HIGH-FREQUENCY RESPONSE OF PREMIXED FLAMES TO WEAK STRETCH AND CURVATURE - A VARIABLE-DENSITY ANALYSIS

We investigate how the local burning speed (u(n),) of laminar premixed flames reacts to weak fluctuating velocity gradients and front distor tions, in situations where the latter stimuli have frequencies (omega) comparable to the reciprocal time of transit (tau) across the front i tself. Our main assumptions are: (i) the one-step burning process invo lves a large Zel'dovich number, beta; (ii) velocity fluctuations and f ront distortions are weak and have much longer transverse wavelengths, similar to d/epsilon, than the front thickness, d; (iii) realistic de nsity 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 t hermal-diffusive model gives; in particular, both analyses predict a u niversal flame response at high frequencies, and a resonance at a well defined frequency and Lewis number. (ii) Density variations bring abo ut noticeable quantitative changes, among which are a slower disappear ance of stretch (and Lewis) number effects, and a marked increase of t he Markstein transfer function for curvature at high frequencies (omeg a tau-->infinity,). The results are compatible with previously unexpla ined experiments and numerical simulations, as well as with all the av ailable analytical results.