Effects of droplet evaporation on negative temperature coefficient phenomenon and a prediction model for two-stage auto-ignition

The effects of droplet evaporation on two-stage auto-ignition are investigated by embedding evaporation source terms into a gaseous homogeneous reactor. The ranges of pressure, temperature, equivalence ratio and droplet diameter are 5-15 bar, 600-1000 K, 0.25-1.5 and 0-100 mu m, respectively. Evaporation Damkholer number (Daeva) is proposed to investigate two-stage auto-ignition and its increase affects two-stage auto-ignition in three aspects: (1) a decrease in gas temperature, (2) an increase in available fuel vapor, and (3) the changed proportion of fuel consumption in low-temperature auto-ignition and high-temperature induction. For the cases without evaporation under low pressure, the negative-temperature-coefficient phenomenon appears and disappears for high and low equivalence ratios, respectively. For the cases with evaporation, three auto-ignition modes are observed with increasing Daeva. The first two modes are obvious two-stage auto-ignition and their difference is whether the evaporation has finished before the low-temperature auto-ignition (mode 1#) or not (mode 2#). The zero-temperature-coefficient phenomenon is observed when entering auto-ignition mode 3#. The evaporation effects are introduced to a new prediction for two-stage auto-ignition, including the first delay, the first temperature jump and the relation between cool-flame temperature and the second delay. The prediction results for the first and second delays are satisfactory in wide ranges.