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

Thermoacoustic Damping Rate Determination From Combustion Noise Using Bayesian Statistics

[+] Author and Article Information
Nicolai V. Stadlmair

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

Tobias Hummel

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

Thomas Sattelmayer

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

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 August 5, 2017; final manuscript received September 12, 2017; published online June 27, 2018. Editor: David Wisler.

J. Eng. Gas Turbines Power 140(11), 111501 (Jun 27, 2018) (7 pages) Paper No: GTP-17-1435; doi: 10.1115/1.4038475 History: Received August 05, 2017; Revised September 12, 2017

In this paper, we present a method to determine the quantitative stability level of a lean-premixed combustor from dynamic pressure data. Specifically, we make use of the autocorrelation function of the dynamic pressure signal acquired in a combustor where a turbulent flame acts as a thermoacoustic driver. In the proposed approach, the unfiltered pressure signal including several modes is analyzed by an algorithm based on Bayesian statistics. For this purpose, a Gibbs sampler is used to calculate parameters like damping rates and eigenfrequencies in the form of probability density functions (PDF) by a Markov-chain Monte Carlo (MCMC) method. The method provides a robust solution algorithm for fitting problems without requiring initial values. A further advantage lies in the nature of the statistical approach since the results can be assessed regarding its quality by means of the PDF and its standard deviation for each of the obtained parameters. First, a simulation of a stochastically forced van-der-Pol oscillator with preset input values is carried out to demonstrate accuracy and robustness of the method. In this context, it is shown that, despite a large amount of uncorrelated background noise, the identified damping rates are in a good agreement with the simulated parameters. Second, this technique is applied to measured pressure data. By doing so, the combustor is initially operated under stable conditions before the thermal power is gradually increased by adjusting the fuel mass flow rate until a limit-cycle oscillation is established. It is found that the obtained damping rates are qualitatively in line with the amplitude levels observed during operation of the combustor.

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Figures

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Fig. 1

Block diagram of the second-order oscillator system to generate synthetic time series

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Fig. 2

Numerical validation test cases for single mode system (a) and multimode system (b): time series of raw signal, probability density of pressure signal p′, normalized PSD of p′, autocorrelation and envelope of the autocorrelation

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Fig. 3

Numerical validation test case A: probability densities of the fitting parameters ν1 and f=ω/2π and its corresponding standard deviations σ(…), autocorrelation function of the signal, fitted autocorrelation

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Fig. 4

Comparison of different simulation test cases A and B: autocorrelation of the signal, fitted autocorrelation, identified parameters ν1, ν2, and simulation parameters

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Fig. 5

Evolution of the error for the damping rates identifying one mode I = 1 and two modes I = 2

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Fig. 6

Atmospheric single burner test-rig with lean-premixed, swirl-stabilized flame

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Fig. 7

Signal characteristics of the measurement data for ϕ=0.63, Pth = 41.80 kW: time series of raw signal, probability density of pressure signal p′, normalized PSD of p′, autocorrelation of the signal and envelope of the autocorrelation function

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Fig. 8

Evolution of the damping rate (top) ν1 and ν2 and normalized modal amplitudes (bottom) η1 and η2 in the combustor for varying equivalence ratios

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