Increasingly stringent emissions regulations have led combustion system designers to look for more environmentally combustion strategies. For gas turbine combustion, one promising technology is lean premixed combustion, which results in lower flame temperatures and therefore the possibility of significantly reduced nitric oxide emissions. While lean premixed combustion offers reduced environmental impacts, it has been observed to experience increased possibility of the occurrence of combustion instabilities, which may damage hardware and reduce efficiency. Thermoacoustic combustion instabilities occur when oscillations in the combustor acoustics and oscillations in the flame heat release rate form a closed feedback loop, through one of two possible mechanisms. The first is direct coupling which occurs due to the mean mass flow oscillations induced by the acoustic velocity. Secondly, the acoustics may couple with the flame due to acoustic interactions with fuel/air mixing, resulting in an oscillating equivalence ratio. Only velocity coupling was considered in this study. The methodology used in this study is analysis of instabilities through linear systems theory, requiring knowledge of the individual transfer functions making up the closed-loop system. Methods already exist by which combustor acoustics may be found. However, significant gaps still remain in knowledge of the nature of flame dynamics. Prior knowledge in literature about the flame transfer function suggests that the flame behaves as a low-pass filter, with cutoff frequency on the order of hundreds of hertz. Nondimensionalization of the frequency by flame length scales has been observed to result in a convenient scaling for the flame transfer function, suggesting that the flame dynamics may be dominated by spatial effects. This work was proposed in two parts to extend and apply the body of knowledge on flame dynamics. The phase one goal of this study was to further understand this relationship between the flame heat release rate dynamics and the dynamics of the reaction zone size. The second goal of this work was to apply this flame transfer function knowledge to predictions of instability, validated against measurements in an unstable combustor. Both of these goals meet an existing practical need, providing a design tool for prediction of potential thermoacoustic instabilities in a combustor at the design stage.Measurements of the flame transfer function were made in a swirl-stabilized, lean-premixed combustor. The novel portion of these measurements was the inclusion of spatial resolution of the heat release rate dynamics. By using a speaker, a sine dwell excitation to the velocity was introduced over the range of 10-400Hz. Measurements were then made of the input (inlet velocity) and output (heat release rate, or flame size) resulting in the flame transfer function. The spatial dynamics measurement was approached through several measures of the flame size: the volume and offset distance to the center of the heat release. Each was obtained from deconvoluted, phase averaged images of the flame, referenced to the speaker excitation signal. The results of these measurements showed that the spatial dynamics for each of these three measures were virtually identical to the heat release rate dynamics. This suggests a quite important result, namely that the flame heat release rate dynamics are completely determined by the dynamics of the flame structure. Therefore, prediction of flow structure interaction with the flame distribution is crucial to predict the dynamics of the flame. These spatially resolved transfer function measurements were used in conjunction with the linear closed-loop model to make predictions of instability. These predictions were made by applying the Bode stability criterion to the open-loop system transfer function. This criterion states that instabilities may occur at frequencies where the heat release rate and acoustic oscillations occur in phase and the system gain has a value greater than unity. Performing this analysis on the combined system transfer function yielded results that agreed quite well with actual instability measurements made in the combustor. Closed-loop predictions identified two possible modes for instability, both of which were observed experimentally. One mode resulted from an acoustic peak around 160 Hz, and occurred at lean equivalence ratios. A second mode occurred at lower frequencies (100-150 Hz) and was associated with the increase in flame transfer function gain at increasing equivalence ratios. These are some of the first successful predictions of combustion instability based on linear systems theory. When multiple modes were predicted, it was assumed that if non-linear effects were to be considered, the lower frequency mode would become the dominant mode at these operating conditions due to its higher gain margin. Also of note is that in the practical system, high frequency oscillations are observed, but not predicted, associated with harmonics of the low frequency mode due to the linear nature of the predictions. While these non-linear effects are not captured, the linear predictive capability is thought to be most important, as from a practical perspective, instabilities should be avoided altogether. The primary findings of this study have significant applications to modeling and prediction of combustion dynamics. The classic heat release rate flame transfer function was observed to coincide almost exactly with the flame size transfer functions. The time scales observed in these transfer functions correspond to convective length scales in the combustor, suggesting a fluid mechanical basis of the heat release rate response. Additionally, linear systems theory predictions of instability based on the measured flame transfer functions were proved capable of capturing the stability of the actual combustor with a reasonable degree of accuracy. These predictions should have considerable application to design level avoidance of combustion instability in practical systems. / Ph. D.

