Hysteresis effects of two interactive droplets burning in convective flows

The hysteresis characteristics of two equal-sized droplets in tandem burning in hot convective flows are investigated numerically. Similar to the results of convective single-droplet burning of Jiang et al. (1995), the present study shows that at certain flow conditions, dual solutions are also exhibited for the flame structure around the two droplets, depending upon the initial conditions assumed. For the lower-branch solution where the droplets are initially merged in a chemically frozen flow, four combustion modes, including pure vaporization, wake flame, transition flame, and envelope flame, are obtained sequentially as the ambient flow temperature varies from a low 600 K to a high 1400 K at Re = 10. The upper-branch solution, where the droplets are initially enclosed by an envelope flame, however, possesses only two modes of wake and envelope flame under the equivalent conditions. The vaporization rates of both the leading and trailing droplets are hence found to be multi-valued at certain flow conditions where multiple flame configurations exist. The effects of droplet interaction are more profound on the trailing droplet so that its vaporization rate is generally lower than that of the leading droplet. However, as a transition flame occurs, the inverse exhibition in contrast to the foregoing result is observed, while the double reaction zones are excited. When the droplet spacing becomes large enough, the leading droplet behaves just like a single droplet in an equivalent flow condition, although it is not true for the trailing one.