Methods for the calculation of thermoacoustic stability margins and Monte Carlo-free uncertainty quantification

[+] Author and Article Information
Georg A. Mensah

Institut fr Strmungsmechanik und Technische Akustik Technische Universiterlin Berlin, Germany

Luca Magri

University of Cambridge Engineering Department Cambridge, UK

Jonas P. Moeck

Institut fr Strmungsmechanik und Technische Akustik Technische Universiterlin Berlin, Germany

1Corresponding author.

ASME doi:10.1115/1.4038156 History: Received July 18, 2017; Revised August 10, 2017


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 CFD computations. Frequency-domain approaches 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, which are obtained by experiments with some uncertainty, may have a great impact on stability. The assessment of how parameter uncertainties propagate to system stability is therefore crucial. This question is addressed by uncertainty quantification. A common strategy for uncertainty quantification in thermoacoustics is risk factor analysis. It quantifies the uncertainty of a set of parameters in terms of the probability of a mode to become unstable. A new and fast way to obtain algebraic parameter models in order to tackle the implicit nature of the eigenfrequency 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 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 validation is available.

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