NDLI: Low-Order Modeling of Nonlinear High-Frequency Transversal Thermoacoustic Oscillations in Gas Turbine Combustors

Content Provider	The American Society of Mechanical Engineers (ASME) Digital Collection
Author	Hummel, Tobias Hammer, Klaus Romero, Pedro Schuermans, Bruno Sattelmayer, Thomas
Copyright Year	2016
Abstract	This paper analyzes transversal thermoacoustic oscillations in an experimental gas turbine combustor utilizing dynamical system theory. Limit cycle acoustic motions related to the first linearly unstable transversal mode of a given 3D combustor configuration are modeled, and reconstructed by means of a low order dynamical system simulation. The source of nonlinearity is solely allocated to flame dynamics, saturating the growth of acoustic amplitudes, while the oscillation amplitudes are assumed to always remain within the linearity limit. First, a Reduced Order Model (ROM), which reproduces the combustor’s modal distribution and damping of acoustic oscillations is derived. The ROM is a low-order state-space system, which results from a projection of the Linearized Euler Equations (LEE) into their truncated eigenspace. Second, flame dynamics are modeled as a function of acoustic perturbations by means of a nonlinear transfer function. This function has a linear and a nonlinear contribution. The linear part is modeled analytically from first principles, while the nonlinear part is mathematically cast into a cubic saturation functional form. Additionally, the impact of stochastic forcing due to broadband combustion noise is included by additive white noise sources. Then, the acoustic and the flame system is interconnected, where thermoacoustic non-compactness due to the transversal modes’ high frequency is accounted for by a distributed source term framework. The resulting nonlinear thermoacoustic system is solved in frequency and time domain. Linear growth rates predict linear stability, while envelope plots and probability density diagrams of the resulting pressure traces characterize the thermoacoustic performance of the combustor from a dynamical systems theory perspective. Comparisons against experimental data are conducted, which allow the rating of the flame modes in terms of their capability to reproduce the observed combustor dynamics. Ultimately, insight into the physics of high-frequency, transversal thermoacoustic systems is created.
Sponsorship	International Gas Turbine Institute
File Format	PDF
ISBN	9780791849767
DOI	10.1115/GT2016-57913
Volume Number	Volume 4B: Combustion, Fuels and Emissions
Conference Proceedings	ASME Turbo Expo 2016: Turbomachinery Technical Conference and Exposition
Language	English
Publisher Date	2016-06-13
Publisher Place	Seoul, South Korea
Access Restriction	Subscribed
Subject Keyword	Damping Stability Dynamic systems Transfer functions Oscillations Probability Acoustics Combustion Limit cycles Modeling Density Pressure Physics Noise (sound) Flames Gas turbines Simulation Dynamics (mechanics) White noise Combustion chambers
Content Type	Text
Resource Type	Article

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