Prediction of the pulsation frequency of flames formed over a semi-infinite horizontal surface

The pulsation frequency of horizontally situated semi-infinite reacting surfaces is studied using linear stability theory. The analysis considers the flow to consist of an initially laminar base flow and a periodic disturbance. The governing equations are cast into a self-similar form analogous to previous analyses of boundary layers. The base flow is analyzed in terms of a flame sheet approximation, the solution to which is required to solve the disturbed flow. Some boundary conditions pertaining to the disturbances are evident but some others are inferred herein. The governing equations are solved for a flame burning n-heptane, and the results of the analysis relate the disturbance frequency of the flame to a Grashof type number which, in turn, is related to the length of the thermal boundary layer. It is determined that the frequency scales according to a power law expressed as (length)0.8.