| Summary: | The effect of upstream velocity perturbations on the response of a premixed flame was investigated in terms of the flame transfer function dependency on excitation frequency. In this study, the assumption of constant flame speed was extended and the effect of flame speed development was considered; i.e., the flame speed would grow with the time after ignition or with the distance from a flame-holder. In the present study, the kinematics of a conical flame was investigated by linearization of the front tracking equation of flame to uniform and convected fluctuations of the flow velocity and the response was compared with that of a V-shaped flame and the experimental data in the previous studies. The results show that the effect of flame speed development could influence a decreasing gain and increase the phase of the flame response to the uniform velocity oscillations in low and moderate frequencies. Comparing the variations in the gain of flame response upon normalized frequency, show that a conical flame has lower values than the V-flame. In other words, these flames might be less susceptible to combustion instabilities than the V-flames. Furthermore, the variations in phase of the V-flames responses, which show a quasi-linear behavior with normalized frequency, have higher values than the saturated behavior in phase of the conical flame responses. Also, considering that the flame speed development induces an increase in the gain and phase of the conical flame response to the convected velocity oscillations in certain frequencies; because the developed flame front has longer length in comparison to the flame front in constant flame speed model. Therefore, the flame length may be longer than convective wavelength and the heat release would be generated in different points of the flame; consequently the flow oscillations might exert a stronger impact on the unsteady heat release fluctuations.
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