Forced Response of a Swirling, Premixed Flame to Flow Disturbances

This paper presents measurements of the nonlinear response of a premixed flame to harmonic oscillations. These measurements were obtained to improve understanding of nonlinear flame dynamics in unstable combustors. Simultaneous measurements of CH* and OH* chemiluminescence, pressure, and velocity were obtained over a range of forcing amplitudes and frequencies. These data show that the flame chemiluminescence response to imposed oscillations saturates at pressure and velocity amplitudes on the order of p'/p0 ~ 0.02 and u'/u0 ~ 0.3. The value of the fluctuating to the mean chemiluminescence signal at saturation varied with equivalence ratio. The phase between the chemiluminescence and acoustic signal also exhibits substantial amplitude dependence, even at driving levels where their amplitude ratios are nearly linear. In contrast, the pressure-velocity relationship remains linear with constant phase over the entire amplitude range. Thus, these results suggest that the nonlinear dynamics of premixed combustors are controlled by the acoustics-heat-release relationship, as opposed to gas dynamical processes. The mechanism for saturation of the flame response appears to be caused by nonlinear interactions between the flow forcing and the parametric flame instability, possibly through their impact on the fluctuating flame position. This parametric instability occurs at half the forcing frequency and is caused by the oscillating flow acceleration in the presence of the density jump at the flame. To our knowledge, this observation of the parametric instability is the first in a turbulent, swirl-stabilized flame. Interactions between the nonlinear heat release and linear combustor acoustics were characterized by sweeping the driving frequency through a resonant combustor frequency. With increasing driving amplitude, the resulting frequency response curves began to saturate in amplitude and bend over toward lower frequencies. Similar to the classical nonlinear Duffing oscillator, this bending of the frequency response curves manifests itself as a subcritical bifurcation in combustor response, whose gain and phase exhibited jumps and hysteresis. The bifurcation structure was measured in detail over a range of conditions and shown to have a two-dimensional dependence upon both amplitude and frequency.