Influence of Gravity on the Propagation of Initially Spherical Flames

We study the evolution of an initially spherical kernel of burned gas in a fresh reactive mixture in the presence of a gravity field. The study is carried out numerically in the framework of an axisymmetric geometry, the chemistry being modeled by an irreversible overall one-step reaction. Attention is focused on the influence of two nondimensional parameters, namely the reciprocal of the Froude number, Fr11, and the Lewis number Le. Dependencing on these parameters, many different flame shapes are observed. The influence of Le is found to be consistent with the present knowledge on stretched flames: For Le , 1, an important reduction in the reaction rate is observed at the back of the hot deformed kernel, which can lead to extinction there. For Le . 1, the same occurs at the front surface but typically the flame persists at the back. For Le 4 1, the combustion characteristics, such as the combustion temperature, are found to be practically independent of Fr11, up to very high values of this parameter. A simple model based on a potential flow assumption in the fresh gas is developed and used to evaluate locally the numerically predicted flow field and hence the local stretch over the flame surface. For intermediate values of Fr11, as they are typical in the case of weak kernel deformation, this model is shown to be valid over the entire flame surface. Finally, the relevance of our study to experimental results, which are mainly concerned with flammability limits, is discussed.