Modeling the Response of Premixed Flames to Mixture Ratio Perturbations

Combustion instabilities continue to cause significant reliability and availability problems in low emissions gas turbine combustors. It is known that these instabilities are often caused by a self-exciting feedback loop between unsteady heat release rate and reactive mixture equivalence ratio perturbations. We present an analysis of the flame’s response to equivalence ratio perturbations by considering the kinematic equations for the flame front. This response is controlled by three processes: heat of reaction, flame speed, and flame area. The first two are directly generated by equivalence ratio oscillations. The third is indirect, as it is generated by the flame speed fluctuations. The first process dominates the response of the flame at low Strouhal numbers, roughly defined as frequency times flame length divided by mean flow velocity. All three processes play equal roles at Strouhal numbers of O(1). The mean equivalence ratio exerts little effect upon this transfer function at low Strouhal numbers. At O(1) Strouhal numbers, the flame response increases with decreasing values of the mean equivalence ratio. Thus, these results are in partial agreement with heuristic arguments made in prior studies that the flame response to equivalence ratio oscillations increases as the fuel/air ratio becomes leaner. In addition, a result is derived for the sensitivity of this transfer function to uncertainties in mean flame position. For example, a sensitivity of 10 means that a 5% uncertainty in flame position translates into a 50% uncertainty in transfer function. This sensitivity is of O(1) for St<<1, but has very high values for St∼O(1).