Experimental assessment of various methods of determination of laminar flame speed in experiments with expanding spherical flames with positive Markstein lengths

Abstract

Experimental data obtained from lean propane–air expanding spherical laminar flames at pressures of 1 and 0.5atm, with all other things being equal, are analyzed using four different extrapolation equations available in the literature and a unified processing algorithm developed in the present work. For comparison, experimental data obtained recently by Zamashchikov et al. (2014) from a very rich hydrogen–air flame are also processed using the same algorithm. Dependencies of (i) rms differences between measured and calculated flame radii, (ii) laminar flame speeds, and (iii) Markstein lengths on the boundaries of the analyzed range of flame radii are studied in order to (i) investigate the sensitivity of processing results to these boundaries, (ii) determine the proper radius range for each extrapolation equation, and (iii) to find an equation that fits the measured data in the widest radius range. For the lean propane–air mixture under room conditions, which is associated with a relatively weak effect of flame stretching on the flame kernel growth, all four equations yield approximately equal flame speeds, but the associated Markstein lengths are different. Moreover, the flame speeds and Markstein lengths are sensitive to the processed range of flame radii and the same measured curve can be fitted with the same equation using substantially different pairs of Markstein length and flame speed. Due to these two sources of errors, choice of a proper processing method does not seem to be a critical issue when analyzing weakly non-linear dependencies of flame radius on time. To the contrary, for two other flames, which are associated with stronger stretch effects, the two aforementioned sources of errors play a minor role, i.e. flame speeds and Markstein lengths are weakly sensitive to the processed range of flame radii provided that it is properly selected, while the rms differences between measured and calculated flame radii are sufficiently sensitive to variations in Markstein length and flame speed. Accordingly, a proper choice of a processing method is of paramount importance when analyzing substantially non-linear dependencies of flame radius on time. Results of present work indicate that the phenomenological Markstein equation, which is linear with respect to flame curvature, fits the experimental data well in a wider range when compared to three other equations. Because, close results were also obtained using a non-linear equation derived theoretically by Kelley et al. (2012), the latter equation is worth being highlighted from the basic standpoint.