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A vortex-dynamical scaling theory for flickering buoyant diffusion flames

Published online by Cambridge University Press:  24 September 2018

Xi Xia Open the ORCID record for Xi Xia [Opens in a new window]  and
Peng Zhang
Xi Xia
Affiliation:
Department of Mechanical Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong
Peng Zhang*
Affiliation:
Department of Mechanical Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong
*
†Email address for correspondence: [email protected]
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Abstract

The flickering of buoyant diffusion flames is associated with the periodic shedding of toroidal vortices that are formed under gravity-induced shearing at the flame surface. Numerous experimental investigations have confirmed the scaling, $f\propto D^{-1/2}$, where $f$ is the flickering frequency and $D$ is the diameter of the fuel inlet. However, the connection between the toroidal vortex dynamics and the scaling has not been clearly understood. By incorporating the finding of Gharib et al. (J. Fluid Mech., vol. 360, 1998, pp. 121–140) that the detachment of a continuously growing vortex ring is inevitable and can be dictated by a universal constant that is essentially a non-dimensional circulation of the vortex, we theoretically established the connection between the periodicity of the toroidal vortices and the flickering of a buoyant diffusion flame with small Froude number. The scaling theory for flickering frequency was validated by the existing experimental data of pool flames and jet diffusion flames.

JFM classification

Reacting Flows: Flames Instability: Instability Vortex Flows: Vortex Flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 855 , 25 November 2018 , pp. 1156 - 1169
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Copyright
© 2018 Cambridge University Press 

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