General unsymmetric laminates exhibit large natural curvatures at room temperature. Additionally, inherent to most unsymmetric laminates is the presence of two stable configurations. Multiple configurations and stability issues arise because of the geometric nonlinearities associated with the large curvatures. The laminate can be changed from one stable configuration to the other by a simple snap-through action. This situation offers the opportunity to use shape memory alloys (SMA) attached to the laminate to generate the snap-through forces and change the shape of the laminate on command. Presented is a model which can predict SMA-induced deformations in general unsymmetric laminates and, particularly, the occurrence of the snap through. First, a methodology is developed to predict the deformations of flat general unsymmetric epoxy-matrix composite laminates as they are cooled from their elevated cure temperature. Approximations to the strain fields are used in the expression for the total potential energy, and the Rayleigh-Ritz approach is used to study equilibrium. To further study the laminate deformations, finite-element analyses are performed. Experimental results are presented which confirm the predictions of the developed theory and the finite-element analyses regarding the existence of multiple solutions and the magnitude of the deformations. Results are compared with those of several other investigators. Next, the deformation behavior of general unsymmetric laminates subjected to applied forces is studied. The principle of virtual work is used to derive the equilibrium equations relating the laminate deformations to the applied forces. By solving the equilibrium equations as a function of the force level, relations between the laminate deformations and the applied force are derived, and the force level at which the laminate changes shape is determined. Finally, an existing SMA constitutive model is implemented into the developed theory to predict the deformations of simple structures to SMA-induced forces. Experiments on a narrow aluminium plate with an externally attached SMA actuator are conducted. The experimental results show good agreement with the predictions from the developed theory. Next, the deformation behavior of general unsymmetric laminates subjected to SMA actuators is predicted using the developed theory. Experiments using SMA actuators to generate the snap through of nsymmetric laminates are conducted. Good correlation with the developed theory is obtained. / Ph. D.

The current driven electrothermal instability (ETI) forms when the material resistivity is temperature dependent, occurring in nearly all Z-pinch-like high energy density platforms. ETI growth for high-mass density materials is predominantly striation form which corresponds to magnetically perpendicular mode growth. The striation form is caused by a resistivity that increases with temperature, which is often the case for high-mass density materials. In contrast, low-density ETI growth is mainly filamentation form, magnetically aligned modes, because the resistivity tends to decrease with temperature. Simulating ETI is challenging due to the coupling of magnetic field transport to equation of state over a large region of state space spanning solids to plasmas. This dissertation presents a code-code verification study to effectively model the ETI. Specifically, this study provides verification cases which ensure the unit physics components essential to modeling ETI are accurate. This provides a way for fluid-based codes to simulate linear and nonlinear ETI. Additionally, the study provides a sensitivity analysis of nonlinear ETI to equation of state, vacuum resistivity, and vacuum density. Simulations of ETI typically use a collisional form of the resistivity as provided, e.g., in a Lee-More Desjarlais conductivity table. In regions of low-mass density, collision-less transport needs to be incorporated to properly simulate the filamentation form of ETI growth. Anomalous resistivity (AR) is an avenue by which these collision-less micro-turbulent effects can be incorporated into a collisional resistivity. AR directly changes the resistivity which will directly modify the linear growth rate of ETI, so a new linear growth rate is derived which includes AR's added dependency on current density. This linear growth rate is verified through a filamentation ETI simulation using an ion acoustic based AR model. Kinetically based simulations of vacuum contaminant plasmas provide a physical platform to study the use of AR models in pulsed-power platforms. Using parameters from the Z-machine pulsed-power device, the incorporation of AR can increase a collisional-based resistivity by upwards of four orders of magnitude. The presence of current-carrying vacuum contaminant plasmas can indirectly affect nonlinear ETI growth through modification of the magnetic diffusion wave. The impact of AR on nonlinear ETI is explored through pulsed-power simulations of a dielectrically coated solid metallic liner surrounded by a low-density vacuum contaminant plasma. / Doctor of Philosophy / High-energy-density physics (HEDP) is the study of materials with pressures