In this paper, we present a method to determine the quantitative stability level of a lean-premixed combustor from dynamic pressure data. Specifically, we make use of the autocorrelation function of the dynamic pressure signal acquired in a combustor where a turbulent flame acts as a thermoacoustic driver. In the proposed approach, the unfiltered pressure signal including several modes is analyzed by an algorithm based on Bayesian statistics. For this purpose, a Gibbs sampler is used to calculate parameters like damping rates and eigenfrequencies in the form of probability density functions (PDF) by a Markov-chain Monte Carlo (MCMC) method. The method provides a robust solution algorithm for fitting problems without requiring initial values. A further advantage lies in the nature of the statistical approach since the results can be assessed regarding its quality by means of the PDF and its standard deviation for each of the obtained parameters. First, a simulation of a stochastically forced van-der-Pol oscillator with preset input values is carried out to demonstrate accuracy and robustness of the method. In this context, it is shown that, despite a large amount of uncorrelated background noise, the identified damping rates are in a good agreement with the simulated parameters. Second, this technique is applied to measured pressure data. By doing so, the combustor is initially operated under stable conditions before the thermal power is gradually increased by adjusting the fuel mass flow rate until a limit-cycle oscillation is established. It is found that the obtained damping rates are qualitatively in line with the amplitude levels observed during operation of the combustor.

The goal of this study is to analyze flame transfer functions (FTFs) locally by quantifying the heat release rate with OH*-chemiluminescence and density fluctuation measurements using laser vibrometry. In this study, both techniques are applied to a swirl burner configuration with known FTFs acquired by multimicrophone-method (MMM) measurements for perfectly premixed and partially premixed cases. The planar fields of the quantities are compared to the FTFs in order to improve the understanding regarding the specific amplitude and phase values. On the global scale values of heat release expected from the MMM are satisfactorily reproduced by both methods for the premixed cases, whereas OH*-chemiluminescence data cannot be used as indicator for heat release in the partially premixed case, where equivalence ratio fluctuations are present. Vibrometry is not affected by fluctuations of equivalence ratio but additionally reveals the periodic oscillation of the conical annular jet of the cold reactants in the combustor filled with hot products.

This paper presents a set of methodologies for the extraction of linear growth and damping rates associated with transversal eigenmodes at screech level frequencies in thermoacoustically non-compact gas turbine combustion systems from time domain data. Knowledge of these quantities is of high technical relevance as an required input for the design of damping devices for high frequency oscillations. In addition, validation of prediction tools and flame models as well as the thermoacoustic characterization of a given unstable/stable operation point in terms of their distance from the Hopf bifurcation point occurs via the system growth/damping rates. The methodologies solely rely on dynamic measurement data (i.e. unsteady heat release and/or pressure recordings) while avoiding the need of any external excitation (e.g. via sirens), and are thus in principle suitable for the employment on operational engine data. Specifically, the following methodologies are presented: 1) The extraction of pure acoustic damping rates (i.e. without any flame contribution) from oscillatory chemiluminescence and pressure recordings. 2) The obtainment of net growth rates of linearly stable operation points from oscillatory pressure signals. 3) The identification of net growth rates of linearly unstable operation points from noisy pressure envelope data. The fundamental basis of these procedures is the derivation of appropriate stochastic differential equations, which admit analytical solutions that depend on the global system parameters. These analytical expressions serve as objective functions against which measured data are fitted to yield the desired growth or damping rates. Bayesian methods are employed to optimize precision and confidence of the fitting results. Numerical test cases given by time domain formulations of the acoustic conservation equations including high-frequency flame models as well as acoustic damping terms are set up and solved. The resulting unsteady pressure and heat release data are then subjected to the proposed identification methodologies to present corresponding proof of principles and grant suitability for employment on real systems.

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This paper presents a set of methodologies for the extraction of linear growth and damping rates associated with transversal eigenmodes at screech level frequencies in thermoacoustically noncompact gas turbine combustion systems from time domain data. Knowledge of these quantities is of high technical relevance as a required input for the design of damping devices for high frequency (HF) oscillations. In addition, validation of prediction tools and flame models as well as the thermoacoustic characterization of a given unstable/stable operation point in terms of their distance from the Hopf bifurcation point occurs via the system growth/damping rates. The methodologies solely rely on dynamic measurement data (i.e., unsteady heat release and/or pressure recordings) while avoiding the need of any external excitation (e.g., via sirens), and are thus in principle suitable for the employment on operational engine data. Specifically, the following methodologies are presented: (1) The extraction of pure acoustic damping rates (i.e., without any flame contribution) from oscillatory chemiluminescence and pressure recordings; (2) The obtainment of net growth rates of linearly stable operation points from oscillatory pressure signals; and (3) The identification of net growth rates of linearly unstable operation points from noisy pressure envelope data. The fundamental basis of these procedures is the derivation of appropriate stochastic differential equations (SDE), which admit analytical solutions that depend on the global system parameters. These analytical expressions serve as objective functions against which measured data are fitted to yield the desired growth or damping rates. Bayesian methods are employed to optimize precision and confidence of the fitting results. Numerical test cases given by time domain formulations of the acoustic conservation equations including HF flame models as well as acoustic damping terms are set up and solved. The resulting unsteady pressure and heat release data are then subjected to the proposed identification methodologies to present corresponding proof of principles and grant suitability for employment on real systems.