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Doctor of Philosophy with a Major in Aerospace Engineering

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Uncertainty-Based Methodology for the Development of Space Domain Awareness Architectures in Three-Body Regimes

2024-04-29 , Gilmartin, Matthew Lane

The past decade has seen a massive growth in interest in lunar space exploration. An increase in global competition has led a growing number of countries and non-governmental organizations towards lunar space exploration as a means to demonstrate their industrial and technological capabilities. This increase in cislunar space activity and resulting increase congestion and conjunction events poses a significant safety impact to spacecraft on or around the moon. This risk was demonstrated on October 18th 2021 when India’s Chandrayaan 2 orbiter was forced to maneuver to avoid a collision with NASA’s Lunar Reconnaissance Orbiter. In order to mitigate the safety impacts of increased congestion, enhanced space traffic management capabilities are needed in the cislunar regime. One foundational component of space traffic management is space domain awareness (SDA). Current SDA infrastructure, a network of earth-based and space-based sensors, was designed to track objects in near-earth orbits, and is not suitable for tracking objects in distant, non-Keplerian cislunar orbits. As a result, new infrastructure is needed to fill this capability gap. The cislunar regime presents a number of challenges and constraints that complicate the SDA architecture design space. Unlike the near-earth regime, cislunar space is a three-body environment, violating many of the simplifying assumptions and models that are used in the near-earth domain. Furthermore, instability in cislunar dynamics means that state uncertainty plays a much more dominant role in system performance. This research identified three technology gaps exposed by the transition to the cislunar regime, that impede the ability of designers to explore the design space and perform many-query analyses, such as design optimization. A new uncertainty-based methodology was then proposed to both address these gaps and enhance design space exploration. The first technology gap identified was a reliance on three-body dynamics violate analytic two-body models of spacecraft motion, meaning that cislunar trajectories must be numerically integrated at much greater computational cost. A method was proposed that combines surrogate modeling techniques with and orbit family approach to develop an analytic parametric model of spacecraft motion. An experiment was carried out in order to interrogate the efficacy of this approach. Multiple surrogate models were generated using the approach, and each was compared to the state-of-the-art numerical integration approach. The surrogate modeling approach was found to greatly reduce the computational cost required to determine the initial state of an arbitrary periodic cislunar trajectory, while maintaining comparable accuracy to existing full-order methods. Of the surrogate model formulations tested, the interpolation methods were found to have the best combination of accuracy and speed for the proposed application. The second technology gap identified was a reliance on Gaussian distributions in most tracking filter implementations. In non-linear domains such as the cislunar regime Gaussian distributions may deviate from a Gaussian shape when propagated through the system's non-linear dynamics. This creates convergence issues that limit the robustness of tracking schemes that rely on Gaussian characterizations of uncertainty. This in turn creates a need to characterize the realism of Gaussian uncertainty approximations of potentially non-Gaussian uncertainty distributions. The characterization of uncertainty realism was identified to be a computationally intensive process, limiting the breadth of potential design space exploration. To ameliorate this issue a surrogate modeling process was proposed for the development of models to characterize the realism of uncertainty estimates produced by tracking filters. An experiment was executed to evaluate the efficacy of this approach. The surrogate modeling process was found to greatly improve the computational cost of the full-order analysis. While the surrogate models were found to have non-negligible errors, these errors were on the same order of magnitude as the variability of the full-order model. Of the models tested, the model based on boosted decision trees was found to have the best balance of speed and accuracy. This massive increase in computational efficiency enables designers to evaluate much larger volumes of design cases using the same hardware. The third identified technology gap was the exponential increases in the computational cost required to evaluate tracking uncertainty using full-order cislunar SDA simulations, as the number and diversity of systems in an SDA system increases. As a result of this ballooning computational cost, detailed uncertainty quantification can rapidly become intractable in a many-query analysis context, limiting the scope of design space exploration and uncertainty quantification. A surrogate modeling method was proposed to provide a volumetric assessment of tracking performance at reduce the computational cost compared to existing methods. As part of this proposed approach, changes in tracking uncertainty were evaluated with respect to the search volume. Changes in uncertainty were evaluated using a novel equivalent radius metric to estimate the rate of information gain of information gain for individual sensor systems which is then aggregated for the overall architecture. As part of this approach, field surrogates and reduced order models were investigated as potential techniques to improve the computational cost and quality of the generated surrogate models. An experiment was performed to investigate the efficacy of the proposed method in comparison to the existing methods. The generated surrogate models were found to significantly reduce the computational cost of the tracking analysis. Furthermore, this experiment found scalar surrogate models to provide the most accurate modeling of the full-order models. The field surrogates generally under-performed their scalar counterparts in terms of goodness-of-fit. Of the models tested, the scalar boosted decision tree model was found to have the best balance of speed and accuracy. In practice, this model offered was able to reduce the computational cost of evaluating SDA architecture tracking performance by several orders of magnitude, enabling designers to increase the breadth of design space exploration by similar orders of magnitude. Finally, each of the developed modeling approaches were integrated into a unified methodology, named VENATOR, to evaluate \gls{SDA} architectures. A demonstration experiment was proposed, wherein the proposed VENATOR uncertainty-based methodology was compared to a state-of-the-art methodology using equivalent full-order analyses. The experiment was broken into two phases. In the first phase, both frameworks were used to evaluate the same architecture. Next, in the second phase, the VENATOR uncertainty-based methodology was used to evaluate a simple optimization problem. The first phase of this analysis found the VENATOR uncertainty-based methodology to offer an improvement in computational cost of over three orders of magnitude. During the second phase, a simple optimization was run using the VENATOR uncertainty-based methodology, evaluating over 82,000 cases in a total of 1.6 days. A short design space exploration was carried out, identifying the Pareto front of non-dominated cases, to demonstrate the utility of this approach. Using the run time of the state-of-the-art system when evaluating a single architecture, it was estimated that using this reference methodology would have taken over 14 years to evaluate the same number of cases using the same hardware. This massive increase in computational efficiency allows designers to greatly increase the breadth of design space exploration, enabling them to examine far larger case loads, reducing design risk and increasing design knowledge. For this reason, the uncertainty-based methodology was deemed to be a significant improvement over the state-of-the-art methodologies.

