APPLICATION OF RATE-RATIO ASYMPTOTICS TO THE PREDICTION OF EXTINCTIONFOR METHANOL DROPLET COMBUSTION

Asymptotic methods are employed to describe the flame structure and ex tinction of quasisteady, spherically symmetrical diffusion flames arou nd methanol droplets. Starting with a short mechanism involving 14 ste ps, five of which are reversible, sequentially reduced overall descrip tions of four, three, and two steps are obtained by investigating the character of the departure of the H atom and its associated radicals f rom steady states and by demonstrating in agreement with earlier work that, contrary to hydrocarbon flames, water-gas equilibrium is an exce llent approximation in the reaction zones of these methanol flames. It is shown that a useful two-step approximation is described qualitativ ely by CH3OH + O-2 --> CO + 2H(2)O and CO + 1/2O(2) --> CO2, in which CO stands for the mixture of CO and H-2 needed to maintain water-gas e quilibrium. The rate of the first of these steps is controlled mainly by that of the elementary step CH3OH + H --> CH2OH + H-2, in which CH2 OH stands for both isomers, and the rate of the second by that of H O-2 + M --> HO2 + M. The flame structure involves a thin fuel-consumpt ion zone on the rich side of a broader but still thin layer of H-2 and CO oxidation. The maximum temperature, that of the fuel-consumption z one, is calculated as a function of the rate of scalar dissipation at the stoichiometric mixture fraction, and extinction conditions are ide ntified from the maximum of this scalar dissipation on the resulting C -shaped curve. Extinction diameters are calculated explicitly from the se results for methanol droplets burning in oxygen-nitrogen mixtures i nitially at 300 K and at normal atmospheric and subatmospheric pressur es. Absorption of water in the liquid methanol is verified to exert a large effect on extinction and is included in the analysis by treating the two limiting cases of time-dependent liquid-phase diffusion and p erfect liquid-phase mixing, along with the quasisteady gas phase. It i s found that the second of these limits is in better correspondence wi th existing experiments and that, for burning in air, typically betwee n about 40% and 80% of the droplet mass is water at extinction. Reason able agreement with previously reported extinction diameters, obtained from detailed time-dependent computations and from microgravity dropl et-combustion experiments, is thereby achieved. The results provide an analytical method for calculating methanol droplet combustion and ext inction.