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

Efficient Computation of Thermoacoustic Modes in Industrial Annular Combustion Chambers Based on Bloch-Wave Theory

[+] Author and Article Information
Georg A. Mensah, Jonas P. Moeck

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

Giovanni Campa

Product Development,
Turbomachinery and Combustion,
Ansaldo Energia S.p.A.,
Genova 16152, Italy

Contributed by the Combustion and Fuels Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received October 5, 2015; final manuscript received November 2, 2015; published online February 23, 2016. Editor: David Wisler.

J. Eng. Gas Turbines Power 138(8), 081502 (Feb 23, 2016) (7 pages) Paper No: GTP-15-1474; doi: 10.1115/1.4032335 History: Received October 05, 2015; Revised November 02, 2015

Most annular combustors feature a discrete rotational symmetry so that the full configuration can be obtained by copying one burner-flame segment a certain number of times around the circumference. A thermoacoustic model based on the Helmholtz equation then admits special solutions of the so-called Bloch type that can be obtained by considering one segment only. We show that a significant reduction in computational effort for the determination of thermoacoustic modes can be achieved by exploiting this concept. The framework is applicable even in complex cases including an inhomogeneous temperature field and a frequency-dependent, spatially distributed flame response. A parametric study on a three-dimensional combustion chamber model is conducted using both the full-scale chamber simulation and a one-segment model with the appropriate Bloch-type boundary conditions. The results for both computations are compared in terms of mode frequencies and growth rates as well as the corresponding mode shapes. The same is done for a more complex industrial configuration. These comparisons demonstrate the benefits of the Bloch-wave based analysis.

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Grahic Jump Location
Fig. 1

The red dots correspond to the centers of the cells, where unsteady heating may occur

Grahic Jump Location
Fig. 2

Illustration of linear elements with periodic and Bloch-periodic boundary conditions; adapted from Ref. [20]

Grahic Jump Location
Fig. 3

Generic annular combustion chamber geometry as proposed in Ref. [7]. Only one unit cell is shown here. The degree of symmetry is N = 12 and thus the full geometry can be restored by respective incremental rotations around the symmetry axis.

Grahic Jump Location
Fig. 4

Schematic representation of the generic combustion chamber setup. The blue faces highlight the Bloch-periodic boundaries. All other boundaries are assumed to be acoustically hard walls where the normal component of the acoustic velocity vanishes. The cones illustrate the position and shape of the domains of heat release.

Grahic Jump Location
Fig. 5

Left: cross-sectional view along the symmetry plane of a unit cell of the generic chamber setup showing the temperature distribution. The dashed hatching indicates the hot gas (1800 K), while the solid hatching highlights the cold gas (300 K). The heat release zone is indicated by the orange area. Right: detailed geometry of the generic heat release zone, i.e., the flame.

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Fig. 6

Comparison of the eigenfrequencies computed with full domain and unit-cell approach. The deviation for higher frequencies can be attributed to the better convergence of the unit-cell computation.

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Fig. 7

Comparison of unstable 228 Hz modes computed with full domain and unit-cell approach. The eigenfunction in the full domain can be restored from the unit-cell solution by means of the extrapolation property (14). The color scheme represents the normalized acoustic pressure amplitude. The angular planes in combustion chamber and plenum are only virtual separations to depict the individual segments; they are not physical walls.

Grahic Jump Location
Fig. 8

Comparison of the real and imaginary parts of the normalized pressure fluctuation amplitude of the unstable 228 Hz mode of the generic chamber. The full chamber result is indicated by an dashed line while the result from the unit-cell computation is drawn with a solid line. The values were sampled along a ring of 0.22 m radius at a height of 0.26 m. This is 0.03 m above the burner outlet in the combustion chamber. The Bloch-periodicity and the occurring mirror symmetry were exploited to recover the full mode. The small deviations can be attributed to different meshes used for the unit cell and the full chamber. However, the excellent agreement of the two results becomes clear.

Grahic Jump Location
Fig. 9

Schematic illustration of the AE94.3A unit-cell model setup. Sound hard boundaries (gray) were set at all walls and the inlet, a complex impedance (green) at the outlet, Bloch-periodic boundaries (cyan) at the azimuthal sides. Transfer matrices (yellow) were used to model the acoustic response of the burner.

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Fig. 10

Comparison of the resulting frequencies and growth rates for the industrial combustion chamber model. The axis has been normalized using the same reference values. Note the different scaling of the axis, causing deviations in the growth rates to appear larger relative to deviations in the frequencies. However, the good match of the results of the two methods can be seen. The arrow indicates the eigenvalues corresponding to the modes in Fig. 11.

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Fig. 11

Comparison of the same mode computed with quarter domain (right) and with unit-cell (left) approach. The color scheme represents the normalized acoustic pressure amplitude. The mode shapes correspond to the eigenfrequencies indicated by the arrow in Fig. 10. The eigenfunction in the full domain can be restored from the unit-cell solution by means of the Bloch-periodicity (14).



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