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Modeling and Simulation of Flow Transients inside a Multi-Stage Axial-Centrifugal Compressor

2024-04-27 , Jing, Zhenhao

In this work, an unsteady mean line flow model for multi-stage axial and centrifugal compressors is developed, where the blade rows, i.e., rotors and stators, are modeled as successive diffusing stream tubes in their own stationary or rotating reference frames. Thus, the compressor flow is “driven” by the added velocity at frame transformations instead of being driven by a user-input aerodynamic force, which is perpendicular to the flow direction. The developed mean line flow model features a series of physics-based modeling approaches that distinguishes itself from most unsteady compressor models. The aforementioned frame transformations between stationary and rotating reference frames are accommodated by inter-domain boundary conditions (interfaces), which allow acoustic waves to propagate the discontinuity in flow properties created by the frame transformation. Such a discontinuity accommodated by the interfaces is also used as a compact loss zone to include various loss models intended to capture the individual physical phenomenon. Thus, the energy addition at frame transformations and the loss models jointly predict the compressor aerodynamic performance, hence removing the need for user-input compressor performance. A series of steady-state and unsteady simulations are performed and presented. Several sensitivity studies on selected individual loss models are presented for steady-state simulations to reveal their influence. During compressor rig tests, the flow transients are simulated to investigate the surge process and choke/unchoke response. A novel rig test approach enabling measurement of equilibrium characteristics on the unstable side is proposed and simulated. In order to simulate compressor flow transient in real working conditions in a gas-turbine engine, a lumped-parameter combustor-turbine model is developed and coupled with the compressor model. Such an approach enabled the simulation of gas turbine transients, including fast engine acceleration and deceleration and the effects of heat transfer in those engine transients. A novel active energy management strategy, which uses an electric starter/generator (ES/G) to enhance gas turbine acceleration, is proposed and simulated. A similar approach using ES/G to assist recovery from surges is also examined by simulation, and the necessary ES/G power for such a task is evaluated.

