Effects of turbulent flame development on thermoacoustic oscillations

Thermoacoustic oscillations of a turbulent flame stabilized behind a bluff body in a duct are considered using (1) a kinematic model of the response of the flame to oncoming flow velocity oscillations and (2) the n–(tau) model of the influence of a localized heat source on longitudinal acoustic waves in a duct. The kinematic model well known in the literature is extended to allow for flame speed increase with the distance from the bluff body. Such an increase is an important peculiarity of practical premixed turbulent flames developing with the distance from a flameholder. For weak, harmonic, uniform fluctuations of the oncoming flow velocity, perturbations in the flame shape and in the total heat release rate are analytically determined. Calculated results show that the development of turbulent flame speed substantially affects both the gain and the phase of the flame transfer function and, in consequence, the stability of the flame studied.