On the validity of quasi-steady assumption in transient droplet combustion

A study on droplet combustion in unsteady force convection at high pressure under microgravity conditions was performed. The hysteresis loop of the instantaneous burning rate of a single suspended 1-butanol droplet was observed for the first time. Results showed that the classical quasi-steady film model cannot describe droplet combustion in an unsteady flow. Based on precise experimental observation and by utilizing dimensional analysis of the energy conservation equation, a new criterion is herein proposed for the condition in which the quasi-steady assumption is valid and for that in which it is not. The dimensional analysis led to formulation of a new time scale. Based on the time scale which we call the response-time-scale, a new Damköhler number, termed the response-Damköhler-number was formulated. Using the definition of the new time scale and that of the Damköhler number, unsteady behaviors of droplet combustion under conditions of various pressures and varying force convection were examined. Finally, using the response-Damköhler-number and the deviation factor between the actual instantaneous burning rate and the burning rate predicted by the quasi-steady theory, droplet combustion was categorized into four specific regimes. This study is also of fundamental interest in terms of the effects of turbulence on droplet evaporation and combustion in spray flames.