An analytical model for the impulse response of laminar premixed flames to equivalence ratio perturbations

The dynamic response of conical laminar premixed flames to fluctuations of equivalence ratio is analyzed in the time domain, making use of a level set method (“G-Equation”). Perturbations of equivalence ratio imposed at the flame base are convected towards the flame front, where they cause modulations of flame speed, heat of reaction and flame shape. The resulting fluctuations of heat release rate are represented in closed form in terms of respective impulse response functions. The time scales corresponding to these mechanisms are identified, their contributions to the overall flame impulse response are discussed. If the impulse response functions are Laplace transformed to the frequency domain, agreement with previous results for the flame frequency response is observed. An extension of the model that accounts for dispersion of equivalence ratio fluctuations due to molecular diffusion is proposed. The dispersive model reveals the sensitivity of the premixed flame dynamics to the distance between the flame and the fuel injector. The model results are compared against numerical simulation of a laminar premixed flame.