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

Acoustic Damper Placement and Tuning for Annular Combustors: An Adjoint-Based Optimization Study

[+] Author and Article Information
Georg A. Mensah

Institut für Strömungsmechanik und
Technische Akustik,
Technische Universität Berlin,
Berlin 10115, Germany
e-mail: georg.a.mensah@tu-berlin.de

Jonas P. Moeck

Institut für Strömungsmechanik und
Technische Akustik,
Technische Universität Berlin,
Berlin 10115, Germany

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 August 11, 2016; final manuscript received September 14, 2016; published online January 18, 2017. Editor: David Wisler.

J. Eng. Gas Turbines Power 139(6), 061501 (Jan 18, 2017) (9 pages) Paper No: GTP-16-1404; doi: 10.1115/1.4035201 History: Received August 11, 2016; Revised September 14, 2016

Thermoacoustic instabilities pose a major threat to modern gas turbines. The use of acoustic dampers, like Helmholtz resonators, has proven useful for the mitigation of such instabilities. However, assessing the effect of acoustic dampers on thermoacoustic modes in annular combustion chambers remains an intricate task. This results from the implicit nature of the thermoacoustic Helmholtz equation associated with the high number of possible parameter values for the positioning of the dampers and their impedance design. In the present work, the principal challenges of the effective placement and the design of the impedance of acoustic dampers in annular chambers are discussed. This includes the choice of an appropriate objective function for the optimization, the combinatorial challenges when dealing with different possible damper arrangements, and the numerical complexities when using the thermoacoustic Helmholtz equation to approach this issue. As a key aspect, the paper proposes a new adjoint-based approach to tackle these problems. The new algorithm establishes algebraic models that predict the effect of acoustic dampers on the growth rates of the thermoacoustic modes. The theory is exemplified on the basis of a generic annular combustor model with 12 burners.

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Figures

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Fig. 1

Considered test geometry and discretization mesh. The black boundaries were assumed to be sound hard while a variable impedance could be specified at the outlet (green). The red shaded elements highlight the flame volume.

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Fig. 2

Comparison of the first neglected term σN+1ϵN+1ωN+1 and the corresponding error ηN. The first neglected term is indicated by a triangle while the error is marked by an asterisk. The different colors cyan, orange, green, blue, and magenta correspond to the perturbation amplification σ=1, 2, 4, 5, and 8, respectively.

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Fig. 3

Schematic illustration of the applied optimization algorithm

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Fig. 4

Illustration of the scaling problem. Cyan lines represent isolines of the objective function. The applied scaling considerably affects the parameter shift.

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Fig. 5

Illustration of the test case geometry and mesh. The numbers indicate the sector labels. Each sector is equipped with two independent impedance BCs close to the burner outlet (yellow and green lines). Cyan lines indicate periodic boundaries and black lines highlight sound hard boundaries. The red elements of the mesh highlight the domain of heat release.

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Fig. 6

Mode shapes of the three considered modes. The graphics represent the mode (0) (bottom right), mode (1) (bottom left), and mode (2) (top right). The color shading represents the real part of the complex pressure amplitude p̂.

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Fig. 7

Comparison of expected (arrows) and actual (stars) growth rate shifts of the first and second considered modes. Orange and green correspond to mode (1); blue and red represent the growth rates of mode (2). The triples indicate the burner segments equipped with dampers. Taking the rotational symmetry of the system into account, all relevant configurations are considered. There are several configurations where the estimate is showing the same low growth rate. This is in accordance with the positioning rule given in Ref. [7].

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Fig. 8

Evolution of the minimum damping rate for the first 60 optimization iteration steps. The algorithm successfully stabilizes the considered modes. The non-monotonic development may be attributed to poor scaling of the design parameters, a weak step size tolerance, or the non-smoothness of the objective function.

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