Logistic-Regression-Based Meta-Analysis of Factors Affecting Flame Stability in a Shock Tube

This work describes a meta-analysis performed in an effort to better understand the parameters controlling flame stability in shock-tube flame experiments. The data set used in the analysis was aggregated from multiple prior studies employing the shock-tube flame speed method, as well as previously unreported results. Flames are first qualitatively classified as being smooth, distorted, or wrinkled based on end-wall images. A subset of trials capturing the stability transition from stable to unstable flames are then selected from each set of experiments. Across all data sets, the transition between stable and unstable flames is analyzed as a binary classification problem using logistic regression. The resulting classification model, cast in terms of a multivariate power-law expression for the critical temperature ((Formula presented.)) at which flames become unstable, is found to be highly predictive of the stability transition. Consideration of the trained model coefficients allows the effects of different experimental parameters on (Formula presented.) to be identified. Model parameters provide significant new insight into the selection of diluents in experiments; the use of a test gas with a high heat capacity ratio is found to have the most beneficial effect toward increasing (Formula presented.), while the effects of Lewis number and molecular weight are determined to be negligible. Ignition-location and pressure effects are less well quantified due to limited available data and are identified as key areas of further study.