The capability to perform rendezvous and proximity operations about space objects is central to the next generation of space situational awareness. The ability to diagnose and respond to spacecraft anomalies is often hampered by the lack of capability to perform inspection or testing on the target vehicle in flight. While some limited ability to perform inspection can be provided by an extensible boom, such as the robotic arms deployed on the space shuttle and space station, a free-flying companion vehicle provides maximum flexibility of movement about the target. Safe and efficient utilization of a companion vehicle requires trajectories capable of minimizing spacecraft resources, e.g., time or fuel, while adhering to complex path and state constraints. This paper develops an efficient solution method capable of handling complex constraints based on a grid search A* algorithm and compares solution results against a state-of-the-art nonlinear optimization method. Trajectories are investigated that include nonlinear constraints, such as complex keep-out-regions and thruster plume impingement, that may be required for inspection of a specific target area in a complex environment. This work is widely applicable and can be expanded to apply to a variety of satellite relative motion trajectory planning problems. / The capability to perform rendezvous and proximity operations about space objects is central to the next generation of space situational awareness. The ability to diagnose and respond to spacecraft anomalies is often hampered by the lack of capability to perform inspection or testing on the target vehicle in flight. While some limited ability to perform inspection can be provided by an extensible boom, such as the robotic arms deployed on the space shuttle and space station, a free-flying companion vehicle provides maximum flexibility of movement about the target. Safe and efficient utilization of a companion vehicle requires trajectories capable of minimizing spacecraft resources, e.g., time or fuel, while adhering to complex path and state constraints. This paper develops an efficient solution method capable of handling complex constraints based on a grid search A* algorithm and compares solution results against a state-of-the-art nonlinear optimization method. Trajectories are investigated that include complex nonlinear constraints, such as complex keep-out-regions and thruster plume impingement, that may be required for inspection of a specific target area in a complex environment. This work is widely applicable and can be expanded to apply to a variety of satellite relative motion trajectory planning problems. / Master of Science / The ability of one satellite to perform actions near a second space satellite or other space object is important for understanding the space environment and accomplishing space mission goals. The development of a method to plan the path that one satellite takes near a second satellite such that fuel usage is minimized and other constraints satisfied is important for accomplishing mission goals. This thesis focuses on developing a fast solution method capable of handling complex constraints that can be applied to plan paths satellite relative motion operations. The solution method developed in this thesis is then compared to an existing solution method to determine the efficiency and accuracy of the method.

Les satellites sont mis en orbite en utilisant des lanceurs dont la conception est une des activités principales d’Airbus Defence and Space. Pour ce faire, se baser sur des expériences n’est pas facile : les souffleries ne permettent pas d’évaluer toutes les situations auxquelles un lanceur est confronté au cours de sa mission. La simulation numérique est donc essentielle pour l’industrie spatiale. Afin de disposer de simulations toujours plus fidèles, il est nécessaire d’utiliser des supercalculateurs de plus en plus puissants. Cependant, ces machines voient leur complexité augmenter et pour pouvoir exploiter leur plein potentiel, il est nécessaire d’adapter les codes existants. Désormais, il semble essentiel de passer par des couches d’abstraction afin d’assurer une bonne portabilité des performances. ADS a développé depuis plus de 20 ans le code FLUSEPA qui est utilisé pour le calcul de phénomènes instationnaires comme les calculs d’onde de souffle au décollage ou les séparations d’étages. Le solveur aérodynamique est basé sur une formulation volume fini et une technique d’intégration temporelle adaptative. Les corps en mouvement sont pris en compte via l’utilisation de plusieurs maillages qui sont combinés par intersections.Cette thèse porte sur la parallélisation du code FLUSEPA. Au début de la thèse, la seule version parallèle disponible était en mémoire partagée. Une première version parallèle en mémoire distribuée a d’abord été réalisée. Les gains en performance de cette version ont été évalués via l’utilisation de deux cas tests industriels. Un démonstrateur du solveur aérodynamique utilisant la programmation par tâche au dessus d’un runtime a aussi été réalisé. / There are different kinds of satellites that offer different services like communication, navigationor observation. They are put into orbit through the use of launchers whose design is oneof the main activities of Airbus Defence and Space. Relying on experiments is not easy : windtunnel cannot be used to evaluate every critical situation that a launcher will face during itsmission. Numerical simulation is therefore mandatory for spatial industry.In order to have more reliable simulations, more computational power is needed and supercomputersare used. Those supercomputers become more and more complex and this impliesto adapt existing codes to make them run efficiently. Nowadays, it seems important to rely onabstractions in order to ensure a good portability of performance. Airbus Defence and Spacedeveloped for more than 20 years the FLUSEPA code which is used to compute unsteady phenomenalike take-off blast wave or stage separation. The aerodynamic solver relies on a finitevolume formulation and an explicit temporal adaptive solver. Bodies in relative motion are takeninto account through the use of multiple meshes that are overlapped.This thesis is about the parallelization of the FLUSEPA code. At the start of the thesis,the only parallel version available was in shared memory through OpenMP. A first distributedmemory version was realized and relies on MPI and OpenMP. The performance improvementof this version was evaluated on two industrial test cases. A task-based demonstrator of theaerodynamic solver was also realized over a runtime system.

