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research-article

Thermoacoustic Damping Rate Determination from Combustion Noise Using Bayesian Statistics

[+] Author and Article Information
Nicolai Stadlmair

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

Tobias Hummel

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

Thomas Sattelmayer

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

1Corresponding author.

ASME doi:10.1115/1.4038475 History: Received August 05, 2017; Revised September 12, 2017

Abstract

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. 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 by a Markov-Chain Monte-Carlo (MCMC) method. The method provides a robust solution algorithm for fitting problems without requiring initial values. First, a simulation of a stochastically forced van-der-Pol oscillator with pre-set input values is carried out to demonstrate accuracy and robustness of the method. In this context it is shown that, despite of a large amount of uncorrelated background noise, the identified damping rates are in a good agreement with the simulated parameters. Secondly, 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.

Copyright (c) 2017 by ASME
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