Effect of cylindrical confinement on the evolution of outwardly propagating flames

Evolution of outwardly propagating flames from a point of ignition into a cylindrical chamber is further explored through both experiments and modeling, and a newly developed correction method is presented to improve the accuracy of experimental burning velocity and Markstein length determination. A flamelet-based model, described herein, demonstrates reasonable quantitative agreement with the experimental data for flame propagation rate and allows for further information about the flame evolution to be ascertained. A cylindrical chamber boundary causes significant distortion of the flame surface and modification of the propagation rate through the interaction of the wall and the flow induced by thermal expansion across the flame. These departures from an unconfined case, especially the violation of spherical symmetry and zero burned gas velocity, result in erroneous values for flame speed calculated using conventional constant-pressure method, based on an unconfined flame. A flow correction factor that accounts for the actual induced fluid motions is developed based on the quantitatively predictive model. The calculated burned gas velocity is used as a correction factor in equations relating the propagation speed and unburned flame speed. The results indicate that use of the flow-corrected flame speed both improves the accuracy of planar burning velocity and Markstein length calculation and doubles the flame radius range valid for calculation. Model predictions reveal that calculations even for some small flame radii relative to the wall radius, where the flame speed-stretch relationship appears to be linear in accordance with the commonly employed theory, yield noticeable errors in the flame speed, burning velocity, and Markstein length.