The use of lean, premixed combustion in gas turbines is now widespread due to their low NOx emissions. Such systems are, however, susceptible to a phenomenon called thermoacoustic instability, which occurs as a result of unstable coupling between the combustion chamber acoustics and the flame. It can lead to large amplitude pressure oscillations within a combustor at frequencies in the hundreds of hertz. These pressure oscillations can result in unacceptably large noise levels, flame blow-out, reduced performance and fatigue failure of the combustor walls. This thesis investigates two problems of particular relevance to thermoacoustic instability. (For complete abstract open document)

Combustion instability is a process which involves unsteady chemical kinetic, fluid mechanic, and acoustic processes. It can lead to unstable behavior and be detrimental in ways ranging from faster part fatigue to catastrophic system failure. In terms of combustion methodology, combustion instability has been a key issue for lean premixed combustion. The primary objective of this work is to improve understanding of combustion dynamics through an experimental study of lean premixed combustion using a low swirl combustor. This special burner was developed at the Lawrence Berkeley National Laboratory and has recently received significant interest from the gas turbine industry. In these experiments, acoustic perturbations (chamber modes) are imposed on a low swirl stabilized methane-air flame using loudspeakers. The flame response is examined and quantified with OH planar laser induced fluorescence. Rayleigh index maps of the flame are computed for each frequency and operating condition. Examining the structures in the Rayleigh maps, it is evident that, while the flame shows no significant response in some cases, acoustic forcing in the 70-150 Hz frequency range induces vortex shedding in the flame shear layer. These vortices distort the flame front and generate locally compact and sparse flame areas. This information about the flow field shows that, besides illuminating the combustion dynamics, the Rayleigh index is a useful way to reveal interesting aspects of the underlying flow. The experiments also revealed other interesting aspects of this flame system. It was found that the flame becomes unstable when the perturbation amplitude reaches 0.7% of the mean pressure. Decreasing the swirl number makes the flame shape more jet-like, but does little to alter the shear-layer coupling. In a similar fashion, increasing the pressure was found to alter the flame shape and flame extent, but the thermo-acoustic coupling and induced large scale structure persisted to 0.34MPa, the highest pressure tested.

This dissertation presents a formulation of the Continuous Sensitivity Equation Method (CSEM) applied to the Computational Fluid Dynamics (CFD) simulation of thermoacoustic instability problems. The proposed sensitivity analysis approach only requires a single run of the CFD simulation. Moreover, the sensitivities of field variables, pressure, velocity and temperature to boundary-condition parameters are directly obtained from the solution to sensitivity equations. Thermoacoustic instability is predicted by the Rayleigh criterion. The sensitivity of the Rayleigh index is computed utilizing the sensitivities of field variables. The application of the CSEM to thermoacoustic instability problems is demonstrated by two classic examples. The first example explores the effects of the heated wall temperature on the one-dimensional thermoacoustic convection. The sensitivity of the Rayleigh index, which is the indicator of thermoacoustic instabilities, is computed by the sensitivity of field variables. As the heat wall temperature increases, the sensitivity of the Rayleigh index decreases. The evolution from positive to negative sensitivity values suggests the transition from a destabilizing trend to stabilizing trend of the thermoacoustic system. Thermoacoustic instabilities in a self-excited Rijke tube are investigated following the relatively simple thermoacoustic convection problem. The complexity of simulating the Rijke tube increases in both dimensions and mechanisms which incorporate the species transport process and chemical reactions. As a representative model of the large lean premixed combustor, Rijke tube has been extensively studied. Quantitative sensitivity analysis sets the present work apart from previous research on the prediction and control of thermoacoustic instabilities. The effects of two boundary-condition parameters, i.e. the inlet mass flow rate and the equivalence ratio, are tested respectively. Small variations in both parameters predict a rapid change in sensitivities of field variables in the early stage of the total time length of 1.2s. The sensitivity of the Rayleigh index "blows up" at a specific time point of the early stage. In addition, variations in the inlet mass flow rate and the equivalence ratio lead to opposite effects on the sensitivity of the Rayleigh index. There exist some common findings on the application of the CSEM. For both thermoacoustic problems, the sensitivities of field variables and the Rayleigh index exhibit oscillatory nature, confirming that thermoacoustic instability is an overall effect of the coupling process between fluctuations of pressure and heat release rate. All the sensitivities of the Rayleigh index show rapid changes and "blow up" in the early stage. Although the numerical errors could influence the fidelity of computational results, it is believed that the rapid changes reflect the susceptibility to thermoacoustic instabilities in the studied systems. It should also be noted that the sensitivities are obtained for small variations in influential parameters. Therefore, the resulting sensitivities do not predict the occurrence of thermoacoustic instabilities under a condition that is far from the reference state determined by either CFD simulation results (employed in this dissertation) or experimental data. The sensitivity solver developed for the present research has the feature of flexibility. Additional mechanisms and more complicated instability criteria could be easily incorporated into the solver. Moreover, the sensitivity equations formulated in this dissertation are derived from the full set of nonlinear governing equations. Therefore, it is possible to extend the use of the sensitivity solver to other CFD problems. The developed sensitivity solver needs to be optimized to gain better performance, which is considered to be the primary future work of this research. / Ph. D.

