The current research focuses on the thermoacoustic instability of lean premixed combustion, which is a promising technique to inhibit Nitrogen Oxides (NOx) emission. Thermoacoustic instability describes the condition that the pressure oscillation is unusually high in the combustion device. It results from the coupling between pressure fluctuation and heat release oscillation, which experiences significant temporal and spatial variations. These variations are closely related to the flame shape deformation and critical in determining the trend of the global instability. Therefore, the current study aims to examine both the global and local flame features created by thermoacoustic instability. The first part of the work is studying the unstable flame induced by artificial acoustic perturbation. The particular focus is on the global and local heat release rate oscillation. In the experiment, the global heat release rate oscillation was indicated by the hydroxyl (OH*) chemiluminescence captured with a photomultiplier tube (PMT). On the other hand, the flame shape and the local mean heat release rate were examined with flame surface density (FSD), which was calculated with the images captured with the planar laser-induced fluorescence of the hydroxide radical (OH-PLIF) method. The main analysis methods used in the current research are Rayleigh criterion and proper orthogonal decomposition (POD), which can efficiently capture the dominant oscillation mode of the flame. The acoustic perturbation study first examined the effect of pressure variation (0.1 - 0.4 MPa) on the flame response to the acoustic perturbation. Results show that the elevated pressure intensifies the fundamental mode of heat release oscillation when the heat release oscillation is in phase with the pressure fluctuation; otherwise, the fundamental oscillation tends to be inhibited. The pressure affects both the strength and the distribution of the local fundamental and the first harmonic oscillations. Furthermore, the effect of the pressure on the distribution is larger than that on the strength. The study also investigated the role of Strouhal numbers in characterizing the flame oscillation induced by acoustic perturbation. Results show that the Strouhal number can characterize the changing trend of the oscillation amplitude, whereas the oscillation phase-delay is less dependent on the Strouhal number. The local analysis reveals that the nonlinear flame behavior results from the flame rollup induced by acoustic perturbation. Furthermore, the reconstruction of the global heat release shows that the cancellation of out-of-phase local oscillations can cause a low-level global oscillation. Results also demonstrate that the local heat release oscillation contains intense harmonic oscillations, which are closely associated with the flame rollup. However, the harmonic oscillation is less likely the main reason causing nonlinear flame behavior. Besides the study with acoustic perturbation, the current study also conducted experimental and modeling studies on the self-excited thermoacoustic instability. The particular focus is examining the effects of hydrogen addition on the instability trend. Results demonstrate that the hydrogen concentration can affect both the oscillation frequency and amplitude. Pressure analysis shows that the low-frequency mode is triggered when the hydrogen concentration is low, whereas a high hydrogen concentration tends to excite a high-frequency mode. Moreover, the frequency tends to increase with an increasing hydrogen concentration. Modeling results illustrate that the change of the oscillation mode, which is determined by the turbulent flame speed, is mainly affected by the delay time between the heat release oscillation and the velocity fluctuation. The modeling work shows that the one-dimensional model is not very efficient in capture the instability trend of the high-frequency mode. It may result from the lack of the knowledge of the mechanism of acoustic damping and flame dynamics.

