On the Rational Interpretation of Data on Laminar Flame Speeds and Ignition Delay Times

Abstract

This article examines a seemingly trivial issue, namely, the apparently large scatter found for the laminar flame speeds of fuel-rich mixtures as compared to those of lean mixtures. Using the hydrogen/air flame speed at atmospheric pressure as an example, it is demonstrated that this perceptive notion is based on rather uninformed data presentation. It is shown that the cause for the notion has little to do with the data itself, but it is the result that the flame speed data are customarily plotted against the equivalence ratio, which by its asymmetric definition, compresses the data for lean mixtures and expands the data for rich ones. When plotting the flame speed against the symmetrized equivalence ratio defined as ≡ φ/(1 + φ), it can be readily shown that the flame speed data have, in fact, similar uncertainties across the entire range of stoichiometric mixtures tested thus far. A statistical analysis of an extensive set of flame speed data further illustrates the above point, namely, a nearly invariant confidence interval across the same range of stoichiometry. The aforementioned result, coupled with a similar statistical analysis performed for a representative set of shock-tube ignition delay time, highlights the importance of the systematic treatment of the uncertainty in these global, yet fundamental combustion property measurements in aiding reaction model development and testing. For this purpose, an impact factor is proposed for combustion experiments, by combining the sensitivity of the response to rate parameters with the inherent uncertainty of the experiment. It is demonstrated that with the exception of some extreme cases, the impact factors of the flame speed and shock tube ignition delay data are quite close to each other, making both indispensable for model testing. Overall the study illustrates that as a quantitative science, fundamental combustion property measurements must consider inherent experimental uncertainty and require a careful analysis of the uncertainty in order to yield useful results.