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Supplemental Material for Charismatic rhetoric, perceptions of charisma and narcissism, and voting behavior: Leadership Under crisis by Tais S Barreto, Ethlyn A Williams, Randi. L Sims, Rajnandini Pillai and Kate McCombs by Leadership

This scoping review aims to explore what is known about students' attitudes towards, ideas about, and perseptions of diversity in higher education.

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Three-dimensional (3D) turbulent boundary layers (TBLs) play a crucial role in determining the aerodynamic properties of most aero-mechanical devices. However, accurately predicting these flows remains a challenge due to the complex nonlinear and nonlocal physics involved, which makes it difficult to develop universally applicable models. This limitation is particularly significant as the industry increasingly relies on simulations to make decisions in high-consequence environments, such as the certification or aircraft, and high-fidelity simulation methods that don't rely on modeling are prohibitively expensive. To address this challenge, it is essential to gain a better understanding of the physics underlying 3D TBLs. This research aims to improve the predictive accuracy of turbulence models in 3D TBLs by examining the impact of model assumptions underpinning turbulent constitutive relations, which are fundamental building blocks of every turbulence model. Specifically, the study focuses on the relevance and necessity of nonlinear and nonlocal model assumptions for accurately predicting 3D TBLs. The study considers the attached 3D boundary layer flow over the textbf{Be}nchmark textbf{V}alidation textbf{E}xperiment for textbf{R}ANS/textbf{L}ES textbf{I}nvestiagtions (BeVERLI) Hill as a test case and corresponding particle image velocimetry data for the investigation. In a first step, the BeVERLI Hill experiment is comprehensively described, and the important characteristics of the flow over the BeVERLI Hill are elucidated, including complex symmetry breaking characteristics of this flow. Reynolds-averaged Navier-Stokes simulations of the case using standard eddy viscosity models are then presented to establish the baseline behavior of local and linear constitutive relations, i.e., the standard Boussinesq approximation. The tested eddy viscosity models fail in the highly accelerated hill top region of the BeVERLI hill and near separation. In a further step, several nonlinear and nonlocal turbulent constitutive relations, including the QCR model, the model by Gatski and Speziale, and the difference-quotient model by Egolf are used as metrics to gauge the impact of nonlinearities and nonlocalities for the modeling of 3D TBLs. It is shown that nonlinear and nonlocal approaches are essential for effective 3D TBL modeling. However, simplified reduced-order models could accurately predict 3D TBLs without high computational costs. A constitutive relation with local second-order nonlinear mean strain relations and simplified nonlocal terms may provide such a minimal model. In a final step, the structure and response of non-equilibrium turbulence to continuous straining are studied to reveal new scaling laws and structural models. Doctor of Philosophy Airplanes and other flying objects rely on the way air flows around them to generate lift and stay in the sky. This airflow can be very complex, especially close to the surface of the object, where it is affected by friction with the object. This friction generates a layer of air called a boundary layer, which can become turbulent and lead to complex patterns of airflow. The boundary layer is generated by the friction between the air and the surface of the object, which causes the air molecules to "stick" to the surface. This sticking creates a layer of slow-moving air that slows down the flow of air around the object. This loss of momentum creates drag, which is one of the main factors that resist the motion of objects in the air. The slowing of the air flow in the boundary layer is due to the viscosity of the air, which is a measure of how resistant the air is to deformation. The molecules in the air have a tendency to stick together, making it difficult for them to move past each other. This resistance causes the momentum of the air to be lost as it flows over the surface of the object because air molecules close to the surface "pull" on the ones farther away. Understanding how turbulent boundary layers (TBLs) work is essential to accurately predict the airflow around these objects using computer simulations. However, it's challenging because TBLs involve complex physics that are difficult to model accurately. This research focuses on a specific type of TBL called a three-dimensional (3D) TBL. This study looks at how different assumptions affect the accuracy of computer simulations that predict this type of airflow. It is found that using more complex models that take into account nonlinear and nonlocal physics can help predict 3D TBLs more accurately. However, these models are computationally expensive, and it is also found that simpler models can work well enough and are cheaper. This research further establishes important physical relations of the mechanisms pertaining 3D TBLs that could support the advancement of current models.

Small unmanned aircraft and electric vertical takeoff and landing (eVTOL) aircraft have recently emerged as vehicles able to perform new missions and stimulate future air transportation methods. This dissertation presents several system identification research advancements for these modern aircraft configurations enabling accurate mathematical model development for flight dynamics simulations based on wind-tunnel and flight-test data. The first part of the dissertation focuses on advances in flight-test system identification methods using small, fixed-wing, remotely-piloted, electric, propeller-driven aircraft. A generalized approach for flight dynamics model development for small fixed-wing aircraft from flight data is described and is followed by presentation of novel flight-test system identification applications, including: aero-propulsive model development for propeller aircraft and nonlinear dynamic model identification without mass properties. The second part of the dissertation builds on established fixed-wing and rotary-wing aircraft system identification methods to develop modeling strategies for transitioning, distributed propulsion, eVTOL aircraft. Novel wind-tunnel experiment designs and aero-propulsive modeling approaches are developed using a subscale, tandem tilt-wing, eVTOL aircraft, leveraging design of experiments and response surface methodology techniques. Additionally, a method applying orthogonal phase-optimized multisine input excitations to aircraft control effectors in wind-tunnel testing is developed to improve test efficiency and identified model utility. Finally, the culmination of this dissertation is synthesis of the techniques described throughout the document to form a flight-test system identification approach for eVTOL aircraft that is demonstrated using a high-fidelity flight dynamics simulation. The research findings highlighted throughout the dissertation constitute substantial progress in efficient empirical aircraft modeling strategies that are applicable to many current and future aeronautical vehicles enabling accurate flight simulation development, which can subsequently be used to foster advancement in many other pertinent technology areas. Doctor of Philosophy Small, electric-powered airplanes flown without an onboard pilot, as well as novel electric aircraft configurations with many propellers that operate at a wide range of speeds, referred to as electric vertical takeoff and landing (eVTOL) aircraft, have recently emerged as aeronautical vehicles able to perform new tasks for future airborne transportation methods. This dissertation presents several mathematical modeling research advancements for these modern aircraft that foster accurate description and prediction of their motion in flight. The mathematical models are developed from data collected in wind-tunnel tests that force air over a vehicle to simulate the aerodynamic forces in flight, as well as from data collected while flying the aircraft. The first part of the dissertation focuses on advances in mathematical modeling approaches using flight data collected from small traditional airplane configurations that are controlled by a pilot operating the vehicle from the ground. A generalized approach for mathematical model development for small airplanes from flight data is described and is followed by presentation of novel modeling applications, including: characterization of the coupled airframe and propulsion aerodynamics and model development when vehicle mass properties are not known. The second part of the dissertation builds on established airplane, helicopter, and multirotor mathematical modeling methods to develop strategies for characterization of the flight motion of eVTOL aircraft. Innovative data collection and modeling approaches using wind-tunnel testing are developed and applied to a subscale eVTOL aircraft with two tilting wings. Statistically rigorous experimentation strategies are employed to allow the effects of many individual controls and their interactions to be simultaneously distinguished while also allowing expeditious test execution and enhancement of the mathematical model prediction capability. Finally, techniques highlighted throughout the dissertation are combined to form a mathematical modeling approach for eVTOL aircraft using flight data, which is demonstrated using a realistic flight simulation. The research findings described throughout the dissertation constitute substantial progress in efficient aircraft modeling strategies that are applicable to many current and future vehicles enabling accurate flight simulator development, which can subsequently be used for many research applications.

Thin filament pyrometry is a proven technique used to measure flame temperature by capturing the spectral radiance produced by the immersion of silicon carbide filaments in a hot gas environment. In this study a commercially available CMOS color camera was used, and the spectral response of each color channel was integrated with respect to the assumed graybody radiation spectrum to form a look up table between color ratio and temperature. Interpolated filament temperatures are then corrected for radiation losses via an energy balance to determine the flame temperature. Verification of the technique was performed on the Holthuis and Associates Flat Flame Burner, formerly known as the Mckenna Burner, and the results are directly compared to literature values measured on a similar burner. The results are also supported by radiation corrected measurements taken using a type B thermocouple on the same burner setup. An error propagation analysis was performed to determine which factors contribute the most to the final measurement uncertainty and confidence intervals are calculated for the results. Uncertainty values for a single point measurement were determined to be between ±15 and ±50 K depending on the color ratio and the total uncertainty associated with day-to-day changes in the measurement setup was found to be ±55 K. Master of Science Determination of flame temperature is an important aspect of combustion research and is often critical to the evaluation of combustion systems as well as the integration of those systems into more complex devices. In this thesis the technique of thin filament pyrometry was implemented and verified through the use of a well characterized calibration flame. This technique involves placing thin filaments usually made from silicon carbide into the flame and capturing the spectrum of light they emit with a detector. Since the amount of light emitted as well as which wavelengths the light is concentrated in is a strong function of temperature, this methodology may be used to calculate the temperature of the flame. Thin filament pyrometry has the advantage compared to other techniques in that it is extremely cheap to implement and requires no advanced scientific equipment. The SiC filaments have been shown to have a very high resistance to the flame environment and do not face many of the same challenges that can cause problems for other techniques. A statistical analysis of the method implemented in this work was also performed and the expected uncertainty was similar to many of the alternative techniques which necessitate a more complex or expensive setup.

Supersonic jet exhaust plumes produce noise in jet engines, which has been a problem in the aerospace field. Researchers are working on ways to reduce this turbulent mixing noise, with little modification to the engine and nozzle. Prior work has shown that total temperature non-uniformity is a noise reduction technique which introduces a stream of cold flow into the heated jet. This method has been shown to cause changes in the exhaust plume and result in a 2±0.5 dB reduction of peak sound pressure levels. The goal of this work is to reveal underlying changes in the spatial-temporal structure of plume instability and turbulence caused by non-uniform total temperature distributions. Studies have demonstrated several methods of jet noise reduction by modifying the turbulent mixing in the exhaust plume. Large-scale turbulent structures have been shown to be the dominant source of noise in heated supersonic jets, especially over long, streamwise distances. Therefore, a large field-of-view measurement is desirable for studying these structures. Time-Resolved Doppler Global Velocimetry (TR-DGV) with a sampling frequency of 50 kHz is used to collect flow velocity data that is resolved in both time and space. The experiments for data collection were performed on a heated supersonic jet at the Virginia Tech Advanced Propulsion and Power Laboratory. A converging-diverging nozzle with a diameter Reynolds number of 850,000 was used to generate a perfectly expanded, heated flow of Mach 1.5 and a nozzle pressure ratio (NPR) of 3.67. The unheated plume was introduced at the center of the nozzle, with a total temperature ratio (TTR) of 2. Comparison of the mean velocity fields shows that the introduction of the cooler temperature flow in the thermally non-uniform case results in a velocity deficit of about 10% compared to the thermally uniform case. The method of spectral proper orthogonal decomposition (SPOD) was used to reveal the large-scale, coherent noise producing mechanisms. SPOD results indicate that the thermally non-uniform case showed a decrease in turbulent kinetic energy compared to the uniform case at all frequencies. Coherent fluctuations start developing further upstream in the thermally non-uniform case. The addition of the unheated plume results in a disruption in the propagation of the Mach waves from the shear layer into the ambient. The results indicate that the total temperature non-uniformity results in a modified exhaust plume and mean flow distribution at the nozzle exit, compared to that of a thermally uniform flow, which past studies have indicated is a method to reduce jet noise. Master of Science Supersonic jet exhaust plumes produce noise in jet engines, which has been a problem in the aerospace field. Researchers are working on ways to reduce this turbulent mixing noise, with little modification to the engine and nozzle. Traditionally, nozzles produce a single stream of uniform temperature flow. This work identifies a method of reducing jet noise, known as thermal non-uniformity. A stream of cold flow is introduced at the center of the nozzle. Applying this method to jet engines can result in quieter aircraft. Large-scale turbulent structures are the dominant noise producing source in supersonic free jets. To further understand the relationship between coherent structures and acoustic jet noise, spectral analysis is used to educe these structures from the flow. This study uses velocity data collected using Time-Resolved Doppler Global Velocimetry (TR-DGV). The study compares the results of a thermally uniform and a thermally non-uniform heated supersonic jet of Mach 1.5. The goal of this study is to determine the effects of thermal non-uniformity on large-scale coherent structures using a modal decomposition analysis known as spectral proper orthogonal decomposition (SPOD). The results from this study show that the thermally non-uniform cases contained less turbulent kinetic energy compared to the thermally uniform cases. Coherent fluctuations start developing further upstream in the thermally non-uniform case. The addition of the unheated plume results in a disruption in the propagation of the Mach waves from the shear layer into the ambient. The results indicate that the total temperature non-uniformity results in a modified exhaust plume and mean flow distribution at the nozzle exit, compared to that of a thermally uniform flow, which past studies have indicated is a method to reduce jet noise.