that exceed 1Mbar, and is difficult to reach here on Earth. Inertial confinement fusion concepts and experiments are the primary source for achieving these pressures in the laboratory. Inertial confinement fusion (ICF) is a nuclear fusion concept that relies on the inertia of imploding materials to compress a light fuel (often deuterium and tritium) to high densities and temperatures to achieve fusion reactions. The imploding materials in ICF are driven in many ways, but this dissertation focuses on ICF implosions driven by pulsed-power devices. Pulsed-power involves delivering large amounts of capacitive energy in the form of electrical current over very short time scales (nanosecond timescale). The largest pulsed-power driver is the Z-machine at Sandia National Laboratory (SNL) which is capable of delivering upwards of 30 MA in 130 ns approximately. During an ICF implosion there exists instabilities that disrupt the integrity of the implosion causing non-ideal lower density and temperature yields. One such instability is the Rayleigh-Taylor instability where a light fluid supports a heavy fluid under the influence of gravity. The Rayleigh-Taylor is one of the most detrimental instabilities toward achieving ignition and was one of the main research topics in the early stages of this Ph.D. The study of this instability provided a nice intro for modeling in the HEDP regime, specifically, in the uses of tabulated equations-of-state and tabulated transport coefficients (e.g., resistivity and thermal conductivity). The magneto Rayleigh-Taylor instability occurs in pulsed-power fusion platforms where the heavy fluid is now supported by a magnetic field instead of a light fluid. The magneto Rayleigh-Taylor instability is the most destructive instability in many pulsed-power fusion platforms, so understanding seeding mechanisms is critical in mitigating its impact. Magnetized liner inertial fusion (MagLIF) is a pulsed-power fusion concept that involves imploding a solid cylindrical metal annulus on laser-induced pre-magnetized fuel. The solid metal liners have imperfections and defects littered throughout the surface. The imperfections on the surface create a perturbation during the initial phases of the implosion when the solid metal liner is undergoing ohmic heating. Because a solid metal has a resistivity that increases with temperature, as the metal heats the resistivity increases causing more heating which creates a positive feedback loop. This positive feedback loop is similar to the heating process in a nichrome wire in a toaster, and is the fundamental bases of the main instability studied in this dissertation, the electrothermal instability (ETI). ETI is present in all pulsed-power fusion platforms where a current-carrying material has a resistivity that changes with temperature. In MagLIF, ETI is dominant in the early stages of a current pulse where the resistivity of the metal increases with temperature. An increasing resistivity with temperature is connected to the axially growing modes of ETI which is denoted as the striation form of ETI. Contrary to the striation form of ETI, the filamentation form of ETI occurs when resistivity decreases with temperature and is associated with the azimuthally growing modes of ETI. Chapter 2 in this dissertation details a study of how to simulate striaiton ETI for a MagLIF-like configuration across different resistive magnetohydrodynamics (MHD) codes. Resistivity that decreases with temperature typically occurs in low-density materials which are often in a gaseous or plasma state. Low density plasmas are nearly collision-less and have resistivity definitions that often overestimate the conductivity of a plasma in certain experiments. Anomalous resistivity (AR) addresses this overestimation by increasing a collisional resistivity through micro-turbulence driven plasma phenomenon that mimic collisional behavior. The creation of AR involves reduced-modeling of micro-turbulence driven plasma phenomenon, such as the lower hybrid drift instability, to construct an effective collision frequency based on drift speeds. Because AR directly modifies a collisional resistivity for certain conditions, it will directly alter the growth of ETI which is the topic of Chapter 3. The current on the Z-machine is driven by the capacitor bank through the post-hole convolute, the magnetically insulated transmission lines, and then into the chamber. Magnetically insulated transmission lines have been shown to create low-density plasma through desorption processes in the vacuum leading to a load surrounded by a low-density plasma referred to as a vacuum contaminant plasmas (VCP). VCP can divert current from the load by causing a short between the vacuum anode and cathode gap. In simulations, this plasma would be highly conducting when represented by a collisionally-based resistivity model resulting in non-physical vacuum heating that is not observed in experiments. VCP are current-carrying low-density and high-temperature plasmas which make them ideal candidates to study the role of AR as described in Chapter 4. Chapter 4 investigates the role AR in a VCP would have on striation ETI for a MagLIF-like load.

