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Equivalence ratio fluctuations are known to he one of the key factors controlling thermoacoustic stability in lean premixed gas turbine combustors. The mixing and thus the spatiotemporal evolution of these perturbations in the combustor flow is, however, difficult to account for in present low-order modeling approaches. To investigate this mechanism, experiments in an atmospheric combustion test rig are conducted. To assess the importance of equivalence ratio fluctuations in the present case, flame transfer functions for different injection positions are measured. By adding known perturbations in the fuel flow using a solenoid valve, the influence of equivalence ratio oscillations on the heat release rate is investigated. The equivalence ratio fluctuations in the reaction zone are measured spatially and temporally resolved using two optical chemiluminescence signals, captured with an intensifled camera. A steady calibration measurement allows for the quantitative assessment of the equivalence ratio fluctuations in the flame. This information is used to obtain a mixing transfer function, which relates fluctuations in the fuel flow to corresponding fluctuations in the equivalence ratio of the flame. The current study focuses on the measurement of the global, spatially integrated, transfer function for equivalence ratio fluctuations and the corresponding modeling. In addition, the spatially resolved mixing transfer function is shown and discussed. The global mixing transfer function reveals that, despite the good spatial mixing quality of the investigated generic burner, the ability to damp temporal fluctuations at low frequencies is rather poor. It is shown that the equivalence ratio fluctuations are the governing heat release rate oscillation response mechanism for this burner in the low-frequency regime. The global transfer function for equivalence ratio fluctuations derived from the measurements is characterized by a pronounced low-pass characteristic, which is in good agreement with the presented convection-diffusion mixing model.

The describing function is a powerful tool to characterize nonlinear dynamical systems in the frequency domain. In some cases, it is the only available description of a nonlinear operator characterizing a certain subcomponent of the system. This paper presents a methodology to provide a state-space realization of one given describing function, in order to allow the study of the system in the time domain as well. The realization is based on Hammerstein models and Fourier-Bessel series. It can be embedded in time domain simulations of complex configurations with many nonlinear elements interacting, accurately describing the nonlinear saturation of the system. The technique is applied to an example application in the field of combustion instability, featuring self-excited thermoacoustic oscillations. We benchmark the performance of the tool comparing the results with a frequency domain analysis of the same system, obtaining good agreement between the two formulations.

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Controlling combustion instabilities by means of open-loop forcing at non-resonantfrequencies is attractive because neither a dynamic sensor signal nor a signal processor is required. On the other hand, since the mechanism by which this type of control suppresses an unstable thermoacoustic mode is inherently nonlinear, a comprehensive explanation for success (or failure) of open-loop control has not been found. The present work contributes to the understanding of this process in that it interprets open-loop forcing at non-resonant fi'equencies in terms of the flame's nonlinear response to a superposition of two approximately sinusoidal input signals. For a saturation-type nonlinearity, the fundamental gain at one frequency may be decrea. sed by increasing the amplitude of a secondary fi-equency component in the input signal. This effect is flrst illustrated on the basis of an elementary model problem. In addition, an experimental investigation is conducted at an atmospheric combustor test-rig to corroborate the proposed explanation. Open-loop acoustic and fuelflow forcing at various frequencies and amplitudes is applied at unstable operating conditions that exhibit high-amplitude limit-cycle oscillations. The effectiveness of specific forcing parameters in suppressing self-e.xcited oscillations is correlated with flame response measurements that include a secondary forcing frequency. The results demonstrate that a reduction in the fundamental harmonic gain at the instability frequency through the additional forcing at a non-resonant frequency is one possible indicator of successful open-loopcontrol. Since this mechanism is independent of the system acoustics, an assessment of favorable forcing parameters, which stabilize thermoacoustic oscillations, may be based solely on an investigation of burner and flame.

The current paper investigates the nonlinear interaction of the flow field and the unsteady heat release rate and the role of swirl fluctuations. The test rig consists of a generic swirl-stabilized combustor fed with natural gas and equipped with a high-amplitude forcing device. The influence of the phase between axial and azimuthal velocity oscillations is assessed on the basis of the amplitude and phase relations between the velocity fluctuations at the inlet and the outlet of the burner. These relations are determined in the experiment with the multimicrophone-method and a two component laser Doppler velocimeter (LDV). Particle image velocimetry (PIV) and OH*-chemiluminescence measurements are conducted to study the interaction between the flow field and the flame. For several frequency regimes, characteristic properties of the forced flow field and flame are identified, and a strong amplitude dependence is observed. It is found that the convective time delay between the swirl generator and the flame has an important influence on swirl-number oscillations and the flame dynamics in the low-frequency regime. For mid and high frequencies, significant changes in the mean flow field and the mean flame position are identified for high forcing amplitudes. These affect the interaction between coherent structures and the flame and are suggested to be responsible for the saturation in the flame response at high forcing amplitudes.