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Research Papers: Gas Turbines: Combustion, Fuels, and Emissions

Extraction of Linear Growth and Damping Rates of High-Frequency Thermoacoustic Oscillations From Time Domain Data

[+] Author and Article Information
Tobias Hummel

Lehrstuhl für Thermodynamik,
Technische Universität München,
Garching 85748, Germany;
Institute for Advanced Study,
Technische Universität München,
Garching 85748, Germany
e-mail: hummel@td.mw.tum.de

Frederik Berger

Lehrstuhl für Thermodynamik,
Technische Universität München,
Garching 85748, Germany
e-mail: berger@td.mw.tum.de

Nicolai Stadlmair

Lehrstuhl für Thermodynamik,
Technische Universität München,
Garching 85748, Germany
e-mail: stadlmair@td.mw.tum.de

Bruno Schuermans

Institute for Advanced Study,
Technische Universität München,
Garching 85748, Germany;
GE Power,
Baden 5401, Switzerland
e-mail: bruno.schuermans@ge.com

Thomas Sattelmayer

Lehrstuhl für Thermodynamik,
Technische Universität München,
Garching 85748, Germany
e-mail: sattelmayer@td.mw.tum.de

1Corresponding author.

Contributed by the Combustion and Fuels Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received July 4, 2017; final manuscript received August 24, 2017; published online December 19, 2017. Editor: David Wisler.

J. Eng. Gas Turbines Power 140(5), 051505 (Dec 19, 2017) (10 pages) Paper No: GTP-17-1274; doi: 10.1115/1.4038240 History: Received July 04, 2017; Revised August 24, 2017

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.

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References

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Figures

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Fig. 2

Computational domain with damping region D, boundary conditions, mean heat release distribution, and T1 mode shape

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Fig. 1

Model combustion system with (a) longitudinal pressure mode and compact flame and (b) transversal pressure mode and noncompact flame

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Fig. 3

System identification results—left: damping rates, middle: net growth rates, and right: pure flame driving via βn = νn + αn

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Fig. 4

Noncompact flame segmentation, mean heat release distribution, and MIMO feedback connections for reduced order modeling

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Fig. 5

Representative signals of Fourier coefficients of the CCW rotating T1 mode for one (a) linearly stable and (b) unstable operation point. Probability density functions p reveal the noisy and limit cyclic nature of the respective signals as per normal and bimodal distributions.

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Fig. 7

Reconstructed autocorrelation function for identification of damping rate shown for unstable operation point OP#5

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Fig. 8

Time traces of slowly varying amplitudes

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Fig. 9

Fit results—unstable case OP#5

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Fig. 6

Integral heat release signal of (a) stable (OP#2) and (b) unstable (OP#5) operation points

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