Helicopter turboshaft engines may ingest large amounts of foreign particles (most commonly sand/dust), which can cause significant compressor blade damage and even engine failure. In many helicopters, this issue is mitigated by separating the particles from the intake airstream. An effective device for engine air-particle separation is the vortex tube separator (VTS), which uses centrifugal forces in a vortical flow to radially filter foreign particles from a duct with an annular exit. Dozens or hundreds of these devices are linked together on a shared manifold known as a VTS array. There is a distinct lack of scientific literature regarding these arrays, which likely feature significantly more complex flowfields than singular VTSs due to aerodynamic interactions between the devices. The research presented in this dissertation identifies and explains flow features unique to arrays by means of an experimental investigation downstream of various VTS configurations in a wind tunnel. Mean PIV flowfields reveal that the VTS array rapidly generates a strong central recirculation zone while a single VTS does not, implying the existence of axial flow gradients within associated separators that could affect filtration efficiency. The key factor here is the global swirl intensity, which is increased in array flows due to high angular momentum contributions from separators that are radially distant from the duct center. A preliminary momentum integral model is constructed to predict the onset of recirculation in VTS flows. Analysis is then extended to the unsteady flowfield, where it is shown that VTS-generated turbulence contains only low levels of anisotropy. Spectral proper orthogonal decomposition is conducted on the array flow; it reveals the existence of low-frequency harmonic behavior composed of back-and-forth pumping motions downstream of the central VTS. Additionally, a unique precession motion is found in the same region at a slightly higher frequency. Similar precessing vortex cores have been shown to reduce separation efficiency in other cyclone separators. Both of these coherent structures may be associated with the central recirculation zone and may interfere with VTS array filtration given their timescales relative to potential particle relaxation timescales. This dissertation opens the door for future experimental and computational studies of fluid and particle dynamics in VTS flows with the goal of improving VTS array-specific design philosophies. Doctor of Philosophy Vortex tube separators (VTSs) help protect helicopter engines by filtering harmful particles (sand, dust, snow, ash, sea spray, etc.) they would otherwise ingest. This is done by creating a vortex in which centrifugal forces eject particles outwards, separating them from the main airstream. These devices are effective when dozens are grouped together into VTS arrays, but little is understood of the complex air and particle dynamics that result from the many interacting vortices both in and around such arrays. This dissertation describes an early effort to study these aerodynamics and open the door for subsequent particle dynamics research. A laser-based measurement technique called particle image velocimetry is used to determine flow velocities downstream of a VTS array placed in a wind tunnel. When velocities are averaged together over time, they reveal a central recirculation zone (a known feature of intensely swirling flows) downstream of the VTS array that vanishes when only a single separator in the array is active. A mathematical model is developed to predict such recirculation. It demonstrates that a VTS array comprises many separators that are far from the center of the duct they are contained within, and these contribute greatly to the overall swirl intensity. Other data analysis techniques are used to investigate the instantaneous velocity flowfield, which differs significantly from averaged quantities. One such technique is spectral proper orthogonal decomposition, which extracts so-called "coherent structures" from the flow - correlated high-energy motions that exist at certain frequencies and may not be visible in the raw data. This analysis finds two interesting structures at the very center of the duct, possibly associated with the recirculation zone: a back-and-forth pumping motion at a very low frequency (and some of its harmonic frequencies), and a "precessing" (unsteadily rotating) vortex at a slightly higher frequency. These motions, as well as the central recirculation zone itself, are impactful because they may affect the filtration process within the VTS upstream of where they were measured. Such effects will be investigated in future experiments and, if confirmed, may influence the design of VTS arrays.

Laminar-turbulent transition has a strong impact on aerodynamic performance in many practical applications. Hence, there is a practical need for developing reliable and efficient transition prediction models, which form a critical element of the CFD process for aerospace vehicles across multiple flow regimes. This dissertation explores machine learning approaches to develop transition models using data from computations based on linear stability theory. Such data provide strong correlation with the underlying physics governed by linearized disturbance equations. In the proposed transition model, a convolutional neural network-based model encodes information from boundary layer profiles into integral quantities. Such automated feature extraction capability enables generalization of the proposed model to multiple instability mechanisms, even for those where physically defined shape factor parameters cannot be defined/determined in a consistent manner. Furthermore, sequence-to-sequence mapping is used to predict the transition location based on the mean boundary layer profiles. Such an end-to-end transition model provides a significantly simplified workflow. Although the proposed model has been analyzed for two-dimensional boundary layer flows, the embedded feature extraction capability enables their generalization to other flows as well. Neural network-based nonlinear functional approximation has also been presented in the context of transport equation-based closure models. Such models have been examined for their computational complexity and invariance properties based on the transport equation of a general scalar quantity. The data-driven approaches explored here demonstrate the potential for improved transition prediction models. Doctor of Philosophy Surface skin friction and aerodynamic heating caused by the flow over a body significantly increases due to the transition from laminar to turbulent flow. Hence, efficient and reliable prediction of transition onset location is a critical component of simulating fluid flows in engineering applications. Currently available transition prediction tools do not provide a good balance between computational efficiency and accuracy. This dissertation explores machine learning approach to develop efficient and reliable models for predicting transition in a significantly simplified manner. Convolutional neural network is used to extract features from the state of boundary layer flow at each location along the body. These extracted features are then processed sequentially using recurrent neural network to predict the amplification of instabilities in the flow, which is directly correlated to the onset of transition. Such an automated nature of feature extraction enables the generalization of this model to multiple transition mechanisms associated with different flow conditions and geometries. Furthermore, an end-to-end mapping from flow data to transition prediction requires no user expertise in stability theory and provides a significantly simplified workflow as compared to traditional stability-based computations. Another category of neural network-based models (known as neural operators) is also examined which can learn functional mapping from input variable field to output quantities. Such models can learn directly from data for complex set of problems, without the knowledge of underlying governing equations. Such attribute can be leveraged to develop a transition prediction model which can be integrated seamlessly in flow solvers. While further development is needed, such data-driven models demonstrate the potential for improved transition prediction models.

Aircraft propulsion systems can be exposed to a variety of solid particulates while operating in either arid or other hazardous environments. For conventional takeoff and landing aircraft, debris can be ingested directly into the gas turbine powerplant which is exposed to the ambient environment. For helicopters and other vertical takeoff and landing (VTOL) aircraft, rotor down wash presents a particular threat during takeoff and landing operations as significant amounts of groundlevel particles can be entrained in the surrounding air and subsequently ingested into the engine. Prolonged exposure to particle ingestion events leads to premature engine wear and, in extreme cases, rapid engine failure. Expanding our current understanding of these events is the first step to enabling engine manufacturers to mitigate these damage mechanisms through novel engine designs. The work described in this dissertation is aimed at increasing the scientific understanding of these ingestion events through the development of two distinct diagnostic instruments. First, an anisokinetic particle sampling probe is designed to be used for in-situ particle sampling inside of a gas turbine engine compressor. Offtake of particles during engine operation in dusty conditions will provide researchers with an improved understanding of particle breakage tendency and component erosion susceptibility. Both experimental and numerical investigations of the probe present a comprehensive realization of probe performance characteristics. Secondly, a novel particle visualization technique is developed to provide users with particle distribution and particle mass flow estimates at the inlet of a gas turbine engine. This technique yields both time-resolved and time-averaged quantities, allowing users to have a comprehensive account of particles entering the engine. Doctor of Philosophy Foreign debris ingested into aircraft engines can cause serious damage and degrade their performance. The source of these ingested particles may be from atmospherically suspended ash due to volcanic eruption, high altitude ice crystals, or ground-level sand and dust. Both conventional takeoff and landing aircraft and vertical takeoff and landing (VTOL) aircraft are at risk. In extreme cases, exposure to a particle-laden atmosphere has resulted in catastrophic engine failure and loss of life. For this reason, researchers are intensely focused on mitigating the effects of these harmful particulates. The work described in this dissertation establishes two novel diagnostic capabilities. These are aimed at providing the research community with an increased understanding of how particles enter an aircraft powerplant as well as describe the behavior of these particles as they traverse the initial stages of an engine. The first instrument described is a particle sampling probe which is meant to be inserted into the compressor section of a gas turbine engine. This probe will offtake particles as they enter the engine after they have had an opportunity to interact with the rotating components of the compressor. In doing so, researchers gain an improved understanding of particle breakage tendency and component erosion susceptibility. The second instrument provides a snapshot of particle distribution at the inlet of the engine as well as estimates of total particle mass flow. This capability allows researchers to have a precise understanding of the quantity of ingested material as well as a qualitative understanding of how the inflow distribution of particles looks. Each of the developed tools represent a first step to enabling engine manufacturers to mitigate these damage mechanisms through novel engine designs.

Doctor of Philosophy Filtered Rayleigh scattering (FRS) is a laser-based measurement technique that makes use of the scattering of light off particles that are much smaller than the wavelength of light that hits them (i.e., Rayleigh scattering of air molecules). The scattered laser light is altered after encountering particles in predictable ways that can be related to changes in velocity, temperature, and density. However, other sources of scattered light interfere with the pure Rayleigh scattering signal such as Mie and background scattering. Mie scattering is the scattering of light off particles that are much bigger than the wavelength of light that hits them (i.e., dust particles suspended in air). Background scattering is the laser light scattered off physical objects that reflect back into the region of interest. The different types of scattering are accounted for with intensive modeling and iterative fitting schemes where the error between simulated data and experimental data is minimized. This fit allows for velocity, temperature, and density information to be extracted from the measured scattered light. This iterative scheme is then applied to experimental measurements on the ground with mini turbojet engines as well as full-scale turbofan engines. A data grouping technique is derived such that the total measured force using FRS can be divided into individual contributions from different parts of the engine. These developed techniques have laid the foundation for future in-flight measurements of engine forces.

