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This thesis is a numerical study of the coupled Burgers equation. The coupled Burgers equation is motivated by the Boussinesq equations that are often used to model the thermal-fluid dynamics of air in buildings. We apply Finite Element Methods to the coupled Burgers equation and conduct several numerical experiments. Based on these results, the Group Finite Element method (GFE) appears to be more stable than the standard Finite Element Method. The design and implementation of controllers heavily relies on rapid solutions to complex models such as the Boussinesq equations. Thus, we further examine the feasibility and efficiency of the Proper Orthogonal Decomposition (POD) for the coupled Burgers equation. Using POD, we reduce the system to a "minimal" number of ODE's and conduct numerous numerical studies comparing the POD and GFE method. Further numerical experiments consider an application where the dynamics are projected on a POD basis and then the governing parameters of the system are varied. / Master of Science

Modern gas turbine combustors implement lean premixed (LPM) combustion system to reduce the formation of NOx pollutants. LPM technology has advanced to have the ability to produce extremely low level of NOx emissions. The current focus of research on LPM is focused on reducing the NOx emission to much smaller scales, which is mandated because of the stricter regulations and environmental concerns. However, LPM combustors are susceptible to lean blowout (LBO), and other corresponding instabilities as the combustor is operated lean. Therefore, it is essential to understand the LBO limits and dynamics of flow in lean operating conditions. One of the other primary parameters for the improved combustion chamber designs is an accurate characterization of the heat loads on the liner walls in the wide range of operating conditions. Currently, there are very limited studies on the flame side heat transfer in reacting conditions. Current gas turbine combustion technology primarily focuses on burning natural gas as the gas fuel option for industrial systems. However, interest in utilizing additional options due to environmental regulations as well as concerns about energy security have motivated interest in using fuel gases that have blends of Methane, Propane, H2, CO, CO2, and N2. For example, fuel blends of 35%/60% to 55%/35% of CH4/CO2 are typically seen in Landfill gases. Syngas fuels are typically composed primarily of H2, CO, and N2. Gases from anaerobic digestion of sewage, used commonly in wastewater treatment plants, usually have 65–75% CH4 with the balance being N2. The objective of this study is to understand the LBO limits and the effects of the instabilities that arise (called near blowout oscillations) as the combustor is operated lean. Near blowout oscillations arise as the equivalence ratio is reduced. These oscillations are characterized by continuous blowout and re-ignition events happening at low frequencies. The low-frequency oscillations have very high-pressure amplitude and can potentially damage the liner wall. The impact of the near blowout oscillations on the flow field and heat transfer on the liner walls are studied. To accomplish this, the experiments were conducted at Advanced Propulsion and Power laboratory located at Virginia Tech. A lean premixed, swirl stabilized fuel nozzle designed with central pilot hub was used for the study. Additionally, this work also studies the lean blowout limits with fuel blends of CH4-C3H8, CH4-CO2, and CH4-N2 and also their effect on the stability limits as the pilot fuel percentage was changed. Flow field during near blowout oscillations was studied using planar particle image velocimetry (PIV) and flame shapes and locations during these oscillations was studied by using high-speed imaging of the flame. A statistical tool called proper orthogonal decomposition (POD) was utilized to post-process the PIV data and high-speed imaging data. Heat transfer on the liner walls was studied using a transient IR thermography methodology. The heat transfer on the liner wall during the near blowout instabilities was resolved. LBO limits and near blowout oscillations were characterized by studying the pressure measurements in the primary combustor region. Fluctuating heat loads on the liner walls with the same frequency as that of near blowout instabilities was observed. The magnitude of fluctuation was found to be very high. Phase sorted POD reconstructed flame images demonstrated the location of the flame during near blowout oscillations. Thus, blowout and re-ignition events are resolved from the high-speed flame images. POD reconstructed flow field from the PIV data demonstrated the statistically significant flow structures during near blowout oscillations. A hypothesis for the mechanism of near blowout oscillations was explained based on the measurements and observations made. Lean Blowout limits (LBO) changed when the percentage of pilot and air flow rates was changed. As the pilot percentage increased, LBO limits improved. Results on the study of fuel mixtures demonstrate that the addition of propane, nitrogen and carbon dioxide has minimal effect on when the flame becomes unstable in lean operating conditions. However, on the other hand, the addition of diluent gas showed a potential blowout at higher operating conditions. It was also observed that Wobbe index might not be a good representation for fuels to study the fuel interchangeability in lean operating conditions. / Ph. D.

