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Non-normality and internal flame dynamics in premixed flame-acoustic interaction
Published in American Institute of Aeronautics and Astronautics Inc.
2011
Volume: 679
   
Pages: 315 - 342
Abstract
This paper investigates the non-normal nature of premixed flame-acoustic interaction. The thermoacoustic system is modelled using the acoustic equations for momentum and energy, together with the equation for the evolution of the flame front obtained from the kinematic G-equation. As the unsteady heat addition acts as a volumetric source, the flame front is modelled as a distribution of monopole sources. Evolutions of the system are characterized with a measure of energy due to fluctuations. In addition to the acoustic energy, the energy due to fluctuations considered in the present paper accounts for the energy of the monopole sources. The linearized operator for this thermoacoustic system is non-normal, leading to non-orthogonality of its eigenvectors. Non-orthogonal eigenvectors can cause transient growth even when all the eigenvectors are decaying. Therefore, classical linear stability theory cannot predict the finite-time transient growth observed in non-normal systems. In the present model, the state space variables include the monopole source strengths in addition to the acoustic variables. Inclusion of these variables in the state space is essential to account for the transient growth due to non-normality. A parametric study of the variation in transient growth due to change in parameters such as flame location and flame angle is performed. In addition to projections along the acoustic variables of velocity and pressure, the optimal initial condition for the self-evolving system has significant projections along the strength of the monopole distribution. Comparison of linear and corresponding nonlinear evolutions highlights the role of transient growth in subcritical transition to instability. The notion of phase between acoustic pressure and heat release rate as an indicator of stability is examined. © 2011 Cambridge University Press.
About the journal
JournalData powered by TypesetJournal of Fluid Mechanics
PublisherData powered by TypesetAmerican Institute of Aeronautics and Astronautics Inc.
ISSN00221120
Impact Factor1.868
Open AccessNo
Citation Styleunsrt
Sherpa RoMEO Archiving PolicyGreen
Concepts (33)
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    Acoustic energy
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    ACOUSTIC EQUATION
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    ACOUSTIC PRESSURES
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    ACOUSTIC VARIABLES
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    Flame dynamics
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    Flame front
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    FLAME LOCATION
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    FLAMES
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    HEAT RELEASE RATES
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    Initial conditions
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    Linear stability theory
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    LINEARIZED OPERATORS
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    MONOPOLE DISTRIBUTION
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    MONOPOLE SOURCE
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    NON-NORMALITY
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    NON-ORTHOGONALITY
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    NONLINEAR EVOLUTIONS
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    Parametric study
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    Premixed
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    Reacting flows
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    State space
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    SUBCRITICAL TRANSITION
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    THERMOACOUSTIC SYSTEMS
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    TRANSIENT GROWTH
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    Acoustic wave scattering
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    ACOUSTIC WAVE TRANSMISSION
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    Eigenvalues and eigenfunctions
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    Thermoacoustics
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    Mathematical operators
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    Acoustics
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    Eigenvalue
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    KINEMATICS
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    Modeling