OCR Text |
Show ) by the droplet radius. Thus, as the droplet evaporates during burning, the numerical grid moves with the droplet surface. The chemical reaction of the nonane fuel is modeled using a two-step reaction mechanism recommended by Westbrook and Dryer6 in which hydrocarbons first oxidize to CO and H20, and then CO oxidizes to CO2. The reactions and rate expressions for this mechanism are6 : (la) (16) and, (2a) (26) (2c) For nonane, the pre-exponential factor, A, in equation (1) is 5.2xl01l, and the effective activation energy, Ea, is 30.kcal/mol. These, and other reaction mechanisms for a variety of hydrocarbon fuels are based on experimental data and reproduce measured ftame speeds and overall heats of reaction. However, such a data base and correlations do not exist for tetrachloroethane (TECA). Experimental data" show that pure TECA droplets will not ignite under the conditions we are modeling. Therefore, as a first approximation, the TECA reaction is modeled using a similar two-step reaction mechanism, with a substantially higher activation energy, (40.kcal/mol), to simulate the resistance of TECA to ignition. One-Dimensional Trajectory Model: , The second model is a one-dimensional Lagrangian solution of the droplet trajectory. Newton's law is applied to the center of gravity of a vaporizing droplet under the inftuence of drag and gravity forces. The drag force and droplet burning rate are specified externally based on the above detailed models and empirical correlations. The purpose of this model is to show the effect of uncertainties in these parameters on droplet trajectory. Thus, the first model is intended to elucidate processes associated within and around single droplets, without external ftow, while the second model examines global droplet behavior in a ftow field. To simulate the drop furnace experimental conditions in Ref. 4, the droplet is assumed to start from rest and fall under its own weight. Variable drag forces are calculated using correlations from Eisenklam et a1.8 and Renksizbulut and Yuen9 • Both of these correlations are based on the standard drag curve, adjusted for mass transfer using the transfer number, B, where B represents the ratio of the "driving force" for gasification to the "resistance" to gasification. Gasification implies either burning or vaporization. For the purposes of this model, the transfer number was assumed constant and related to the droplet gasification rate by the expression derived from the D2_Law1o. Since the actual droplet will undergo a heat-up period, |