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Research Papers

Effects of Asymmetry on Thermoacoustic Modes in Annular Combustors: A Higher-Order Perturbation Study

[+] Author and Article Information
Georg A. Mensah

Institut für Strömungsmechanik und
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

Alessandro Orchini

Institut für Strömungsmechanik und
Technische Akustik,
Technische Universität Berlin,
Berlin 10623, Germany

Jonas P. Moeck

Institut für Strömungsmechanik und
Technische Akustik,
Technische Universität Berlin,
Berlin 10623, Germany;
Department of Energy and
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 141(4), 041030 (Dec 07, 2018) (8 pages) Paper No: GTP-18-1358; doi: 10.1115/1.4041007 History: Received June 26, 2018; Revised July 10, 2018

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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References

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Figures

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Fig. 1

Annular combustor geometry used for the present study. The combustor is referred to as MICCA [20]. The domain of heat release is highlighted in orange and is defined as in [23].

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Fig. 2

Discretization mesh used in this study (left) and mean speed of sound c0 (right). The color scale ranges from 348 m/s to 784 m/s.

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Fig. 3

Comparison between the state space model approximation of the FTF evaluated at purely real values of ω (solid line) and the data from experiments [23] (dots)

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Fig. 4

Pressure mode shapes of the three thermoacoustic modes considered in this study. They correspond to an axial mode (#0) and plenum-dominant azimuthal modes (#1 and #2).

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Fig. 5

Perturbation patterns under consideration. We set Δεn = 1 at the burners highlighted in orange in these patterns, and Δεn = 0 at the others.

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Fig. 6

Eigenvalue evolution of various modes (rows) for different perturbation patterns (columns). The black curves with markers denote the exact results for perturbation parameters μ of 0.00 (☆), 0.25 (◯), 0.50 (◯), 0.75 (◯), and 1.00 (⎔). The degenerate eigenvalues might split into two branches – orange line with (x)-markers and blue line with (+)-markers. The darker the shading, the higher the applied order of the perturbation theory. Note that for cases #1A, #2A, and #2B, an eigenvalue is unaffected by the perturbations, and therefore, it reduces to a single (blue) point.

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Fig. 7

Eigenvalue evolution for mode #1 when a modified version of pattern C is applied such that the average change to the FTFs is 0. As expected, the first-order theory predicts a shift of the eigenvalues in opposite directions.

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