Filtered Rayleigh scattering (FRS) is a non-intrusive, optical measurement technique that can currently provide time-averaged, simultaneous planar measurements of three-component velocity, static temperature, and static density of aerodynamic flows. Development of the FRS technique has typically employed 532 nm Nd:YAG lasers coupled with the use of iodine vapor cells as the molecular filter. One method to improve the effective signal-to-noise ratio (SNR), and therefore the performance of an FRS system, is to use shorter wavelengths. This takes advantage of the dependence of the Rayleigh scattering signal on the inverse of the wavelength of the incident laser light to the fourth power: even small shifts to shorter wavelengths can offer significant gains in SNR as a result. This study explores the implementation of an ultraviolet (UV) FRS system nominally at 387 nm with the use cesium vapor as the molecular filter. The cesium absorption lineshapes (corresponding to the 62S1/2 → 82P3/2 atomic transitions around 387 nm) are considered along with camera specifications to simulate an ultraviolet filtered Rayleigh scattering (UV FRS) measurement of aerodynamic flows. A signal model is developed using numerical functions for the cesium vapor cell transmission, camera specifications, signal-dependent shot noise, and signal-independent electronic detector read noise. Using this noise-inclusive model (over a 2.4 GHz scan bandwidth with a 7.5 cm long cesium vapor cell corresponding to current Virginia Tech FRS capabilities) velocity, static temperature, and static density measurement sensitivities for this proposed configuration are analyzed by evaluating and deriving the Cramér-Rao lower bound (CRLB) for each quantity. The effects of different flow conditions, Mie and geometric scattering levels, cesium vapor cell temperature, and spectral resolution are demonstrated. It is found that the best possible theoretical measurement results are obtained for high-speed wind tunnel flow conditions with high spectral resolution, and that the CRLB for velocity, static temperature, and static density for a 387 nm system approaches or exceeds that of a 532 nm system for a given signal-to-noise ratio (SNR). Master of Science One type of non-intrusive measurement technique that can be applied to aerodynamic flows is filtered Rayleigh scattering (FRS). Unlike other non-intrusive techniques such as particle image velocimetry (PIV) and Doppler global velocimetry (DGV), FRS does not require that the flow be seeded with particles and can provide simultaneous measurements of three-component velocity, static temperature, and static density. Current FRS measurement systems commonly use 532 nm green-light lasers and iodine cells for filtering. However, a stronger Rayleigh scattering signal (and therefore better measurement) can be attained by using shorter laser wavelengths as the strength of the Rayleigh scattering is related to the inverse of the incident wavelength to the fourth power. This study takes advantage of this fact to propose an FRS measurement system using ultraviolet laser light at nominally 387 nm. The implementation of a commercially available 387 nm laser system with the use of cesium cells for filtering is investigated. In order to simulate the performance of the system, a signal model is developed that includes both signal-dependent shot noise, and signal-independent electronic detector read noise. The signal model is combined with the transmission profile of cesium vapor, commercially available camera specifications, and typical FRS measurement parameters to simulate a 387 nm FRS system measurement. The measurement sensitives and performance of the proposed UV FRS system at 387 nm are investigated by deriving and evaluating the Cramér-Rao lower bound (CRLB) for velocity, static temperature, and static density. The effects of different flow conditions, Mie and geometric scattering levels, cesium vapor cell temperature, and scan resolution are demonstrated. The best performance is attained at high-speed conditions with high spectral resolution, and this approaches or exceeds the simulated performance of a 532 nm system with an iodine vapor cell over the same range of conditions.

Master of Science Particulate ingestion has been an ongoing issue in the aviation industry as aircraft are required to operate in hostile environments. Ingesting particulates such as sand or dust can erode and damage engine components. This damage will affect the life cycle of parts and compromise the safety of the aircraft. This issue is very costly and dangerous. In order to combat these issues, a particle sensor with the ability to monitor in-stream particulate size, shape, and mass flow rate is necessary. Our team with the Advanced Propulsion and Power Laboratory developed a non-intrusive optical sensor that is able to characterize non-spherical particles. This sensor has been used in various applications through the years; however, most recently, the sensor has been demonstrated at the Virginia Tech M250 engine inlet. This was the first time that the sensor was directly attached to an engine's inlet and subjected to engine conditions. For this validation, highly erosive, coarse quartz was used. Utilizing laser and cameras, the sensor is able to deduce the particles' average shape and size distributions. From those measurements, the mass flow rate of the particle can be calculated. The works provided in the thesis show that particle ingestion rates can be measured to an acceptably high accuracy. In contrast, refinement of the processing techniques can provide spatially resolved measurements of particle characteristics as well.

Shape morphing in aerospace structures has the potential to reduce noise, improve efficiency, and increase the adaptability of aircraft. Among the many challenges in developing morphing technologies is finding suitable wing skin materials that can be both stiff to support the structural loads, while being elastic and compliant to support this shape morphing an minimize actuation energy. This remains an open challenge, but many possible solutions have been found in smart materials, namely shape memory alloys and polymers. Of these, shape memory polymers have received more attention for wing skins due to their low density and cost, and high elastic limits in excess of 100% strain, but they suffer from generally low overall moduli. Shape memory polymer composites have been considered to address this, typically in the form of particulate/nanoscale reinforcements or by using them as matrix materials in laminate composites. While these can serve to increase the stiffness of the composite, there is still a present need for reinforcement strategies that can also maintain the large changes in stiffness of shape memory polymers. An alternative shape memory composite relies on honeycomb materials with shape memory polymer infills. Previous research has shown that polymer filled honeycombs exhibit greater in-plane moduli greater than the infill or honeycomb alone, but there has been little research focused on understanding this behavior. Moreover, while most engineered cellular structures are comprised of symmetric and periodic cells, cellular structures in nature are commonly spatially varying, asymmetric networks, which have not been considered in these composites. Motivated by these challenges in designing materials for shape morphing, this work seeks to explore the use of shape memory polymer-filled honeycomb composites for use as variable stiffness materials. First, the interaction between infill and the honeycomb, and the relationship between the honeycomb geometry and the effective composite properties is not well understood. This research first investigates the mechanisms of stiffening in these composites through both unit cell finite element models and through experimental characterization. Parametric studies are completed for selected honeycomb geometry design variables, and three key mechanisms of stiffening are identified. Next, these mechanisms are further supported by experimental studies, and comparisons are made showing the limitations of the few existing analytic models. With the knowledge gained from these studies, shape memory polymer infills are considered to create variable stiffness composites. In the first study, sizing design variables are selected to parametric the honeycomb cell geometry, with the designs constrained to be symmetric in-plane. A constrained multiobjective design optimization is completed for two chosen performance objectives, and corresponding local sensitivity studies are completed as well. The results predict that these composites meet and exceed the current bounds of both shape memory polymers and their composites, but also variable stiffness materials in general. A great degree of tailorability is demonstrated, and the model predictions are validated against experimental results from fabricated honeycomb composite samples. Next, generally asymmetric cell geometries are considered by defining shape design variables for the cell geometry. These cells are constrained to be periodic but not symmetric, allowing for the possible benefits of asymmetric to be investigated. Additionally, interconnected and spatially varying multicell unit cells are considered, further allowing for the study of spatially varying cell geometries. Multiobjective optimizations are completed for two unit cell cases, and Pareto fronts are identified. The results are compared to both those from the sizing optimization study and to the current state of the art, and are similarly found to demonstrate high performance and a great degree of tailorability in effective properties. Doctor of Philosophy Vehicle shape morphing, the smooth, continuous change of an aircraft's external shape, can greatly improve the efficiency and reduce noise in modern and future vehicles. Among the is challenges in this field is finding suitable skin materials that can be both stiff to support the forces exerted on an aircraft, while being soft and compliant to support this shape morphing. Smart materials, namely shape memory polymers, present many attractive options for this need, but generally need to have a higher stiffness to be suitable for large scale applications. To address this, adding reinforcements to shape memory polymers has been of interest, and current work has largely been focused on using long fiber composites or particulate and nano-reinforcements. As an alternative to these strategies, inspiration can be found in nature where polygon cells are a common means of reinforcement in both plants and animals. Motivated by the current state of the art and the promise of shape morphing structures, this work seeks to investigate cellular structures in the form of hexagonal honeycombs as a means of increasing the stiffness of shape memory polymer infills. This is done by first improving the understanding of more general polymer-filled honeycomb, which exhibit effective stiffnesses greater than the honeycomb or polymer alone. With a working understanding of how the honeycomb stiffens the infill and how the cell geometry influences this behavior, variable modulus infills are next considered. First, sizing design variables (i.e. the lengths and thicknesses of the honeycomb geometry) are selected to describe cell geometries. Design optimization problems are considered and used to estimate the bounds of possible performance for these composites. Relationships between the design variables and the composite performance are investigated, and an improved understanding of these composites is developed. Next, shape design variables are selected to allow for the asymmetry and spatial variation found in natural cellular structures, and similar design optimizations are completed. The results of this work are experimentally validated, and demonstrate that these composites allow for combinations of stiffness and stiffness change that meet and exceed the current state of the art. Furthermore, tailoring the cell geometry allows for an easy means of changing the behavior of the composite. This work represents a great improvement and an important step in overcoming the challenges in developing shape morphing systems.

A computational model is developed to simulate the impact dynamics of a droplet on solid substrates with the purpose of predicting the droplet spreading characteristics over time. Previous studies focused on finding relations between the impact parameters and outcome dynamics. A modified approach like the one used in this project revolves around modeling the moving contact lines at the interface in a multiphase flow environment. Focusing on research from an aircraft de-icing point of view, this study is considered a prerequisite in understanding the physics of droplet impact. The primary focus is on extending the application to incorporate super-cooled environments. Development of the model involved the use of the Volume-of-Fluid function coupled with the High-Resolution Interface Capturing scheme to model the moving contact line. The evolution of the moving contact line is modeled with contact angles as their inputs to understand the effect of the surface tension forces. Contact angle modeling is based on the Blended-Kistler method, which captures the contact angle evolution based on the surface tension and capillary number. Preliminary validation performed on the model proves its effectiveness in accurately simulating the impact behavior when compared to the literature, where the spread diameter and height agree well with experiments. The validated model is also compared to the in-house experiments performed at the Cavitation and Multiphase flow laboratory using different substrate materials. The substrates each show unique behavior - Impact on Glass results in the droplet depositing on the surface. Aluminum results in a full rebound and PET-G, results in a drop ejection. Based on inputs from the experiments - contact angles, spread diameter, and the maximum spread $beta$, show good agreement in comparison to the literature. Master of Science Computational model developed to simulate the impact dynamics of the droplet on solid surfaces, which predicts the evolution of the droplet over time in order to analyze the effect of the surface and properties of the fluid on the behavior of the droplet on impact. Focusing on research from an aircraft de-icing point of view, this study is considered a pre-requisite in understanding the physics of droplet impact, with potential scope in extending the simulation to applications at temperatures lower than $0^{circ}$ C. A model developed with the help of basic governing equations in fluid mechanics helps capture the effect of interactions between different physical states. The angle at which the droplet interacts with the surface (Contact Angle) and the diameter evolution (d/D) help us understand the effectiveness of the model to simulate droplet impact. Preliminary validation of the model is performed with respect to the literature where the droplet diameter evolution and the height variation match well with the experiments, which was the major criterion in determining the accuracy of the model. This model is compared to the in-house experiments performed at the Cavitation and Multiphase flow laboratory on different surfaces such as Glass, Aluminum, and Plastic (PET-G). The surfaces each show unique behavior with impact on Glass having the droplet deposit on the surface, aluminum resulting in the droplet bouncing after hitting the surface, and PET-G resulting in a small droplet being ejected from the bigger droplet which eventually deposits on the surface. Conclusions from the comparison between the experiments and the numerical simulation show how the model is effective in capturing the impact behavior on surfaces like glass in comparison to surfaces like Aluminum in this case that repels water.

