A computational study on propagating spherical and cylindrical premixed flames

Perfectly spherical and cylindrical premised methane/air flames are numerically investigated in order to analyze the inner structure of the flame, the flame propagation, and stretch effects. Three kinds of flames are studied: steady, expanding, and imploding flames. To model the flames in detail, while minimalizing computational costs, a flamelet model is adapted to the spherical and cylindrical flames in combination with a skeletal reaction mechanism. The expression for the flame stretch rate follows directly from its mass-based definition and is shown to consist of two terms, one due to the propagation of the flame itself and the other one due to the variation of the flame thickness. This last term is usually ignored in literature. It is shown to be small compared with the other term, but important if one is interested in the dynamics of the flame itself. Parameters related to flame stretch such as the Karlovitz and Markstein numbers are obtained and analyzed. Furthermore, the flame propagation velocities of these expanding and imploding flames are shown to change only slightly throughout the flame. Both the gas and burning velocities, however, vary significantly when changing the position in the flame. The flame propagation velocity of the expanding spherical flame is in excellent agreement with experimental data.