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EXTRACTION OF LINEAR GROWTH AND DAMPING RATES OF HIGH-FREQUENCY THERMOACOUSTIC OSCILLATIONS FROM TIME DOMAIN DATA

[+] Author and Article Information
Tobias Hummel

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

Frederik M. Berger

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

Nicolai Stadlmair

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

Bruno Schuermans

Institute for Advanced Study, Technische Universität München, 85748 Garching, GermanyGE Power, 5401 Baden, Switzerland
bruno.schuermans@ge.com

Thomas Sattelmayer

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

1Corresponding author.

ASME doi:10.1115/1.4038240 History: Received July 04, 2017; Revised August 24, 2017

Abstract

This paper presents a set of methodologies for the extraction of linear growth and damping rates associated with transversal eigenmodes at screech level frequencies in thermoacoustically non-compact gas turbine combustion systems from time domain data. Knowledge of these quantities is of high technical relevance as an required input for the design of damping devices for high frequency oscillations. In addition, validation of prediction tools and flame models as well as the thermoacoustic characterization of a given unstable/stable operation point in terms of their distance from the Hopf bifurcation point occurs via the system growth/damping rates. The methodologies solely rely on autonomous dynamic measurement data. Three methodologies are presented: 1) Extraction of pure acoustic damping rates from oscillatory chemiluminescence and pressure recordings. 2) Obtainment of net growth rates of linearly stable operation points from oscillatory pressure signals. 3) Identification of net growth rates of linearly unstable operation points from noisy pressure envelope data. The basis of these procedures is the derivation of stochastic differential equations, which admit analytical solutions that depend on the desired parameters. These analytical expressions serve as objective functions against which measured data are fitted to yield the desired growth or damping rates. Bayesian methods are employed to optimize precision and confidence of the fitting results. Numerically obtained unsteady pressure and heat release data are then subjected to the proposed identification methodologies to present corresponding proof of principles and grant suitability for employment on real systems.

Copyright (c) 2017 by ASME
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