Laminar premixed flame response to equivalence ratio oscillations

Self-excited oscillations in low emission, premixed combustion systems are often caused by feedback between unsteady heat release rates and reactive mixture equivalence ratio perturbations. This paper presents an analysis of the flame response to equivalence ratio perturbations, showing that the heat release response is controlled by the superposition of three disturbances: heat of reaction, flame speed, and flame area. The first two disturbances are directly generated by equivalence ratio oscillations. The third is indirect, as it is generated by the flame speed fluctuations. Heat of reaction disturbances dominate the flame response at low Strouhal numbers, roughly defined as (frequency × flame length)/(axial flow velocity). All three disturbances play equal roles at Strouhal numbers of O(1). In addition, 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, this result is in partial agreement with heuristic arguments made in prior studies that the flame response to equivalence ratio oscillations increases as the mixture becomes leaner. In addition, results are derived for the sensitivities of this transfer function to uncertainties in mean flame position; i.e., a sensitivity of 2 implies that a 5% uncertainty in flame position translates into a 10% uncertainty in transfer function. It is shown that this sensitivity is generally of O(1) at low Strouhal numbers, grows with increasing Strouhal numbers, and reaches a maximum value of O(10) for high Strouhal numbers.