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research-article

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, 10623, Berlin, Germany
georg.a.mensah@tu-berlin.de

Luca Magri

Engineering Department, University of Cambridge, CB2 1PZ, Cambridge, United Kingdom
lm547@cam.ac.uk

Alessandro Orchini

Institut für Strömungsmechanik, und Technische Akustik, Technische Universität Berlin, 10623, Berlin, Germany
aorchini@gmail.com

Jonas P. Moeck

Institut für Strömungsmechanik, und Technische Akustik, Technische Universität Berlin, 10623, Berlin, Germany; Department of Energy and, Process Engineering, Norwegian University of Science and Technology, 7491, Trondheim, Norway
jonas.moeck@pi.tu-berlin.de

1Corresponding author.

ASME doi:10.1115/1.4041007 History: Received June 26, 2018; Revised July 10, 2018

Abstract

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 non-uniform 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 to 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, which is solved with a Helmholtz solver. Results for modes of zeroth, first, and second azimuthal mode 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.

Copyright (c) 2018 by ASME
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