Three-dimensional (3D) turbulent boundary layers (TBLs) are ubiquitous in most engineering applications, but most turbulence models used to simulate these flows are built on two-dimensional turbulence theory, limiting the accuracy of simulation results. To improve the accuracy of turbulence modeling capabilities, a better understanding of 3DTBL physics is required. This dissertation outlines the experimental investigation of the attached 3D TBL flow over the Benchmark Validation Experiments for RANS/LES Investigations (BeVERLI) Hill using laser Doppler velocimetry in the Virginia Tech Stability Wind Tunnel. The mean flow and turbulence behavior of the boundary layer are studied and compared with turbulence theories to identify the validity of these assumptions in the BeVERLI Hill flow. It is shown that the pressure gradients and curvature of the hill have a significant effect on the turbulence behavior, including significant history effects at all stations due to the changing pressure gradient impact through the height of the boundary layer. Supplementing the experimental results with analysis from rapid distortion theory and simulations, it is shown that the stations lower on the hill are significantly affected by the non-linear history effects due to the varying upstream origins of the flow passing through those stations. Stations closer to the hill apex pass through a region of extremely strong favorable pressure gradient and hill constriction, resulting in behavior that matches qualitatively with the results from rapid distortion theory and provides insights into the physical mechanisms taking place in these regions of the flow. Despite the misalignment of the mean flow angle (γFGA) and turbulent shear stress angle (γSSA) throughout all of the profiles, the proposed 3D law of the wall of van den Berg (1975), which incorporates pressure gradient and inertial effects and relies on the assumption that γFGA=γSSA, is able to predict the flow behavior at more mildly non-equilibrium stations. This suggests that models that currently rely on assumptions founded on the two-dimensional law of the wall could be improved by incorporating van den Berg's model instead. The total shear stress distribution at selected stations on the BeVERLI Hill are all significantly reduced below equilibrium two-dimensional (2D) levels, indicating that turbulence models built on this assumptions will not be able to accurately simulate the 3D turbulence behavior. Doctor of Philosophy As an object moves through a fluid or a fluid moves past an obstacle, fluid sticks to the solid boundary of the object because of the fluid's viscosity, resulting in zero velocity on the surface (known as the "no-slip" condition). There then exists a region where the flow velocity increases from zero to the freestream velocity - this region is known as the boundary layer. The nature of the boundary layer developing around a body significantly influences how the body and fluid interact and is critical to practical items of engineering interest, such as estimating how much drag a vehicle will experience. Most bodies of engineering interest are three-dimensional (3D), like an aircraft or a car, and thus induce a three-dimensional boundary layer, but many turbulence theories used in computational fluid dynamics simulations are based on simplified two-dimensional (2D) flow behavior studied in laboratories. To further improve the accuracy of simulations, a better understanding of three-dimensional turbulent boundary layer flows is required. This dissertation outlines a study of three-dimensional turbulent flows by analyzing the three-dimensional turbulent boundary layer over the Benchmark Validation Experiments for RANS/LES Investigations (BeVERLI) Hill using laser Doppler velocimetry (LDV) in the Virginia Tech Stability Wind Tunnel. LDV uses the Doppler shift principle to measure the fluid velocity and turbulence at different points in the flow. Through analysis of the fluid velocity and turbulence in the flow, it is shown that the turbulence and flow behavior at certain stations are heavily influenced on the upstream flow history. Stations closer to the bottom of the hill are more influenced by the upstream flow history, while stations closer to the top of the hill experience such strong acceleration due to the local favorable pressure gradient and hill curvature that the upstream history has a more linear influence. In general, the turbulence on the hill is reduced due to the acceleration over the surface below 2D levels and does not match with the 2D fundamental relationships often used in turbulence theories for simulations. Thus, simulations that rely on these assumptions will not be able to accurately predict the details of the 3D flow. A proposed 3D model for the mean velocity behavior by van den Berg (1975) will perform better in simulations than the typical 2D law used in some turbulence model assumptions.

Viscous drag reduction plays a vital role in increasing the performance of vehicles. However, there are only so many measurement techniques that can quickly and accurately measure this when compared to pressure drag measurement techniques. The current study makes use of one of the direct and robust measurement techniques that exist, called the Oil Film Interferometry (OFI) to estimate skin friction on the NASA/Virginia Tech BeVERLI (Benchmark Validation Experiment for RANS and LES Investigations) hill. This project aims to develop a detailed database of non-equilibrium, separated turbulent boundary layer flows obtained through wind tunnel experiments for CFD validation. Skin friction measurements are obtained at specific critical locations on the hill and in its close proximity. The challenges involved in obtaining skin friction data from these locations are discussed in detail. Detailed discussions on the experimental setup and data processing methodology are presented. Qualitative and quantitative results from each measurement location are discussed along with uncertainties to explain certain key flow physics. Additionally, skin friction coefficients from selected overlapping measurement locations from another experimental flow measurement technique called Laser Doppler Velocimetry (LDV) are compared with OFI, and a cross-instrument study is performed. Finally, results from well-refined RANS CFD simulations are assessed with the experimental results, and critical improvement areas are identified. Master of Science Drag force is a parameter that significantly contributes to the performance efficiency of any vehicle moving in a fluid. This force is categorised into two types - pressure and viscous drag- both of which need to be minimised as much as possible to contribute towards higher vehicle performance. While there are numerous measurement techniques and documentation currently available to measure pressure drag, this is not the case with the measurement of viscous drag. Skin friction measurement directly relates to the estimation of viscous drag, but accurate and quick measurement of this quantity highly challenging with countable measurement techniques currently available. Through this project, BeVERLI (Benchmark Validation Experiment for RANS and LES Investigations), a detailed documentation is developed for accurate measurement of skin friction through Oil Film Interferometry (OFI). The results obtained through this measurement is explained with a detailed experimental procedure as well as using a data processing code. The accuracy of these results are then discussed with the results from another flow measurement technique called Laser Doppler Velocimetry (LDV) and from Computational Fluid Dynamics (CFD).

The velocity fields of high Reynolds number, turbulent, wall boundary layers in non-equilibrium pressure gradients are experimentally investigated. Experiments in two wall configurations were performed; one with a hydrodynamically smooth test wall composed of flat aluminum panels, and the other with a rough surface consisting of 2 mm tall, staggered, circular cylindrical elements. A representative set of pressure gradient distributions were generated on the research wall by a systematically rotated NACA 0012 airfoil placed in a wind tunnel section to determine the functional dependence of the boundary layer formation on pressure gradient. Particle image velocimetry (PIV) was the primary measurement technique used to determine time-resolved features of the velocity flow field. newline{}newline{} It is shown that regardless of wall condition and Reynolds number, the non-equilibrium turbulent boundary layers exhibit increasingly non-local behavior with streamwise development. This is apparent as a lag to the pressure gradient distribution observed in the streamwise developing integrated boundary layer parameters. These ``history effects" are also prevalent in mean velocity profiles which are exhibited as a cross-over of the favorable and adverse pressure gradient profiles in the logarithmic layer. Similar cross-over points are observed in the Reynolds shear and normal stresses, particularly at the streamwise station downstream of the pressure gradient switch. The primary effect of the rough wall is to increase the magnitude of flow scales, and, while they exhibit the same qualitative history effects as the smooth wall, the rough wall flows show an earlier relaxation to equilibrium. Despite inherent uncertainties of indirect skin friction methods for the rough wall, the effective sandgrain roughness parameter k_s does not show a functional dependency to pressure gradient history. An evaluation of the wall-similarity hypothesis solely based on boundary layer thickness to roughness parameter ratios delta/k_s is insufficient and additional parameters such as pressure gradient histories, local roughness Reynolds numbers, and bias uncertainties due to instrument spatial resolution must be considered. Doctor of Philosophy In the interface between a surface and a moving fluid is the boundary layer where high shear and viscous stresses cause the bulk velocity to decrease to zero. When turbulent, this region of fluid is characterized by random, chaotic, and fluctuating motions of varying sizes. Parameters such as pressure gradients and geometric irregularities of the surface, referred to as roughness, can increase fluctuating pressures and velocities within the boundary layer and cause unwanted noise, vibration, and increased drag. Although many studies have evaluated boundary layers with either roughness or pressure gradient independently, most surfaces in practical application are susceptible to the compounding influences of both of these parameters. Thus, it is necessary to expand the current knowledge database to include complex flow fields necessary to improve data driven modeling and vehicle design.newline{}newline{} This study focuses on experimental observations of the turbulent velocity field developing in both a rough and smooth wall boundary layer that is induced to a family of bi-directional pressure gradients generated by the pressure field of a rotating airfoil inside in a wind tunnel. Through statistical observations of the velocity field it was found that the varying pressure gradients caused the flow to develop non-local dependencies such that the response of the downstream boundary layer was dependent on the upstream flow history. The principal effect of roughness was to increase the magnitude of turbulent scales, but to show the same qualitative response to the pressure gradient history as seen in a smooth wall flow. However, direct comparison of rough and smooth wall turbulence statistics by means of the ``wall-similarity hypothesis" requires careful consideration of multiple parameters including these flow histories, scales prescribed by roughness parameters, and bias errors from experiment under-resolution of the velocity field.

There has been lots of interest in designing more fuel efficient aircraft using concepts such as boundary layer ingestion (BLI) that cause large amounts of pressure and swirl distortion that enter the jet engines. To enable ground testing the performance of these engines in different distortion patterns, the StreamVane and ScreenVane systems have been developed. A StreamVane consists of a complex vane pack that is custom designed for each distortion profile and the ScreenVane combines the StreamVane with a pressure distortion screen for testing engines under both pressure and swirl distortions. The complexity and uniqueness of these devices make predicting their structural integrity and propensity to flutter a challenge, necessitating the need for studying flutter in these complex vane packs. In order to study flutter of these complex vane packs, a methodology was created to obtain trailing edge displacements and frequencies from high speed video of a StreamVane and was used on a quad swirl StreamVane and a Simplified model. Unsteady CFD with periodic mesh deformation based off of its modal analysis was used to validate if it can predict the flutter velocity as well as understanding what the unsteady aerodynamic response to flutter is. A parameter study was then conducted along with oilflow visualization to better understand the potential causes of flutter and the impact of different design parameters. A harmonic response analysis was conducted on each of these designs and a correlation between the amplitude from the harmonic response and the flutter Mach number was obtained that can be used to predict when a StreamVane will flutter. A new series of StreamVanes were designed and based off of computational analysis, two were selected for manufacture. They both successfully avoided fluttering in flutter tests and were found to accurately replicate the goal swirl profile when measured with a 5 hole probe. These results provide a basis for understanding and predicting flutter in StreamVanes. Master of Science There has been lots of interest in designing more fuel efficient aircraft using concepts such as boundary layer ingestion (BLI) that cause large amounts of pressure and swirl distortion that enter the jet engines. To enable ground testing the performance of these engines in different distortion patterns, the StreamVane and ScreenVane systems have been developed. A StreamVane consists of a complex vane pack that is custom designed for each distortion profile and the ScreenVane combines the StreamVane with a pressure distortion screen for testing engines under both pressure and swirl distortions. The complexity and uniqueness of these devices make predicting their structural integrity and propensity to flutter a challenge, necessitating the need for studying flutter in these complex vane packs. Flutter is when a structure experiences excess vibration when exposed to unsteady aerodynamic loads. In order to study flutter of these complex vane packs, a methodology was created to obtain trailing edge displacements and frequencies from high speed video of a StreamVane and was used on a quad swirl StreamVane and a Simplified model. Unsteady computation fluid dynamics (CFD) with periodic mesh deformation was used to validate if it can predict the flutter velocity as well as understanding what the unsteady aerodynamic response to flutter is. A parameter study was then conducted along with oilflow visualization to better understand the potential causes of flutter and the impact of different design parameters. A harmonic response analysis, which consists of a dynamic structural analysis with sinusoidal loading applied, was conducted on each of these designs. A correlation between the amplitude from the harmonic response and the flutter Mach number was obtained that can be used to predict when a StreamVane will flutter. A new series of StreamVanes were then designed and based off of computational analyses, two were selected for manufacture. They both successfully avoided fluttering in flutter tests and were found to accurately replicate the goal swirl profile when measured with a 5 hole probe downstream of the StreamVane. These results provide a basis for understanding and predicting flutter in StreamVanes and other complex vane packs.

