Combustion dynamics of lean-premixed axial fuel-staged combustor: self-excited instability, flame transfer function, and low-order modeling

Abstract

Advanced gas turbine engines are expected to play a crucial role as a stabilizer in the rapid, widespread electrification and renewable transformation of energy systems. Axial staged combustion methods, whether for newly developed or retrofitted gas turbine combustors, are promising candidates for enhancing combined cycle efficiency by more than 65$\%$ without significantly increasing nitric oxide emissions. In this concept, the majority of the fuel is supplied to the primary reaction region operating under lean-premixed conditions, and the remaining fuel/air mixtures are then injected into the vitiated crossflow near the combustor exit to increase the turbine inlet temperature. However, combustion instabilities under axial-fuel-staging conditions can become more complex than those in conventional single-flame combustion, due to the presence of multiple discrete reaction zones and their various interactions. A proper understanding of these dynamics is essential for the successful application of the technique. Driven by both physical and practical motivations, this doctoral dissertation intensively addresses the combustion dynamics of a lean-premixed axial fuel-staged system, in an attempt to significantly expand our understanding of these phenomena. Using a lean-premixed axially staged combustor, several experimental investigations are conducted under various operating conditions, which are meticulously designed for systematic examination of the dynamics. During the investigations, thermophysical data regarding self-excited conditions, related flame dynamics, and forced responses are measured using various methods

these include dynamic pressure measurements, photomultiplier tubes, hot-wire anemometers, high-speed OH* chemiluminescence and OH planar laser-induced fluorescence image measurements, and acoustic external forcing. Numerical and analytical approaches---specifically finite element methods-based and reduced-order model-based linear acoustic calculations---are also carried out to support empirical findings. Initially, the study investigates the link between first- and second-stage flame dynamics in the lean-premixed axially staged combustor with various inlet conditions. The findings indicate that the second-stage jet-in-vitiated-crossflow flame is preferentially coupled to higher-order acoustic modes than the upstream primary flame with the same characteristic nozzle dimension. The excitations driven by each flame appear to be mutually incompatible, with this selective behavior critically dependent on the secondary flame's position relative to the acoustic mode shape. When the second-stage flame is located near a pressure node or a velocity antinode, the dynamics of the flame feature conspicuous flapping motion in the crossflow direction due to the influence of the primary flame-induced crossflow velocity fluctuations. On the other hand, when located near a pressure antinode, the secondary jet flame periodically exhibits combined dynamics of jet merging-induced flame front annihilation and the growth of non-axisymmetric coherent structures. In this case, high-intensity pressure oscillations are sustained by the local heat release fluctuations generated solely from the transverse reacting jets, while the upstream primary flame remains nearly unperturbed, or decoupled from the underlying feedback processes. In addition, to understand the synchronized or isolated dynamics of the system, the $\rm H_{2}$ concentration in the primary flame was varied without altering the secondary operating conditions. The results reveal two new phenomena: the simultaneous excitation of both flames sharing the same acoustic mode under higher $\rm H_{2}$ conditions, and instabilities induced by the secondary flame in isolation, without noticeable modulations in the primary flame. The following study investigates the distinctive characteristics of the transfer function of transverse reacting jets in vitiated crossflow, fundamentally important yet largely unknown. During the research, reduced-order modeling combined with two different flame transfer functions (for the primary and secondary flames)—an approach that has not been previously demonstrated—is performed to predict the stability of the axially staged system. From detailed measurements of transfer functions of lean-premixed primary and secondary flames in response to harmonic velocity disturbances, the results show that the transfer function of the second-stage flame is described as having relatively larger gain without undulating patterns, near-linear slow decay in magnitude with respect to the forcing frequency, and remarkably shorter duration response time. Using the reduced-order modeling approach that considers the crucial finite time delay between two distinct transfer functions, validated against empirical data, we demonstrate that self-induced instabilities in the axially staged system can be driven simultaneously by the dynamics of both primary and secondary flames. Additionally, the triggering of second-stage-induced instability is characteristically connected to higher-order acoustic modes, consistent with the aforementioned results. Such non-axisymmetric intra-combustor interactions generate a cascade of spectral peaks, including combinations of the first and third longitudinal modes and their intermodulation frequencies. Here, the secondary jet flame exhibits more complicated modal dynamics, manifested as the L3 mode-coupled jet merging-related flame surface annihilation and the L1 mode-coupled lateral movements of the transverse jet column. Additionally, the analysis reveals a close relationship between the amplitude of the secondary flame's fluctuations and the direction of the crossflow. Results from the consecutive experimental investigations are remarkable, revealing previously unknown findings about the combustion dynamics of the axially staged combustor and elucidating the underlying mechanisms of the complex thermoacoustic interactions in the two lean-premixed flames. The current integrated empirical and analytical findings are projected to serve as both foundational knowledge and an effective tool for the future development and operation of axial fuel-staged gas turbine engines.