Theoretical examination of assumptions commonly used for the gas phase surrounding a burning droplet
A finite reaction-rate model is compared to three commonly used flame-sheet models. The latter differ in their treatment of the evaporation from the surface and the value used for the molecular weights in the evaporation law. All four models are applicable to both steady and unsteady burning of droplets. Further, they account for variations of droplet radii and allow for differences in ambient conditions. Numerical results (obtained forn-decane) show that if the radius of the droplet is 10^(−2) cm the thin-flame approximation is excellent at 10 atm if the droplet surface temperature is not close to either the boiling point or the ambient temperature. However, this approximation is unacceptable at 1 atm. Among the three flame-sheet models, the one using non equilibrium evaporation at the surface and individual molecular weights best approximates the finite reaction-rate theory. However, this agreement breaks down for smaller droplets with lower surface temperatures, or for air with a larger oxygen content. These conclusions are independent of the chosen kinetics. The Clausius-Clapeyron approximation is shown to be excellent away from the boiling point for R = 10^(−2) cm. However, as the droplet surface temperature approaches the boiling point, or the droplet radius decreases, this assumption leads to considerable errors in the evaporation rate and also distortion of the thermal layer. Even larger errors are obtained when an average molecular weight is used. Here, large underestimates of the evaporation rate and great distortions of the thermal layer of the droplet are obtained. In spite of these errors, all models agree well at wet-bulb conditions.