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The entropy wave generation in a heated one-dimensional duct
Published online by Cambridge University Press: 28 November 2019
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.
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- © 2019 Cambridge University Press
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