Numerical study of synthetic spherically expanding flames for optimization of laminar flame speed experiments

This study presents the performances of four commonly-used extrapolation models, including the linear stretch and linear curvature models, the nonlinear model in expansion form, and the nonlinear quasi-steady model, using synthetic data sets generated over a wide range of conditions. The effects of a number of experimental limitations, such as the facility size, the finite camera framing rate, and the noise in the image detected flame radius, were investigated. Two types of error, model and noise error, which constitute the overall extrapolation uncertainty were investigated. Relative model error is primarily driven by Markstein length (L-b) and the flame radius range; however, it is weakly sensitive to laminar flame speed (S-b(0)). Noise error is controlled by the size of flame radius data set which depends on framing rate and the selected flame radius range. For small values of vertical bar L-b vertical bar, the model error is negligible. For large values of vertical bar L-b vertical bar, the two error types are equally prevalent in the overall uncertainty and they cannot be simultaneously minimized. Experimentally, large experimental facilities and high camera framing rates should be favored to reduce the noise error. For extrapolation to zero-stretch, the model that best reproduces the flame propagation evolution should be favored. The Markstein length demonstrates a high sensitivity to the choice of model and noise addition when compared to the laminar flame speed. The procedures developed in this study can be used to predict extrapolation-induced error under various experimental conditions and can be used to optimize laminar flame speed experiments.