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Autonomous and Robust Monocular Simultaneous Localization and Mapping-Based Navigation for Robotic Operations in Space

2024-04-27 , Dor, Mehregan

The theoretical background, the synthesis, and the implementation details of estimation frameworks for target-relative spacecraft rendezvous and proximity operations (RPO) and small body probing and surveying (SBPS) predicated on modern simultaneous localization and mapping (SLAM) are considered. The challenges arising in the application of pure visual monocular SLAM to spacecraft relative navigation by testing an off-the-shelf algorithm, ORB-SLAM, on real satellite servicing image sequences, were identified. It is additionally determined that the inclusion of inertial measurement unit-based (IMU) factors, predominantly used in visual-inertial simultaneous localization and mapping (viSLAM), may not provide observability of the ambiguous scale or of the inertial motion over extended arcs, and moreover would not facilitate the smoothing problem. A comprehensive SLAM framework, predicated on monocular image feature point tracking and sensor fusion for on-the-fly navigation and map building is proposed. The work is contrasted to the state-of-the-art methods which instead exploit stereo imaging. A factor graph approach, allowing for the incorporation of asynchronous measurements of diverse modalities, and the inclusion of kinematic and dynamic constraints, is selected. A new relative dynamics factor predicated on the chaser-target relative orbital mechanics is devised and then augmented with the existing relative kinematics factor of Setterfield et al. to account for non-inertial motion of the target center of mass. AstroSLAM, an algorithm solving for the navigation solution of a spacecraft under motion in the vicinity of a small body by exploiting monocular SLAM, sensor fusion, and RelDyn motion factors, is proposed. The developed motion factor encodes a hybrid inertial rate gyro sensor model and vehicle dynamics model, based on the spacecraft-small-body-Sun system, incorporating realistic perturbing effects, which affect the motion of the spacecraft in a non-negligible manner. The RelDyn factor is readily specialized to the spacecraft rendezvous problem by removing the target gravitational pull variable. The data shows that RelDyn out-performs the state-of-the-art preintegrated IMU accelerometer factors, commonly used in visual-inertial SLAM solutions, in one instance of a legacy NASA small body surveying mission and in one instance of an in-lab-generated dataset. On-the-fly target dynamical parameter estimation, such as the center of mass location, the spin vector, and the gravity parameter, is also demonstrated. An existing robotics procedure, dubbed structure from small-motion (SfSM), is leveraged to tackle the challenge of map initialization with small camera baseline and weak-perspective projection

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A Data-driven Methodology for Aircraft Trajectory Analysis to Improve Mid-air Conflict Detection in Terminal Airspace

