Gas-turbine combustion chambers typically consist of nominally identical sectors arranged in a rotationally symmetric pattern. However, in practice, the geometry is not perfectly symmetric. This may be due to design decisions, such as placing dampers in an azimuthally nonuniform fashion, or to uncertainties in the design parameters, which break the rotational symmetry of the combustion chamber. The question is whether these deviations from symmetry have impact on the thermoacoustic-stability calculation. The paper addresses this question by proposing a fast adjoint-based perturbation method. This method can be integrated into numerical frameworks that are industrial standard such as lumped-network models, Helmholtz and linearized Euler equations. The thermoacoustic stability of asymmetric combustion chambers is investigated by perturbing rotationally symmetric combustor models. The approach proposed in this paper is applied to a realistic three-dimensional combustion chamber model with an experimentally measured flame transfer function (FTF). The model equations are solved with a Helmholtz solver. Results for modes of zeroth, first, and second azimuthal order are presented and compared to exact solutions of the problem. A focus of the discussion is set on the loss of mode-degeneracy due to symmetry breaking and the capability of the perturbation theory to accurately predict it. In particular, an “inclination rule” that explains the behavior of degenerate eigenvalues at first order is proven.
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April 2019
Research-Article
Effects of Asymmetry on Thermoacoustic Modes in Annular Combustors: A Higher-Order Perturbation Study
Georg A. Mensah,
Georg A. Mensah
Institut für Strömungsmechanik und
Technische Akustik,
Technische Universität Berlin,
Berlin 10623, Germany
e-mail: georg.a.mensah@tu-berlin.de
Technische Akustik,
Technische Universität Berlin,
Berlin 10623, Germany
e-mail: georg.a.mensah@tu-berlin.de
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Luca Magri,
Luca Magri
Engineering Department,
University of Cambridge,
Cambridge CB2 1PZ, UK
University of Cambridge,
Cambridge CB2 1PZ, UK
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Alessandro Orchini,
Alessandro Orchini
Institut für Strömungsmechanik und
Technische Akustik,
Technische Universität Berlin,
Berlin 10623, Germany
Technische Akustik,
Technische Universität Berlin,
Berlin 10623, Germany
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Jonas P. Moeck
Jonas P. Moeck
Institut für Strömungsmechanik und
Technische Akustik,
Technische Universität Berlin,
Berlin 10623, Germany;
Technische Akustik,
Technische Universität Berlin,
Berlin 10623, Germany;
Department of Energy and
Process Engineering,
Norwegian University of
Science and Technology,
Trondheim 7491, Norway
Process Engineering,
Norwegian University of
Science and Technology,
Trondheim 7491, Norway
Search for other works by this author on:
Georg A. Mensah
Institut für Strömungsmechanik und
Technische Akustik,
Technische Universität Berlin,
Berlin 10623, Germany
e-mail: georg.a.mensah@tu-berlin.de
Technische Akustik,
Technische Universität Berlin,
Berlin 10623, Germany
e-mail: georg.a.mensah@tu-berlin.de
Luca Magri
Engineering Department,
University of Cambridge,
Cambridge CB2 1PZ, UK
University of Cambridge,
Cambridge CB2 1PZ, UK
Alessandro Orchini
Institut für Strömungsmechanik und
Technische Akustik,
Technische Universität Berlin,
Berlin 10623, Germany
Technische Akustik,
Technische Universität Berlin,
Berlin 10623, Germany
Jonas P. Moeck
Institut für Strömungsmechanik und
Technische Akustik,
Technische Universität Berlin,
Berlin 10623, Germany;
Technische Akustik,
Technische Universität Berlin,
Berlin 10623, Germany;
Department of Energy and
Process Engineering,
Norwegian University of
Science and Technology,
Trondheim 7491, Norway
Process Engineering,
Norwegian University of
Science and Technology,
Trondheim 7491, Norway
Manuscript received June 26, 2018; final manuscript received July 10, 2018; published online December 7, 2018. Editor: Jerzy T. Sawicki.
J. Eng. Gas Turbines Power. Apr 2019, 141(4): 041030 (8 pages)
Published Online: December 7, 2018
Article history
Received:
June 26, 2018
Revised:
July 10, 2018
Citation
Mensah, G. A., Magri, L., Orchini, A., and Moeck, J. P. (December 7, 2018). "Effects of Asymmetry on Thermoacoustic Modes in Annular Combustors: A Higher-Order Perturbation Study." ASME. J. Eng. Gas Turbines Power. April 2019; 141(4): 041030. https://doi.org/10.1115/1.4041007
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