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Atomization and Sprays
MULTIPLE-STATE PHENOMENA AND HYSTERESIS OF A COMBUSTING ISOLATED DROPLET
Institute of Aeronautics and Astronautics, National Cheng Kung University, Tainan, Taiwan,70101, ROC
Department of Mechanical Engineering, Technology and Science Institute of Northern Taiwan, Taipei, Taiwan, 112, R.O.C.
A study is presented on transition duality and phenomena related to a multiple state involving upper and lower branches for different flame configurations, flow structures, principal interphase mechanisms, and therefore different laws and correlations of droplet gasification in the ranges of Reynolds number and Damköhler number. Analytically derived canonical laws of droplets provide a theoretical basis for laws and correlations accommodating the multiplicity of interphase exchange rates to aid in spray calculation. The irreversibilities associated with the extinction and reattachment of an envelope flame are identified as the primary mechanism of the duality, which is characterized by the presence of two different states and burning rates of a droplet at a given Reynolds number and environmental temperature. The region and strength of duality are characterized by the difference in the burning rate of the two branches, both of which diminish at large values of Damköhler number. Burning rates and Reynolds numbers at the extinction and reattachment points are found to obey a law of proportionality within good approximation, whereas the percentile gasification of all the interphase exchange mechanisms and the global correction factor for gasification follow size-similarity rules for all the droplet sizes in the range of Reynolds numbers for a given environmental temperature. A universal droplet state chart provides an integrated view of the various states of a droplet through its life in a spray combustion chamber. Droplet acoustic response characteristics in the duality region are divided into three classifications: in-branch mode, which refers to oscillation that is limited to a single branch; trans-branch mode, an oscillation that starts at a branch and transfers to another branch; and loop oscillation, which is oscillation covering both branches. Oscillations involving transition among different branches and wake flame modes are identified as the principal causes of self-sustained oscillations in combusting droplets.
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