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Characterizing energy growth during combustion instabilities: Singularvalues or eigenvalues?
Published in Elsevier Ltd
2009
Volume: 32 II
   
Pages: 2933 - 2940
Abstract
Non-normality in thermoacoustic systems has received attention recently. It has been shown that in a non-normal but classically linearly stable system, there can be significant transient energy growth of small perturbations before their eventual decay. This growth occurs in the absence of non-linear effects. This phenomenon can be explained by the non-normality of the governing linear operator or the non-orthogonality of the eigenvectors of the system. In this paper, we study various aspects of this transient energy growth for a general combustor, with localized heat release approximated by the popular n-r model. Galerkin technique is used to simplify the governing acoustic equations in a duct in the presence of a localized heat source with appropriate boundary conditions. Singularvalue decomposition (SVD) is used to compute the transient energy growth. SVD is used as a tool to obtain the maximum possible energy amplification and the optimal initial conditions required for this amplification. The necessary and sufficient conditions for no energy growth are discussed. A parametric analysis is performed to highlight the effect of system parameters on the maximum transient growth rate and to obtain regions of stability of the thermoacoustic system. © 2009 The Combustion Institute. Published by Elsevier Inc. All rights reserved.
About the journal
JournalData powered by TypesetProceedings of the Combustion Institute
PublisherData powered by TypesetElsevier Ltd
ISSN15407489
Open AccessNo
Concepts (14)
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    Combustion instabilities
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    Growth factor
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    NON-NORMALITY
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    PSEUDOSPECTRA
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    TIME LAG MODEL
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    Amplification
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    Bioactivity
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    Combustion
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    Mathematical operators
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    Peptides
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    Singular value decomposition
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    Smoke
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    Thermochemistry
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    Explosives