Effects of Turbulent Flame Speed Development on Ducted Flame Oscillations
Paper in proceedings, 2004
A confined premixed turbulent flame that oscillates behind a bluff body under the influence of imposed velocity perturbations is studied as a model of thermo-acoustic oscillations in the afterburner of an aeroengine, caused by the interaction between acoustic waves and unsteady heat release. A kinematic model of the flame dynamics, developed by Dowling, is extended to allow for the effects of turbulent flame speed development on the heat release in the system. For this purpose, an expression for developing turbulent flame speed, obtained by two of us , is incorporated into the model of Dowling. A theoretical solution for the transfer function between the oncoming flow velocity and total heat release rate is found by considering weak velocity oscillations and using a simplified expression for the developing flame speed. Numerical solutions are obtained for various magnitudes of the velocity oscillations and using the full model for the flame speed. Both solutions indicate that the development of turbulent flame speed notably changes the phase difference between the oscillations of the oncoming flow velocity and total heat release rate in the combustor. Consequently, according to the Rayleigh criterion, the flame speed development should be properly addressed when numerically investigating the stability of a combustor with respect to acoustic waves.