Analysis of degenerate mechanisms triggering finite-amplitude thermo-acoustic oscillations in annular combustors

Sandeep R. Murthy, Taraneh Sayadi, Vincent Le Chenadec, Peter J. Schmid, Daniel J. Bodony

Research output: Contribution to journalArticle

Abstract

A simplified model is introduced to study finite-amplitude thermo-acoustic oscillations in -periodic annular combustion devices. Such oscillations yield undesirable effects and can be triggered by a positive feedback between heat-release and pressure fluctuations. The proposed model, comprising the governing equations linearized in the acoustic limit, and with each burner modelled as a one-dimensional system with acoustic damping and a compact heat source, is used to study the instability caused by cross-sector coupling. The coupling between the sectors is included by solving the one-dimensional acoustic jump conditions at the locations where the burners are coupled to the annular chambers of the combustion device. The analysis takes advantage of the block-circulant structure of the underlying stability equations to develop an efficient methodology to describe the onset of azimuthally synchronized motion. A modal analysis reveals the dominance of global instabilities (encompassing the large-scale dynamics of the entire system), while a non-modal analysis reveals a strong response to harmonic excitation at forcing frequencies far from the eigenfrequencies, when the overall system is linearly stable. In all presented cases, large-scale, azimuthally synchronized (coupled) motion is observed. The relevance of the non-modal response is further emphasized by demonstrating the subcritical nature of the system's Hopf point via an asymptotic expansion of a nonlinear model representing the compact heat source within each burner.

Original languageEnglish (US)
Pages (from-to)384-419
Number of pages36
JournalJournal of Fluid Mechanics
Volume881
DOIs
StatePublished - Dec 25 2019

Fingerprint

combustion chambers
Combustors
burners
Acoustics
Fuel burners
oscillations
acoustics
heat sources
sectors
harmonic excitation
positive feedback
Modal analysis
Damping
chambers
damping
methodology
Feedback
heat
expansion
Hot Temperature

Keywords

  • nonlinear instability

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

Cite this

Analysis of degenerate mechanisms triggering finite-amplitude thermo-acoustic oscillations in annular combustors. / Murthy, Sandeep R.; Sayadi, Taraneh; Le Chenadec, Vincent; Schmid, Peter J.; Bodony, Daniel J.

In: Journal of Fluid Mechanics, Vol. 881, 25.12.2019, p. 384-419.

Research output: Contribution to journalArticle

Murthy, Sandeep R. ; Sayadi, Taraneh ; Le Chenadec, Vincent ; Schmid, Peter J. ; Bodony, Daniel J. / Analysis of degenerate mechanisms triggering finite-amplitude thermo-acoustic oscillations in annular combustors. In: Journal of Fluid Mechanics. 2019 ; Vol. 881. pp. 384-419.
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