Turbulent boundary layers flowing over a smooth surface were studied to understand the influence of varying pressure gradients and flow Reynolds number on the boundary layer growth and mean turbulent properties. The test was conducted in the Virginia Tech Stability Wind Tunnel with a 0.914 m chord length, NACA 0012 Airfoil in the test section. This airfoil was rotated to different angles of attack to induce varying pressure gradients on the boundary layer developing on the test section walls. Mean pressure measurements, boundary layer pressure measurements, and time-resolved, wall-normal, stereoscopic particle image velocimetry (TR-PIV) measurements were made. The TR-PIV data was acquired at a chord-based Reynolds number of 1.2 million, 2 million, and 3.5 million, at a sampling rate of 1 kHz, in two different camera configurations. The boundary layer pressure measurements were acquired at different flow Reynolds numbers ranging between 0.76 million and 3.5 million. Both adverse and favorable pressure gradients of varying intensities were imposed on the boundary layer by rotating a 0.914 m chord NACA 0012 airfoil to angles of attacks between -{10}^o and {12}^o. Measurements at varying streamwise locations enabled the study of boundary layer flow development under changing pressure gradients. The pressure gradient influences were observed in the boundary layer characteristic properties, on the mean velocities, and on the Reynolds stresses present in the flow. The pressure gradient influences were found to be consistent at varying Reynolds numbers, but the intensity of their effects was influenced by the flow Reynolds number. Moreover, the influence of pressure gradients and flow Reynolds numbers was evident in both outer and inner scales. The test data acquired was also validated with previous works. M.S. The interaction of turbulent boundary layers and smooth surfaces is prevalent in our world. It plays a vital role in various phenomena, such as, aircraft stall, cabin noise, and structural vibrations. Varying flow conditions influence the behavior of boundary layers and the extent of their implications. The effects of pressure gradients and the level of turbulence, described by the Reynolds numbers, on turbulent boundary layer flow was studied. This was done through an experiment conducted at the Virginia Tech Stability Wind Tunnel facility. The test data was acquired through boundary layer pressure measurements and Time-Resolved, Stereoscopic Particle Image Velocimetry (TR-PIV) at varying streamwise locations in the test section. A 0.914 m chord, NACA 0012 airfoil was placed in the test section and its angle of attack was varied to -{10}^o,0^o,\ \ and\ {12}^o to induce a favorable, minimum, and an adverse pressure gradient, respectively. The TR-PIV measurements were acquired at a sampling rate of 1 kHz and in two different camera configurations. The flow Reynolds number was based on the airfoil chord length (Re_c) and was varied to 1.2 million, 2 million, and 3.5 million for the TR-PIV tests. The boundary layer pressure measurements were acquired using an array of 30 Pitot probes placed in the boundary layer of the flow. The flow Reynolds number for these test runs ranged between 0.76 million and 3.5 million. The acquired data was used to analyze the mean statistical properties of turbulent boundary layers primarily focusing on the mean velocities, boundary characteristic parameters, Reynolds normal stresses, and Reynolds shear stresses. The results showed that the nature of pressure gradient influences on the mean properties of turbulent boundary layers remained consistent regardless of the flow Reynolds number. However, the intensity of the pressure gradient effects was influenced by the flow Reynolds number. These observations were made at various streamwise data acquisition locations through which the evolution of the flow was also studied. Lastly, the results obtained in this experiment were validated with previous works.

It is one thing to have evidence that demonstrates “what works” for First Nations students, but quite another to have a shared understanding of the assumptions underpinning evidence-based policy. In this chapter, we explore these philosophical foundations with the aim of catalysing effective research translation. In concluding this volume, we consider first the prerequisite foundations of epistemology, axiology, and ontology which enable policy to support the aspirations of First Nations communities, families, and students. Second, we consider the power relations that pave the way for self-determined agency within classrooms and across educational systems. Third, we theorise the role of pedagogy and curriculum within the frame of an education system designed to provide First Nations students with the knowledge and skills they need to thrive.

High Reynolds number turbulent boundary layers over both smooth and rough surfaces subjected to a systematically defined family of continually varying, bi-directional pressure gradient distributions are investigated in both wind tunnel experiments and steady 2D and 3D Reynolds Averaged-Navier-Stokes (RANS) computations. The effects of pressure gradient, pressure gradient history, roughness, combined roughness and pressure gradient, and combined roughness and pressure gradient history on boundary growth and the behavior of the underlying surface pressure spectrum are examined. Special attention is paid to how said pressure spectra may be effectively modeled and predicted by assessing existing empirical and analytical modeling formulations, proposing updates to those formulations, and assessing RANS flow modeling as it pertains to successful generation of spectral model inputs. It is found that the effect of pressure gradient on smooth wall boundary layers is strongly non-local. The boundary layer velocity profile, turbulence profiles, and associated parameters and local skin friction at a point that has seen non-constant upstream pressure gradient history will be dependent both on the local Reynolds number and pressure gradient as well as the Reynolds number and pressure gradient history. This shows itself most readily in observable downstream lagging in key observed behaviors. Steady RANS solutions are capable of predicting this out-of-equilibrium behavior if the pressure gradient distribution is captured correctly, however, capturing the correct pressure gradient is not as straightforward as may have previously been thought. Wind tunnel flows are three-dimensional, internal problems dominated by blockage effects that are in a state of non-equilibrium due to the presence of corner and juncture flows. Modeling a 3D tunnel flow is difficult with the standard eddy viscosity models, and requires the Quadratic Constitutive Relation for all practical simulations. Modeling in 2D is similarly complex, for, although 3D effects can be ignored, the absence of two walls worth of boundary layer and other interaction flows causes the pressure gradient to be captured incorrectly. These effects can be accounted for through careful setup of meshed geometry. Pressure gradient and history effects on the pressure spectra beneath smooth wall boundary layers show similar non-locality, in addition to exhibiting varying effects across different spectral regions. In general, adverse pressure gradient steepens the slope of the mid-frequency region while favorable shallows it, while the high frequency region shows self-similarity under viscous normalization independent of pressure gradient. The outer region is dominated by history effects. Modeling of such spectra is not straightforward; empirical models fail to incorporate the subtle changes in spectral shape as coherent functions of flow variables without becoming overly-defined and producing non-physical spectral shapes. Adopting an analytical formulation based on the pressure Poisson equation solves this issue, but brings into play model inputs that are difficult to predict from RANS. New modeling protocols are proposed that marry the assumptions and limitations of RANS results to the analytical spectral modeling. Rough surfaces subjected to pressure gradients show simplifications over their smooth wall relatives, including the validity of Townsend's outer-layer-Reynolds-number-similarity Hypothesis and shortened history effects. The underlying pressure spectra are also significantly simplified, scaling fully on a single outer variable scaling and showing no mid-frequency slope pressure gradient dependence. This enables the development of a robust and accurate empirical model for the pressure spectra beneath rough wall flows. Despite simplifications in the flow physics, modeling rough wall flows in a steady RANS environment is a challenge, due to a lack of understanding of the relationship between the rough wall physics and the RANS model turbulence parameters; there is no true physical basis for a steady RANS roughness boundary condition. Improvements can been made, however, by tuning a shifted wall distance, which also factors heavily into the mathematical character of the pressure spectrum and enables adaptations to the analytical model formulations that accurately predict rough wall pressure spectra. This work was sponsored by the Office of Naval Research, in particular Drs. Peter Chang and Julie Young under grants N00014-18-1-2455, N00014-19-1-2109, and N00014-20-2821. This work was also sponsored by the Department of Defense Science, Mathematics, and Research for Transformation (SMART) Fellowship Program and the Naval Air Warfare Center Aircraft Division (NAWCAD), in particular Mr. Frank Taverna and Dr. Phil Knowles. Doctor of Philosophy Very near to a solid surface, air or water flow tends to be highly turbulent: chaotic and random in nature. This is called a boundary layer, which is present on almost every system that involves a fluid and a solid with motion between them. When the boundary layer is turbulent, the surface of the solid body experiences pressures that fluctuate very rapidly, and this can fatigue the structure and create noise that radiates both into the structure to passengers and out from the structure to observers far away. These pressure fluctuations can be described in a statistical nature, but these statistics are not well understood, particularly when the surface is rough or the average pressure on the surface is changing. Improving the ability to predict the statistics of the pressure fluctuations will aid in the design of vehicles and engineering systems where those fluctuations can be damaging to the structure or the associated noise is detrimental to the role of the system. Wind turbine farm noise, airport community noise, and air/ship-frame longevity are all issues that stand to benefit from improved modeling of surface pressure fluctuations beneath turbulent boundary layers. This study aims to improve said modeling through the study of the effects of changing average surface pressure and surface roughness on the statistics of surface pressure fluctuations. This goal is accomplished through a combination of wind tunnel testing and computer simulation. It was found that the effect of gradients in the surface pressure is not local, meaning the effects are felt by the boundary layer at a different point than where the gradient was actually applied. This disconnect between cause and effect makes understanding and modeling the flow challenging, but adjustments to established modeling ideas are proposed that prove more effective than what exists in the literature for capturing those effects. Roughness on the surface causes the flow to become even more turbulent and the surface pressure fluctuations to become louder and more damaging. Fortunately, it is found that the combination of roughness with a gradient in surface pressure is actually simpler than equivalent smooth surfaces. These simplifications offer significant insight into the underlying physics at play and enable the development of the first analytically based model for rough wall pressure fluctuations.

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.

Master of Science Aviation gas turbine engine particle ingestion is known to reduce engine lifespans and even pose a threat to safe operation in the worst case. Particles being ingested into an engine can be modeled using multiphase flow techniques. Devices called inertial particle separators are designed to remove particles from the flow into the engine. One challenge with designing such a separator is figuring out how to efficiently expel the small particles from the flow while not unnecessarily increasing pressure loss with excessive twists and turns in the geometry. Designers usually have to develop such geometries using multiphase flow computational fluid dynamics (CFD) that solve the fluid and particle dynamics. The abundance of data associated with CFD, and especially multiphase flows make it an ideal application to study with machine learning (ML). Because such multiphase simulations are very computationally expensive, it is desirable to develop "cheaper" methods. This is the long term goal of this work; we want to create ML surrogates that decrease the computational cost of simulating the particle and fluid flow in particle separator geometries such that designs can be iterated more quickly. In this work we introduce how artificial neural networks (ANNs), which are a tool used in ML, can be used to predict particle acceleration in fluid flow. The ANNs are shown to learn the acceleration predictions with acceptable accuracy for the training data generated with canonical flow cases. However, the ML model struggles to become generalizable to actual CFD simulations.

