The predictive design of fuel injection hardware used for active combustion control is not well established in the gas turbine industry. The primary reason for this is that the underlying mechanisms governing the flow rate authority downstream of the nozzle are not well understood. A detailed investigation of two liquid fuel flow modulation configurations is performed in this thesis: a piston and a throttle-valve configuration. The two systems were successfully built with piezoelectric actuation to drive the prime movers proportionally up to 800 Hz. Discussed in this thesis are the important constituents of the fuel injection system that affect heat release authority: the method of fuel modulation, uncoupled dynamics of several components, and the compressibility of air trapped in the fuel line. Additionally, a novel technique to model these systems by way of one-dimensional, linear transmission line acoustic models was developed to successfully characterize the principle of operation of the two systems. Through these models, insight was gained on the modes through which modulation authority was dissipated and on methods through which successful amplitude scaling would be possible. At high amplitudes, it was found that the models were able to successfully predict the actual performance reasonably well for the piston device. A proportional phase shifting controller was used to test the authority on a 40-kW rig with natural longitudinal modes. Results show that, under limited operating conditions, the sound pressure level at the limit cycle frequency was reduced by about 26 dB and the broadband energy was reduced by 23 dB. Attenuation of the fuel pulse at several combustor settings was due to fluctuating vorticity and temporal droplet distribution effects. / Master of Science

Experiments on the DIII-D device in the negative triangularity (NT) regime of tokamak operation demonstrate core conditions that offer advantageous stability properties. Long duration, stationary discharges in this scenario maintain performance metrics that scale to viable reactor gain. Deleterious global modes of toroidal mode number n=1 are infrequent in these plasmas, which operate free of core instability cycles that can kick off global instabilities. These plasmas operate free of edge instability cycles that would damage reactor components, as do all strongly shaped NT plasmas. Reproducible access to high-power stationary states was developed at two values of q95, the edge magnetic winding number or “safety factor”. Core MHD instabilities manifest in one form of internal ideal mode, the quasi-interchange mode (QI), found to be consistent with modeling of the profiles and parameter space in which NT operates. The GATO and DCON ideal MHD codes are used to characterize the limits to normalized pressure in NT, finding global kink modes with strong poloidal harmonic m=1,2 components at normalized plasma pressure βN=3-3.5. Limits to β_N are predicted to be mostly insensitive to plasma boundary shape in NT and similar at both q95 values obtained in experiments. Average triangularity is shown to affect ideal limits, when modified at the outer midplane. A similar result is obtained with the RDCON resistive MHD code, which is used to characterize the stability to resistive “tearing modes”. Experimental NT equilibria and equilibria across shape scans were investigated. Only outer midplane modifications affected tearing calculations. Ideal kink modeling and experimental observations of sporadic QI mode provide an explanation for current diffusion not predicted by neoclassical theory. This effect is found in experiments at q95=3, analyzed with the ONETWO transport code’s facility to evolve magnetic flux over a discharge consistently with measured profiles and reconstructed magnetic flux surfaces. This result is compared with GATO calculations and ONETWO flux diffusion analysis of a conventional shape, ITER baseline demonstration discharge that is shown to have an intrinsically 3D core. Radiation from accumulated plasma impurities seems to alter the core q profile. This makes unstable a QI mode that spurs formation of a helical core, sustained by anomalous magnetic flux diffusion. NT experiments at q95=4 are limited in energy confinement by poor fast ion confinement, as a result of nondisruptive core 3/2 tearing modes. Analysis with ONETWO shows agreement with neoclassical flux diffusion predictions in these cases, corresponding to a removal of core instabilities and elevation of minimum safety factor values qmin to unity. This understanding of the core MHD, performance, and operational limits of NT scenarios in DIII-D advances the development of negative triangularity scenarios and informs the core phenomena observed in experiments spanning the regime.

Lean, premixed combustion has enjoyed increased application due to the need to reduce pollutant emissions. Unfortunately, operating the flame at lean conditions increases susceptibility to thermoacoustic (TA) instability. Self-excited TA instabilities are a result of the coupling of the unsteady heat release rate of the flame with the acoustics of the combustion chamber. The result is large pressure oscillations that degrade performance and durability of combustion systems. Industry currently has no reliable tool to predict instabilities a priori. CFD simulations of full-scale, turbulent, reacting flows remain unrealizable. The work in this paper is part of a study that focuses on developing compact models of TA instabilities, i.e. acoustics and flame dynamics. Flame dynamics are defined as the response in heat release to acoustic perturbations. Models of flame dynamics can be coupled with models of combustor enclosure acoustics to predict TA instabilities. In addition, algorithms to actively control instabilities can be based on these compact models of flame dynamics and acoustics. The work outlined in this thesis aims at determining the flame dynamics model experimentally. Velocity perturbations are imparted on laminar and turbulent flames via a loudspeaker upstream of the flame. The response of the flame is observed through two measurements. Hydroxyl radical (OH*) chemiluminescence indicates the response in chemical reaction rate. Tunable Diode Laser Absorption Spectroscopy (TDLAS), centered over two water absorption features, allows a dynamic measurement of the product gas temperature. The response in product gas temperature directly relates to the enthalpy fluctuations that couple to the acoustics. Experimental frequency response functions of a laminar, flat-flame burner and a turbulent, swirl-stabilized combustor will be presented as well as empirical low-order models of flame dynamics. / Master of Science

