There still is a practical need for improved closure models for the Reynolds-averaged Navier-Stokes (RANS) equations. This dissertation explores two different approaches for using experimental data to provide improved closure for the Reynolds stress tensor field. The first approach uses machine learning to learn a general closure model from data. A novel framework is developed to train deep neural networks using experimental velocity and pressure measurements. The sensitivity of the RANS equations to the Reynolds stress, required for gradient-based training, is obtained by means of both variational and ensemble methods. The second approach is to infer the Reynolds stress field for a flow of interest from limited velocity or pressure measurements of the same flow. Here, this field inversion is done using a Monte Carlo Bayesian procedure and the focus is on improving the inference by enforcing known physical constraints on the inferred Reynolds stress field. To this end, a method for enforcing boundary conditions on the inferred field is presented. The two data-driven approaches explored and improved upon here demonstrate the potential for improved practical RANS predictions. / Doctor of Philosophy / The Reynolds-averaged Navier-Stokes (RANS) equations are widely used to simulate fluid flows in engineering applications despite their known inaccuracy in many flows of practical interest. The uncertainty in the RANS equations is known to stem from the Reynolds stress tensor for which no universally applicable turbulence model exists. The computational cost of more accurate methods for fluid flow simulation, however, means RANS simulations will likely continue to be a major tool in engineering applications and there is still a need for improved RANS turbulence modeling. This dissertation explores two different approaches to use available experimental data to improve RANS predictions by improving the uncertain Reynolds stress tensor field. The first approach is using machine learning to learn a data-driven turbulence model from a set of training data. This model can then be applied to predict new flows in place of traditional turbulence models. To this end, this dissertation presents a novel framework for training deep neural networks using experimental measurements of velocity and pressure. When using velocity and pressure data, gradient-based training of the neural network requires the sensitivity of the RANS equations to the learned Reynolds stress. Two different methods, the continuous adjoint and ensemble approximation, are used to obtain the required sensitivity. The second approach explored in this dissertation is field inversion, whereby available data for a flow of interest is used to infer a Reynolds stress field that leads to improved RANS solutions for that same flow. Here, the field inversion is done via the ensemble Kalman inversion (EKI), a Monte Carlo Bayesian procedure, and the focus is on improving the inference by enforcing known physical constraints on the inferred Reynolds stress field. To this end, a method for enforcing boundary conditions on the inferred field is presented. While further development is needed, the two data-driven approaches explored and improved upon here demonstrate the potential for improved practical RANS predictions.

The design method for marine propulsor (propeller/stator) is presented for an autonomous underwater vehicle (AUV) that operates at a very high loading condition. The design method is applied to Virginia Tech Dragon AUV. It is based on the parametric geometry definition for the propulsor, use of high-fidelity CFD RANSE solver with the transition model, construction of the surrogate model, and multi-objective genetic optimization algorithm. The CFD model is validated using the paint pattern visualization on the surface of the propeller for an open propeller at model scale. The CFD model is then applied to study hydrodynamics of ducted propellers such as forces and moments, tip leakage vortex, leading-edge flow separation, and counter-rotating vortices formed at the duct trailing edge. The effect of variation of thickness for stator blades and different approaches for modeling the postswirl stator is presented. The field trials for Dragon AUV shows that there is a good correlation between expected and achieved design speed under tow condition with the designed base propulsor. The marine propulsor design is further improved with an objective to maximize the propulsive efficiency and minimize the rolling of AUV. The stator is found to eliminate the swirl component of velocity present in the wake of the propeller to the maximum extent. The propulsor designed using this method (surrogate-based optimization) is demonstrated to have an improved torque balance characteristic with a slight improvement in efficiency than the base propulsor design. / Master of Science / The propulsion system is the critical design element for an AUV, especially if it is towing a large payload. The propulsor for towing AUVs has to provide a very large thrust and hence the propulsor is highly loaded. The propeller has to rotate at very high speed to produce the required thrust and is likely to cavitate at this high speed. Also at this high loading condition, the maximum ideal efficiency of the propulsor is very less. Another challenge is the induced torque from the propeller on AUV that can cause the rolling of an AUV which is undesirable. This problem can be addressed by installing the stator behind the propeller that will produce torque in the opposite direction of the propeller torque. In this work, we present a design methodology for marine propulsor (propeller/stator) that can be used in AUV towing a large payload. The propulsor designed using this method has improved torque characteristics and has the efficiency close to 80 % of the ideal efficiency of ducted propeller at that loading condition.

