An experimental study: laminar flame speed sensitivity from spherical flames in stoichiometric CH₄–air mixtures

Further improvements in modern chemical kinetics mechanisms using laminar flame speeds require an understanding of the uncertainty and precision of the measurement and hence its limitations. From an inspection of the literature, it was found that laminar flame speed values of a basic methane–air mixture could depend on what measuring technique is employed. One way to reconcile these differences and understand the limitations of the various techniques is to quantify both their uncertainties and sensitivities to various parameters such as vessel size, detailed data reduction method, and igniter influences. To this end, a detailed experimental sensitivity analysis of a spherically expanding flame experiment and its contributing factors was performed. A simple mixture involving stoichiometric CH₄–air was emphasized since there is still unreasonable uncertainty in its laminar flame speed and those measured values from spherical flames are consistently lower than those observed through the years with other methods by at least 1.7 cm/s. The effect of experimental vessel diameter on the inferred laminar flame speed for CH₄ was also systematically explored in the same apparatus for the first time. It was found that ignition energy (when properly accounted for) and mixture preparation time were negligible factors. Smoothing experimental data was shown to decrease the fit uncertainty, but it can also lead to higher repeatability uncertainty. The best way to approach smoothing, if it must be done, is to incrementally increase the smoothing span so as not to over smooth data. Additionally, the derivative method was found to be sensitive to the maximum size of the flame radius for experiments in smaller vessels (). Smaller vessels also have more-limited data in the healthy region that is neither ignition nor confinement affected, and it is therefore suggested that extreme care be taken to ensure that the data used in extrapolation are unaffected. A new method of eliminating cutoff bias and sensitivity could be to compute all reasonable permutations of cutoffs and use a histogram for the flame speed. A complete uncertainty quantification was performed which showed that the largest source of uncertainty was the repeatability of the experiments (77% of the total uncertainty), and this result is largely influenced by the data reduction and analysis. Other important factors were the mixture and temperature uncertainties, where the latter, if not fixed or corrected to a single initial temperature, can contribute as much as 55% of the overall uncertainty. This paper confirms the general results observed in recent works in the literature while further quantifying and highlighting the experimental uncertainty in laminar flame speeds obtained from spherical flames in confined vessels. Based on the results herein, we believe that the unburned laminar flame speed for a stoichiometric CH₄–air mixture at 1 atm and 298 K is 34.1 ± 0.3 cm/s.