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

Linearized Euler Equations for the Prediction of Linear High-Frequency Stability in Gas Turbine Combustors

[+] Author and Article Information
Moritz Schulze

Lehrstuhl für Thermodynamik,
Technische Universität München,
Garching D-85748, Germany
e-mail: schulze@td.mw.tum.de

Tobias Hummel

Lehrstuhl für Thermodynamik,
Technische Universität München,
Garching D-85748, Germany;
Institute for Advanced Study,
Technische Universität München,
Garching D-85748, Germany

Noah Klarmann, Frederik Berger, Thomas Sattelmayer

Lehrstuhl für Thermodynamik,
Technische Universität München,
Garching D-85748, Germany

Bruno Schuermans

Institute for Advanced Study,
Technische Universität München,
Garching D-85748, Germany;
GE Power,
Baden 5400, Switzerland

1Corresponding author.

Manuscript received July 9, 2016; final manuscript received July 12, 2016; published online October 4, 2016. Editor: David Wisler.

J. Eng. Gas Turbines Power 139(3), 031510 (Oct 04, 2016) (10 pages) Paper No: GTP-16-1319; doi: 10.1115/1.4034453 History: Received July 09, 2016; Revised July 12, 2016

A novel methodology for linear stability analysis of high-frequency thermoacoustic oscillations in gas turbine combustors is presented. The methodology is based on the linearized Euler equations (LEEs), which yield a high-fidelity description of acoustic wave propagation and damping in complex, nonuniform, reactive mean flow environments, such as encountered in gas turbine combustion chambers. Specifically, this work introduces three novelties to the community: (1) linear stability analysis on the basis of linearized Euler equations. (2) Explicit consideration of three-dimensional, acoustic oscillations at screech level frequencies, particularly the first-transversal mode. (3) Handling of noncompact flame coupling with LEE, that is, the spatially varying coupling dynamics between perturbation and unsteady flame response due to small acoustic wavelengths. Two different configurations of an experimental model combustor in terms of thermal power and mass flow rates are subject of the analysis. Linear flame driving is modeled by prescribing the unsteady heat release source term of the linearized Euler equations by local flame transfer functions, which are retrieved from first principles. The required steady-state flow field is numerically obtained via computational fluid dynamics (CFD), which is based on an extended flamelet-generated manifold (FGM) combustion model, taking into account heat transfer to the environment. The model is therefore highly suitable for such types of combustors. The configurations are simulated, and thermoacoustically characterized in terms of eigenfrequencies and growth rates associated with the first-transversal mode. The findings are validated against experimentally observed thermoacoustic stability characteristics. On the basis of the results, new insights into the acoustic field are discussed.

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Figures

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Fig. 1

Model burner experimental setup [16]

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Fig. 2

Normalized mean heat release fields for marginally stable LP (left) and stable LP (right) [21]

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Fig. 3

Discretized computational domain with boundary conditions (top) and detailed grid topology in the vicinity of the burner with mesh refinement

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Fig. 4

Grid convergence study in terms of eigenfrequency and growth rate

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Fig. 5

Experimentally determined PSDs for stable LP (top) and marginally stable load point (bottom) as well as comparison of eigenfrequencies to numerical findings [16]

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Fig. 6

Axially distributed mean temperature T¯

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Fig. 7

Mode shapes in terms of normalized ℜ(p̂T1l) for the T1l mode: stable load point for a realistic distribution of speed of sound as well as for constant speed of sound (top) and marginally stable load point (bottom)

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Fig. 8

Axial distributions of normalized pressure ℜ(p̂T1l) and normalized axial velocity ℜ(ûT1l) along the pressure antinodal line for stable and marginally stable load points

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Fig. 9

T1l mode normalized transverse velocity v̂ (top) and density ρ̂ (bottom) for marginally stable load point at two phase instants

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Fig. 10

Imaginary part of T1 wave number ℑ(kT1+) for marginally stable LP (top) and stable LP (bottom)

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Fig. 11

Normalized pressure along the antinodal line and exponential fit for stable and marginally stable operation

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