The response of a conical laminar premixed flame to equivalence ratio oscillations in rich conditions

Responses of conical premixed methane/air mixture flames with equivalence ratio oscillations were numerically investigated at three different oscillation frequency regimes; low, medium and high (10, 50 and 150 s^-1) under a rich condition. One-step and two-step reaction mechanism have been investigated. The pre-exponential factors for the one-step and two-step reaction mechanism were calibrated at minimum and maximum equivalence ratio of this study, Ø= 1.1 and 1.5, by comparing the flame length of the numerical results with the experimental results. The two-step reaction mechanism predicted well the variation in the flame shape under a steady state condition with equivalence ratio variations while the one-step reaction mechanism failed to predict the variation in the flame shape especially under the near rich flammability limit condition. This is because of the CO formation inclusion in the two-step reaction mechanism. The effects of the equivalence ratio oscillation frequency towards flame dynamics were discussed. The amplitude of the flame tip movement attenuates following the attenuation of the equivalence ratio oscillation towards the downstream direction at high oscillation frequency. The dynamic response of the flame tip for low, medium and high oscillation frequency regimes shows interesting behavior. The quasi-steady manner of the flame tip movement was observed at the low frequency regime. In the medium and high frequency regime cases, we found that the attenuation of the flame tip motion is affected by the wrinkling of the flame surface in addition to the attenuation of the equivalence ratio oscillation amplitude. Moreover, an increase in the number of wrinkles as the equivalence ratio oscillation frequency is increased induces large attenuation of the flame tip oscillation amplitude. Furthermore, we found that the period of the equivalence ratio oscillation, T and the convective transport time, τ control the flame response in that T/τ, is a controlling parameter of the conical flame response in quasi-steady (T/τ ≥ 1.0) or unsteady (T/τ ≤ 1.0) manner.