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

Kojourimanesh, M.Department of Mechanical Engineering, Eindhoven University of Technology, Netherlands (author)

Part of proceedings: ISBN 978-83-7880-799-5QC 20220517
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.

Kornilov, V.Department of Mechanical Engineering, Eindhoven University of Technology, Netherlands (author)
de Goey, P.Department of Mechanical Engineering, Eindhoven University of Technology, Netherlands (author)
Lopez Arteaga, InesKTH,Department of Mechanical Engineering, Eindhoven University of Technology, Netherlands(Swepub:kth)u1gy0h8d (author)
KTHDepartment of Mechanical Engineering, Eindhoven University of Technology, Netherlands (creator_code:org_t)

In:"Advances in Acoustics, Noise and Vibration - 2021" Proceedings of the 27th International Congress on Sound and Vibration, ICSV 2021: Silesian University Press

By the author/editor: Kojourimanesh, M ...; Kornilov, V.; de Goey, P.; Lopez Arteaga, I ...

About the subject

ENGINEERING AND TECHNOLOGY: ENGINEERING AND ...; and Mechanical Engin ...; and Energy Engineeri ...

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