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Self-excited systems are open loop unstable plants having a nonlinearity that prevents an exponentially increasing time response. The resulting limit cycle is induced by any slight disturbance that causes the response of the system to grow to the saturation level of the nonlinearity. Because there is no external disturbance, control of these self-excited systems requires that the open loop system dynamics are altered so that any unstable open loop poles are stabilized in the closed loop. This work examines a variety of adaptive control approaches for controlling a thermoacoustic instability, a physical self-excited system. Initially, a static feedback controller loopshaping design and associated system identification method is presented. This design approach is shown to effectively stabilize an unstable Rijke tube combustor while preventing the creation of additional controller induced instabilities. The loopshaping design method is then used in conjunction with a trained artificial neural network to demonstrate stabilizing control in the presence of changing plant dynamics over a wide variety of operating conditions. However, because the ANN is designed specifically for a single combustor/actuator arrangement, its limited portability is a distinct disadvantage. Filtered-X least mean squares (LMS) adaptive feedback control approaches are examined when applied to both stable and unstable plants. An identification method for approximating the relevant plant dynamics to be modeled is proposed and shown to effectively stabilize the self-excited system in simulations and experiments. The adaptive feedback controller is further analyzed for robust performance when applied to the stable, disturbance rejection control problem. It is shown that robust stability cannot be guaranteed because arbitrarily small errors in the plant model can generate gradient divergence and unstable feedback loops. Finally, a time-averaged-gradient (TAG) algorithm is investigated for use in controlling self-excited systems such as the thermoacoustic instability. The TAG algorithm is shown to be very effective in stabilizing the unstable dynamics using a variety of controller parameterizations, without the need for plant estimation information from the system to be controlled. / Ph. D.

Lean premixed combustors have been designed to lower NOx and other pollutant levels in land based gas turbines. These combustors are often susceptible to thermo-acoustic instabilities, which manifest as pressure and heat release oscillations in the combustor. To be able to predict and control these instabilities, it is required that both the acoustics of the system, and a frequency-resolved response of the combustion process to incoming perturbations be understood. Currently, a system-level approach is being used widely to predict the thermoacoustic instabilities. This approach requires simple, yet accurate models which would describe the behavior of each dynamic block within the loop. The present study is directed toward using computational fluid dynamics (CFD) as a tool in developing reduced order models for the dynamics of laminar flat flames and swirl stabilized turbulent flames. A finite-volume based approach is being used to simulate reacting flows in both laminar and turbulent combustors. The study has been divided into three parts -- the first part involves the modeling of a self-excited combustor (the acoustics of the combustor are coupled with the unsteady heat release); the second part of the research aims to study the effect of velocity perturbations on the unsteady heat release rate from a burner stabilized laminar flat flame; the third and final part of work involves an extension of the laminar flat flame study to turbulent reacting flows in a swirl stabilized combustor, and study the effects on the turbulent heat release due to the velocity perturbations. A Rijke tube combustor was selected to study self-excited combustion phenomenon. A laminar premixed methane-air flat flame was stabilized on a honeycomb flame-stabilizer. The flame stabilizer was placed at the center of the 5 feet vertical tube. The position of the flame at the center of the tube leads to a thermoacoustic instability of the 2nd acoustic mode. The fundamental thermoacoustic frequency was predicted accurately by the CFD model and the amplitude was reasonably matched (for a flow rate of Q = 120 cc/s and equivalence ratio phi = 1.0). Other characteristics of the pressure power spectrum were captured to a good degree of accuracy. This included the amplitude modulation of the fundamental and the harmonics due to a subsonic pulsating instability. The flat flame study has been being conducted for Q = 200 cc/s and equivalence ratio phi = 0.75. The objective has been to obtain a frequency response function (FRF) of the unsteady heat release rate (output) due to incoming velocity perturbations (input). A range of frequencies (15 Hz - 500 Hz) have been selected for generating the FRF. The aim of this part of the study has been to validate the computational model against the experimental results and propose a physics based interpretation of the flame response. Detailed heat transfer modeling (including radiation heat transfer) and two-step chemistry models have been implemented in the model. The FRF generated has been able to reproduce the experimentally observed phenomena, like the low frequency pulsating instability occurring at 30 Hz. A heat transfer study has been conducted to explain the pulsating instability and a fuel variability study has been performed. Both the heat transfer study and the fuel variability study proved the role of heat transfer in creating the pulsating instability. The final part of the study involves simulation of reacting flow in a turbulent swirl stabilized combustor. The effect of velocity perturbations on the unsteady heat release has been studied by creating an FRF between the unsteady velocity and the unsteady heat release rate. A Large Eddy Simulation (LES) approach has been selected. A swirl number of S = 1.19 corresponding to a flow rate of Q = 20 SCFM with an equivalence ratio of phi = 0.75 have been implemented. Reduced reaction chemistry modeling, turbulence-chemistry interaction and heat transfer modeling have been incorporated in the model. The LES of reacting flow has shown vortex-flame interaction occurring inside the combustor. This interaction has been shown to occur at 255 Hz. The FRF obtained between unsteady velocity and unsteady heat release rate shows good comparison with the experimentally obtained FRF. / Ph. D.

