Thermoacoustic instabilities are a major threat for modern gas turbines. Frequency-domain-based stability methods, such as network models and Helmholtz solvers, are common design tools because they are fast compared to compressible flow computations. They result in an eigenvalue problem, which is nonlinear with respect to the eigenvalue. Thus, the influence of the relevant parameters on mode stability is only given implicitly. Small changes in some model parameters, may have a great impact on stability. The assessment of how parameter uncertainties propagate to system stability is therefore crucial for safe gas turbine operation. This question is addressed by uncertainty quantification. A common strategy for uncertainty quantification in thermoacoustics is risk factor analysis. One general challenge regarding uncertainty quantification is the sheer number of uncertain parameter combinations to be quantified. For instance, uncertain parameters in an annular combustor might be the equivalence ratio, convection times, geometrical parameters, boundary impedances, flame response model parameters, etc. A new and fast way to obtain algebraic parameter models in order to tackle the implicit nature of the problem is using adjoint perturbation theory. This paper aims to further utilize adjoint methods for the quantification of uncertainties. This analytical method avoids the usual random Monte Carlo (MC) simulations, making it particularly attractive for industrial purposes. Using network models and the open-source Helmholtz solver PyHoltz, it is also discussed how to apply the method with standard modeling techniques. The theory is exemplified based on a simple ducted flame and a combustor of EM2C laboratory for which experimental data are available.
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June 2018
Research-Article
Methods for the Calculation of Thermoacoustic Stability Boundaries and Monte Carlo-Free Uncertainty Quantification
Georg A. Mensah,
Georg A. Mensah
Institut für Strömungsmechanik
und Technische Akustik,
Technische Universität Berlin,
Berlin 10623, Germany
e-mail: georg.a.mensah@tu-berlin.de
und Technische Akustik,
Technische Universität Berlin,
Berlin 10623, Germany
e-mail: georg.a.mensah@tu-berlin.de
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Luca Magri,
Luca Magri
Engineering Department,
University of Cambridge,
Cambridge CB2 1PZ, UK
University of Cambridge,
Cambridge CB2 1PZ, UK
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Jonas P. Moeck
Jonas P. Moeck
Institut für Strömungsmechanik
und Technische Akustik,
Technische Universität Berlin,
Berlin 10623, Germany
und Technische Akustik,
Technische Universität Berlin,
Berlin 10623, Germany
Search for other works by this author on:
Georg A. Mensah
Institut für Strömungsmechanik
und Technische Akustik,
Technische Universität Berlin,
Berlin 10623, Germany
e-mail: georg.a.mensah@tu-berlin.de
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
University of Cambridge,
Cambridge CB2 1PZ, UK
Jonas P. Moeck
Institut für Strömungsmechanik
und Technische Akustik,
Technische Universität Berlin,
Berlin 10623, Germany
und Technische Akustik,
Technische Universität Berlin,
Berlin 10623, 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 July 18, 2017; final manuscript received August 10, 2017; published online January 17, 2018. Editor: David Wisler.
J. Eng. Gas Turbines Power. Jun 2018, 140(6): 061501 (10 pages)
Published Online: January 17, 2018
Article history
Received:
July 18, 2017
Revised:
August 10, 2017
Citation
Mensah, G. A., Magri, L., and Moeck, J. P. (January 17, 2018). "Methods for the Calculation of Thermoacoustic Stability Boundaries and Monte Carlo-Free Uncertainty Quantification." ASME. J. Eng. Gas Turbines Power. June 2018; 140(6): 061501. https://doi.org/10.1115/1.4038156
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