Response of a laminar premixed flame to flow oscillations: A kinematic model and thermoacoustic instability results

Combustion instability is a resonance phenomenon that arises due to the coupling between the system acoustics and the unsteady heat release. The constructive feedback between the two processes, which is known to occur as a certain phase relationship between the pressure and the unsteady heat release rate is satisfied, depends on many parameters among which is the acoustic mode, the flame holder characteristics, and the dominant burning pattern. In this paper, we construct an analytical model to describe the dynamic response of a laminar premixed flame stabilized on the rim of a tube to velocity oscillation. We consider uniform and nonuniform velocity perturbations superimposed on a pipe how velocity profile. The model results show that the magnitude of heat release perturbation and its phase with respect to the dynamic perturbation depend primarily on the flame Strouhal number, representing the ratio of the dominant frequency times the tube radius to the laminar burning velocity. In terms of this number, high-frequency perturbations pass through the flame while low frequencies lead to a strong response. The phase with respect to the velocity perturbation behaves in the opposite way. Results of this model are shown to agree with experimental observations and to be useful in determining how the combustion excited mode is selected among all the acoustic unstable modes. The model is then used to obtain a time-domain differential equation describing the relationship between the velocity perturbation and the heat release response over the entire frequency range.