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Predicting the secondary dynamic mode interference phenomenon in thermoacoustic instability control.

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Summary

This study introduces a new mathematical method to understand how secondary dynamic modes become unstable when suppressing thermoacoustic instability in a Rijke tube. The analysis reveals how controller gains can inadvertently destabilize these modes.

Keywords:
Rijke tubefeedback controllinear systemsstabilitythermoacousticstime delay

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Area of Science:

  • Fluid Dynamics
  • Control Theory
  • Acoustics

Background:

  • Thermoacoustic instability is a significant challenge in combustion systems.
  • Previous studies observed secondary dynamic modes during instability suppression but lacked complete analytical explanations.
  • Rijke tubes are common experimental setups for studying thermoacoustic instabilities.

Purpose of the Study:

  • To develop a novel mathematical framework for analyzing the emergence of secondary dynamic modes during thermoacoustic instability suppression.
  • To investigate the parametric stability of a Rijke tube system with passive and active control.
  • To identify conditions under which secondary modes become unstable despite primary mode stabilization.

Main Methods:

  • Modeling the Rijke tube dynamics as a linear time-invariant multiple time-delay system of neutral type.
  • Employing the cluster treatment of characteristic roots paradigm for stability analysis.
  • Utilizing a time-delayed integral feedback control strategy.
  • Experimental validation using a laboratory-scale Rijke tube.

Main Results:

  • The cluster treatment of characteristic roots method provides exhaustive stability analysis in the parameter space.
  • Stability is assessed with and without a Helmholtz resonator.
  • The study identifies specific controller gain ranges that lead to secondary dynamic mode instability.
  • Experimental results confirm the analytical predictions regarding mode stabilization and destabilization.

Conclusions:

  • The novel analytical tool effectively predicts the behavior of secondary dynamic modes in controlled thermoacoustic systems.
  • Inappropriate selection of control gains can lead to unexpected instabilities in secondary modes.
  • This research offers a more complete analytical understanding of complex dynamic behaviors in combustion instabilities.