2024-04-27 , Zhang, Wenxin

A mid-air collision occurs when two aircraft come into contact while airborne. It stands as one of the most devastating accidents in aviation history and remains a pressing safety issue in current flight operations. Presently, Air Traffic Control (ATC) serves as the primary means to ensure safe separation between aircraft and prevent mid-air collisions. This heavily relies on human operators, Air Traffic Controllers (ATCOs), who manage critical tasks under significant workload. The anticipated expansion of aviation, both in terms of traffic volume and diversity, particularly in terminal airspace, presents substantial challenges to the existing ATC system. The workload on ATCOs may exceed their capacity, potentially compromising safety. To address forthcoming aviation demands and maintain high safety standards, ATC is gradually integrating automated systems to assist ATCOs in transitioning from manual to supervisory roles. This dissertation is driven by the need for advanced analytics and automated decision supports concerning air traffic within terminal airspace. By leveraging Global Navigation Satellite System (GNSS) technologies, specifically Automatic Dependent Surveillance–Broadcast (ADS-B), ATC is able to access real-time and extensive historical operational data. Hence, this research presents a novel data-driven methodology to conduct thorough aircraft trajectory analysis, aiming to improve mid-air conflict detection within terminal airspace. The outlined methodology comprises three key steps: (1) traffic flow identification and recognition, (2) trajectory prediction, and (3) conflict detection. The traffic flow identification and recognition step entails two key requirements: (1) an effective method to identify air traffic flows in terminal airspace, and (2) a fast and accurate method to recognize the air traffic flow of individual flights. Achieving the first requirement demands a clustering approach capable of filtering out non-nominal trajectories commonly encountered in daily operations. While Density-Based Spatial Clustering of Applications with Noise (DBSCAN) may be applied, it can struggle with density variations in traffic flows observed in historical trajectories. Thus, Ordering Points to Identify the Clustering Structure (OPTICS) is proposed as an alternative clustering algorithm. Additionally, Weighted Euclidean Distance is suggested as a distance metric to account for the significance of different trajectory points. An experiment is designed to implement the OPTICS and DBSCAN algorithms using Weighted Euclidean Distance as the distance metric to identify air traffic flows in terminal airspace, and the results have demonstrated OPTIC's superior effectiveness in enhancing identification over DBSCAN. Addressing the second requirement involves employing a method capable of multi-class classification with rapid training and high accuracy. Ensemble models such as Random Forest and Extreme Gradient Boosting (XGBoost) provide a favorable balance between accuracy and efficiency, rendering them viable choices. Conversely, the Long Short-Term Memory (LSTM) model is anticipated to yield even higher accuracy, albeit with longer training time. An experiment is designed to implement Random Forest, XGBoost, and LSTM models for multi-class classification of aircraft trajectory segments, aiming to recognize air traffic flows of individual flights. Subsequently, their performance in terms of accuracy and training time is compared. The results of the experiment indicate that Random Forest achieves accuracy levels comparable to LSTM while significantly reducing training times. The trajectory prediction step necessitates a method for aircraft trajectory prediction. Existing methods typically employ an encoder-decoder architecture with LSTM trained on entire trajectory sets, leading to potential challenges: (1) difficulty in effectively learning hidden features due to significant differences in input trajectories, and (2) sequential nature of LSTM resulting in prolonged training durations. To overcome the first challenge, this study proposes to train multiple predictors on subsets with distinct traffic flows identified earlier, rather than a monolithic predictor on the entire dataset. An experiment is devised to implement the encoder-decoder architecture with LSTM to train a monolithic predictor and multiple predictors, on datasets containing all trajectories and subsets with distinct traffic flows respectively, then compare the accuracy and training time of the two approaches. The results have revealed that employing multiple predictors leads to increased accuracy and decreased training time compared to the single predictor approach. To address the second challenge, Transformer is proposed as an alternative to LSTM, benefiting from attention mechanisms to eliminate sequential operations and enable parallelization. An experiment is designed to train trajectory predictors for distinct traffic flows using the encoder-decoder architecture, first with LSTM and then with Transformer, followed by a comparison of the prediction accuracy and training time between the two approaches. The implementation results indicate a considerable reduction in training time and comparable accuracy achieved by Transformer compared to LSTM, particularly for extended prediction horizons. The conflict detection step requires an automated method to identify conflicts within terminal airspace, with a critical focus on addressing uncertainty. Utilizing historical trajectory data is crucial, especially in the context of aircraft position estimation, which conventionally relies solely on mathematical tools without leveraging real-world data. Kernel Density Estimation (KDE), a statistical technique for deriving Probability Density Functions (PDFs) from sampled data, emerges as a promising tool to enable robust estimation of aircraft positions based on historical trajectories. Furthermore, the intersection of PDFs from different flights serves as a means to identify potential conflicts. Hence, a novel Weighted KDE method is proposed to estimate aircraft positions by integrating outputs from traffic recognition and trajectory prediction, subsequently facilitating conflict detection in terminal airspace through the intersection of flight PDFs. To validate the proposed method, an experiment is designed to implement Weighted KDE to synthesize the outcomes of traffic flow recognition and trajectory prediction to estimate aircraft positions and then perform conflict detection by representing conflict with the intersection of aircraft position PDFs. The implementation results reveal that the conflict probabilities calculated by the Weighted KDE method show an inverse relationship with actual distances between aircraft, in both horizontal and vertical planes, thereby demonstrating the effectiveness the proposed conflict detection method. Several representative real flight scenarios serve as use cases to showcase the efficacy of the proposed data-driven methodology for analyzing aircraft trajectories to improve mid-air conflict detection in terminal airspace. The exploratory nature of this research suggests its potential evolution into a real-time decision support tool that offers conflict detection advisories for ATCOs. Transitioning from research to practical application may require real flight tests and incorporation of Real-time Assurance (RTA) mechanisms.

