Response of flame speed to positively and negatively curved premixed flames

We address flame stretch effects on two-dimensional premixed 'regular' (RF) and 'inverted' (UF) flames burning methane-air and propane-air mixtures through an experimental investigation. The regular flames have a negative curvature and are concave to the unburned mixture, while the inverted flames are positively curved and convex. The response to stretch (that addresses the influence of curvature) differs along the planar and curved regions of a premixed flamefront. A curved flame behaves as a lens that focuses (negative curvature) or defocuses heat from the burned to the unburned side depending upon its curvature, but defocuses (negative curvature) or focuses the concentration of the deficient reactant from the unburned side into the premixed reaction zone. The focusing of heat into the unburned side of the negatively curved RF raises the local temperature in the unburned region and increases the upstream velocity. The positive curvature of the UF induces a positive stretch rate, which decreases the flame propagation speed by lowering the local reaction and heat generation rates. However, the combined effects of stretch and curvature are more complex. The planar and curved regions have different responses to stretch. The planar regions behave in accord with the Markstein Su(K) linear relation and the unstretched flame speeds S^ou thus inferred are in accord with the literature. The flame speed, however, changes dramatically along the curved regions due to curvature effects. Although curvature effects are included in the definition of stretch, they are not fully accounted for by the Su(K) Markstein linear relation. Even after considering the effect of curvature in the definition of K, strong negative curvature raises the value of the flame speed above the prediction of the Su(K) expression, while strong positive curvature reduces its magnitude below that predicted by the relation. This implies that the curvature has an influence on Su through K and through the sign of curvature and Lewis number.