### Abstract

Effects of the Lewis number and radiative heat loss on flame bifurcations and extinction of CH_{4}/O_{2}-N_{2}-He flames are investigated numerically with detailed chemistry. Attention is paid to the interaction between radiation heat loss and the Lewis number effect. The Planck mean absorption coefficients of CO, CO_{2}, and H_{2}O are calculated using the statistical narrow-band model and compared with the data given by Tien. The use of Tien's Planck mean absorption coefficients overpredicts radiative heat loss by nearly 30% in a counterflow configuration. The new Planck mean absorption coefficients are then used to calculate the extinction limits of the planar propagating flame and the counterflow flame when the Lewis number changes from 0.967 to 1.8. The interaction between radiation heat loss and the Lewis number effect greatly enriches the phenomenon of flame bifurcation. The existence of multiple flames is shown to be a physically intrinsic phenomenon of radiating counterflow flames. Eight kinds of typical patterns of flame bifurcation are identified. The competition between radiation heat loss and the Lewis number effect results in two distinct phenomena, depending on if the Lewis number is greater or less than a critical value. Comparisons between the standard limits of the unstrained flames and the flammability limits of the counterflow flames indicate that the flammability limit of the counterflow flame is lower than the standard limit when the Lewis number is less than the critical value and is equal to the standard limit when the Lewis number is higher than this critical value. Finally, a G-shaped curve and a K-shaped curve which respectively represent the flammable regions of the multiple flames for Lewis numbers lower and higher than the critical value are obtained. The G- and K-shaped curves show a clear relationship between the stretched counterflow flame and the unstrained planar flame. The present results provide a good explanation of the physics revealed experimentally in microgravity.

Original language | English |
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Pages (from-to) | 165-190 |

Number of pages | 26 |

Journal | Journal of Fluid Mechanics |

Volume | 379 |

DOIs | |

Publication status | Published - 1999 Jan 25 |

### ASJC Scopus subject areas

- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering

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## Cite this

_{4}/O

_{2}-N

_{2}-He flames.

*Journal of Fluid Mechanics*,

*379*, 165-190. https://doi.org/10.1017/S0022112098003231