Computational fluid dynamics methods have seen an increasing role in aerodynamic analysis since their first implementation. However, there are several major limitations is these methods of analysis, especially in the area of modeling separated flow. There exists a large demand for high-fidelity experimental data for turbulence modeling validation. Virginia Tech has joined NASA in a cooperative project to design and perform an experiment in the Virginia Tech Stability Wind Tunnel with the purpose of providing a benchmark set of data for the turbulence modeling community for the flow over a three-dimensional bump. This process requires thorough risk mitigation and analysis of potential flow sensitivities. The current study investigates several aspects of the experimental design through the use of several computational fluid dynamics codes. An emphasis is given to boundary condition matching and uncertainty quantification, as well as sensitivities of the flow features to Reynolds number and inflow conditions. Solutions are computed for two different RANS turbulence models, using two different finite-volume CFD codes. Boundary layer inflow parameters are studied as well as pressure and skin friction distribution on the bump surface. The shape and extent of separation are compared for the various solutions. Pressure distributions are compared to available experimental data for two different Reynolds numbers. / Master of Science / Computational fluid dynamics (CFD) methods have seen an increasing role in engineering analysis since their first implementation. However, there are several major limitations is these methods of analysis, especially in the area of modeling of several common aerodynamic phenomena such as flow separation. This motivates the need for high fidelity experimental data to be used for validating computational models. This study is meant to support the design of an experiment being cooperatively developed by NASA and Virginia Tech to provide validation data for turbulence modeling. Computational tools can be used in the experimental design process to mitigate potential experimental risks, investigate flow sensitivities, and inform decisions about instrumentation. Here, we will use CFD solutions to identify risks associated with the current experimental design and investigate their sensitivity to incoming flow conditions and Reynolds number. Numerical error estimation and uncertainty quantification is performed. A method for matching experimental inflow conditions is proposed, validated, and implemented. CFD data is also compared to experimental data. Comparisons are also made between different models and solvers.

Computational fluid dynamics (CFD) methods and schemes have been evolving at a rate that significantly outpaces the equipment needed to readily utilize them at scale. This lack of computational resources has resulted in an increased reliance on turbulence models and the need to know where turbulence models do well, where they do poorly, and where/how they can be improved upon. The BeVERLI Hill experiments aim to address this issue by providing experimental data that achieves a completeness level of three, which has never been done for this type of project. The experimental data collected is studied along side computational results from CFD solvers in order to help address and answer these questions. This paper provides an overview of the current computational status of the BeVERLI Hill project at Virginia Tech. The computational grids used for the analyses are presented such that the reader can gain an appreciation for the modeling techniques and methods being implemented. An analysis of the numerical error associated with the computational results is presented to provide confidence in the results obtained. An in-depth analysis will be presented that shows the results for the various grid levels that are being utilized to determine any grid based effects that are occurring within the solutions. Then, an analysis of the influence of the Reynolds numbers being run is shown. An investigation into the differences between the two different solvers being utilized, SENSEI and Fluent, is shown. An analysis of the effects on the solutions due to numerical limiters is presented to assist in increasing the computational efficiency of the workflow while not adversely affecting the results. Finally, an analysis of the differences between the two turbulence models being utilized is presented. Computational results are compared to available experimentally obtained data to further motivate and identify flow features. / Master of Science / An analysis has been done with high-fidelity computational fluid dynamic solvers that are utilized in order to solve for the flow over a three-dimensional bump called BeVERLI. An analysis is provided that discusses the use of different computational meshes, solvers, turbulence models, and numerical limiters within the computational tools to characterize the flow over the bump. An analysis of the estimated amount of numerical error within the solutions is provided along with a comparison to experimentally obtained data.

