Theoretical Modeling of Cool Flames

Abstract

In order to understand the interaction of the physical and chemical processes which result in cool flames, a theoretical investigation of flame propagation has been undertaken. For this study, a mathematical model has been formulated which takes into account the conservation of mass, momentum, and energy; and assumes Fick's law for mass diffusion. To account for the flame separation property associated with these flames, a chemical model consisting of two exothermic, monomolecular, series reactions has been considered in order to have several chemical reactions proceeding at different rates. The resulting flame equations have been solved analytically for an ignition temperature approximation to the chemical kinetics and numerically for Arrhenius kinetics. The results for the two kinetics models compare favorably for the cases in which double flames are produced. A general comparison of the theoretical results to experimental results appearing in the literature shows a general agreement in the shape of the temperature profiles. The conclusion is drawn that the two flame phenomenon can be viewed as literally two flames with weak but sufficient interaction to maintain a separation distance.