Uncertainty reduction in laminar flame speed extrapolation for expanding spherical flames

The quantification and reduction of the uncertainties in the extrapolation process in laminar flame speed measurements were studied using expanding spherical flames under positive Markstein length (Lb> 0) conditions. The experimental and computational results were first compared showing their differences. The performance of three extrapolation formulas was then examined under a wide range of experimental conditions using various extrapolation ranges and pressures. It is found that the extrapolation uncertainty contains two sources of error, namely model error and random error. The individual effects of the upper and lower bounds of the extrapolation range under various Lb conditions were studied and the ratio of Lb and the flame radius range is found to be the controlling parameter of the model error. Small value of |Lb/Rf| allows the neglect of the model error by increasing the upper or the lower bound of the flame radius range. A new empirical parameter, Lb/Rf,new, was defined according to the experimental results, while it is recognized that the random error is mainly affected by the number of points for extrapolation and that at least 30 points should be used to remove the random error.