Effects of data point number on laminar flame speed extrapolation

Abstract

This study aims to investigate the effects of data points number on the accuracy of flame speed extrapolation using expanding spherical flame, which is a practical issue in high flame speed experimental measurement. Monte Carlo simulations were conducted based on the flame radius data obtained from one-dimensional spherical flame simulation. Given number of points were randomly picked from 70 points to obtain the unstretched flame speed by linear and nonlinear extrapolation under different Lewis number, fuel type, and initial pressures. The results were statistically analyzed and show that the least number for flame speed extrapolation is related to the Lewis number of mixtures. Mixtures with Lewis number smaller than unity need more data points to ensure accurate extrapolating results. In addition, the accuracy of flame speed determination is very sensitive to the error in flame radius when data points are sparse. When 0.1% of Gauss noise was added to flame radius data, additional dozens of points are required to keep the same accuracy. At least 30 data points were suggested to be adopted in the extrapolation of flame speed to reduce the uncertainty from data points number to less than 1%. The effects of the flame radius range on the determination of flame speed again validated by the current study, indicating a wide range of flame radius should be used to avoid uncertainty. It was also shown that the nonlinear extrapolation method needs fewer data points than the linear method to achieve the same accuracy for mixtures.