Une des pistes majeures pour obtenir des turbines à gaz moins polluantes est l'utilisation de chambres de combustion fonctionnant en régime prémélangé pauvre. Cependant, dans de tels régimes de fonctionnement, la flamme obtenue est cependant plus facilement sujette aux instabilités thermo-acoustiques.Dans cette thèse, un brûleur étagé swirlé fonctionnant au propane a été employé pour illustrer une méthode d'analyse de la combustion prémélangée. Cette installation a été étudiée à l'aide de diagnostics classiques (micros, PLIF, film à haute cadence de la flamme).La stratégie de post-traitement développée dans cette thèse utilise par contre des outils eux aussi classiques (PSD, moyenne de phase) mais aussi une méthode d'analyse avancée, la Décomposition en Modes Dynamiques. Celle-ci est notamment étudiée em détail afin d'en cerner les avantages et les limitations dans le cadre de l'analye des instabilités de combustion. / One of the major ways of reducing pollutant emissions in gas turbines is using combustion chambers with lean premixed mixtures. However, in such operating conditions the flame is more susceptible to thermo-acoustic instabilities. In the present work, a propane-fed swirled burner using two injection stages is used to illustrate a post-processing strategy for premixed combustion analysis. This model burner has been studied using classic diagnostics (microphones, PLIF, highspeed imaging).The strategy developed in the present work uses both classic postprocessing tools (PSD, phase averaging) and an advanced method, the Dynamic Mode Decomposition. In particular, this method is studied in detail and compared to more lassic ones in order to clearly point its advantages as well as its shortcomings when used to study combustion instabilities.

L’objectif est de développer et de tester des instruments peu côuteux pour la simulation, l’estimation et le contrôle d’écoulements. La décomposition orthogonale aux valeurs propres (POD) et une projection de Galerkin des équations sur les modes POD sont utilisées pour construire des modèles d’ordre réduit des équations de Navier-Stokes incompressibles. Dans ce travail, un écoulement autour d’un cylindre carré est considéré en configuration bidimensionnelle et tridimensionnelle. Des actionneurs de soufflage/aspiration sont placés sur la surface du cylindre. Quelques techniques de calibration sont appliquées, fournissant des modèles précis, même pour les écoulements tridimensionnels avec des structures tourbillonaires compliquées. Une méthode d’estimation d’état, impliquant des mesures, est ensuite mise au point pour des écoulements instationnaires. Une calibration multi-dynamique et des techniques d’échantillonnage efficaces sont appliquées, visant à construire des modèles robustes à des variations des paramètres de contrôle. Nous amorçons une analyse de stabilité linéaire en utilisant des modèles d’ordre réduit linéarisés autour d’un état d’équilibre contrôlé. Les techniques présentées sont appliquées à écoulements autour du cylindre carré à des nombres de Reynolds compris entre Re = 40 et Re = 300. / The aim is to develop and to test tools having a low computational cost for flow simulation, estimation and control applications. The proper orthogonal decomposition (POD) and a Galerkin projection of the equations onto the POD modes are used to build low order models of the incompressible Navier-Stokes equations. In this work a flow past a square cylinder is considered in two-dimensional and three-dimensional configurations. Two blowing/suction actuators are placed on the surface of the cylinder. Calibration techniques are applied, providing stable and rather accurate models, even for three-dimensional wake flows with complicated patterns. A state estimation method, involving flow measurements, is then developed for unsteady flows. Multi-dynamic calibrations and efficient sampling techniques are applied to build models that are robust to variations of the control parameters. A linear stability analysis by using linearized low order models around a controlled steady state is briefly addressed. The presented techniques are applied to the square cylinder configuration at Reynolds numbers that range between Re = 40 and Re = 300.

The Naval Postgraduate School is currently developing their first CubeSat, the Solar Cell Array Tester CubeSat, or NPS-SCAT. Launching a CubeSat, such as NPS-SCAT, requires environmental testing to ensure not only the success of the mission, but also the safety of other CubeSats housed in the same deployer. This thesis will address the development of CubeSat vibration testing methodology at NPS, including subsystem testing, engineering unit qualification, and flight unit testing. In addition, the new Cal Poly CubeSat Test POD Mk III will be introduced and evaluated based upon comparison with the Poly Picosatellite Orbital Deployer (P-POD). Using examples from the development of NPS-SCAT and test data from Cal Poly’s Test POD Mk III and P-POD, the current CubeSat testing methodology will be verified and an improved method for NPS CubeSat subsystem testing will be presented.