This study focuses on deposition processes from sediment laden buoyant river plumes in deltaic regions. The goal is to experimentally examine the effects of various physical phenomena influencing the rate at which sediment is removed from the plume. Previous laboratory and field measurements have suggested that, at times, sedimentation can take place at rates higher than that expected from individual particle settling (i.e., C{W}_{s}). Two potential drivers of enhanced sedimentation are flocculation and interfacial instabilities. We experimentally measured the sediment fluxes from each of these processes using two sets of laboratory experiments that investigate two different modes of instability, one driven by sediment settling and one driven by fluid shear. The settling-driven and shear-driven instability sets of experiments were carried out in a stagnant stratification tank and a stratification flume respectively. In both sets, continuous interface monitoring and concentration measurement were made to observe developments of instabilities and their effects on the removal of sediment. Floc size was measured during the experiments using a separate floc camera setup and image analysis routines. Results from the stratification tank experiments suggest that the settling-driven gravitational instabilities do occur in the presence of flocs, and that they can produce sedimentation rates higher than those predicted from floc settling. A simple cylinder based force balance approach adopting the concept of critical Grashof number was used to develop a model for the effective settling velocity under settling-driven instabilities that is a function of sediment concentration in the plume only. Results from the stratification flume experiments show that under shear instabilities, the effective settling velocity is greater than the floc settling velocity, and increases with plume velocity and interface mixing. The difference between effective and floc settling velocity was denoted as the shear-induced settling velocity. This settling rate was found to be a strong function of the Richardson number, and was attributed to mixing processes at the interface. Conceptual and empirical analysis shows that the shear-induced settling velocity is proportional to U{Ri}^{-2}. Following the experiments, analyses were made among contributions of different mechanisms on the total deposition rate, and the locations that the various mechanisms may be active in the length of a plume. This analysis leads to a conceptual discretization of a plume into three zones of sedimentation behavior and Richardson number. The first zone is the supercritical near-field plume with intense interface mixing. Zone two represents the subcritical region where interface mixing still occurs, and zone three is the high Richardson number zone where mixing at the interface is effectively nonexistent. In zones one and two, individual floc settling and shear-induced settling mechanisms play the major roles in removing sediment from the plume. While, shear-induced settling rate was found to be maximum near the river mouth, its share of the total settling rate increases in the crossshore direction, since sand and large particulates deposit near the inlet and only small particles (with relatively low settling velocity) remain as the plume propagates. The third zone, starts when the interfacial mixing diminishes and leaking commences. / Ph. D.

Particle accelerators are machines to accelerate and store charged particle beams, such as electrons or protons, to the energy levels for various scientific applications. There are three basic types of particle accelerators: linear accelerators (linac), storage-ring (or circular) accelerators, and recirculating accelerators. The third type, also the most recent one, is designed to accelerate a particle beam in a short section of linac, circulate and then continue to accelerate it for energy boost or decelerate it for energy recovery. The modern recirculating machines possess the advantages to both accelerate and preserve the beam with high beam quality, as well as efficiently reuse the accelerating components. As modern accelerators push toward the high-brightness or high-intensity frontier by demanding particles in a highly charged bunch to concentrate in an ever-decreasing beam phase space, the interaction amongst particles via their self-generated electromagnetic fields can potentially lead to coherent instabilities of the beam and thus pose significant challenges to the machine design and operation. Microbunching instability (MBI) has been one of the most challenging issues for such high-brightness or high-intensity beam transport, as it would degrade lasing performance in the fourth-generation light sources, reduce cooling efficiency in electron cooling facilities, and eventually compromise the luminosity of colliding beams in lepton or lepton-hadron colliders. The dissertation work will focus on the MBI in modern recirculating electron accelerators. The research attempts to develop a comprehensive theoretical formulation of MBI with aspects including among various degrees of freedoms the beam itself, the beamline lattice optics, and incorporation of all relevant collective effects that the beam encounters, for example the coherent synchrotron radiation (CSR) and the longitudinal space charge (LSC) effects. This dissertation includes the following seven themes: 1) Development and generalization of MBI theory to arbitrary linear lattices and coupled beams with constant and varying energies; 2) Construction of CSR impedance models from steady state to transient state and from high to low energy regime; 3) Numerical implementation of the developed theory as a fast and numerical-noise-free Vlasov solver and benchmarking with massive particle tracking simulation; 4) Exploration of multistage cascaded amplification mechanism of CSR microbunching development; 5) Control of CSR-induced MBI in multi-bend transport or recirculation arcs; 6) Study of more aspects of microbunched structures in beam phase spaces; and 7) Study of MBI for magnetized beams and confirming the suppression of MBI for a recent cooler design for Jefferson Lab Electron Ion Collider project. / Ph. D.

