Modeling tools for the prediction of premixed flame transfer functions

The response of flames to incident perturbations is of central interest in combustion dynamics analysis. The problem can be described in the linear regime by a transfer function. It is shown in this article that the description of the perturbed velocity field incident on the flame front is of crucial importance when dealing with the flame transfer function. This is demonstrated in the special case of a premixed flame anchored on the rim of a burner submitted to flow perturbations. Previous studies of this problem have shown that in the low-frequency range the flame dynamics was governed by a single dimensionless frequency, and that a first-order model described the general behavior of the flame response when the disturbance wavelength exceeds the flame height. Complementary experiments reported in this article indicate that this model fails when the modulation frequency is increased. On this experimental basis, a revised formulation of the velocity perturbation incident on the flame is proposed which accounts for the flame cusping phenomenon when more than one wavelength wrinkles the flame front. Combining this more realistic velocity field with a level set approach for the flame dynamics, a full numerical integration of the G-equation is carried out. The transfer function is computed over the whole useful range of frequencies. Experimental data are then compared with analytical and numerical predictions. It is shown that the current first-order models underestimate the phase lag between velocity and heat release fluctuations. A constant phase shift is obtained in the high-frequency limit which does not correspond to observations. The new velocity model yields a better representation of the flame response in a wider range of frequencies. It is shown in particular that the modeled phase lag between combustion and flow perturbations increases with frequency, as is effectively observed.