As the world moves towards environmental sustainability, the civil aviation enterprise has responded by setting challenging goals for significantly increased energy efficiency and reduced harmful emissions into the atmosphere as codified by National Aeronautics and Space Administration (NASA) and Advisory Council for Aircraft Innovation and Research in Europe (ACARE). The airline industry supports these goals because of their positive impact on operational cost and the environment. Achieving such goals requires introduction of novel technologies and aircraft concepts. Previous studies have shown that electrified aircraft can be effective in meeting these challenges.While there are several mechanisms to incorporate novel technologies for electrified aircraft, two such technologies: turbo-electric propulsion and distributed propulsion, are used in this research. Integration of these two technologies with the airframe leverages the well-known favorable interference between the wing and the tractor propeller wake to provide increased lift during takeoff.In the present research, the advantages and disadvantages of integrating a turbo-electric distributed propulsion (TEDiP) system are assessed for a regional transport aircraft (RTA). With near term motor technology, an improvement in trip fuel burn was observed on the four and six propeller variants of the TEDiP aircraft. The takeoff field length(TOFL) also improved in all three design variants which is a direct result of the working of distributed propulsion leading to better aerodynamic performance at takeoff conditions.The approach and findings for this research are reported in this thesis. Master of Science While air transportation system is considered the fastest means to travel, the avi-ation industry is responsible for 2.1% of all human-induced CO2 emissions, whichputs a renewed emphasis on environmental sustainability. There is heightenedinterest in exploring alternative propulsion technologies for aviation to mitigatethe effects of ever increasing demand for air travel coupled with fossil fuel pricevolatility.Ambitious plans have been outlined by leading aerospace organizations to reduceharmful emissions into the atmosphere. Achieving these ambitious goals requiresdevelopment and introduction of game changing technologies and aircraft con-cepts. Few such concepts include novel propulsion systems like all electric andhybrid-electric propulsion, distributed propulsion, and boundary layer ingestion.The X-57 is a novel all-electric aircraft being developed by NASA as a technologydemonstrator and makes use of multiple electric motors and propellers placedon the wing.Owing to battery technology limitations, all-electric and hybrid-electric propul-sion are not considered as viable options. In the near term, incorporatingdistributed propulsion alongside turbo-electric propulsion, for a Turbo-ElectricDistributed Propulsion(TEDiP) system may be a promising option in the near--to-mid-term. The overall goal of the present study is to investigate potentialbenefits and penalties of TEDiP systems for regional transport aircraft (RTA).To perform this study, the aerodynamics module of Pacelab Aircraft PreliminaryDesign (APD) Multi-Disciplinary Optimization (MDAO) framework is alteredto account for changes in wing-propeller aerodynamics due to the interactionof wing and multiple propellers. This required selection of a cost-effective toolthat captures aerodynamic data for multiple propellers and wing. VSPAEROis the aerodynamic tool of choice for this research. Aerodynamic data fromVSPAERO is coupled to APD and three TEDiP design variants with four, sixand eight propeller are designed with the ATR 72-500 as the baseline. Thebenefits and penalties of integrating the TEDiP system onto these variants isinvestigatedThe results show that a performance comparable to the baseline can be achievedin the near term with the four propeller variant even with current electricalsystems technology trends with a small weight penalty, and in the medium termon a six propeller variant. A decrease in trip fuel burn and improved takeofffield length(TOFL) performance justifies the usage of TEDiP systems.

Reduction of surface pressure fluctuations is desirable in various aerodynamic and hydrodynamic applications. Over the past few years, studies on canopy surface treatments have been conducted to investigate the fundamental mechanisms of surface pressure attenuation termed as pressure shielding. This work talks about the design, development and experimental testing of unidirectional canopy surface treatments which are evenly spaced arrays of streamwise rods placed parallel to the wall without an entrance condition. The canopy designs are based on surface treatments tested by Clark et al. (2014) inspired by the downy coating on owl wings. The main objective of the work is to establish fundamental physical and mathematical basis for treatments that shield aerodynamic surfaces from turbulent pressure fluctuations, while maintaining the wall-normal transport of momentum and low aerodynamic drag. Experimental testing of these canopy treatments are performed in the Anechoic Wall-Jet facility at Virginia Tech. Different canopy configurations are designed to understand the effect of various geometric parameters on the surface pressure attenuation. The treatment is found to exhibit broadband reduction in the surface pressure spectrum. Attenuation develops in two frequency regions which scale differently depending on two different mechanisms. Canopies seems to reduce the large-scale turbulent fluctuations up to nearly twice the height. Semi-analytical model is developed to predict surface pressure spectra in a wall-jet and canopy flow. The rapid term model shows that the inflection in the streamwise mean velocity profile is the most dominant source of surface pressure fluctuations. Synchronized pressure and velocity measurements elucidate significant features of the sources that could be affecting surface pressure fluctuations. Overall, this study explores the qualitative and quantitative physics behind pressure shielding mechanism which find application particularly in trailing edge noise reduction. Doctor of Philosophy Unsteady pressure fluctuations originating from interaction of turbulent flow over surfaces often cause undesirable effects. Trailing edge noise in wind turbines and helicopter blades, cabin noise and interior wind noise are some of noise sources which originate from surface pressure fluctuations. Previous studies have demonstrated that surface treatments help in reducing the unsteady surface pressure fluctuations therefore shielding surfaces and this phenomenon is termed as 'Pressure Shielding'. These are surface treatments inspired from the downy coating on owl's wings. This study is motivated by recent works conducted at Virginia Tech on experimental investigation of unidirectional canopy treatments. These are evenly spaced arrays of streamwise rods held horizontal at the downstream end. Most previous surface treatments contain some entrance condition such as steps, supports or gaps which effect the surface pressure measurements and disturb the incoming flow. In this study, the canopies are developed without any entrance condition therefore assist in capturing the fundamental mechanisms of the flow interaction with the canopy rods.

This study documents the integration and testing of a new variety of unsteady surface temperature gages designed to operate in high speed flow. Heat flux through the surface of the test article was determined from the unsteady temperature by applying a 3D reconstruction algorithm based on a Green's function approach. The surface temperature gages used in this work were 1.59 mm inserts designed to maximize material matching with the test article, in this case 316 stainless steel. A series of benchtop experiments were first performed to understand the individual properties of the gage and determine measurement uncertainty. Prior to testing, all temperature gages are calibrated using an environmental chamber. Gages were installed into slugs of several materials and subjected to a heated jet with a total temperature of 620 K to examine the effects of material mismatch. A shock tube with a notional operating Mach of 2.6 was used to determine the thermal response of the gages as a function of time. In both tests, reference Medtherm Schmidt-Boelter gages ensure consistent heat fluxes are applied across all runs. The time response of the entire electrical system was determined by subjecting the gage to a nanosecond scale laser pulse. Two experimental campaigns were conducted in Virginia Tech's Hypersonic Wind Tunnel. First, gages were integrated into a flat plate test article and subjected to a notionally 2D Mach 3 flow. Tunnel total pressures and temperatures ranged from 793-876 kPa and 493-594 K, respectively. A reference 3.18 mm Medtherm Schmidt-Boelter gage was also installed for comparison. All temperature data are reconstructed using the algorithm to determine heat flux. The second test campaign utilized a flat-faced cylindrical test article in a notionally axisymmetric Mach 6 flow environment. Flow total pressures and temperatures ranged from 8375-8928 kPa and 485.5-622 K. respectively. The Fay-Riddell analytical method was applied to the resulting temperature traces in order to infer the heat flux at the stagnation point for comparison with the reconstructed heat flux. This experiment was complimented with steady, 3D CFD in order to understand the temperature variation across the test article. Both campaigns demonstrate good agreement between the heat flux reconstructed from surface temperatures measured using the new gage, reference measurements, and simulations/analytical methods. The importance of material matching is highlighted during this study. The performance of this gage is shown to exceed the current state-of-the-art, opening the possibility for future analysis of phenomenon present in high-speed flow. Doctor of Philosophy At very fast speeds, it is important to understand how the temperatures of surfaces change with time. Traditional devices which can measure surface temperatures have a number of weaknesses, and to address these a new type of surface temperature device has been designed. By using computational methods, one can determine how much energy is being transferred through the surface by measuring how the surface temperature changes over time. A series of laboratory experiments were conducted to understand how this new instrument compares to the current state-of-the-art. Two experimental campaigns were then conducted to test the temperature gages. The first experiment used a simple flat plate geometry in a flow 3 times the speed of sound to serve as a benchmark test case, as the flow over a flat plate is well understood. The second test utilized a flat-faced cylindrical test article in a flow 6 times the speed of sound. The results of this test was compared to exact solutions and flow simulations. The result of this study is a well quantified tool to study how energy flows through a body subjected to very high speed flow, which will enable further study of the complicated thermal environments experienced at high speeds.

Refereed/Peer-reviewed In late 2013, under the leadership of Prime Minister Abbott, the Australian Government announced a new policy designed to increase attendance rates in remote community schools—the Remote School Attendance Strategy (RSAS). The model assumed that employing local people in the program, which was designed to support parents get their children to school, would yield significant improvements and consequently improve educational outcomes. After a slight initial increase in school attendance rates, RSAS schools have seen average attendance rates decline since 2016, which now stand more than eight percentage points lower than at commencement. This article analyses My School data for Very Remote Aboriginal schools, showing how the RSAS school attendance results compare with similar non-RSAS schools. We question why the Australian Government continues to invest in a program that is not meeting its objectives, asking, what went wrong? We do this by critically analysing 36 policy-related documents, looking for ideological clues that show why the government continues to invest in the program and how it sees it as “successful”. We conclude by raising ethical and accountability concerns about the RSAS, which lacks evidence of attendance improvement, and which potentially causes harm to its objects: First Nations students.

Computed tomography for flame chemiluminescence emissions allows for 3D spatially resolved flame measurements to be acquired using a series of discrete viewing angle camera images. To determine fuel/air ratios, the ratio of excited radical species (OH*/CH*) emissions using chemiluminescence can be employed. Following the process of high-resolution tomography reconstructions in this work allowed for flame tomography coupled with chemiluminescence emissions to be used for spatially resolved phase averaged equivalence ratio measurements. This is important as variations in local equivalence ratios can have a profound effect on flame behavior including but not limited to thermoacoustic instability, NOx and CO formation, and flame stabilization. Local equivalence ratios are determined from a OH*/CH* ratio of tomographically reconstructed intensity fields and relating them to equivalence ratio. The correlation of OH*/CH* to equivalence ratio is derived from an axisymmetric, commercially available flat flame burner (Holthuis and Associates Burner). To relate intensity field imaging (camera coordinate system) during the tomographic reconstruction to the real-world coordinate system of the burner a calibration procedure was performed and then validated. A calibration plate with 39 non-coplanar points was used in this procedure. It was then validated by comparing the Abel inverted flame images of the axisymmetric Holthuis and Associates burner with the tomographic reconstructed images. Results show a successful tomographic reconstruction of thermoacoustic self-excited cycle concluding equivalence ratio fluctuations coinciding with the 1st dominate frequency of the pressure fluctuations and influenced by a 2nd harmonic frequency. Master of Science In recent years tomographic reconstruction of flames have gained significant focus in understanding different flame phenomenon. One specific flame phenomenon is known as a thermoacoustic instability. Using highspeed cameras for chemiluminescence imaging of specific species can help define heat release rate, air/fuel ratio/equivalence ratio spatially. Coupling of pressure measurements to imaging methods can be used to determine the flames response to acoustic perturbations in the flow field. Every optics system has inherently different light transmission characteristics and therefore, needs to be calibrated/correlated using a known flame source. The work done in this paper used a Holthuis and Associates flat flame as the known flame source in conjunction with an optics system to correlate OH*/CH* ratio to equivalence ratio. This is possible due to the perfectly premixed nature the flat flame provides. The correlation curve for the optics system is then applied to the tomographically reconstructed chemiluminescence intensities during a self-excited thermo-acoustic instability. In addition, a flat flame burner was used to validate the tomography approach and calibration procedure. In conclusion the objective of this work develops and validates a method for use in tomographic reconstruction of spatially varying equivalence ratios.