<p dir="ltr">Thermo-acoustic interactions, characterized by the coupling between heat release and acoustic waves, are a phenomenon that can lead to combustion instability in high-speed propulsion devices. These interactions are highly undesirable as they can damage engine components and, in severe cases, cause catastrophic failure of the entire propulsion system. Mitigating these instabilities is crucial for ensuring reliable combustor operation. This work presents a computational investigation of combustion instability in Purdue's Continuously Variable Resonance Combustor (CVRC), focusing on the prediction of instability trend over the entire oxidizer-post length range. Computational fluid dynamics (CFD) studies in the past mainly focused on individual CVRC cases with specific oxidizer-post lengths. Those studies help understand the instability mechanism for individual CVRC cases but are limited in examining the applicability of model predictions over a wide range of instability conditions. No studies have been reported to assess the model predictivity over the entire oxidizer-post range in CVRC. </p><p dir="ltr">In this work, we first conduct a series of CFD simulations that cover the entire oxidizer-post length in CVRC to assess the models for a wide range of instability conditions. It is found that the CFD models generally fail to capture the instability trend over the entire oxidizer-post length although they can capture some individual cases. To understand the model failure, parametric studies are often deemed the first step of investigation. Such parameter studies, however, are expensive for CVRC since more than ten simulation cases to cover the entire oxidizer-post range are needed for each parametric study. Multiple parametric studies are typically needed to cover various uncertainties from numerics and physical models and those involved in the experimental conditions, making parametric studies for CVRC a computationally expensive task. Therefore, our focus next is on developing faster approaches.</p><p dir="ltr">The second part of this work is to develop a reduced-order model to quickly conduct the needed parametric studies. The developed reduced-order model leverages the instability mechanisms observed from the CFD simulations conducted in the first part. Monte Carlo approaches are employed to replace expensive CFD simulations by replicating the randomness in the combustor through statistical sampling. The developed reduced-order model is first validated by comparing its predictions with the CFD simulation results in a number of cases. The reduced-order model, despite its simplicity, reasonably reproduced the overall trend of instability from CFD simulations, making it an attractive alternative to the detailed model simulations for parametric studies. </p><p dir="ltr">The validated reduced-order model is then applied to parametric studies of CVRC to help identify the uncertainties of CFD predictions of CVRC. Four sets of parametric studies are conducted to provide a rapid examination of the effect of heat loss, the effect of oxidizer temperature, the effect of equivalence ratio, and the effect of turbulence on the instability predictions in CVRC. From the rapid reduced-order parametric studies, we found that the heat losses in upstream of the oxidizer inlet and the combustor wall are the two most contributing factors to the uncertainties of CFD model predictions. The turbulence level and the error involved in the equivalence ratio due to experimental uncertainties play an insignificant role in contributing to the CFD prediction uncertainties. </p><p dir="ltr">This work is a significant contribution to the combustion instability community by enabling an alternative rapid assessment of CFD model predictions. This capability facilitates the identification of major contributing factors of CFD modeling uncertainties with much less computational cost, thereby allowing for a more focused approach to CFD analysis and ultimately accelerating the improvement of CFD models for combustion instability studies. </p>

In the effort to reduce emission and fuel consumption in industrial gas turbines, lean premixed combustion is utilized but is susceptible to thermoacoustic instabilities. These instabilities occur due to an in-phase relationship between acoustic pressure and unsteady heat release in a combustor. Thermoacoustic instabilities have been shown to cause structural damage and limit operability of combustors. To mitigate these instabilities, a variety of active and passive methods can be employed. The addition of porous inert media (PIM) is a passive mitigation technique that has been shown to be effective at mitigating an instability. Practical industrial application of a mitigation strategy requires early-stage design considerations such as reduced order modeling, which is often used to study a systems' stability response to