Scaling turbulent flame speeds of negative Markstein length fuel blends using leading points concepts

This work describes analyses of turbulent flame speeds, ST, of negative Markstein length fuel blends using leading point models. One implication of these models is that the maximum laminar burning velocity, SL,max, of highly stretched flames or “critically stretched flames”, is the appropriate flame speed scale with which to parameterize the turbulent flame speed. More specifically, it leads to a scaling approach for the turbulent flame speed of the form S T S L ,max = f 〈 u rms ′ 〉 LP S L ,max , τ S L ,max τ flow , where τ S L ,max and τflow are the chemical time-scale associated with the leading point and a characteristic fluid mechanical time-scale, respectively. In this paper, we apply these scalings to data sets from the literature which explore pressure and fuel composition effects on ST. Amongst these data sets are new measurements, acquired by our group, of ST,GC for H2/CO mixtures at pressures up to 20 atm. It is shown that this approach can scale turbulent burning velocities from a range of different data sets, with significantly different fuel compositions, pressures, and stoichiometries. This result is particularly significant in understanding the strong pressure effects manifested in these data. Nonetheless, we also emphasize that time-scale, length scale, and Reynolds number effects on these correlations are difficult to differentiate as they exhibit similar pressure sensitivities, and further work is needed to conclusively understand the coupled (and very strong) effects of mixture stretch sensitivity and pressure on turbulent burning velocities.