Impact of stretch on the flame dynamics of laminar premixed flames

Flame transfer functions (FTF) of laminar premixed flames acoustically forced are analytically investigated and modelled. The study is based on the linearized G-equation, which is used to kinematically track the flame front. In order to incorporate combustion properties, the laminar consumption speed is considered varying depending on the flame front stretch. Once written in dimensionless form, the G-equation reveals that the FTF depends on 3 dimensionless parameters: a Strouhal number (St₂) that accounts for the convective time of the flow perturbation along the flame-front, the flame aspect-ratio (Lf/R) and the dimensionless Markstein length, adimensionalized by the injector radius. It is shown that the latter term is responsible for a flame-flow feedback that acts as damper or amplifier of the flame perturbation, respectively for thermodiffusively stable or unstable flames. A LOM FTF is derived both for Conical and V-flames, highlighting the impact of stretch for each configuration. Ultimately the obtained FTFs are compared to previously proposed analytical FTFs from the literature, underlining the importance of stretch at high frequency.