Brief Communication: A Simplified Approach to Transient Convective Droplet Evaporation and Burning
Empirical correlations for evaporation rates from single fuel droplets have existed since the 1930s. These correlations, which will be referred to in this article as Froessling/Ranz-Marshall types of correlations, are appropriate to the special cases of steady-state evaporation in the absence of chemical reaction. In a previous article by the authors, the quasi-steady evaporation and burning processes associated with a fuel drop in a convective environment are examined through a droplet model based on the boundary layer approach. For droplet Reynolds numbers of practical interest, this model produces very reasonable steady state as well as quasi-time-dependent droplet simulations, requiring relatively short computational times and yielding good agreement with the above-mentioned empirical correlations. The steady-state case, however, is usually relevant to practical combustor situations only when the drop has reached a nearly uniform temperature since the heating process of the drop cannot be considered to be quasi-steady. In the present study, the transient heating process of the droplet interior during evaporation and/or burning is taken into account, and thus calculations pertaining to the entire life-time of the droplet are carried out. It is of particular interest here to obtain simplified correlations to describe the transient behavior of evaporating and burning droplets; these may be incorporated with greater ease into spray calculations. Accordingly, we have chosen to use stagnation conditions in the present model in a modification of the Froessling/Ranz-Marshall correlations. These modified correlations, incorporating an effective transfer number, produce a fairly accurate representation of droplet evaporation and burning, while requiring only one tenth the computational effort used in a full boundary layer solution.