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A Multi-Objective Deep Learning Methodology for Morphing Wings

2024-04-27 , Achour, Gabriel

Due to design constraints, conventional aircraft cannot achieve maximum aerodynamic performance when operating under varying missions and weather conditions. One of these constraints is the traditional approach of optimizing aircraft wings to achieve the best average aerodynamic performance for a specific mission while maintaining structural integrity. Previous studies have shown that changing the shape of wings at different points of a mission profile improves the aerodynamic performance of aircraft. As such, stakeholders have explored the viability and feasibility of changing or morphing the shape of aircraft wings to enable aircraft to adapt to varying missions and weather conditions. However, as with any other aspect of aircraft design, some challenges currently exist that hinder the development of conventional aircraft with morphing wings. First, the computational cost of flow solvers makes aerodynamic shape optimization time-consuming and computationally expensive due to its iterative nature. When designing a morphing wing, different configurations are computed for different points in the flight envelope, multiplying the computational cost necessary for morphing wing aircraft design. Consequently, a framework capable of performing shape optimization at a reduced computational cost is needed. Second, morphing can lead to a high variation of wing shapes, generating high aerodynamic loads and minimizing the aerodynamic benefits of morphing wings. Moreover, structural analyses are also computationally expensive, replicating the same challenges as aerodynamic optimization. As such, a multi-objective framework capable of optimizing morphing wings to increase aerodynamic efficiency while addressing aeroelastic constraints at a lower computational cost is needed. Finally, even though changing the shape of an aircraft’s wing at each segment of a mission profile is the most efficient approach to maximize the benefits of morphing wings, this is not ideal as flight and weather conditions are not constant throughout the flight segment. A framework that can adapt the wing shapes to varying flow conditions during the flight is needed. Consequently, this thesis aims to address these gaps by 1) developing a Conditional Generative Adversarial Network-based algorithm capable of generating optimal wing shapes of a morphing wing vehicle for each segment of a given mission profile, 2) training a Reinforcement Learning agent to modify the optimized shape and design the wing structure to ensure the structural integrity of morphing wings throughout the flight while maintaining a high aerodynamic performance 3) implementing a Meta Reinforcement Learning agent to make aircraft wings adapt their shapes to variations in flow conditions during each mission segment. The experiments outlined in this thesis involve designing each network architecture, collecting the training datasets, and training each model. These models are then applied to various aerodynamic and aero-structural optimization tasks across various demonstrated morphing wing mechanisms. Each model demonstrated accurate optimization results when compared to classical optimization methods. Additionally, the results indicate a significant reduction in computational power required by the deep learning models. As such, this thesis demonstrates the immense benefits of training and implementing deep learning models to perform various optimization tasks related to morphing wing aircraft design at a lower computational cost than traditional optimization algorithms. Furthermore, this thesis demonstrates the benefits of morphing wings throughout flight to maximize aerodynamic efficiency while minimizing structural constraints, which can lead to a non-negligible fuel consumption economy. Finally, this thesis demonstrates how meta-learning can be applied to continuously adapt the shape of a wing to unexpected changes in flow conditions throughout flight.

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An Approach for Risk-Informed UAS Mission Planning in Urban Environments to Support First Responders

2024-04-27 , Pattison, Jeffrey T.

