## Abstract

Linear stability of planar, laminar premixed flames to longitudinal periodic perturbations is theoretically investigated within the thermo-diffusive flame model. An explicit dispersion relation is introduced that relates the rate of growth of oscillations ω_{o}, the wave number of longitudinal disturbances k_{o}, and the first order perturbation of the Lewis number from unity l_{1}, thus revealing the domain of flame instability in (k_{o}-l_{1}) plane. For large-wavelength disturbances, k_{o} = 0, the dispersion relation becomes identical to that found in previous studies for the stability of adiabatic flames subjected to transverse perturbations. In particular, it is predicted that outside of the critical minimum and maximum values of l_{1} = {-2, 4 (1+ 3^{1/2})}, flames are acoustically unstable to long-wavelength longitudinal perturbations. For finite values of k_{o}, on the other hand, the stability contours for longitudinal disturbances are different from those for transverse ones. In terms of the wave length, stable flames are predicted to exist only in a small region 6.3816 < l_{1} < 17.699 for short wave-length perturbations λ_{o} = ≪1, in (λ_{o}-l_{1})-plane. Also, it is shown that there exists a most dangerous critical minimum (maximum) wave number k_{o}* ≈ 35.3 (wave length λ_{o}* ≈ 0.178 ) at l_{1}* ≈ 10.1, below (above) which all flames are unstable to longitudinal disturbances. The stability analysis is extended to include non-adiabatic flames, and volumetric heat loss (gain) is found to increase (decrease) the total area of unstable flame regions within the (k_{o}-l_{1}) plane, in agreement with previous findings. Possible resonance between the frequency of externally-applied (forced) acoustic oscillations, and that associated with the intrinsic flame acoustic instabilities identified herein, may have importance to the combustion technology.

Original language | English (US) |
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Pages (from-to) | 119-129 |

Number of pages | 11 |

Journal | American Society of Mechanical Engineers, Heat Transfer Division, (Publication) HTD |

Volume | 341 |

State | Published - Dec 1 1997 |

## ASJC Scopus subject areas

- Mechanical Engineering
- Fluid Flow and Transfer Processes