Theoretical, and experimental determinations of the transfer function of a laminar premixed flame

The dynamical behavior of laminar premixed flames is investigated in this article. The flame response to incident perturbations is characterized with a transfer function relating the flow velocity modulations and the heat release fluctuations. This function is obtained using the assumptions introduced in previous studies by Fleifil et al., but the model is extended to account for any flame angle (i.e., any operating condition). The modeling shows that the phenomena can be described using a single control parameter taking the form of a reduced frequency omega*. This quantity is derived as omegaR/S-L cos alpha (0), where omega is the angular frequency, R is the burner radius, S-L is the laminar burning velocity, and alpha (0) in the half-cone angle of the steady flame, this parameter may be used to describe the response of the burner to accoustic modulation, knowing its geometry and the flame properties. Two characteristics times have been determined. The first one defines the cut-off frequency of the low-pass filter associated with the flame response. The second one enables the prediction of the time lag between the velocity modulation at the burner exit and the flame heat release, the exact transfer function and an approximation in the form of a first-order model are compared with an extensive set of experimental data corresponding to a range of equivalence ratios and two burner diameters. Good agreement is obtained for low values of the reduced frequency. In an intermediate range of frequencies, the experimental phase exceeds the theoretical values by a significant amount, the difference between theory and experiment is due to the simplifying assumptions used in the model.