Mobius transformation between reflection coefficients at upstream and downstream sides of flame in thermoacoustics systems

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Abstract

An alternative approach to assess the conditions for the onset of thermoacoustics combustion instability is proposed. The method is based on the analysis of the relation between the reflection coefficient of combustor upstream section (subsystems) with respect to the burner/flame, Rup, and the input reflection coefficient, Rin, as observed from the inlet of the burner with flame and all downstream subsystems of a combustion appliance. The instability of the combustor can be determined by evaluating the system dispersion relation expressed in the terms of these two reflection coefficients. The properties of the relation between Rin, the reflection coefficient of the burner downstream subsystems, Rdn, and elements of the flame transfer matrix, TM, of the burner are investigated. This relation has the form of the well-known Mobius transformation. Using the well-developed theory of the transformation, we derive the necessary conditions of Rdn to ensure that the magnitude of Rin becomes less than 1 in a frequency range. This condition results in a passive thermoacoustics stability of the system's operation. Furthermore, an optimum value of Rdn is derived which provides a minimum value of Rin at given entries of the burner TM. The practical application of the developed theory provides suitable criteria and guidelines for designing passive acoustic properties at the downstream side of the combustion appliance.

Original languageEnglish
Title of host publicationAdvances in Acoustics, Noise and Vibration - 2021 : Proceedings of the 27th International Congress on Sound and Vibration, ICSV 2021
EditorsEleonora Carletti, Malcolm Crocker, Marek Pawelczyk, Jiri Tuma
PublisherSilesian University Press
Number of pages8
ISBN (Electronic)9788378807995
Publication statusPublished - 11 Jul 2021
Event27th International Congress on Sound and Vibration, ICSV 2021 - Prague, Virtual, Czech Republic
Duration: 11 Jul 202116 Jul 2021
Conference number: 27
https://icsv27.org/index.php

Conference

Conference27th International Congress on Sound and Vibration, ICSV 2021
Abbreviated title(ICSV27)
Country/TerritoryCzech Republic
CityPrague, Virtual
Period11/07/2116/07/21
Internet address

Bibliographical note

Publisher Copyright:
© "Advances in Acoustics, Noise and Vibration - 2021" Proceedings of the 27th International Congress on Sound and Vibration, ICSV 2021. All rights reserved.

Keywords

  • Combustion
  • Flame transfer function
  • Instability
  • Passive termination

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