment has been utilized to evaluate the new hybrid transitional approach. The assessment has proven the efficiency of the new hybrid model, and it has provided a transformative advancement to the modeling of dynamic stall.

Horizontal-axis wind turbines operate in a complex, inherently unsteady aerodynamic environment. The flow over the blades is dominated by 3-D effects, particularly during stall, which is accompanied by massive flow separation and vortex shedding. There is always bluff-body shedding from the turbine nacelle and support structure which interacts with the rotor wake. In addition, the high aspect ratios of wind turbine blades make them very flexible, leading to substantial aeroelastic deformation of the blades, altering the aerodynamics. Finally, when situated in a wind farm, turbines must operate in the unsteady wake of upstream neighbors. Though computational fluid dynamics (CFD) has made significant inroads as a research tool, simple, inexpensive methods, such as blade element momentum theory, are still the workhorses in wind turbine design and aeroelasticity applications. These methods are unable to accurately predict rotor loads near the edges of the operating envelope. In this work, a range of unstructured grid CFD techniques for predicting wind turbine loads and aeroelasticity has been developed and applied to the NREL Unsteady Aerodynamics Experiment Phase VI rotor. First, a kd-tree based nearest neighbor search algorithm was used to improve the computational efficiency of an approximate unsteady actuator blade method. This method was then shown to predict root and tip vortex locations and strengths similar to an overset method, but without the computational expense of modeling the blade surfaces. A hybrid Reynolds-averaged Navier-Stokes / Large Eddy Simulation (HRLES) turbulence model was extended to an unstructured grid framework and demonstrated to improve predictions of unsteady loading and shedding frequency in massively separated cases. For aeroelastic predictions, a methodology for tight coupling between an unstructured CFD solver and a computational structural dynamics tool was developed. Finally, time-accurate overset rotor simulations of a complete turbine---blades, nacelle, and tower---were conducted using both RANS and HRLES turbulence models. The HRLES model was able to accurately predict rotor loads when stalled. In yawed flow, excellent correlations of mean blade loads with experimental data were obtained across the span, and wake asymmetry and unsteadiness were also well-predicted.

Ce travail porte sur l’évaluation de la méthode ZDES pour la simulation de jets propulsifs. L’analyse se concentre sur le positionnement des cellules de chocs et le développement des couches de mélange d’une tuyère double-flux avec plug externe, typique des moteurs d’avions modernes. Les champs statistiques sont comparés aux résultats expérimentaux et discutés en termes de grandeurs moyennes, fluctuantes et dans le domaine fréquentiel. L’intérêt d’utiliser un schéma spatial peu dissipatif ainsi qu’une échelle de longueur sous-maille basée sur la vorticité locale est mis en évidence, notamment pour le dévelopement de la couche de mélange interne, et le mode 2 ("automatique") de la ZDES a démontré un comportement similaire au mode 1 ("manuel") dans les couches de mélange. Par ailleurs, la technique Random Flow Generation (RFG) mise en oeuvre afin de reproduire la turbulence amont existant au coeur des jets primaire et secondaire a permis d’accélérer la transition RANS-LES dans les deux couches de mélanges, plus conformément à l’expérience. La transition est d’autant plus rapide que le taux de turbulence est élevé et l’échelle de la turbulence injectée est petite. Le positionnement des cellules de choc est également amélioré, soulignant l’importance de prendre en compte la turbulence amont dans les simulations de jets. / In this thesis, the ZDES method is assessed for the simulation of propulsive jets. This work focuses on the shock-cell positioning and the mixing layer development of a dual-stream nozzle configuration with an external plug, typical of modern aircraft engines. Reynolds averaged data are discussed in terms of mean and fluctuating quantities as well as in the frequency domain and compared with experimental data. First, the advantage of using a low dissipative spatial scheme as well as a subgrid length scale based on the local vorticity is demonstrated, especially for the development of the core mixing layer. Besides, the "automatic" mode of ZDES (mode 2) is found to provide similar mixing layers as the user defined mode.Then, the use of the Random Flow Generation (RFG) technique at the inlet boundaries of the core and fan channels in order to reproduce the turbulence rate at the center of the nozzle ducts is shown to accelerate the RANS-to-LES transition in both external and internal mixing layers, which is in better agreement with the experimental results. The transition length is further reduced when the injected turbulent ratio is higher, but also when the injected turbulent length scale is smaller. Of interest, the shock-cell positioning in the fan jet is also improved using RFG, which emphasizes the importance of accounting for upstream turbulence for this type of simulations.

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.

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.

In this work, the mathematical implications of merging two different turbulence modeling approaches are addressed by deriving the exact hybrid RANS/LES Navier-Stokes equations. These equations are derived by introducing an additive-filter, which linearly combines the RANS and LES operators with a blending function. The equations derived predict additional hybrid terms, which represent the interactions between RANS and LES formulations. Theoretically, the prediction of the hybrid terms demonstrates that the hybridization of the two approaches cannot be accomplished only by the turbulence model equations, as it is claimed in current hybrid RANS/LES models. The importance of the exact hybrid RANS/LES equations is demonstrated by conducting numerical calculations on a turbulent flat-plate boundary layer. Results indicate that the hybrid terms help to maintain an equilibrated model transition when the hybrid formulation switches from RANS to LES. Results also indicate, that when the hybrid terms are not included, the accuracy of the calculations strongly relies on the blending function implemented in the additive-filter. On the other hand, if the exact equations are resolved, results are only weakly affected by the characteristics of the blending function. Unfortunately, for practical applications the hybrid terms cannot be exactly computed. Consequently, a reconstruction procedure is proposed to approximate these terms. Results show, that the model proposed is able to mimic the exact hybrid terms, enhancing the accuracy of current hybrid RANS/LES approaches. In a second effort, the Two Level Simulation (TLS) approach is proposed as a near-wall model for LES. Here, TLS is first extended to compressible flows by deriving the small-scale equations required by the model. The full compressible TLS formulation and the hybrid TLS/LES approach is validated simulating the flow over a flat-plate turbulent boundary layer. Overall, results are found in reasonable agreement with experimental data and LES calculations.