Thermoacoustic instabilities in gas turbine operation arise due to unsteady fluctuations in heat release coupled with acoustic oscillations, often caused by varying equivalence ratio perturbations within the flame field. These instabilities can cause irreparable damage to critical turbine components, requiring an understanding of the spatial/temporal variations in equivalence ratio values to predict flame response. The technique of computed tomography for flame chemiluminescence emissions allows for 3D spatially resolved flame measurements to be acquired using a series of integral projections (camera images). High resolution tomography reconstructions require a selection of projection angles around the flame, while captured chemiluminescence of radical species intensity fields can be used to determine local fuel-air ratios. In this work, a tomographic reconstruction algorithm program was developed and utilized to reconstruct the intensity fields of CH* and OH*, and these reconstructions were used to quantify local equivalence ratios in an acoustically forced flame. A known phantom function was used to verify and validate the tomography algorithm, while convergence was determined by subsequent monitoring of selected iterative criteria. A documented method of camera calibration was also reproduced and presented here, with suggestions provided for future calibration improvement. Results are shown to highlight fluctuating equivalence ratio trends while illustrating the effectiveness of the developed tomography technique, providing a firm foundation for future study regarding heat release phenomena. / Master of Science / Acoustic sound amplification occurs in the combustion chamber of a gas turbine due to the machine ramping up in operation. These loud sound oscillations continue to grow larger and can damage the turbine machinery and even threaten the safety of the operator. Because of this, many researchers have attempted to understand and predict this behavior in hopes of ending them altogether. One method of studying these sound amplifications is looking at behaviors in the turbine combustion flame so as to potentially shed light on how these large disturbances form and accumulate. Both heat release rate (the steady release of energy in the form of heat from a combustion flame) and equivalence ratio (the mass ratio of fuel to air burned in a combustion process) have proven viable in illustrating oscillatory flame behavior, and can be visualized using chemiluminescence imaging paired with computed tomography. Chemiluminescence imaging is used to obtain intensity fields of species from high resolution camera imaging, while computed tomography techniques are capable of reconstructing these images into a three-dimensional volume to represent and visualize the combustion flame. These techniques have been shown to function effectively in previous literature and were further implemented in this work. A known calibration technique from previous work was carried out along with reconstructing a defined phantom function to show the functionality of the developed tomography algorithm. Results illustrate the effectiveness of the tomographic reconstruction technique and highlight the amplified acoustic behavior of a combustion flame in a high noise environment.

Thermoacoustic instability is one of the most significant problems faced in the design of some combustion systems. Thermoacoustic oscillations arise due to feedback between acoustic waves and unsteady heat release rate when the fluctuating heat release rate is sufficiently in phase with the unsteady pressure. The primary aim of designers is to design linearly stable thermoacoustic systems in which these dangerous oscillations do not arise. In thermoacoustics, adjoint-based sensitivity analysis has shown promise at predicting the parameters which have the most influence on the linear growth and decay rates as well as oscillation frequency observed during periods of linear growth and decay. Therefore, adjoint-based methods could prove to be a valuable tool for developing optimal passive control solutions. This thesis aims to develop novel experimental sensitivity analysis techniques and provide a first comparison with the predictions of adjoint-based sensitivity analysis. In this thesis experimental sensitivity analysis is performed on (i) a vertical electrically-driven Rijke tube, and (ii) a vertical flame-driven Rijke tube. On the electrically-driven Rijke tube, the feedback sensitivity is studied by investigating the shift in linear growth and decay rates and oscillation frequency observed during periods of linear growth and decay due to the introduction of a variety of passive control devices. On the flame-driven Rijke tube, the base-state sensitivity is studied by investigating how the linear growth and decay rates as well as oscillation frequency during periods of linear growth and decay change as the convective time delay of the flame is modified. Adjoint-based sensitivity analysis gives the shift in linear growth and decay rate and the oscillation frequency when parameters are changed. This thesis provides experimental measurements of the same quantities, for comparison with the numerical sensitivity analysis, opening up new avenues for the development, implementation and validation of optimal passive control strategies for more complex thermoacoustic systems.

