Uncertainty in stretch extrapolation of laminar flame speed from expanding spherical flames

The present work investigated the uncertainties associated with the extrapolation of stretched flames to zero stretch in flame speed measurements using expanding spherical flames. Direct numerical simulations of time evolution of expanding spherical flames from a small ignition kernel to a propagating front with sufficiently large radius provide the relations between stretched flame speed and stretch rate that can be used to assess the uncertainty of extrapolation models. It is found that the uncertainties of flame extrapolation largely depend on the mixture Lewis numbers. While the uncertainty is minimized for stoichiometric H₂/air and n-heptane/air flames, the uncertainty can be as high as 60% for lean H₂/air mixtures, and 10% for lean and rich n-heptane/air mixtures. The present findings show that the weakly stretched flame assumption fails for lean hydrogen mixtures, and give a good explanation to the discrepancies between experiments and model predictions for H₂/air as well as the discrepancies between measurements of n-heptane/air using spherical and counterflow flames. A relation between extrapolation uncertainties and the product of Markstein number and Karlovitz number is provided, which can be useful for uncertainty quantification of future and existing measurements.