Increasing concerns over the condition of our environment and its long term health have led to the development of greener combustion techniques for use in turbomachinery applications. Lean Direct Injection is an active area of research for how fuel is introduced and burned in the combustor section of a jet engine or land based liquid fuel turbine. Overall lean combustion results in lower NOx emmisions while direct injection insures shorter combustor lengths. Lean Direct Injection and other lean burning combustor designs are susceptible to thermoacoustic instabilities. The SARA or Synchronously Actuated Response Atomizer is a liquid fuel atomizer and supply system designed to allow for the active control of droplet size, cone angle, and mass flow rate. These three parameters have been shown to be important in controlling combustion quality and heat release. This research investigates the capabilities of the SARA design in a series of non-reacting tests. Static and Dynamic tests were performed on the SARA nozzle with a maximum actuation of 400 Hz. Also, a novel use of hot-film anemometry was developed to measure the dynamic flow rate fluctuations. / Master of Science

In order to predict the linear stability of combustion systems in industrial-scale gas turbines, a stability analysis was completed using models generated for each of the major dynamic components. Changes in the combustion process of gas turbines to reduce emissions has resulted in large amplitude pressure oscillations associated with a coupling between the natural acoustic modes of the combustor and the unsteady heat release from the flame. Detailed models of the acoustics and the heat release processes were created and assembled, with a time delay element and the appropriate scaling, into a system block diagram to investigate the stability of the system using linear system theory. Wherever possible the analytical models were validated with experimental data. The main goal of this work was to create a design methodology which could be used by industry to predict where instabilities were likely to occur during the design phase. Results show that the system based stability analysis can predict some of the instability frequencies seen in the experimental data, but more refined models are needed to predict every instability. Future work will involve designing experiments to validate and refine the dynamic models already developed. / Master of Science

Investigating the mechanical dynamics of bacterial motility has led to a deeper understanding of the behaviors and lifecycle of many bacterial species. We discuss chain driven sliding motility where the bacteria maintain connections between daughter cells following division, resulting in long chains that expand across the viscous substrate. These chains grow exponentially, suggesting the chain tips may accelerate to very fast speeds. We devise multiple mathematical frameworks encapsulating the key physical dynamics and interactions to investigate the dynamics of bacterial chains and the biological implications of this motility. Our first framework, the rigid rod model, provides a set of equations describing the chain growth dynamics. Analysis of these equations reveals the stress maintaining cell-cell linkages increases unsustainably at an exponential rate. We devise a perturbation analysis of the rigid rod model in order to predict the critical stress associated with mechanical failure of these linkages. A phenomenological population model reveals that repeated chain breakages limit the expansion of the entire population to linear growth. Through experimental observation and computer simulations, we identify two key mechanical instabilities that emerge in growing bacterial chains. The first is sharp localized kinking that leads to the chain breakage mentioned above. In the second dynamic, the chain buckles due to compressive drag forces resulting in the emergence of large curvatures throughout the chain. We devise a continuum mechanics framework to examine the curvature dynamics in the growing chain. Through linear stability analysis of the rigid rod model and the continuum mechanics framework, we predict the dominant instability dynamic based on the physical properties of the chain and its environment. We use rigid rod model simulations to investigate the biological implications of these dynamics. Lastly, we introduce a number of methods that extend the rigid rod model to allow for the investigation of interacting chains. We consider methods that implement forces due to the entanglement of cell body appendages as well as collision dynamics. In total these models provide generic frameworks for investigating mechanical dynamics of growing bacterial chains. Our models provide testable predictions and suggest biological motivations for the typical behaviors that are observed in these cell chains. / Doctor of Philosophy / Motility is crucial in the life of many bacterial species. Effective motility allows bacteria to obtain nutrients and avoid dangerous hazards. Since motility is such an important part of bacterial survival, understanding bacterial motility has strong implications in bacterial control and utilization. We consider a motility in which the bacteria move by forming long, often straight chains of many cell bodies that expand across the surface. This is known as chain-mediated sliding motility and can allow the bacteria to move at very high speeds. We present multiple physics based mathematical frameworks that provide the tools to investigate chain-mediated sliding motility. These frameworks are generic and can be applied to study any bacterial species that use chain growth as a means for motility. Using these tools, we learn the speed at which these chains can expand is limited by the mechanical strength of the linkages connecting adjacent cells with in the chain. This limitation means the chains will repeatedly break into shorter chains, a pattern that limits the speed at which the entire bacterial population can expand. Additionally, we discover two interesting behaviors exhibited by these bacterial chains, one in which the chain kinks before breaking into two shorter chains, and a second in which the chain buckles, resulting in curved chains. We apply our mathematical frameworks to determine how the physical conditions dictate which of these two behaviors will emerge and learn the chains may curve and bend as a means to avoid breaking. Lastly we introduce additional methods that extend these frameworks to allow for investigating the behavior of the bacteria when multiple chains interact with one another. The mathematical frameworks we present allow for investigation into the specific mechanical properties that make chain growth possible as well as the mechanics that limit its efficiency. The models also give insight into the biological impact of this motility, suggesting how it affects the growth-coupled spreading of an entire bacterial population.

