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The entropy wave generation in a heated one-dimensional duct

Published online by Cambridge University Press:  28 November 2019

Myunggon Yoon Open the ORCID record for Myunggon Yoon [Opens in a new window]
Myunggon Yoon*
Affiliation:
Department of Mechanical Engineering, Gangneung-Wonju National University, Wonju26403, Republic of Korea
*
†Email address for correspondence: mgyoon@gwnu.ac.kr
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Abstract

This paper presents a theoretical analysis on entropy wave generation in a heated one-dimensional duct, which is a simple thermoacoustic model of a combustor. Following a new observation that an entropy wave is caused by the fluctuations of heat/flow power ratio, the entropy transport equation is analytically solved for a heat input uniformly distributed over an acoustically compact zone. Investigating transfer functions from heat and acoustic fluctuations to the entropy wave, we obtain a deeper understanding on the low-pass filtering property of entropy waves with a closed-form expression of the entropic cutoff frequency. A theoretical explanation on why a thinner flame generally results in a stronger entropy wave is also given. These findings are extended to a general flame distribution from a temporal-spatial filtering interpretation of the entropy transport equation. Furthermore, the thin flame limits of our entropy wave models are compared with a popular entropy model based on the thin flame assumption and jump conditions. A numerical example supporting our theoretical findings is also presented.

JFM classification

Acoustics: Aeroacoustics Reacting Flows: Combustion Compressible Flows: Gas dynamics

Information

Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 883 , 25 January 2020 , A44
Copyright
© 2019 Cambridge University Press

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