APPLICATION OF THE MARKSTEIN NUMBER CONCEPT TO CURVED TURBULENT FLAMES

Abstract

Effects of large-scale stretching of premixed turbulent flames on flame speed are discussed and an extension of the classical Markstein number concept is proposed to parameterize flame speed modifications by the stretch rate. The concept is applied to fit various experimental data on the growth of the radius of expanding, statistically spherical, premixed, turbulent flames, obtained by different groups under different conditions. In all the cases studied, the suggested extension approximates the experimental data very well. It is shown also that this phenomenological approach may be utilized to determine the values of unperturbed turbulent flame speeds, , by processing the experimental data for spherical flames. The difference between the obtained values of unperturbed and the mean speeds of spherical flames, observed during expansion, may be as large as 200–300%. The strong influence of the perturbations discussed shows that such effects should be properly addressed when analyzing experimental data or invoking a presumed turbulent flame speed in simulations, for example, in large-eddy simulation based on the G-equation approach.

Keywords:

• premixed turbulent combustion
• flame speed
• Markstein number

This work was supported by the Swedish Research Council for Engineering Sciences.

Notes

¹Here the term unperturbed flame means a fully developed, planar, statistically one- dimensional flame of a steady thickness, which propagates with a steady speed against a stationary and spatially uniform unburned mixture flow.

²In the turbulent case, the problem is more pronounced because δ_t ≫ δ_L

³Since the evolution of mean flame brush thickness was not controlled in these experiments, the observed time independence (or weak time dependence?) of turbulent flame speed does not prove that these flames are fully developed. It is worth noting that a typical developing turbulent flame is characterized by substantial growth of δ_t(t) but weak (if t > τ_t) growth of S _t, which is close to (Liputuikov and Chomiak, 2001, 2002a; Prudnikov, 1964).

^a u ₀′ = 1 m/s, L ₀ = 1 m, and τ_{t, 0} = 1 s.

^bCorrelation coefficient.