Flow strain and curvature Markstein numbers of edge flame in the counterflow configuration

Abstract

Based on the counterflow configuration, the Markstein numbers of one-dimensional premixed flame and two-dimensional edge flame of hydrogen-air system are numerically studied and compared with each other. By varying the inlet velocity and mixing layer thickness, the proportional relationship between flame stretch caused by flow strain (Kas) and by flame curvature (Kac) disappears, and therefore two corresponding Markstein numbers Mas and Mac at different flame markers (or iso-contours of temperature) within flame front could be obtained through linear fitting between normalized flame displacement speed Sd∗ and bivariate (Kas,Kac). With the flame marker shifting from unburnt to burnt side, Mac profile of edge flame exhibits a decreasing trend while Mas profiles of premixed flame and edge flame both display an increasing trend with its sign changing from negative to positive. Moreover, a good agreement of Mas profiles between two kinds of flames is observed while the discrepancy begins to appear when normalized temperature θ ≥5, which should be attributed to the shift of flame marker from premixed branch into diffusion branch rather than the decrease of heat release rate. The comparison between simulation and theory reveals differences of Mas values except for 2.5 < θ < 4 and those of Mac values except for θ = 2.5, which might be accounted for a moderate Zel'dovich number Ze, i.e. 3.9, based on detailed hydrogen-air chemical mechanism. Therefore, the “larger activation energy” assumed in asymptotic theory may not be valid for hydrogen-air flames whose equivalence ratio is 1.6 in this study.