The past decade has seen a tremendous increase in the use of Unmanned Aerial Systems (UAS). What was once exclusively used by the military is now a critical component for a wide range of applications, including deliveries and logistics, construction, and law enforcement. Police departments around the world are beginning to see the potential UAS have for responding to emergency events. These UAS can reduce response times, be used to deescalate events, and provide crucial information to ground personnel prior to arrival. However, introducing UAS provides significant difficulties. Human operators and pilots are required to ensure safe operations and regulatory compliance. The Federal Aviation Administration has imposed strict regulations on the use of UAS in populated areas, restricting the autonomous capabilities of UAS. For UAS to be able to operate more autonomously with less human input, additional safety measures and assurance of acceptably safe operations are required. This thesis explores how to incorporate risk assessment into UAS mission planning for emergency response to introduce additional safeguards without significantly sacrificing the UAS response capability. The major areas of research studied in this thesis include UAS risk estimation methods, UAS route planning with risk incorporated, and optimizing a system of UAS to respond to emergencies when risk is considered. Because UAS are relatively new compared to manned aircraft, UAS lack historical flight data required for risk assessment like manned aircraft. A new machine learning model is proposed that can be used for evaluating UAS risk in a more time efficient manner than the physics-based modeling and simulation methods commonly used for risk estimation. Response time is critical for emergency events, and the route a UAS takes to reach the emergency directly affects its ability to respond. This work also studies various route planning methods that can account for UAS risk to find a suitable route planning configuration that meets the demands for using UAS as a first responder. Another critical component to the response time is intelligently selecting UAS launch locations. The performance of Integer Linear Programming, Genetic Algorithms, and a hybrid algorithm are compared to determine the most suitable method for finding the optimal launch locations to minimize response time for a system of three UAS when ground risk is incorporated into the emergency response route planning. Using a software in the loop flight simulator and a vehicle simulation environment, an overarching experiment demonstrates the effectiveness of the proposed approach for incorporating risk into mission planning to see how the proposed approach impacts UAS emergency response.

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Permuted proper orthogonal decomposition for analysis of advecting structures

2024-04-27 , Ek, Hanna Maria

This work is motivated by the large and ever-increasing amounts of data from studies in experimental and computational fluid dynamics, and the desire to extract and analyze coherent structures from such datasets. Specifically, this thesis is concerned with vortex patterns in turbulent shear flows, which appear as advecting structures in planar measurements or slices through three-dimensional computational domains. Space-only proper orthogonal decomposition (POD) is one of the most widely used techniques for the analysis of coherent structures and decomposes mean-subtracted data into the space-time separated form q^' (x,t)=∑_j =〖a_j (t) ϕ_j (x) 〗. This method is optimal in the spatial inner product and targets high energy spatial structures, but it is sensitive to input data alignment and cannot effectively handle translations. This work applies a re-orientation of the space-time coordinates in the POD framework, and the modified POD method, referred to as permuted POD (PPOD), is the focus of this thesis. PPOD decomposes data as q^' (x,t)=∑_j =〖a_j (n) ϕ_j (s,t) 〗, where x=(s,n) is a general spatial coordinate system, s is the coordinate along the bulk advection direction in curvilinear space, and n=(n_1,n_2 ) are the mutually-orthogonal directions normal to s. PPOD is optimal in the s,t inner product and, thus, targets advecting structures via their s,t correlations. Specifically, the PPOD modes, ϕ_j (s,t), portray advection as diagonal features in s,t space, where the slope of the features corresponds to the phase speed. Hence, these speeds are a natural output of the decomposition and can vary in an arbitrary and dispersive manner along the s coordinate. Generally, the PPOD modes have arbitrary s,t dependences, and a single mode can describe a broadband or multi-frequency disturbance, as well as time-varying characteristics, such as transient and intermittent dynamics. Additionally, one- and two-dimensional Fourier transforms of the PPOD modes provide useful alternative ways to portray the modal characteristics. For example, the wavenumber-frequency spectrum provides a compact visualization of disturbance advection velocity or dispersion. The PPOD properties are considered through the analysis of data from three high Reynolds number advection-dominated flows: an acoustically forced reacting wake, a swirling annular jet, and a jet in cross flow (JICF), and the results are compared with those from space-only POD. In the wake and swirling jet cases, the leading PPOD and space-only POD modes focus on similar features: advecting shear layer structures. However, low-rank approximations of the wake flow, which is characterized by a broad range of spectral and wavenumber content, show clear differences in the methods’ ability to capture the spatial and temporal information. For equal low-rank approximations, space-only POD provides higher-fidelity spatial reconstructions, while PPOD provides higher-order frequency content. In contrast, the leading PPOD and space-only POD modes for the JICF datasets capture different types of flow structures: advecting shear layer vortices (SLVs) and bulk jet flapping, respectively, while the SLVs are spread over lower energy modes in the case of space-only POD. This shows that the s,t inner product allows the PPOD method to directly target the SLVs, despite them containing a smaller fraction of the energy compared to the jet flapping. Additionally, the leading PPOD mode captures key characteristics of the SLV dynamics for each of the JICF cases, including those typical of convectively and globally unstable JICF, as well as intermittent characteristics and minor time-dependent differences or shifts in the dynamics. On the other hand, higher-order space-only POD approximations are required for comparable descriptions of these dynamics, and the rank depends on the operating conditions and stability characteristics of the JICF.