Future generations of unmanned spacecraft, aircraft, ground, and submersible vehicles will require precise relative navigation capabilities to accomplish missions such as formation operations and autonomous rendezvous and docking. The development of relative navigation sensing and control techniques is quite challenging, in part because of the difficulty of accurately simulating the physical relative navigation problems in which the control systems are designed to operate. A hardware testbed that can simulate the complex relative motion of many different relative navigation problems is being developed. This testbed simulates near-planar relative motion by using software to prescribe the motion of an unmanned ground vehicle and provides the attached sensor packages with realistic relative motion. This testbed is designed to operate over a wide variety of conditions in both indoor and outdoor environments, at short and long ranges, and its modular design allows it to easily test many different sensing and control technologies. / Master of Science

Coulomb forces acting between close flying charged spacecraft provide near zero propellant relative motion control, albeit with added nonlinear coupling and limited controllability. This novel concept has numerous potential applications, but also many technical challenges. In this dissertation, two- and three-craft Coulomb formations near GEO are investigated, using a rotating Hill frame dynamical model, that includes Debye shielding and differential gravity. Aspects of dynamical systems theory and optimization are applied, for insights regarding stability, and how inherent nonlinear complexities may be beneficially exploited to maintain and maneuver these electrostatic formations. Periodic relative orbits of two spacecraft, enabled by open-loop charge functions, are derived for the first time. These represent a desired extension to more substantially studied, constant charge, static Coulomb formations. An integral of motion is derived for the Hill frame model, and then applied in eliminating otherwise plausible periodic solutions. Stability of orbit families are evaluated using Floquet theory, and asymptotic stability is shown unattainable analytically. Weak stability boundary dynamics arise upon adding Coulomb forces to the relative motion problem, and therefore invariant manifolds are considered, in part, to more efficiently realize formation shape changes. A methodology to formulate and solve two-craft static Coulomb formation reconfigurations, as parameter optimization problems with minimum inertial thrust, is demonstrated. Manifolds are sought to achieve discontinuous transfers, which are then differentially corrected using charge variations and impulsive thrusting. Two nonlinear programming algorithms, gradient and stochastic, are employed as solvers and their performances are compared. Necessary and sufficient existence criteria are derived for three-craft collinear Coulomb formations, and a stability analysis is performed for the resulting discrete equilibrium cases. Each specified configuration is enabled by non-unique charge values, and so a method to compute minimum power solutions is outlined. Certain equilibrium cases are proven maintainable using only charge control, and feedback stabilized simulations demonstrate this. Practical scenarios for extending the optimal reconfiguration method are also discussed. Lastly, particular Hill frame model trajectories are integrated in an inertial frame with primary perturbations and interpolated Debye length variations. This validates qualitative stability properties, reveals particular periodic solutions to exhibit nonlinear boundedness, and illustrates higher-fidelity solution accuracies. / text

This dissertation presents results from a thorough study of the tip-gap turbulent flow structure in a low-speed linear compressor cascade wind tunnel at Virginia Tech that includes a moving belt system to simulate the relative motion between the tip and the casing. The endwall pressure measurements and the surface oil flow visualizations were made on a stationary endwall to obtain the flow features and to determine the measurement profiles of interest. A custom-made miniature 3-orthogonal-velocity-component fiber-optic laser-Doppler velocimetry (LDV) system was used to measure all three components of velocity within a 50 mm spherical measurement volume within the gap between the endwall and the blade tip, mainly for the stationary wall with 1.65% and 3.30% tip gaps as well as some initial experiments for the moving wall. Since all of the vorticity in a flow originates from the surfaces under the action of strong pressure gradient, it was very important to measure the nearest-wall flow on the endwall and around the blade tip. The surface skin friction velocity was measured by using viscous sublayer velocity profiles, which verified the presence of an intense lateral shear layer that was observed from surface oil flow visualizations. All second- and third-order turbulence quantities were measured to provide detailed data for any parallel CFD efforts. The most complete data sets were acquired for 1.65% and 3.30% tip gap/chord ratios in a low-speed linear compressor cascade. This study found that tip gap flows are complex pressure-driven, unsteady three-dimensional turbulent flows. The crossflow velocity normal to the blade chord is nearly uniform in the mid tip-gap and changes substantially from the pressure to suction side. The crossflow velocity relies on the local tip pressure loading that is different from the mid-span pressure loading because of tip leakage vortex influence. The tip gap flow is highly skewed three-dimensional flow throughout the full gap. Normalized circulation within the tip gap is independent of the gap size. The tip gap flow interacts with the primary flow, separates from the endwall, and rolls up on the suction side to form the tip leakage vortex. The tip leakage vortex is unsteady from the observation of the TKE transport vector and oil flow visualizations. The reattachment of tip separation vortex on the pressure side strongly depends on the blade thickness-to-gap height ratio after the origin of tip leakage vortex but is weakly related to it before the origin of tip leakage vortex for a moderate tip gap. Other than the nearest endwall and blade tip regions, the TKE does not vary much in tip gap. The tip leakage vortex produces high turbulence intensities. The tip gap flow correlations of streamwise and wall normal velocity fluctuations decrease significantly from the leading edge to the trailing edge of the blade due to flow skewing. The tip gap flow is a strongly anisotropic turbulent flow. Rapid distortion ideas can not apply to it. A turbulence model based on stress transport equations and experimental data is necessary to reflect the tip gap flow physics. For the moving endwall, relative motion skews the inner region flow and is decorrelated with the outer layer flow. Hence, the TKE and correlations of streamwise and wall normal velocity fluctuations decrease. / Ph. D.