geometric changes and mitigation approaches. These reduced order models rely on flame transfer functions (FTF) which numerically represent the relationship between heat release and acoustic perturbations. The accurate quantification of heat release is critical in the study of these instabilities and is a necessary component to improve the reduced order model's predictive capability. Heat release quantification presents numerous challenges. Previous work resolving heat release has used optical diagnostics. For perfectly premixed, laminar flames, it has been shown there are proportional relationships between OH* or CH* chemiluminescence to heat release. This is an ideal case; in reality, practical burners produce turbulent and partially premixed flames. Due to the additional straining of the flame caused by turbulence, the heat release is no longer proportional to chemiluminescence quantities. Also, partially premixed systems have spatially varying equivalence ratios and heat release rates, meaning analysis reliant on perfectly premixed assumptions cannot be used and techniques that can handle spatial variations is needed. The objective of this thesis is to incorporate PIM effects into a reduced order model and resolve quantities vital to understand how PIM is mitigating thermoacoustic instabilities in a partially premixed, turbulent combustion environment. The initial work presented in this thesis is the development of a reduced order model for predicting mode shapes and system stability with and without PIM. This was the first time that a reduced order model was developed to study PIM effects on the thermoacoustic response. Model development used a linear FTF and can predict the system frequency and stability response. Through the frequency response, mode shapes can be constructed which show the axial variation in acoustic values, along with node and anti-node locations. Stability trends can be predicted, such as the independent effects of system parameter variation, to determine its stability response. The model was compared to canonical case studies as well as experimental data with reasonable agreement. With PIM addition, it was shown that a combustor would be under stable operation at more flow conditions than without PIM. The work also shows the stability sensitivity to different porous parameters and PIM locations within the combustor. The model has been used to aid in the design of other combustion systems developed at Virginia Tech's Advanced Propulsion and Power Laboratory. To better understand how PIM is affecting the system stability and demonstrate measurements for the improvement of a numerical FTF, experimental work to resolve the spatially varying equivalence ratio fluctuations was conducted in an atmospheric, swirl-stabilized combustor. The experimental studies worked to improve the fundamental understanding of PIM and its mitigation effects through spatially and temporally resolved equivalence ratios during a self-excited instability. The experimental combustor has an optically accessible flame region which allowed for high speed chemiluminescence to be captured during the instability. Equivalence ratio values were calculated from a relation involving OH*/CH* chemiluminescence ratio. The acoustic perturbations were studied to show how the equivalence ratio fluctuations were being generated and coupling with the acoustic waves. The fluctuation in equivalence ratio showed about 65% variation around its mean value during the period of an instability cycle. When porous media was added to the system, the fluctuation in equivalence ratio was mitigated and a reduction in peak frequency (sound pressure level) SPL of 38 dB was observed. Changes in the spatial distribution of equivalence ratio with PIM addition were shown to produce a more stable operation. Effects such as locally richer burning and changes to recirculation zones promoted more stable operation with PIM addition. Testing with forced acoustic input was also conducted to quantify the flame response. The results demonstrated that a flame in a system with PIM responds differently than without PIM, highlighting the need to develop FTF for systems with PIM. This experimental study was the first to study equivalence ratio in a turbulent, partially premixed combustor using PIM as a mitigation technique. A final experimental investigation was conducted to resolve the spatially defined heat release and its fluctuation during a thermoacoustic instability period. This was the first time that heat release had been investigated in a partially premixed, thermoacoustically unstable system, using PIM as a migration method. Heat release was quantified using equivalence ratio, strain rate, OH* intensity, and a correction factor determined from a chemical kinetic solver. The heat release analysis built upon the equivalence ratio study with additional flow field analysis using PIV. The