Gas-phase quasi-steadiness and fuel vapor accumulation effects in droplet burning

The present investigation demonstrates that due to volume effects the amount of fuel vapor in the inner region to the flame during droplet combustion can be substantial. By properly accounting for its initial accumulation and the subsequent depletion, but still assuming gas-phase quasi-steady transport, we can formulate simplified theories for droplet vaporization and combustion. The present results generally agree with those obtained from more detailed studies allowing for transient transport in the gas phase. In particular it is shown that for low ambient oxidizer concentrations the flame-front standoff ratio increases without bound and some fuel vapor still remains at complete droplet vaporization, whereas in richer environments a steady state may be reached such that complete fuel consumption coincides with complete fuel vaporization. Effects due to droplet heating are also investigated. Experimental results on almost spherically symmetric droplet combustion conducted under subatmospheric pressure agree with the theoretical predictions. It is emphasized that when instantaneous rate of fuel vaporization is assumed to be equal to that of fuel consumption at the flame, and therefore not accounting for the amount stored in the inner region, the d² law yields inaccurate estimates on the rate of chemical heat release from droplet burning. The extent to which a porous-sphere experiment can simulate droplet combustion is also discussed.