This paper analyzes transversal thermoacoustic oscillations in an experimental gas turbine combustor utilizing dynamical system theory. Limit-cycle acoustic motions related to the first linearly unstable transversal mode of a given 3D combustor configuration are modeled and reconstructed by means of a low-order dynamical system simulation. The source of nonlinearity is solely allocated to flame dynamics, saturating the growth of acoustic amplitudes, while the oscillation amplitudes are assumed to always remain within the linearity limit. First, a reduced order model (ROM) which reproduces the combustor's modal distribution and damping of acoustic oscillations is derived. The ROM is a low-order state-space system, which results from a projection of the linearized Euler equations (LEE) into their truncated eigenspace. Second, flame dynamics are modeled as a function of acoustic perturbations by means of a nonlinear transfer function. This function has a linear and a nonlinear contribution. The linear part is modeled analytically from first principles, while the nonlinear part is mathematically cast into a cubic saturation functional form. Additionally, the impact of stochastic forcing due to broadband combustion noise is included by additive white noise sources. Then, the acoustic and the flame system is interconnected, where thermoacoustic noncompactness due to the transversal modes' high frequency (HF) is accounted for by a distributed source term framework. The resulting nonlinear thermoacoustic system is solved in frequency and time domain. Linear growth rates predict linear stability, while envelope plots and probability density diagrams of the resulting pressure traces characterize the thermoacoustic performance of the combustor from a dynamical systems theory perspective. Comparisons against experimental data are conducted, which allow the rating of the flame modes in terms of their capability to reproduce the observed combustor dynamics. Ultimately, insight into the physics of high-frequency, transversal thermoacoustic systems is created.
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July 2017
Research-Article
Low-Order Modeling of Nonlinear High-Frequency Transversal Thermoacoustic Oscillations in Gas Turbine Combustors
Tobias Hummel,
Tobias Hummel
Lehrstuhl für Thermodynamik,
Technische Universität München,
Garching 85748, Germany;
Technische Universität München,
Garching 85748, Germany;
Institute for Advanced Study,
Technische Universität München,
Garching 85748, Germany
e-mail: hummel@td.mw.tum.de
Technische Universität München,
Garching 85748, Germany
e-mail: hummel@td.mw.tum.de
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Klaus Hammer,
Klaus Hammer
Lehrstuhl für Thermodynamik,
Technische Universität München,
Garching 85748, Germany
e-mail: klaus.hammer@tum.de
Technische Universität München,
Garching 85748, Germany
e-mail: klaus.hammer@tum.de
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Pedro Romero,
Pedro Romero
Lehrstuhl für Thermodynamik,
Technische Universität München,
Garching 85748, Germany
e-mail: romero@td.mw.tum.de
Technische Universität München,
Garching 85748, Germany
e-mail: romero@td.mw.tum.de
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Bruno Schuermans,
Bruno Schuermans
Institute for Advanced Study,
Technische Universität München,
Garching 85748, Germany;
Technische Universität München,
Garching 85748, Germany;
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Thomas Sattelmayer
Thomas Sattelmayer
Lehrstuhl für Thermodynamik,
Technische Universität München,
Garching 85748, Germany
e-mail: sattelmayer@td.mw.tum.de
Technische Universität München,
Garching 85748, Germany
e-mail: sattelmayer@td.mw.tum.de
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Tobias Hummel
Lehrstuhl für Thermodynamik,
Technische Universität München,
Garching 85748, Germany;
Technische Universität München,
Garching 85748, Germany;
Institute for Advanced Study,
Technische Universität München,
Garching 85748, Germany
e-mail: hummel@td.mw.tum.de
Technische Universität München,
Garching 85748, Germany
e-mail: hummel@td.mw.tum.de
Klaus Hammer
Lehrstuhl für Thermodynamik,
Technische Universität München,
Garching 85748, Germany
e-mail: klaus.hammer@tum.de
Technische Universität München,
Garching 85748, Germany
e-mail: klaus.hammer@tum.de
Pedro Romero
Lehrstuhl für Thermodynamik,
Technische Universität München,
Garching 85748, Germany
e-mail: romero@td.mw.tum.de
Technische Universität München,
Garching 85748, Germany
e-mail: romero@td.mw.tum.de
Bruno Schuermans
Institute for Advanced Study,
Technische Universität München,
Garching 85748, Germany;
Technische Universität München,
Garching 85748, Germany;
Thomas Sattelmayer
Lehrstuhl für Thermodynamik,
Technische Universität München,
Garching 85748, Germany
e-mail: sattelmayer@td.mw.tum.de
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 11, 2016; final manuscript received November 30, 2016; published online February 23, 2017. Editor: David Wisler.
J. Eng. Gas Turbines Power. Jul 2017, 139(7): 071503 (11 pages)
Published Online: February 23, 2017
Article history
Received:
July 11, 2016
Revised:
November 30, 2016
Citation
Hummel, T., Hammer, K., Romero, P., Schuermans, B., and Sattelmayer, T. (February 23, 2017). "Low-Order Modeling of Nonlinear High-Frequency Transversal Thermoacoustic Oscillations in Gas Turbine Combustors." ASME. J. Eng. Gas Turbines Power. July 2017; 139(7): 071503. https://doi.org/10.1115/1.4035529
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