Cette thèse s’inscrit dans le cadre de l’amélioration des prévisions aérothermiques qui suscite l’intérêt croissant des industriels aéronautiques. Elle consiste à évaluer l’apport des méthodes URANS avancées de type SAS dans la prévision des flux de chaleur turbulents et pariétaux pour des écoulements turbulents chauffés. Elle vise aussi à situer ces approches par rapports aux modèles URANS classiques de type DRSM et hybrides RANS/LES comme la ZDES. Une extension de l’approche SAS à un modèle DRSM a d’abord été proposé afin d’obtenir une meilleure restitution des tensions de Reynolds résolues et modélisées. Ce modale SAS-DRSM a été implanté dans le code elsA de l’ONERA. Nous avons ensuite évalué les approches SAS disponibles avec ce code sur la prévention d’écoulements aérothermiques rencontrés sur avion dans un compartiment de moteur. Ces études ont montré que les approches SAS améliorent la représentation des écoulements par rapport aux modèles URANS classiques. Elles aboutissent à des écoulements fortement tridimensionnels avec de nombreuses structures turbulentes. Ces structures induisent un mélange turbulent accru et donc une meilleure prévision du flux de chaleur pariétal. De plus, nos travaux ont situé les approches de type SAS comme des méthodes plus précises que les méthodes URANS classiques sans augmentation importante du coût de calcul. Les modèles SAS ne résolvent pas les plus petites structures caractéristiques du mouvement turbulent par rapport à la ZDES qui montre des prévisions supérieures. Le modèle SAS-RDSM offre néanmoins la meilleur alternative de type SAS. Enfin, l’étude du flux de chaleur turbulent semble retrouver le fait que l’hypothèse classique de nombre de Prandtl turbulent constat n’est pas valable dans toutes les zones de l’écoulement. / The improvement of aerothermal predictions is a major concern for aeronautic manufacturers. In line with this issue, SAS approaches are assessed on the prediction of wall and turbulent heat fluxes for heated-turbulent flows. This study also aims at evaluating these advanced URANS methods in regard to DRSM models and hybrid RANS/LES approaches as ZDES. Firstly, we proposed to combine the SAS approach and a DRSM model in order to better reproduce both resolved and modelled Reynolds stresses. This new model, called SAS-DRSM, was implemented in ONERA Navier-Strokes code elsA. Unsteady simulations of two heated turbulent flows encountered in an aircraft engine compartment were then performed to evaluate all the SAS models available in the code. These numerical studies demonstrated that SAS approaches improve prediction of the flows compared to classical URANS models. They lead to full 3D flows with many turbulent structures. These structures favour turbulent mixing and thus induce a better prediction of the wall heat fluxes. Moreover, the numerical simulations showed that SAS methods are more accurate than classical URANS models without increasing significantly calculation costs. SAS approaches are not able to resolve the smallest turbulent structures in relation to ZDES which provides better predictions. Finally, the investigation of the turbulent heat flux suggested that the constant turbulent Prendtl number assumption, that is characteristic of classical URANS models, may not be valid in some regions of the flow.

Dans le domaine de la modélisation des écoulements turbulents, les approche hybrides RANS/LES ont reçu récemment beaucoup d’attention car ils combinent le coût de calcul raisonnable du RANS et la précision de la LES.Parmi elles, le TPITM (Temporal Partially Integrated Transport Model) est une approche hybride RANS/LES temporelle qui surmonte les inconsistances du raccordement continu du RANS et de la LES grâce à un formalisme de filtrage temporel. Cependant, le modèle TPITM est relativement difficile à mettre en œuvre et, en particulier, nécessite l’utilisation d’une correction dynamique, contrairement à d’autres approches, notamment la DES (Detached Eddy Simulation).Cette thèse propose alors une approche hybride RANS/LES similaire à la DES, mais basée sur un filtrage temporel, déduite du modèle TPITM par équivalence, c’est-à-dire en imposant la même partition entre énergies résolue et modélisée. Ce modèle HTLES (Hybrid Temporal LES) combine les caractéristiques de la DES (facilité de mise en œuvre) et du TPITM (formalisme consistant, justification théorique des coefficients).Après calibration en turbulence homogène, l’approche est appliquée à des cas d’écoulements autour de cylindres carrés puis rectangulaires. La modélisation des tensions de sous-filtre est une adaptation au contexte hybride du modèle RANS k-wSST. / In the field of modelling of turbulent flows, hybrid RANS/LES approaches have recently received a considerable attention due to the combination of the computational cost of RANS and the accuracy of LES.Among them, TPITM (Temporal Partially Integrated Transport Model) is a hybrid RANS/Temporal LES approach that overcomes the inconsistency of the continuous bridging of RANS and LES by using a temporal filtering formalism. However, TPITIM is relatively difficult to implement and, in particular, requires a dynamic correction, contrary to other approaches, in particular DES (Detached Eddy Simulation).The present thesis then proposes a hybrid RANS/LES approach similar to DES, but based on temporal filtering, derived from TPITM using an equivalence criterion, i. e., imposing the same partition of among resolved and modeled energies. This HTLES approach (Hybrid Temporal LES) combines the characteristics of DES (ease of implementation) and of TPITM (consistent formalism, theoretical justification of the coefficients).