velocity vectors showed prominent corner and central recirculation zones in the no PIM case which have been shown to be feedback mechanisms that support instability formation. With PIM addition, these flow features were reduced and decoupled from the combustor inlet reactants. The velocity results were decomposed using a spectral proper orthogonal decomposition (SPOD) method. The energy breakdown showed how PIM reduced and distributed the energy in the flow structures, creating a more stable flow field. Heat release results with velocity information demonstrated the significant coupling mechanisms in the flow field that were mitigated with the PIM addition. The no PIM case showed high heat release areas being directly influenced by the incoming flow fluctuations. The feedback mechanisms, both mean flow and acoustic, have a direct path to the incoming flow to the combustor. In the PIM case, there is significant mixing and burning taking place in locations where it is less likely that feedback can reach the incoming flow to couple to form an instability. The methodology to quantify heat release provides a framework for quantifying a non-linear FTF with PIM. The development and testing to determine a non-linear FTF with PIM are reserved for future work and discussed in the final chapter. The methodologies and modeling conducted here provided insight and understanding to answer why PIM is effective at mitigating a thermoacoustic instability and how it can be studied using a reduced order numerical tool. / Doctor of Philosophy / In the effort to reduce emission and fuel consumption in industrial gas turbines, lean premixed combustion is utilized but is susceptible to thermoacoustic instabilities. These instabilities occur due to a relationship between acoustic pressure and unsteady heat release in a combustor. Thermoacoustic instabilities have been shown to cause structural damage and limit operability of combustors. To mitigate these instabilities, a variety of active and passive methods can be employed. The addition of porous inert media (PIM) is a passive mitigation technique that has been shown to be effective at mitigating an instability. Implementation of these mitigation strategies require early-stage design considerations such as reduced order modeling, which is often used to study a systems' stability response to geometric changes and mitigation approaches. These reduced order models rely on flame transfer functions (FTF) which numerically model the flame response. The accurate quantification of heat release is critical in the study of these instabilities and is a necessary component to improve the reduced order model's predicative capability. Heat release quantification presents numerous challenges. Previous work resolving heat release has used optical diagnostics with varying levels of success. For perfectly premixed, laminar flames, it has been shown there are proportional relationships between flame light emission and heat release. This is an ideal case; in reality, practical burners produce complex turbulent flames. Due to complex turbulent flame, the heat release is no longer proportional to the flame light emission quantities. Also, partially premixed systems have spatially variant flame quantities, meaning analyses reliant on perfectly premixed assumptions cannot be used and techniques that can handle spatial variations are required. The objective of this thesis is to incorporate PIM effects into a reduced order model and resolve quantities vital to understand how PIM is mitigating thermoacoustic instabilities in a partially premixed, turbulent combustion environment. The initial work presented in this thesis is the development of a reduced order model for predicting mode shapes and system stability with and without PIM. The model uses a simple relationship to model the flame response in an acoustic framework. To improve the model and understanding of PIM mitigation, experimental data such as the local heat release rates and equivalence ratios need to be quantified. An experimental technique was utilized on an optically accessible atmospheric, swirl-stabilized combustor, to resolve the spatially variant equivalence ratio and heat release rates. From these results, better understanding of how PIM is improving the stability in a combustion environment is shown. Quantities such as velocity, acoustic pressure, equivalence ratio, and heat release are all studied and used to explain the improved stability with PIM addition. The methodologies and modeling conducted here provided insight and understanding to answer why PIM is effective at mitigating a thermoacoustic instability and how it can be studied using a reduced order numerical tool. Furthermore, the present work provides a framework for quantifying spatially varying heat release measurements, which can be used to develop FTF for use with thermoacoustic modeling approaches.

