The critical lower radius limit approach for laminar flame speed measurement from spherically expanding stretched flames

Spherically expanding flames are severely affected by flame stretch in the early stage of combustion and therefore stretch models are of great importance in determining the uncertainty of experimental laminar flame speeds (S-L) and burned gas Markstein lengths (L-b). In order to prevent the existing large scatter in experimental data of these two fundamental flame parameters, the effect of the lower radius limit for the flame speed calculation on extrapolation results of the stretch models was investigated through spherically expanding flames under constant pressure. Methane, hydrogen, propane, and iso-octane fuels were tested to account for both hydrocarbon and non-hydrocarbon fuels with different evolutions in the burned gas Markstein length when equivalence ratio is increased. Results show that there is a critical lower radius limit (R-L,R-critical), where all laminar flame speed and burned gas Markstein length values obtained by the extrapolation of the stretch models converge to the same laminar flame speed and burned gas Markstein length. The value of the critical lower radius limit strongly depends on the burned gas Markstein number (Ma(b)) and this dependency can be shown with vertical bar Ma(b)vertical bar = 0.8424*R-L,R-critical for fuel/oxidizer mixtures with -0.48 mm <= L-b <= 1.23 mm (or, -0.62 <= Ma(b) <= 2.60). Finally, laminar flame speeds and burned gas Markstein lengths of methane, hydrogen, propane, and iso-octane flames that were corrected according to the critical lower radius limit approach proposed in the present study were compared to previously published experimental results.

Automated summary

The study investigated the effect of lower radius limits on extrapolation results of stretch models for spherically expanding flames, identifying a critical lower radius limit (R-L,R-critical) that converges laminar flame speed and burned gas Markstein length values. The critical lower radius limit strongly depends on the burned gas Markstein number (Ma(b)), with a correlation shown as |Ma(b)| = 0.8424*R-L,R-critical. This approach was used to correct laminar flame speeds and burned gas Markstein lengths for methane, hydrogen, propane, and iso-octane flames, resulting in comparisons with previously published experimental data.