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Identification of heat transfer dynamics for non-modal analysis of thermoacoustic stability
Published in
2011
Volume: 217
   
Issue: 11
Pages: 5134 - 5150
Abstract
A systematic approach for non-modal stability analysis of thermoacoustic systems with a localized heat source is proposed. The response of the heat source to flow perturbations is obtained from unsteady computational fluid dynamics combined with correlation-based linear system identification. A model for the complete thermoacoustic system is formulated with a Galerkin expansion technique, where the heat source is included as an acoustically compact element. The eigenvalues of the resulting system are obtained from discretization of the solution operator, the maximum growth factor is estimated from the pseudospectra using Kreiss' theorem. The approach is illustrated with a simple Rijke tube configuration. Results obtained with a simple "baseline" model for the heat source dynamics based on King's law - widely used in hot wire anemometry - are compared against the more advanced treatment developed here. Analysis of pseudospectra diagrams shows that the choice of the heat source model does influence the sensitivity of eigenvalues to perturbations and hence the non-normal behavior. The maximum growth factor for the system with the heat source model based on King's law is more sensitive to changes in the heat source location than the CFD-based heat source model. © 2010 Elsevier Inc. All rights reserved.
About the journal
JournalApplied Mathematics and Computation
ISSN00963003
Open AccessNo
Concepts (27)
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    ADVANCED TREATMENT
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    Delay systems
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    Discretizations
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    Eigenvalues
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    FLOW PERTURBATIONS
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    Galerkin
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    Growth factor
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    HEAT SOURCE MODELS
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    Heat sources
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    HEAT TRANSFER DYNAMICS
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    HOT WIRE ANEMOMETRY
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    LINEAR SYSTEM IDENTIFICATION
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    LOCAL HEAT SOURCE
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    NORMAL BEHAVIOR
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    PSEUDOSPECTRA
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    RIJKE TUBE CONFIGURATION
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    SENSITIVITY OF EIGENVALUES
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    Stability analysis
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    THERMO-ACOUSTIC STABILITY
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    THERMOACOUSTIC SYSTEMS
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    TRANSIENT GROWTH
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    Eigenvalues and eigenfunctions
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    Linear systems
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    Modal analysis
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    Peptides
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    Thermoacoustics
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    Computational fluid dynamics