From spherical expanding flames to laminar burning properties: a step-by-step analysis

The analysis is proposed of the process of deriving laminar burning parameters from high-speed, high-resolution shadowgraph recording of spherical expanding flames. Data processing and analysis are critically discussed, starting from the extraction of flame radius from the experimental recordings. A specific test case is used as a reference: CH4-air mixtures have been tested in the high-pressure DHARMA reactor, at starting pressure of 6 bar and ambient temperature, varying the equivalence ratio within the flammability range. Even in a simplified configuration, real flames are anyway affected by stretch: the critical point is processing the measured data to obtain the unstretched flame speed and, ultimately, the laminar burning velocity. A linear relationship is usually assumed between flame speed and stretch. In recent years, non-linear methodologies have been proposed as a more accurate approach to the deconvolution of experimental, stretch-affected data. The comparison has been drawn in terms of unstretched laminar burning velocity and burned-gas Markstein length: the results have been referred to available literature. An overall picture of the applicability of the various options has been obtained, together with an estimate of each method's accuracy and of the associated errors (either physical or mathematical in nature).