Reduction of the pollutant emissions is a challenge for the gas turbine industry. A solution to this problem is to employ the low swirl burner which can operate at lower equivalence ratios than a conventional swirl burner. However, flames in the lean regime of combustion are susceptible to flow perturbations and combustion instability. Combustion instability is the coupling between unsteady heat release and combustor acoustic modes where one amplifies the other in a feedback loop. The other method for significantly reducing NOx and CO2 is increasing fuel reactivity, typically done through the addition of hydrogen. This helps to improve the flammability limit and also reduces the pollutants in products by decreasing thermal NOx and reducing CO2 by displacing carbon. In this work, the flammability limits of a low swirl burner at various operating conditions, is studied and the effect of pressure, bulk velocity, burner shape and percent of hydrogen (added to the fuel) is investigated. Also, the flame structure for these test conditions is measured using OH planar laser induced fluorescence and assessed. Also, the OH PLIF data is used to calculate Rayleigh index maps and to construct averaged OH PLIF intensity fields at different acoustic excitation frequencies (45-155, and 195Hz). Based on the Rayleigh index maps, two different modes of coupling between the heat release and the pressure fluctuation were observed: the first mode, which occurs at 44Hz and 55Hz, shows coupling to the flame base (due to the bulk velocity) while the second mode shows coupling to the sides of the flame. In the first mode, the flame becomes wider and the flame base moves with the acoustic frequency. In the second mode, imposed pressure oscillations induce vortex shedding in the flame shear layer. These vortices distort the flame front and generate locally compact and sparse flame areas. The local flame structure resulting from these two distinct modes was markedly different.

Diese Arbeit zielt darauf ab, die raumzeitlichen Regelmäßigkeiten an Übergängen aufzudecken, die in saisonalen Klima- und Ingenieursystemen beobachtet werden, indem moderne Methoden der komplexen Systemwissenschaft verwendet werden. Das erste System ist der indische Sommermonsun - eine Regenzeit, deren jährliche Schwankungen das Leben und den Wohlstand von mehr als einer Milliarde Menschen auf dem indischen Subkontinent beeinflussen und die Wirtschaft des von der Landwirtschaft abhängigen Landes stark beeinträchtigen. Insbesondere die Kenntnis des zeitlichen Ablaufs des Übergangs vom Vormonsun zum Monsun ist für die Planung landwirtschaftlicher Aktivitäten dringend erforderlich. Die Vorhersage des Monsunzeitpunkts über dem indischen Kontinent bleibt jedoch eine große wissenschaftliche Herausforderung. Das zweite ist ein Verbrennungssystem, das anfällig für ein katastrophales Phänomen namens thermoakustische Instabilität ist, das verhindert, dass das Verbrennungssystem unter klimafreundlichen Bedingungen betrieben wird. Eine solche Brennkammer ist typisch für Energie- und Antriebssysteme wie Gasturbinentriebwerke, Boiler und Raketen. Zu verstehen, wann der Übergang zur thermoakustischen Instabilität auftritt und wie dieser Übergang unterdrückt werden kann, sind Schlüsselfragen für die Entwicklung klimafreundlicher Motoren. Diese Dissertation liefert ein neues Verständnis des indischen Sommermonsuns und der thermoakustischen Instabilität durch auf statistischer Physik basierende Ansätze, die verborgene Merkmale in diesen Systemen nahe ihren jeweiligen Übergängen aufdecken. / This thesis aims to reveal the spatiotemporal regularities at transitions observed in seasonal climate and engineering systems by utilizing modern methods of complex systems science. The first system is the Indian Summer Monsoon - a rainy season whose yearly variability affects the life and prosperity of more than a billion people in the Indian subcontinent and strongly impacts the economy of the agriculture-dependent country. In particular, knowledge of the timing of the transition from pre-monsoon to monsoon is greatly needed for the planning of agriculture activities. However, the prediction of monsoon timing over the Indian continent remains a significant scientific challenge. The second is a combustion system prone to a catastrophic phenomenon called thermoacoustic instability, which prevents the combustion system from being operated in climate-friendly conditions. Such a combustor is typical in power and propulsion systems such as gas turbine engines, boilers, and rockets. Understanding when the transition to thermoacoustic instability occurs and how to suppress this transition are key questions for developing climate-friendly engines. This thesis provides a new understanding of the Indian Summer Monsoon and thermoacoustic instability through statistical physics-based approaches that reveal hidden features in these systems near their respective transitions.