Accurate physical modeling and accelerated numerical simulation of turbulent flows remain primary challenges in CFD for aerospace engineering and related fields. This dissertation tackles these challenges with a focus on Reynolds-Averaged Navier--Stokes (RANS) models, which will continue to serve as the backbone for many practical aircraft applications. Specifically, in RANS turbulence modeling, the challenges include developing more efficient ensemble filters to learn nonlinear eddy viscosity models from observation data that move beyond the classical Boussinesq hypothesis, as well as developing non-equilibrium models that break away from the weak equilibrium assumption while maintaining computational efficiency. For accelerating RANS simulations, the challenges include leveraging existing simulation data to optimize the computational workflow while maintaining the method's adaptability to various computational settings. From a fundamental and mathematical perspective, we view these challenges as problems of modeling and learning complex nonlinear and nonlocal mappings, which we categorize into three types: field-to-point, field-to-field, and ensemble-to-ensemble. To model and resolve these mappings, we build up on recent advancements in machine learning and develop novel neural operator-based methods that not only possess strong representational capabilities but also preserve critical physical and mathematical principles. With the developed tools, we have demonstrated promising preliminary results in addressing these challenges and have the potential to significantly advance the state of the art in RANS turbulence modeling and simulation acceleration. / Doctor of Philosophy / Understanding and accurately predicting turbulent flows, such as those around airplanes or ships, are among the biggest challenges in computational fluid dynamics (CFD). This research aims to improve Reynolds-Averaged Navier--Stokes (RANS) models, which are widely used in practical engineering applications. Traditional RANS turbulence models are based on simplified assumptions that are linear and local, making it difficult to capture the true complexity of turbulent flows. My work addresses this limitation by developing new models that leverage advanced machine learning techniques to better represent turbulence. Specifically, I have focused on developing methods that extend beyond conventional approaches by learning more accurate local nonlinear constitutive relations and incorporating nonlocal effects---an important step toward improving simulation accuracy. In addition, I have explored strategies to accelerate RANS simulations by making more effective use of existing data, providing better initial conditions for simulations, and ultimately reducing computational costs. Preliminary results indicate that these new methods have the potential to push the boundaries of RANS turbulence modeling, enabling more accurate and efficient simulations.

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.

A new approach to large-eddy simulation (LES) based on the use of explicit spatial filtering combined with backscatter forcing is presented. The forcing uses a discrete dynamical system (DDS) called the compressible ``poor man's'' Navier--Stokes (CPMNS) equations. This DDS is derived from the governing equations and is shown to exhibit good spectral and dynamical properties for use in a turbulence model. An overview and critique of existing turbulence theory and turbulence models is given. A comprehensive theoretical case is presented arguing that traditional LES equations contain unresolved scales in terms generally thought to be resolved, and that this can only be solved with explicit filtering. The CPMNS equations are then incorporated into a simple forcing in the OVERFLOW compressible flow code, and tests are done on homogeneous, isotropic, decaying turbulence, a Mach 3 compression ramp, and a Mach 0.8 open cavity. The numerical results validate the general filter-forcing approach, although they also reveal inadequacies in OVERFLOW and that the current approach is likely too simple to be universally applicable. Two new proposals for constructing better forcing models are presented at the end of the work.

