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.

We consider the inverse source problem arising in thermo-and photoacoustic tomography. It consists in reconstructing the initial pressure from the boundary measurements of the acoustic wave. Our goal is to extend versatile time reversal techniques to the case when the boundary of the domain is perfectly reflecting, effectively turning the domain into a reverberant cavity. Standard time reversal works only if the solution of the direct problem decays in time, which does not happen in the setup we consider. We thus propose a novel time reversal technique with a nonstandard boundary condition. The error induced by this time reversal technique satisfies the wave equation with a dissipative boundary condition and, therefore, decays in time. For larger measurement times, this method yields a close approximation; for smaller times, the first approximation can be iteratively refined, resulting in a convergent Neumann series for the approximation.

An experimental study was performed on a low frequency transcritical thermoacoustic engine developed at Maurice J. Zucrow Laboratories. The goal of the experiment was to characterize the effects of engine geometry on the thermoacoustic production of the working fluid and to use insights gained to design a power extraction device for the transcritical thermoacoustic engine. The effects of geometry were investigated by parametrically varying the length of the resonator and the diameter of the resonator and measuring the pressure amplitude and frequency of thermoacoustic instabilities developed at varying ∆T and one bulk pressure of P Pcr = 1.1. It was found that increasing resonator length increases pres?sure amplitude, decreases frequency, and increases acoustic power developed. Increasing resonator diameter decreases pressure amplitude, increases frequency, and increases acoustic power developed. It was also experimentally proven that coiled tube sections in the res?onator attenuate the thermoacoustic pressure wave. After testing, the knowledge gained was applied to the design of a bidirectional impulse turbine for eventual integration into a scaled-up version of the current thermoacoustic engine to be used to extract power from the thermoacoustic instabilities developed in the rig.

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

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

Identification of thermoacoustic dynamics that exhibit limit cycle behavior is needed to gain a better intuitive feel of the system, to design complex control strategies, and to validate modeling efforts. Limit cycle oscillations arise in thermoacoustic systems due to the coupling between a nonlinear heat release process and the acoustic dynamics of the combustor. This response arises in lean premixed gaseous power generating turbines and is a concern due to the detrimental effect of the pressure oscillations on the structural integrity of the combustor. Due to the volatile environment intrinsic in the combustor, multiple sensing apparatuses are not available. Therefore, in the current study, an identification approach is assessed considering only a single output from the thermoacoustic system. As a means to further investigate the thermoacoustic limit cycle behavior, a scaled version of the industry-based turbine was constructed. By anchoring a flame halfway from end-to-end of a closed-open tube, a similar nonlinear response is achieved. A harmonic balance technique that linearly incorporates the nonlinearity is developed which uses frequency entrainment to offer sufficient information for the identification. Its validity is assessed on a model, which is based on known dynamics of the thermoacoustic system. The structure of the identification algorithm is based on a two-mode acoustic model with both dynamics and nonlinearity in the feedback loop. The limitations of using only a two-mode identification structure for a system with more than two modes is discussed as well as future efforts that may alleviate this problem. / Master of Science

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