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Direct and Large-Eddy Simulations of Spatially Evolving Supercritical Turbulent Shear Layers

2024-04-27 , Purushotham, Dhruv

A given pure component supercritical fluid at a thermodynamic state in the vicinity of its critical point exhibits significant susceptibility to perturbations in the state. The variation of the thermodynamic and transport properties at these loci are strongly nonlinear as a result of non-negligible intermolecular forces in the fluid. These nonlinearities stress the formulations of existing LES subfilter closures, which are derived based on assumptions that break down at these states. The performance of certain subfilter closures under these conditions is largely unclear and the extension of this argument to multi-component settings adds further uncertainty. The research in this dissertation aims to address a judiciously selected subset of these concerns through a multi-faceted approach based on the joint application of the DNS and LES techniques. Specific outcomes of the research are as follows. First, the DNS data set produced for this work shows that Lagrangian enstrophy is amplified by baroclinicity in an instantaneous sense, and is likely associated with highly-strained local vortical structures. At certain times, the baroclinic contribution can be as much as roughly half the dominant vortex stretching contribution. However, the importance of baroclinicity in the mean diminishes. Enstrophy generation through elemental dilatation is also instantaneously significant, but diminishes in the mean. A detailed analysis of turbulence anisotropy shows that some select points within the shear layer are subject to statistically two, or even one-component turbulence, implying attenuation likely stemming from regions of high density gradient magnitude which are known to appear in systems at these conditions. This is a particular manifestation of the thermo-fluid coupling present in such flows. Comparisons between three LES calculations indicate that coarser grids result in higher shear layer growth rates relative to that predicted by the reference DNS data. An evaluation of turbulent kinetic energy spectra and transport property ratios indicates that this could be a result of over-active subfilter models. Mean molecular transport properties are found to rival their corresponding turbulent analogs, and this is likely a unique behavior due to the thermodynamic setting. The rough equivalence of the molecular transport properties to their turbulent counterparts essentially doubles the action of the diffusive operator in the filtered system of equations, thus imparting additional diffusion to the field. This helps correct for amplified field anisotropies which likely arise not only naturally from the lack of grid resolution at the coarse limit, but also from the presence of regions of high density gradient magnitude which attenuate turbulent fluctuations and inhibit mixing. In this light, the extra diffusion imparted by the models serves as a corrective mechanism, however, it appears that in this thermodynamic setting in the coarse grid limit, the specific models employed ought to be attenuated to some level, given the mismatch in shear layer growth rates. Finally, to isolate and analyze subfilter model performance in a rigorous fashion, an a priori analysis of three classes of subfilter closures is performed. The results indicate that, as expected, the dynamic mixed class of closure performs best. However, quantitative data from this analysis indicates that performing LES using the mixed dynamic closures at grid resolutions 4-5x coarser in each coordinate direction than the required DNS resolution at a given Reynolds number yields acceptable performance. At these resolutions, modeled subfilter stresses remain well correlated with the true subfilter stresses, however, the coarsening represents significant computational savings which can aid engineering design in practical settings. The specific resolution guideline here in particular represents a novel outcome of this research in the area of subfilter modeling for LES.

