High-frequency response of premixed flames to weak stretch and curvature: a variable-density analysis

We investigate how the local burning speed (Un) of laminar premixed flames reacts to weak fluctuating velocity gradients and front distortions, in situations where the latter stimuli have frequencies () comparable to the reciprocal time of transit () across the front itself.Our main assumptions are: (i) the one-step burning process involves a large Zel'dovich number, ; (ii) velocity fluctuations and front distortions are weak and have much longer transverse wavelengths, ~d/, than the front thickness, d; (iii) realistic density changes are retained; (iv) the heat conductivity is proportional to the local temperature.It is shown analytically that: (i) despite the variable density, the trends are qualitatively similar to what a thermal-diffusive model gives; in particular, both analyses predict a universal flame response at high frequencies, and a resonance at a well defined frequency and Lewis number. (ii) Density variations bring about noticeable quantitative changes, among which are a slower disappearance of stretch (and Lewis) number effects, and a marked increase of the Markstein transfer function for curvature at high frequencies ().The results are compatible with previously unexplained experiments and numerical simulations, as well as with all the available analytical results.