# Flame stretch and flame displacement speed

The objective of the present work is to provide a systematic and consistent comparison between theory and simulations for stationary spherical premixed flames. In particular, an GM 6001 for the flame displacement speed – derived from asymptotic theory – was evaluated using numerical simulations in a flame configuration which is not subject to stretch but has finite curvature. The results demonstrated a very good agreement between the asymptotic theory and the simulations. It was shown that only when the flame curvature and the total stretch rate are proportional to each other (as in the case of spherically-expanding flames), a single Markstein length emerges. This is not the case in the stationary flame configuration, where a distinction is made between the Markstein length associated with total stretch rate and the curvature Markstein length . The latter proved to be independent of Lewis and Zel’dovich numbers, which implies that its notion does not involve any diffusion and chemical reaction effects. Moreover, it was found that only iso-surfaces close to the burned side of the flame give results which are not sensitive to the chosen isovalue. In this region, the curvature Markstein length is zero and the flame displacement speed is equal to the laminar flame speed SLSL. Otherwise, large variations in the calculated/measured Markstein length and the FDS should be expected. This is also true for spherically expanding flames as shown in [21]. Finally, it is worth pointing out that the stationary flame configuration examined in this study allows the determination of the unstretched flame speed SLSL without the need for extrapolation to zero stretch, which often leads to inconsistencies.