The persistent thrust for a cleaner, greener environment has prompted air pollution regulations to be enforced with increased stringency by environmental protection bodies all over the world. This has prompted gas turbine manufacturers to move from non-premixed combustion to lean, premixed combustion. These lean premixed combustors operate quite fuel-lean compared to the stochiometric, in order to minimize CO and NOx productions, and are very susceptible to oscillations in any of the upstream flow variables. These oscillations cause the heat release rate of the flame to oscillate, which can engage one or more acoustic modes of the combustor or gas turbine components, and under certain conditions, lead to limit cycle oscillations. This phenomenon, called thermoacoustic instabilities, is characterized by very high pressure oscillations and increased heat fluxes at system walls, and can cause significant problems in the routine operability of these combustors, not to mention the occasional hardware damages that could occur, all of which cumulatively cost several millions of dollars. In a bid towards understanding this flow-flame interaction, this research works studies the heat release response of premixed flames to oscillations in reactant equivalence ratio, reactant velocity and pressure, under conditions where the flame preheat zone is convectively compact to these disturbances, using the G-equation. The heat release response is quantified by means of the flame transfer function and together with combustor acoustics, forms a critical component of the analytical models that can predict combustor dynamics. To this end, low excitation amplitude (linear) and high excitation amplitude (nonlinear) responses of the flame are studied in this work. The linear heat release response of lean, premixed flames are seen to be dominated by responses to velocity and equivalence ratio fluctuations at low frequencies, and to pressure fluctuations at high frequencies which are in the vicinity of typical screech frequencies in gas turbine combustors. The nonlinear response problem is exclusively studied in the case of equivalence ratio coupling. Various nonlinearity mechanisms are identified, amongst which the crossover mechanisms, viz., stoichiometric and flammability crossovers, are seen to be responsible in causing saturation in the overall heat release magnitude of the flame. The response physics remain the same across various preheat temperatures and reactant pressures. Finally, comparisons between the chemiluminescence transfer function obtained experimentally and the heat release transfer functions obtained from the reduced order model (ROM) are performed for lean, CH4/Air swirl-stabilized, axisymmetric V-flames. While the comparison between the phases of the experimental and theoretical transfer functions are encouraging, their magnitudes show disagreement at lower Strouhal number gains show disagreement.

In the mid-1920s, the great Albert Einstein proposed that at extremely low temperatures, a gas of bosonic particles will enter a new phase where a large fraction of them occupy the same quantum state. This state would bring many of the peculiar features of quantum mechanics, previously reserved for small samples consisting only of a few atoms or molecules, up to a macroscopic scale. This is what we today call a Bose-Einstein condensate. It would take physicists almost 70 years to realize Einstein's idea, but in 1995 this was finally achieved. The research on Bose-Einstein condensates has since taken many directions, one of the most exciting being to study their behavior when they are placed in optical lattices generated by laser beams. This has already produced a number of fascinating results, but it has also proven to be an ideal test-ground for predictions from certain nonlinear lattice models. Because on the other hand, nonlinear science, the study of generic nonlinear phenomena, has in the last half century grown out to a research field in its own right, influencing almost all areas of science and physics. Nonlinear localization is one of these phenomena, where localized structures, such as solitons and discrete breathers, can appear even in translationally invariant systems. Another one is the (in)famous chaos, where deterministic systems can be so sensitive to perturbations that they in practice become completely unpredictable. Related to this is the study of different types of instabilities; what their behavior are and how they arise. In this thesis we compare classical and quantum mechanical nonlinear lattice models which can be applied to BECs in optical lattices, and also examine how classical nonlinear concepts, such as localization, chaos and instabilities, can be transfered to the quantum world.

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