Historically turbulence modeling has been sharply divided into Reynolds averaged Navier-Stokes (RANS), in which all the turbulent scales of motion are modeled, and large-eddy simulation (LES), in which only a portion of the turbulent spectrum is modeled. In recent years there have been numerous attempts to couple these two approaches either by patching RANS and LES calculations together (zonal methods) or by blending the two sets of equations. In order to create a proper bridging model, that is, a single set of equations which captures both RANS and LES like behavior, it is necessary to place both RANS and LES in a more general framework.The goal of the current work is threefold: to provide such a framework, to demonstrate how the Flow Simulation Methodology (FSM) fits into this framework, and to evaluate the strengths and weaknesses of the current version of the FSM. To do this, first a set of filtered Navier-Stokes (FNS) equations are introduced in terms of an arbitrary generalized filter. Additional exact equations are given for the second order moments and the generalized subfilted dissipation rate tensor. This is followed by a discussion of the role of implicit and explicit filters in turbulence modeling.The FSM is then described with particular attention to its role as a bridging model. In order to evaluate the method a specific implementation of the FSM approach is proposed. Simulations are presented using this model for the case of separating flow over a "hump" with and without flow control. Careful attention is paid to error estimation, and, in particular, how using flow statistics and time series affects the error analysis. Both mean flow and Reynolds stress profiles are presented, as well as the phase averaged turbulent structures and wall pressure spectra. Using the phase averaged data it is possible to examine how the FSM partitions the energy between the coherent resolved scale motions, the random resolved scale fluctuations, and the subfilter quantities.The method proves to be qualitatively successful at reproducing large turbulent structures. However, like other hybrid methods, it has difficulty in the region where the model behavior transitions from RANS to LES> Consequently the phase averaged structures reproduce the experiments quite well, and the forcing does significantly reduce the length of the separated region. Nevertheless, the recirculation length is signficantly too large for all cases.Overall the current results demonstrate the promise of bridging models in general and the FSM in particular. However, current bridging techniques are still in their infancy. There is still important progress to be made and it is hoped that this work points out the more important avenues for exploration.

The fow around bluff bodies is an essential topic in fuid dynamics. This fow is characterized by large vortical fow regions separating from the surface of the bluff body, and they cause oscillating drag and lift forces on the structure. The fow around an infinite long cylinder is a well-known case being studied in the literature. However, a cylinder with low aspect-ratio piercing the free surface has not been studied much although such an arrangement can be found in many floating offshore structures. In this thesis the results of CFD calculations are presented for a fixed, free surface piercing cylinder with an aspect-ratio L/D equals to 2. The Reynolds number was equal to 4:3 x 104 indicating that the flow is in the sub-critical turbulent regime. An extensive methodology of verication and validation is followed to investigate the reliability of the results. To investigate the effect of the free surface on the calculated hydrodynamic loads, two approaches have been considered: a double-body symmetry condition and an interface capturing Volume-of-Fluid (VoF) method. Additionally, two turbulence models are investigated: a two-equation turbulence model; a non-linear Explicit Algebraic Reynolds Stress Model (EARSM); and the Improved Delayed Detached Eddy Simulation (IDDES) turbulence model. The results are presented in terms of integral results (drag and lift coefficients) and flow visualizations. Based on the results of the cases in which the free surface was modeled as a double body symmetry boundary condition, it is concluded that the model is not suitable for this type of flow as the model damps out the flow dynamics due to over-production of eddy-viscosity. Hence, the characteristic oscillating lift forces are not captured using this turbulence model. However, this turbulence model showed good agreements regarding the flow fields in comparison with experimental PIV measurements. Results of the case modeled with EARSM turbulence model shows better agreement with the experimental results compared with the turbulence model. In the cases where the free-surface is considered, results with the EARSM turbulence model show similar results for the drag forces whereas the lift uctuations were one order of magnitude smaller, compared with the double body case. Lastly, the results using the IDDES turbulence model and free-surface VoF modeling are shown to produce the best comparison with the experimental results, regarding both, integral values and flow field results. / O escoamento ao redor de corpos rombudos é um tópico essencial na dinâmica de fluidos. O escoamento é caracterizado por regiões com grande vorticidade que se separam do corpo e causam oscilações das forças de arrasto e sustentação sobre a estrutura. O escoamento ao redor de cilindros longos é um tema que tem sido extensivamente estudado com muitos trabalhos encontrados na literatura. Entretanto, o cilindro com baixa razão de aspecto perfurante à superfície livre é um caso pouco estudado, apesar desta estrutura ser encontrada em várias estruturas oceânicas flutuantes. Esta dissertação apresenta cálculos numéricos para o escoamento ao redor de um cilindro fixo, que trespassa a superfície livre com razão de aspecto L/D igual a 2. O problema é estudado em um regime subcrítico de turbulência, com número de Reynolds igual a 4:3 x 104. Uma vasta metodologia de verificação e validação foi seguida para avaliar a confiabilidade dos resultados obtidos numericamente. Para investigar os efeitos da superfície livre nas cargas hidrodinâmicas, duas abordagens s~ao consideradas: condição de simetria de duplo corpo e um método de captura de interface Volume of Fluid. Além disso, dois modelos de turbulência foram investigados: o modelo não linear Explicit Algebraic Reynolds Stress Model (EARSM), e o modelo de turbulência Improved Delayed Detached Eddy Simulation (IDDES). Os resultados relacionados aos coeficientes de arrasto e sustentação são apresentados a partir de análise estatística, complementados através de ilustrações que permitem visualizar os campos de escoamento e pressão. Com base nos resultados de casos em que a superfície livre é modelada com uma condição de contorno de simetria, conclui-se que o modelo de turbulência não é adequado para este tipo de escoamento, pois o modelo amortece a dinâmica do escoamento devido à superprodução de viscosidade turbulenta. Consequentemente, as oscilações na força de sustentação não são capturadas usando este modelo. Entretanto, resultados dos campos médios do escoamento mostram-se concordantes com imagens experimentais obtidas com técnicas de PIV - Particle Image Velocimetry. Resultados do caso modelado com o modelo de turbulência EARSM mostram melhores concordâncias na comparação dos parâmetros estatísticos com experimentos do que o modelado com o modelo EARSM. Nos casos em que a superfície livre é modelada com o método VoF, o modelo de turbulência EARSM mostra resultados semelhantes para o arrasto, enquanto as flutuações da sustentação apresentam-se uma ordem de grandeza menores, quando comparadas ao caso de duplo corpo. Resultados usando o modelo de turbulência IDDES e VoF apresentam melhores comparações aos resultados experimentais, tanto para os parâmetros estatísticos quando para as visualizações do escoamento.

