Twenty-Seventh Symposium (International) on Combustion/The Combustion Institute, 1998/pp. 1943±1950 ROLE OF FLAMEFRONT MOTION AND CRITERION FOR GLOBAL QUASI-STEADINESS IN DROPLET BURNING

A theoretical study has been conducted on the role of the ¯amefront motion in droplet burning to determine the range of validity of the classical quasi-steady theory in predicting the ¯ame standoff ratio, as well as its implication on transient fuel vapor accumulation/depletion. Recognizing that ¯amefront motion can be induced by droplet surface regression, by initial conditions, and by far-®eld unsteadiness, and that the ¯amefront standoff ratio is in general large, of the order of 10, it is phenomenologically anticipated that small ¯amefront velocities can lead to large variations of the mass ¯ow rate. Furthermore, it is demonstrated that the in¯uence of this ¯amefront motion can be characterized by a quasi-steady parameter Qs, which is the product of the cube of the standoff ratio and the ratio of the gas to liquid densities, such that the in¯uence is large when it is O(1), and small otherwise. By working in the ¯ame coordinate and, hence, naturally allowing for this motion, and by further assuming gas-phase quasi-stead-iness (in this coordinate), calculated results show that the standoff ratio continuously increases with time for O(1) values of Qs but approaches a constant, which is close to but exceeds the d2-law prediction, when it is suf®ciently small. The present generalized transient formulation also provides a rigorous description of fuel vapor accumulation effects related to the initial condition, demonstrates that these effects can indeed be accounted for on the basis of gas-phase quasi-steadiness, and allows for the simultaneous inclu-sion of far-®eld transient diffusion effects