Particle ingestion remains an important concern for turbine engines, specifically those in aircraft. Sand and related particles tend to become suspended in air, posing an omnipresent health threat to engine components. This issue is most prevalent during operation in sandy environments at low altitudes. Takeoffs and landings can blow a significant quantity of particulates into the air; these particulates may then be ingested by the engine. Helicopters and other Vertical Takeoff and Landing (VTOL) aircraft are at high risk of engine damage in these conditions. Compressor blades are especially vulnerable, as they may encounter the largest of particles. Robust and thorough experimental and computational studies have been conducted to understand the relationships between particle type, shape, and size and their effects on compressor and turbine blade wear. However, there is a lack of literature that focuses on sampling particles directly from the flow inside an engine. Instead, experimental studies that estimate the trajectories and behavior of particles are based upon the resulting erosion of blades and the expected aerodynamics and physics of the region. It is important to close this gap to fully understand the role of particulates in eroding engine components. This study investigated the performance of a particle-sampling probe designed to collect particles after the first compressor stage of a Rolls-Royce Allison Model 250 turboshaft engine. The engine was not used in this investigation; rather, a rig that creates a particle-laden jet was developed in order to determine probe sampling sensitivity with respect to varying angles of attack and flow Mach number. Particle image velocimetry (PIV) was utilized to understand the aerodynamic effects of the probe on smaller particles. Master of Science Aircraft jet engines are constantly exposed to particles suspended in the atmosphere. Most jet engines contain several stages of spinning blades. The first series of stages near the front of the engine comprise the compressor, while the series towards the end of the engine comprise the turbine. Engines depend on compressor blades to add energy to the flow via compression and turbine blades to extract energy from the flow after combustion. Thus, they are critical for the successful operation of the engine. The constant impact of airborne particulates against these blades causes erosion, which alters blade geometry and thereby engine performance. Depending on the turbine inlet temperature, particles may melt and clog the cooling passages in turbine blades, causing serious damage as the blades reach temperatures above their intended operating regime. These damages inhibit the ability of the engine to operate properly and pose a serious safety risk if left unchecked. In literature, experimental engine erosion correlations and numerical models of particle trajectories through the engine have been developed; however, none of these studies collected particles directly from the compressor region of the engine. In this study, a probe was developed and evaluated for the purpose of sampling particulates between the first and second compressor stages of a Rolls-Royce Allison Model 250 turboshaft engine. The probe's efficacy and aerodynamic properties were analyzed such that the probe will provide processable data when inserted into the engine. The methods to obtain this data include particle-sampling and particle image velocimetry (PIV).

The instability modes and non-linear behavior of a cavitating flow have been studied based on the experimental data obtained from planar Particle Image Velocimetry (PIV). Three data-driven techniques, Proper Orthogonal Decomposition (POD), Dynamic Mode Decomposition (DMD), and Clustered-based Reduced Order Modeling (CROM), are applied to the snapshots of the fluctuating component of velocity to investigate instability modes of the cavitating flow. DMD and POD analysis yield multiple modes are corresponding to slow-varying drift flow, cloud-shedding, and Kelvin-Helmholtz (KH) instability for a fixed inlet flow condition. The high coherence measure obtained from the instabilities suggests a transfer of energy from the largest scales, fluctuating mean flow, to the smaller scales such as cloud cavitation and Kelvin-Helmholtz (KH) instability. It is demonstrated that the POD decorrelation of length scales yields inherently quasi-periodic time dynamics, e.g., incommensurate frequencies. Moreover, the eigenvalue obtained from DMD revealed multiple harmonic with different decay rates associated with the cloud cavitation. The above-mentioned intermittent transition between distinct cloud shedding regimes is investigated via Clustered-based Reduced Order Modeling (CROM). Four aperiodic shedding regimes are identified. 68% of the time, triplets of vortices are formed, while 28% of the time, a pair of vortices are formed in the near wake of the throat. Dominant mechanisms governing the momentum transport and the turbulence kinetic energy production, destruction, and redistribution in distinct regions of the flow field have been identified using Gaussian Mixture Models (GMMs). The preceding data-driven techniques and in-depth analysis of the results facilitated modeling of the cavitation inception and break-up. Accordingly, a phase transition field model is developed using the ultra-fast Time-Resolved Particle Image Velocimetry (TR-PIV) and vapor void fraction spatial and temporal data. The data acquisition is implemented in a Venturi-type test section. The approximate Reynolds number based upon the throat height is 10,000, and the approximate cavitation number is 1.95. The non-equilibrium cavitation model assumes that the phase production and destruction are correlated to the static pressure field, pressure spatial derivatives, void fraction, and divergence of the velocity field. Finally, the dependence of the model on the empirical constants has been investigated. Doctor of Philosophy A cavitation bubble occurs where the pressure field is below the saturation pressure of the liquid. Accumulation of the cavitation bubble forms a cavitating flow. This phenomenon is observed in pumps, propulsion systems, internal combustion engines, and rocket engines. Identifying the mechanisms leading to cavitation-induced damages is imperative in the design of the devices. In this regard, investigation of the cavitation bubble inception, deformation, collapse, and intermittent regime change is mandatory in learning the primary mechanisms of the stresses imposed on the device. Experiments and high-fidelity numerical and analytical methods can be employed to shed light on flow physics. The current study adopted joint experimental methods, data analysis techniques, and computational approaches to scrutinize the unsteady cavitating flow underlying physics as it occurs past the throat of a Venturi-type profile. Different mechanisms of instabilities are identified by applying the data-driven techniques to the raw images of the cavitating flow. The path of the transitions between physically different instabilities mechanisms is examined. The local dominant balance between stress terms in the conservation of momentum equation is identified, and the stress terms roles in cavitating flow instabilities and advective acceleration are determined. A new cavitation model is developed and validated against the experimental results. The new model improves the prediction of the void fraction in different regions of the flow field, making it feasible to simulate different regimes of cavitating flow. Finally, the dominant mechanism governing the liquid-vapor transition and the transport of the void fraction is described.

For decades noise-induced hearing loss has been a concern of the Department of Defense (DoD). My research investigates noise generation and dispersion in supersonic jets and focuses on the fluid-dynamic regime typical of high-performance turbojet and turbofan engines. The goal of my research is to understand how dispersion and propagation of wavepackets can be modified by noise reduction strategies based on secondary injections of fluid with a different temperature from the main jet. The research is organized into three studies that focus on instability, large eddy simulations, and resolvent modes. The first study is a computational investigation of the role of thermal non-uniformity on the development of instability modes in the shear-layer of a supersonic $M= 1.5$, $Re=850,000$ jet. Cold fluid is injected at the axis of a heated jet to introduce radial non-uniformity and control the spatial development of the shear layer. The mean flow is analyzed with an efficient 2D and 3D Reynolds-averaged Navier-Stokes (RANS) approach using the SU2 code platform for 3 different cases -baseline, centered, and offset injection. Different turbulence models are tested and compared with the experiments. The coherent perturbation is analyzed using linear parallel and parabolized stability equations (PSEs). The second study investigates novel formulations of large eddy simulation models using an arbitrary high order discontinuous Galerkin scheme. The LES analysis focuses on both numerical issues (such as convergence against the polynomial order of the mesh), modeling issues (such as the choice of subgrid model), and underlying physics (such as vortex stretching and noise generation). Wall models are used to capture the viscous sublayer at the nozzle. The Ffowcs Williams-Hawkings (FW-H) method is used for far-field noise predictions for all cases. Three-dimensionality is studied to investigate how injection in the shear layer acts to create a rotational inviscid core and affects the mixing of the cold fluid and noise dispersion. The third study extends the (first) instability study by considering (global) resolvent modes. Such optimally forced modes of the turbulent mean flow field will identify the turbulent coherent structures (wavepackets) for different turbulence models at $M=1.5$. The LES simulations performed in the second study will be used to extract the mean flow and the dynamic modes for comparison. My research plan is to perform the resolvent analysis of the axisymmetric mean flow fields for the thermally activated case (i.e., the centered injection) and compare it to the baseline jet case. Different turbulence models will be investigated to determine the correct alignment of dynamic and resolvent modes. Finally, I will consider the three-dimensional, non-axisymmetric mean flow created by offset injection described in the second study, which requires evaluating the convolution products of resolvent modes and base flow. Such three-dimensional resolvent compressible modes have never been identified in the context of supersonic jets. Doctor of Philosophy For decades noise-induced hearing loss has been a concern of the Department of Defense (DoD). Research in this area is critical to US national security and valued by both the aircraft industry and government. The noise generated during take-off and landing is hazardous to the crew personnel who work around this vicinity. A reduction of noise can significantly decrease medical expenditure and allow the aircraft industry to meet the stringent community noise requirements. Among the various techniques of noise reduction analyzed over the years, thermal non-uniformity stands out for its simple implementation and cost-effectiveness, especially in after-burner turbojets. Thermal non-uniformity with a cold secondary stream introduces low-velocity fluid in a supersonic jet by locally increasing the density while matching the mass flow rate. Changes to the velocity profile are localized; different regions of the jet emit sound at different frequencies and radiation angles, thus the link between injection location and noise control is not well understood. Using different computational tools this research investigates the link connecting thermal non-uniformity, turbulent production, and sound generation. Injection at different radial locations affects the two mechanisms of sound radiation in different ways. The first mechanism, the Kelvin Helmholtz instability, can be studied as an eigenvalue problem that represents the spatial growth of normal modes. De-coherence of these modal fluctuations can be obtained by injecting secondary fluid directly into the shear layer. This injection mode is called offset injection. The present research shows that the thickening of the shear layer due to low-velocity fluid delays the formation of Kelvin-Helmholtz modes in the offset case. Thus, the outskirts of the jet produce pressure fluctuations with a lower spectral energy density. The second mechanism, the Orr instability, can be analyzed as non-modal growth of acoustic perturbation forced by the breakdown of the core of the jet. LES and stability analysis shows that centered injection is highly effective in reducing the Orr radiation. Resolvent modes explain that the rationale is the delay and reduction of a secondary resonant peak between spatial eddies and forcing caused by changes in the mean profile responsive to secondary injection. Our analysis also explains why the offset injection is more effective at a low polar angle, while centered injection reduces acoustic radiation towards high polar angles. Parametric studies of different injection strategies, i.e., location and number of injection ports are performed to demonstrate the best strategy for noise level reductions.

