Simplified model for droplet combustion in a slow convective flow

An idealized model for droplet vaporization or combustion in the Burke-Schumann reaction-sheet approximation is analyzed in terms of a Peclet number based on the Stefan velocity, taken to be of order unity, for Lewis numbers of unity and for small values of a parameter ɛ, defined as the ratio of the convective velocity far from the droplet to the Stefan velocity at its surface. Asymptotic solutions for the velocity, pressure, and mixture-fraction fields are obtained through second order in ɛ. The results are employed to calculate the effects of convection on the burning rate and on the flame shape. The prediction that the burning-rate constant increases linearly with ɛ for small values of ɛ is shown to be consistent with available experimental data. It is demonstrated that reasonable values of diffusivities provide approximate agreement of predicted burning rates and flame shapes with results of measurements.