A full solar eclipse is going to be visible from a range of states in the contiguous United States on August 21, 2017. Since the atmosphere of the Earth is charged by the sun, the blocking of the sunlight by the moon may cause short term changes to the atmosphere, such as density and temperature alterations. There are many ways to measure these changes, one of these being ionospheric scintillation. Ionospheric scintillation is rapid amplitude and phase fluctuations of signals passing through the ionosphere caused by electron density irregularities in the ionosphere. At mid-latitudes, scintillation is not as common of an occurrence as it is in equatorial or high-altitude regions. One of the theories that this paper looks into is the possibility of the solar eclipse producing an instability in the ionosphere that will cause the mid-latitude region to experience scintillations that would not normally be present. Instabilities that could produce scintillation are reviewed and altered further to model similar conditions to those that might occur during the solar eclipse. From this, the satellites that are being used are discuses, as is hardware and software tools were developed to record the scintillation measurements. Although this work was accomplished before the eclipse occurred, measurement tools were developed and verified along with generating a model that predicted if the solar eclipse will produce an instability large enough to cause scintillation for high frequency satellite downlinks. / Master of Science

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.

The mid-latitude ionosphere is more complicated than previously thought, as it includes many different scales of wave-like structures. Recent studies reveal that the mid-latitude ionospheric irregularities are less understood due to lack of models and observations that can explain the characteristics of the observed wave structures. Since temperature and density gradients are a persistent feature in the mid-latitude ionosphere near the plasmapause, the drift mode growth rate at short wavelengths may explain the mid-latitude decameter-scale ionospheric irregularities observed by the Super Dual Auroral Radar Network (SuperDARN). In the context of this dissertation, we focus on investigating the plasma waves responsible for the mid-latitude ionospheric irregularities and studying their influence on Global Positioning System (GPS) scintillations. First, the physical mechanism of the Temperature Gradient Instability (TGI), which is a strong candidate for producing mid-latitude irregularities, is proposed. The electro- static dispersion relation for TGI is extended into the kinetic regime appropriate for High- Frequency (HF) radars by including Landau damping, finite gyro-radius effects, and tem- perature anisotropy. The kinetic dispersion relation of the Gradient Drift Instability (GDI) including finite ion gyro-radius effects is also solved to consider decameter-scale waves gen- eration. The TGI and GDI calculations are obtained over a broad set of parameter regimes to underscore limitations in fluid theory for short wavelengths and to provide perspective on the experimental observations. Joint measurements by the Millstone Hill Incoherent Scatter Radar (ISR) and the Su- perDARN HF radar located at Wallops Island, Virginia have identified the presence of decameter-scale electron density irregularities that have been proposed to be responsible for low-velocity Sub-Auroral Ionospheric Scatter (SAIS) observed by SuperDARN radars. In order to investigate the mechanism responsible for the growth of these irregularities, a time series for the growth rate of both TGI and GDI is developed. The time series is computed for both perpendicular and meridional density and temperature gradients. The growth rate comparison shows that the TGI is the most likely generation mechanism for the observed quiet-time irregularities and the GDI is expected to play a relatively minor role in irregular- ity generation. This is the first experimental confirmation that mid-latitude decameter-scale ionospheric irregularities are produced by the TGI or by turbulent cascade from primary irregularity structures produced from this instability. The quiet- and disturbed-times plasma wave irregularities are compared by investigating co-located experimental observations by the Blackstone SuperDARN radar and the Millstone Hill ISR under various sets of geomagnetic conditions. The radar observations in conjunction with growth rate calculations suggest that the TGI in association with the GDI or a cascade product from them may cause the observations of disturbed-time sub-auroral ionospheric irregularities. Following this, the nonlinear evolution of the TGI is investigated utilizing gyro-kinetic Particle-In-Cell (PIC) simulation techniques with Monte Carlo collisions for the first time. The purpose of this investigation is to identify the mechanism responsible for the nonlinear saturation as well as the associated anomalous transport. The simulation results indicate that the nonlinear E x B convection (trapping) of the electrons is the dominant TGI sat- uration mechanism. The spatial power spectra of the electrostatic potential and density fluctuations associated with the TGI are also computed and the results show wave cascad- ing of TGI from kilometer scales into the decameter-scale regime of the radar observations. This suggests that the observed mid-latitude decameter-scale ionospheric irregularities may be produced directly