To quantify primary side aerosol retention, an Eulerian/Lagrangian approach was used to investigate aerosol transport in a compressible, turbulent, adiabatic, internal, wall-bounded flow. The ARTIST experimental project (Phase I) served as the physical model replicated for numerical simulation. Realizable k-ε and standard k-ω turbulence models were selected from the computational fluid dynamics (CFD) code, FLUENT, to provide the Eulerian description of the gaseous phase. Flow field simulation results exhibited: a) onset of weak secondary flow accelerated at bend entrance towards the inner wall; b) flow separation zone development on the convex wall that persisted from the point of onset; c) centrifugal force concentrated high velocity flow in the direction of the concave wall; d) formation of vortices throughout the flow domain resulted from rotational (Dean-type) flow; e) weakened secondary flow assisted the formation of twin vortices in the outflow cross section; and f) perturbations induced by the bend influenced flow recovery several pipe diameters upstream of the bend. These observations were consistent with those of previous investigators. The Lagrangian discrete random walk model, with and without turbulent dispersion, simulated the dispersed phase behavior, incorrectly. Accurate deposition predictions in wall-bounded flow require modification of the Eddy Impaction Model (EIM). Thus, to circumvent shortcomings of the EIM, the Lagrangian time scale was changed to a wall function and the root-mean-square (RMS) fluctuating velocities were modified to account for the strong anisotropic nature of flow in the immediate vicinity of the wall (boundary layer). Subsequent computed trajectories suggest a precision that ranges from 0.1% to 0.7%, statistical sampling error. The aerodynamic mass median diameter (AMMD) at the inlet (5.5 μm) was consistent with the ARTIST experimental findings. The geometric standard deviation (GSD) varied depending on the scenario evaluated but ranged from 1.61 to 3.2. At the outlet, the computed AMMD (1.9 μm) had GSD between 1.12 and 2.76. Decontamination factors (DF), computed based on deposition from trajectory calculations, were just over 3.5 for the bend and 4.4 at the outlet. Computed DFs were consistent with expert elicitation cited in NUREG-1150 for aerosol retention in steam generators.