Lean premix technology is widely spread in gas turbine combustion systems, allowing modern power plants to fulfill very stringent emission targets. These systems are, however, also prone to thermoacoustic instabilities, which can limit the engine operating window. The thermoacoustic analysis of a combustor is thus a key element in its development process. An important ingredient of this analysis is the characterization of the flame response to acoustic fluctuations, which is straightforward for lean-premixed flames that are propagation stabilized, since it can be measured atmospherically. Ansaldo Energia's GT26 and GT36 reheat combustion systems feature a unique technology where fuel is injected into a hot gas stream from a first combustor, which is propagation stabilized, and auto-ignites in a sequential combustion chamber. The present study deals with the flame response of mainly auto-ignition stabilized flames to acoustic and temperature fluctuations for which a computational fluid dynamics system identification (SI) approach is chosen. The current paper builds on recent works, which detail and validate a methodology to analyze the dynamic response of an auto-ignition flame to extract the flame transfer function (FTF) using unsteady large-Eddy simulations (LES). In these studies, the flame is assumed to behave as a single-input single-output (SISO) or a multi-input single-output (MISO) system. The analysis conducted in GT2015-42622 qualitatively highlights the important role of temperature and equivalence ratio fluctuations, but these effects are not separated from velocity fluctuations. Hence, this topic is addressed in GT2016-57699, where the flame is treated as a multiparameter system and compressible LES are conducted to extract the frequency-dependent FTF to describe the effects of axial velocity, temperature, equivalence ratio, and pressure fluctuations on the flame response. For lean-premixed flames, a common approach followed in the literature assumes that the acoustic pressure is constant across the flame and that the flame dynamics are governed by the response to velocity perturbations only, i.e., the FTF. However, this is not necessarily the case for reheat flames that are mainly auto-ignition stabilized. Therefore, in this paper, we present the full 2 × 2 transfer matrix of a predominantly auto-ignition stabilized flame, and hence, describe the flame as a multi-input multi-output (MIMO) system. In addition to this, it is highlighted that in the presence of temperature fluctuations, the 2 × 2 matrix can be extended to a 3 × 3 matrix relating the primitive acoustic variables as well as the temperature fluctuations across the flame. It is shown that only taking the FTF is insufficient to fully describe the dynamic behavior of reheat flames.

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