by the TGI or by turbulent cascade from primary longer-wavelength irregularity structures produced from this instability. Finally, the potential impact of the mid-latitude ionospheric irregularities on GPS signals is investigated utilizing modeling and observations. The recorded GPS data at mid-latitude stations are analyzed to study the amplitude and phase fluctuations of the GPS signals and to investigate the spectral index variations due to ionospheric irregularities. The GPS measurements show weak to moderate scintillations of GPS L1 signals in the presence of ionospheric irregularities during disturbed geomagnetic conditions. The GPS spectral indices are calculated and found to be in the same range of the numerical simulations of TGI and GDI. Both simulation results and GPS spectral analysis are consistent with previous in-situ satellite measurements during disturbed periods, showing that the spectral index of mid- latitude density irregularities are of the order 2. The scintillation results along with radar observations suggest that the observed decameter-scale irregularities that cause SuperDARN backscatter, co-exist with kilometer-scale irregularities that cause L-band scintillations. The alignment between the experimental, theoretical, and computational results of this study suggests that turbulent cascade processes of TGI and GDI may cause the observations of GPS scintillations that occur under disturbed conditions of the mid-latitude F-region ionosphere. The TGI and GDI wave cascading lends further support to the belief that the E-region may be responsible for shorting out the F-region TGI and GDI electric fields before and around sunset and ultimately leading to irregularity suppression. / Ph. D.

The main goal of this work was to develop adaptive filter algorithms and test their performance in active combustion control. Several algorithms were incorporated, which are divided into gradient descent algorithms and pattern searches. The algorithms were tested on three separate platforms. The first was an analog electronic simulator, which uses a second order acoustics model and a first order low pass filter to simulate the flame dynamics of an unstable tube combustor. The second was a flat flame, methane-air Rijke tube. The third can be considered a quasi-LDI liquid fuel combustor with a thermal output of approximately 30 kW. Actuation included the use of an acoustic actuator for the Rijke tube and a proportional throttling valve for the liquid fuel rig. Proportional actuation, pulsed actuation, and subharmonic control were all investigated throughout this work. The proportional actuation tests on the Rijke tube combustor have shown that, in general, the gradient descent algorithms outperformed the pattern search algorithms. Although, the pattern search algorithms were able to suppress the pressure signal to levels comparable to the gradient descent algorithms, the convergence time was lower for the gradient descent algorithms. The gradient algorithms were also superior in the presence of actuator authority limitations. The pulsed actuation on the Rijke tube showed that the convergence time is decreased for this type of actuation. This is due to the fact that there is a fixed amplitude control signal and algorithms did not have to search for sufficient magnitude. It was shown that subharmonic control could be used in conjunction with the algorithms. Control was achieved at the second and third subharmonic, and control was maintained for much higher subharmonics. The cost surface of the liquid fuel rig was obtained as the mean squared error of the combustor pressure as a function of the magnitude and phase of the controller. The adaptive algorithms were able to achieve some suppression of the pressure oscillations but did not converge to the optimal phase as shown in the cost surface. Simulations using the data from this cost surface were also performed. With the addition of a probing function, the algorithms were able to converge to a near-optimal condition. / Master of Science

Active control of combustion instabilities through secondary fuel injection is a control method that has gained a lot of attention in the past decade. Previous control schemes with acoustic loudspeakers are not practical in full-scale gas turbines due to the extreme temperatures and acoustic power requirements. Much work has gone into controlling these thermoacoustic instabilities with secondary fuel control. Control of a laminar premixed tube combustor through secondary fuel actuation is the concentration of this work. It is the first known published attempt to control a laminar premixed tube combustor through secondary fuel actuation. Due to the low flow rates within the tube combustor an innovative injection technique had to be constructed to perform the secondary fuel actuation. The gaseous fuel is injected only one millimeter above the location of the flame through one, two, or four injectors. These injectors were designed to overcome the serious problem of pulse diffusion. This technique enabled the tube combustor to be controlled through secondary fuel injection. Accompanying the innovative fuel injection technique is a duty cycle modulation technique that was a prime contributor to the success of the control system. This method enabled the system to be controlled at conditions that were uncontrollable with a fixed duty cycle. The overall result was a 35 dB suppression of the limit cycle amplitude with 20% secondary fuel injection. / Master of Science