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Nonlinear response of swirling premixed flames to helical flow disturbances

Published online by Cambridge University Press:  27 May 2020

Vishal Acharya Open the ORCID record for Vishal Acharya [Opens in a new window]  and
Timothy Lieuwen
Vishal Acharya*
Affiliation:
School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA30332, USA
Timothy Lieuwen
Affiliation:
School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA30332, USA
*
†Email address for correspondence: vishal@aerospace.gatech.edu
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Abstract

This paper considers the relationship between nonlinearly interacting helical flow disturbances and flame area response in a swirling premixed flame. The present study was performed to determine whether there are nonlinear mechanisms through which helical modes ($m_{u}\neq 0$) can lead to non-zero unsteady heat release rate oscillations. The results show that for single frequency content (at $\unicode[STIX]{x1D714}_{0}$), helical modes excite unsteady heat release rate response of $O(\unicode[STIX]{x1D716}^{3})$ and that two-frequency excitation (e.g. at $\unicode[STIX]{x1D714}_{0}$ and $2\unicode[STIX]{x1D714}_{0}$), leads to a response of $O(\unicode[STIX]{x1D716}^{2})$ at $\unicode[STIX]{x1D714}_{0}$. There are two mechanisms through which this can occur: First, helical flow disturbances can distort the time-averaged flame shape to have an azimuthal component that matches that of the incident disturbance, $\exp (im_{u}\unicode[STIX]{x1D703})$. Second, multiple helical modes can nonlinearly interact to cause axisymmetric unsteady flame wrinkling. The paper derives the various modal contributions in the incident velocity disturbance that satisfy these criteria. These results suggest that it is only the $m_{u}=0$ mode which controls the linear dynamics (e.g. instability inception conditions) of these flames (where $\unicode[STIX]{x1D716}\ll 1$), but that their nonlinear dynamics is also controlled by the $m_{u}\neq 0$ helical modes.

JFM classification

Reacting Flows: Flames

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Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 896 , 10 August 2020 , A6
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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