On the uncertainty of extrapolation of laminar flame speed and markstein length from expanding spherical flames

Expanding spherical flames are frequently used to determine laminar flame speeds. One of the largest errors associated with this technique is the extrapolation of the experimental data to remove the influence of flame stretch, using a linear or nonlinear relation between the local flame speed and stretch. The present work investigated the uncertainties of various extrapolation equations based on the computation results of the 1-D planar flame and the expanding spherical flame. Computation of the expanding spherical flame starts from ignition to a sufficiently large radius (~50 cm), thereby providing the relation between the local flame speed and stretch for a wide range. It is shown that the computed flame speeds of expanding flames at large radii agree closely with the results of the 1-D planar flame, and that the uncertainties of flame extrapolation largely depend on the Lewis number, Le. While the uncertainties for large Le or near-unity Le flames fall within 5%, those for small Le flames can be as high as 50%. It is suggested that previous measurements at small Le need to be re-analyzed, and that future measurements for such flames need to be conducted with great care. The present work also investigated the effect of pressure on the uncertainties of extrapolation.