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

Acoustic Transfer Functions Derived from Finite Element Modeling for Thermoacoustic Stability Predictions of Gas Turbine Engines Design and prediction of thermoacoustic instabilities is a major challenge in aerospace propulsion and the operation of power generating gas turbine engines. This is a complex problem in which multiple physical systems couple together. Traditionally, thermoacoustic models can be reduced to dominant physics which depend only on flame dynamics and acoustics. This is the general approach adopted in this research. The primary objective of this thesis is to describe how to obtain acoustic transfer functions using finite element modeling. These acoustic transfer functions can be coupled with flame transfer functions and other dynamics to predict the thermoacoustic stability of gas turbine engines. Results of this research effort can go beyond the prediction of instability and potentially can be used as a tool in the design stage. Consequently, through the use of these modeling tools, better gas turbine engine designs can be developed, enabling expanded operating conditions and efficiencies. This thesis presents the finite element (FE) methodology used to develop the acoustic transfer functions of the Combustion System Dynamics Laboratory (CSDL) gaseous combustor to support modeling and prediction of thermoacoustic instabilities. In this research, several different areas of the acoustic modeling were addressed to develop a representative acoustics model of the hot CSDL gaseous combustor. The first area was the development and validation of the cold acoustic finite element model. A large part of this development entailed finding simple but accurate means for representing complex geometries and boundary conditions. The cold-acoustic model of the laboratory combustor was refined and validated with the experimental data taken on the combustion rig. The second stage of the research involved incorporating the flame into the FE model and has been referred to in this thesis as hot-acoustic modeling. The hot-acoustic model also required the investigation and characterization of the flame as an acoustic source. The detailed mathematical development for the full reacting acoustic wave equation was investigated and simplified sufficiently to identify the appropriate source term for the flame. It was determined that the flame could be represented in the finite element formulation as a volumetric acceleration, provided that the flame region is small compared to acoustic wavelengths. For premixed gas turbine combustor flames, this approximation of a small flame region is generally a reasonable assumption. Both the high temperature effects and the flame as an acoustic source were implemented to obtain a final hot-acoustic FE model. This model was compared to experimental data where the heat release of the flame was measured along with the acoustic quantities of pressure and velocity. Using these measurements, the hot-acoustic FE model was validated and found to correlate with the experimental data very well. The thesis concludes with a discussion of how these techniques can be utilized in large industrial-size combustors. Insights into stability are also discussed. A conclusion is then presented with the key results from this research and some suggestions for future work. / 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.

Thermoacoustic instability is of fundamental and applied interest in both scientific research and practical applications. This study aims to explore several very important sub-aspects in this field and contribute to a better understanding of thermoacoustic instability as encountered in typical gas turbines and rocket engines. Atomization has been recognized as a key mechanism in driving applied thermoacoustic instability. In this regard, this study mainly focuses on the atomization process relevant for delineation of thermoacoustic instability, contributing to a comprehensive understanding of the effect of acoustics on primary and secondary atomization. Firstly, a tree-based adaptive solver and VOF method are employed to simulate the jet primary atomization. The code is validated by theoretical, numerical and experimental results to demonstrate its capability and accuracy in terms of atomization in both low-speed and high-speed regime. Perturbation frequency and amplitude have shown to affect the atomization significantly. Besides, the effect of acoustic forcing on liquid ligament has also been numerically investigated. A volume source term is introduced to extend the solver to model the compressible effects in the presence of acoustic forcing. The influence of acoustic wave number, amplitude and frequency has been examined in detail. In terms of modelling the thermoacoustic instability, bifurcation analysis is carried out for a time-delayed thermoacoustic system using the Method of Line approach. Good predictions have been obtained to capture the nonlinear behaviors inherent in the system. Moreover, model-based simulation and control of thermoacoustic instability have been conducted. A low-order wave-based network model for acoustics is coupled with nonlinear flame describing function to predict the nonlinear instability characteristics in both frequency and time domain. Furthermore, active feedback control is implemented. Two different controllers have been designed to eliminate the thermoacoustic instability to an acceptably low level and may be employed in a practical manner.