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

    Source: Journal of Engineering for Gas Turbines and Power:;2017:;volume( 139 ):;issue: 007::page 71503
    Author:
    Hummel, Tobias
    ,
    Hammer, Klaus
    ,
    Romero, Pedro
    ,
    Schuermans, Bruno
    ,
    Sattelmayer, Thomas
    DOI: 10.1115/1.4035529
    Publisher: The American Society of Mechanical Engineers (ASME)
    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 noncompactness due to the transversal modes' high frequency (HF) 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.
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      Low-Order Modeling of Nonlinear High-Frequency Transversal Thermoacoustic Oscillations in Gas Turbine Combustors

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    contributor authorHummel, Tobias
    contributor authorHammer, Klaus
    contributor authorRomero, Pedro
    contributor authorSchuermans, Bruno
    contributor authorSattelmayer, Thomas
    date accessioned2017-11-25T07:15:54Z
    date available2017-11-25T07:15:54Z
    date copyright2017/23/2
    date issued2017
    identifier issn0742-4795
    identifier othergtp_139_07_071503.pdf
    identifier urihttp://138.201.223.254:8080/yetl1/handle/yetl/4233733
    description abstractThis 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 noncompactness due to the transversal modes' high frequency (HF) 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.
    publisherThe American Society of Mechanical Engineers (ASME)
    titleLow-Order Modeling of Nonlinear High-Frequency Transversal Thermoacoustic Oscillations in Gas Turbine Combustors
    typeJournal Paper
    journal volume139
    journal issue7
    journal titleJournal of Engineering for Gas Turbines and Power
    identifier doi10.1115/1.4035529
    journal fristpage71503
    journal lastpage071503-11
    treeJournal of Engineering for Gas Turbines and Power:;2017:;volume( 139 ):;issue: 007
    contenttypeFulltext
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