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Methodological Improvements for the Integration of Spacecraft Trajectory Optimization into Conceptual Space Mission Design

2024-04-27 , Bender, Theresa Elizabeth

As humans continue to send spacecraft further into space and explore uncharted territories, the implementation of space mission design becomes of paramount importance. Trajectory design and optimization is a key element of space mission design that provides information on the specific route a vehicle will take, as well as numerical estimates pertaining to fuel consumption and transfer time. Due to the complexity, high computational costs, and long runtimes of high-fidelity trajectory analyses, less accurate methods are typically used. Low-fidelity estimates provide sufficient accuracy for initial analyses; however, they often lack valuable information about the trajectory that is important to consider during the conceptual design phase. The overall objective of this research is to develop methodological improvements for spacecraft trajectory design and optimization that provide increased flexibility and better enable trajectory considerations to be incorporated into conceptual mission design studies. This research proposes a design space exploration-based approach to the integration of trajectory design and optimization into conceptual space mission design. It aims to provide a strong characterization of the design space and understanding of the problem behavior, as well as be better suited for early phase design studies that possess unknown or evolving mission requirements. The first phase of this research introduces a design of experiments and sensitivity analysis into the traditional trajectory design process in order to identify the behaviors, sensitivities, and trends of trajectory optimization problems. A regression-based approach for the selection of initial guesses is proposed in order to perform more efficient design studies and gain additional insight about the relationships between variables. The second phase of this research investigates the integration of additional evaluation criteria, namely robustness and sensitivity analyses, that are often performed independent of the trajectory design problem. A methodology is proposed for their quantification and integration into design space exploration studies so that they may be analyzed and visualized alongside performance-based metrics. The third phase of this research integrates mission design considerations into this parametric environment through the superimposition of constraints onto the design space, which results in a set of feasible trajectories that meets performance, robustness, stability, and mission design requirements and constraints. The overarching methodology is then applied to a cislunar demonstration in order to illuminate how its application results in trade studies between trajectory design and other mission design considerations that are more comprehensive and flexible than the traditional design approach allows.

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Laser Thomson Scattering Measurements of the Plasma Structure in the Front Pole Region of a Magnetically-shielded Hall Effect Thruster

2024-04-27 , Suazo Betancourt, Jean Luis

Laser Thomson scattering (LTS) is a diagnostic that provides direct access to electron properties in a plasma. This diagnostic is calibrted via laser Raman scattering (LRS). The goal of this thesis was to probe the electron properties in the near field plasma plume of a magnetically shielded (MS) Hall effect thruster (HET), a type of electrostatic electric propulsion device (EP), to provide insight into the applicability of the isothermal magnetic field line model and a notional description of the electron-property-predicted plasma structure traversing the front pole region from the discharge to cathode centerline. To this end, this thesis provides the following contributions: 1. Implementation of a Bayesian analysis and model selection framework for LRS-calibrated LTS diagnostics. 2. Detailed design and implementation of a discharge plasma cell and LTS system for near plasma boundary and laser plasma and laser neutral interactions. 3. Detailed design and implementation of a large vacuum test facility LTS system for measurements in live EP devices benchmarked on a hollow cathode. 4. Detailed upgrade to the large vacuum test facility LTS system for measurements in the near field discharge of a high current density MS HET. Specifically, axially resolved electron property measurements along the discharge channel centerline, spatially resolved method traversing the front pole region from the channel centerline to the cathode centerline, and measurements along two distinct magnetic field lines.

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