In the effort to reduce emission and fuel consumption in industrial gas turbines, lean premixed combustion is utilized but is susceptible to thermoacoustic instabilities. These instabilities occur due to an in-phase relationship between acoustic pressure and unsteady heat release in a combustor. Thermoacoustic instabilities have been shown to cause structural damage and limit operability of combustors. To mitigate these instabilities, a variety of active and passive methods can be employed. The addition of porous inert media (PIM) is a passive mitigation technique that has been shown to be effective at mitigating an instability. Practical industrial application of a mitigation strategy requires early-stage design considerations such as reduced order modeling, which is often used to study a systems' stability response to geometric changes and mitigation approaches. These reduced order models rely on flame transfer functions (FTF) which numerically represent the relationship between heat release and acoustic perturbations. The accurate quantification of heat release is critical in the study of these instabilities and is a necessary component to improve the reduced order model's predictive capability. Heat release quantification presents numerous challenges. Previous work resolving heat release has used optical diagnostics. For perfectly premixed, laminar flames, it has been shown there are proportional relationships between OH* or CH* chemiluminescence to heat release. This is an ideal case; in reality, practical burners produce turbulent and partially premixed flames. Due to the additional straining of the flame caused by turbulence, the heat release is no longer proportional to chemiluminescence quantities. Also, partially premixed systems have spatially varying equivalence ratios and heat release rates, meaning analysis reliant on perfectly premixed assumptions cannot be used and techniques that can handle spatial variations is needed. The objective of this thesis is to incorporate PIM effects into a reduced order model and resolve quantities vital to understand how PIM is mitigating thermoacoustic instabilities in a partially premixed, turbulent combustion environment. The initial work presented in this thesis is the development of a reduced order model for predicting mode shapes and system stability with and without PIM. This was the first time that a reduced order model was developed to study PIM effects on the thermoacoustic response. Model development used a linear FTF and can predict the system frequency and stability response. Through the frequency response, mode shapes can be constructed which show the axial variation in acoustic values, along with node and anti-node locations. Stability trends can be predicted, such as the independent effects of system parameter variation, to determine its stability response. The model was compared to canonical case studies as well as experimental data with reasonable agreement. With PIM addition, it was shown that a combustor would be under stable operation at more flow conditions than without PIM. The work also shows the stability sensitivity to different porous parameters and PIM locations within the combustor. The model has been used to aid in the design of other combustion systems developed at Virginia Tech's Advanced Propulsion and Power Laboratory. To better understand how PIM is affecting the system stability and demonstrate measurements for the improvement of a numerical FTF, experimental work to resolve the spatially varying equivalence ratio fluctuations was conducted in an atmospheric, swirl-stabilized combustor. The experimental studies worked to improve the fundamental understanding of PIM and its mitigation effects through spatially and temporally resolved equivalence ratios during a self-excited instability. The experimental combustor has an optically accessible flame region which allowed for high speed chemiluminescence to be captured during the instability. Equivalence ratio values were calculated from a relation involving OH*/CH* chemiluminescence ratio. The acoustic perturbations were studied to show how the equivalence ratio fluctuations were being generated and coupling with the acoustic waves. The fluctuation in equivalence ratio showed about 65% variation around its mean value during the period of an instability cycle. When porous media was added to the system, the fluctuation in equivalence ratio was mitigated and a reduction in peak frequency (sound pressure level) SPL of 38 dB was observed. Changes in the spatial distribution of equivalence ratio with PIM addition were shown to produce a more stable operation. Effects such as locally richer burning and changes to recirculation zones promoted more stable operation with PIM addition. Testing with forced acoustic input was also conducted to quantify the flame response. The results demonstrated that a flame in a system with PIM responds differently than without PIM, highlighting the need to develop FTF for systems with PIM. This experimental study was the first to study equivalence ratio in a turbulent, partially premixed combustor using PIM as a mitigation technique. A final experimental investigation was conducted to resolve the spatially defined heat release and its fluctuation during a thermoacoustic instability period. This was the first time that heat release had been investigated in a partially premixed, thermoacoustically unstable system, using PIM as a migration method. Heat release was quantified using equivalence ratio, strain rate, OH* intensity, and a correction factor determined from a chemical kinetic solver. The heat release analysis built upon the equivalence ratio study with additional flow field analysis using PIV. The velocity vectors showed prominent corner and central recirculation zones in the no PIM case which have been shown to be feedback mechanisms that support instability formation. With PIM addition, these flow features were reduced and decoupled from the combustor inlet reactants. The velocity results were decomposed using a spectral proper orthogonal decomposition (SPOD) method. The energy breakdown showed how PIM reduced and distributed the energy in the flow structures, creating a more stable flow field. Heat release results with velocity information demonstrated the significant coupling mechanisms in the flow field that were mitigated with the PIM addition. The no PIM case showed high heat release areas being directly influenced by the incoming flow fluctuations. The feedback mechanisms, both mean flow and acoustic, have a direct path to the incoming flow to the combustor. In the PIM case, there is significant mixing and burning taking place in locations where it is less likely that feedback can reach the incoming flow to couple to form an instability. The methodology to quantify heat release provides a framework for quantifying a non-linear FTF with PIM. The development and testing to determine a non-linear FTF with PIM are reserved for future work and discussed in the final chapter. The methodologies and modeling conducted here provided insight and understanding to answer why PIM is effective at mitigating a thermoacoustic instability and how it can be studied using a reduced order numerical tool. Doctor of Philosophy In the effort to reduce emission and fuel consumption in industrial gas turbines, lean premixed combustion is utilized but is susceptible to thermoacoustic instabilities. These instabilities occur due to a relationship between acoustic pressure and unsteady heat release in a combustor. Thermoacoustic instabilities have been shown to cause structural damage and limit operability of combustors. To mitigate these instabilities, a variety of active and passive methods can be employed. The addition of porous inert media (PIM) is a passive mitigation technique that has been shown to be effective at mitigating an instability. Implementation of these mitigation strategies require early-stage design considerations such as reduced order modeling, which is often used to study a systems' stability response to geometric changes and mitigation approaches. These reduced order models rely on flame transfer functions (FTF) which numerically model the flame response. The accurate quantification of heat release is critical in the study of these instabilities and is a necessary component to improve the reduced order model's predicative capability. Heat release quantification presents numerous challenges. Previous work resolving heat release has used optical diagnostics with varying levels of success. For perfectly premixed, laminar flames, it has been shown there are proportional relationships between flame light emission and heat release. This is an ideal case; in reality, practical burners produce complex turbulent flames. Due to complex turbulent flame, the heat release is no longer proportional to the flame light emission quantities. Also, partially premixed systems have spatially variant flame quantities, meaning analyses reliant on perfectly premixed assumptions cannot be used and techniques that can handle spatial variations are required. The objective of this thesis is to incorporate PIM effects into a reduced order model and resolve quantities vital to understand how PIM is mitigating thermoacoustic instabilities in a partially premixed, turbulent combustion environment. The initial work presented in this thesis is the development of a reduced order model for predicting mode shapes and system stability with and without PIM. The model uses a simple relationship to model the flame response in an acoustic framework. To improve the model and understanding of PIM mitigation, experimental data such as the local heat release rates and equivalence ratios need to be quantified. An experimental technique was utilized on an optically accessible atmospheric, swirl-stabilized combustor, to resolve the spatially variant equivalence ratio and heat release rates. From these results, better understanding of how PIM is improving the stability in a combustion environment is shown. Quantities such as velocity, acoustic pressure, equivalence ratio, and heat release are all studied and used to explain the improved stability with PIM addition. The methodologies and modeling conducted here provided insight and understanding to answer why PIM is effective at mitigating a thermoacoustic instability and how it can be studied using a reduced order numerical tool. Furthermore, the present work provides a framework for quantifying spatially varying heat release measurements, which can be used to develop FTF for use with thermoacoustic modeling approaches.

Fan system efficiency for modern aircraft engine design is increasing to the point that bypass duct geometry is becoming a significant contributor and could ultimately become a limiting factor. To investigate this, a number of methods are available to provide qualitative and quantitative analysis of the flow around the loss mechanisms present in the duct. Particle image velocimetry (PIV) is a strong candidate among experimental techniques to address this challenge. Its use has been documented in many other locations within the engine and it can provide high spatial resolution data over large fields of view. In this work it is shown that these characteristics allow the PIV user to reduce the spatial sampling error associated with sparsely spaced point measurements in a large measurement region with high order gradients and small spatial scale flow phenomena. A synthetic flow featuring such attributes was generated by computational fluid dynamics (CFD) and was sampled by a virtual PIV system and a virtual generic point measurement system. The PIV sampling technique estimated the average integrated velocity field about five times more accurately than the point measurement sampling due to the large errors that existed between each point measurement location. Despite its advantages, implementation of PIV can be a significant challenge, especially for internal measurement where optical access is limited. To reduce the time and cost associated with iterating through experiment designs, a software package was developed which incorporates basic optics principles and fundamental PIV relationships, and calculates experimental output parameters of interest such as camera field of view and the amount of scattered light which reaches the camera sensor. The program can be used to judge the likelihood of success of a proposed PIV experiment design by comparing the output parameters with those calculated from benchmark experiments. The primary experiment in this work focused on the Pratt and Whitney Canada JT15D-1 aft support strut wake structure in the bypass duct and was comprised of three parts: a simulated engine environment was created to provide a proof of concept of the PIV experiment design; the PIV experiment was repeated in the full scale engine at four fan speeds ranging from engine idle up to 80% of the maximum corrected fan speed; and, finally, a CFD simulation was performed with simplifying assumptions to provide insight and perspective into the formation of the wake structures observed in the PIV data. Both computational and experimental results illustrate a non-uniform wake structure downstream of the support strut and support the hypothesis that the junction of the strut and the engine core wall is creating a separate wake structure from that created by the strut main body. The PIV data also shows that the wake structure moves in the circumferential direction at higher fan speeds, possibly due to bulk swirl present in the engine or a pressure differential created by the support strut. The experiment highlights the advantages of using PIV, but also illustrates a number of the implementation challenges present, most notably, those associated with consistently providing a sufficient number of seeding particles in the measurement region. Also, the experiment is the first to the author's knowledge to document the use of PIV in a full scale turbofan engine bypass duct. Master of Science

The measurement of temperature in hot gases plays an important role in many engineering applications, such as the efficiency and performance of an engine. As such, understanding the accuracy of these temperature measurements is also important. One of the common ways in which temperature is measured is through the use of total temperature probes. Previous research both at Virginia Tech and in outside studies has been performed to quantify the errors associated with total temperature probe measurements. This work has led to the development of low-order models which can be used to calculate the performance of a total temperature probe as a first-order estimate. These low-order models require knowledge of the heat transfer to the total temperature sensor in order to calculate the probe performance. However, the heat transfer to the sensor is a difficult quantity to calculate and has only been quantified over a set range of operating conditions for a single probe design. This research seeks to expand the range of applicability of the Virginia Tech low-order model by quantifying the heat transfer to the sensor of a total temperature probe over a range of probe geometries through the use of computational models. Key geometry parameters were altered to understand how altering these geometry features would impact the heat transfer to the sensor. In order to quantify the heat transfer to the sensor for varied probe geometries, a new method of characterizing the flow conditions about the sensor was also developed. By characterizing the flow conditions about the sensor, a better quantification of the heat transfer can be obtained. This thesis presents the correlation that was developed to quantify the changes in the flow about the sensor caused by varying the key geometry parameters. The flow conditions encompassed total temperatures from 294 K to 727 K at a Mach number of 0.4. The changes in the flow conditions about the sensor are then used to develop a heat transfer correlation to allow the heat transfer to the sensor to be calculated based off the changes in the flow conditions. The heat transfer to the sensor can then be substituted into the low-order model and used to calculate the performance of a total temperature probe. Master of Science The measurement of temperature in hot gases plays an important role in many engineering applications, such as the efficiency and performance of an engine. As such, understanding the accuracy of these temperature measurements is also important. One of the common ways in which temperature is measured is through the use of total temperature probes. Previous research has been performed to quantify the errors associated with total temperature probe measurements. This work has led to the development of low-order models which can be used to calculate probe errors. These low-order models require knowledge of the heat transfer to the total temperature sensor in order to calculate the probe errors. However, the heat transfer to the sensor is a difficult quantity to calculate and has only been quantified over a set range of flow conditions for a single probe design. This research seeks to quantify how the heat transfer to the sensor of a total temperature probe changes for different probe designs. Key geometry parameters were altered to understand how changing these geometry features would impact the heat transfer to the sensor. This thesis presents how the heat transfer to the total temperature sensor can be calculated over a range of different probe designs. The heat transfer to the sensor can then be substituted into the low-order model and used to calculate the performance of a total temperature probe.