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Show Recent results from a two-dimensional, axisymmetric full Navier-Stokes solution of a single-component burning droplet 7 show that convection has a strong effect on the burning and heat transfer rates of pure hydrocarbon droplets. Results from this model provide insight into the flame structure around the droplet in the presence of convection. When the droplet is large and the Reynolds number high, the flame is confined to the wake region of the droplet. As the droplet gasifies, the Reynolds number decreases, the flame wraps around the droplet, increasing the average temperature and therefore mass transfer from the droplet . As the Reynolds number is lowered further, the flame becomes more symmetric around the droplet, until at zero Reynolds number complete spherical symmetry is achieved. Although these results are limited to single-component droplets, the flame structures they describe are qualitatively the same for multicomponent droplets. This complex flame structure, even at low Reynolds numbers, creates asymmetrical temperature profiles which must be accounted for to quantitatively match experimental data. One-dimensional Trajectory Model: This model calculates the penetration distance of a single droplet using gasification rates calculated from the above detailed models and measured in experiments, and drag correlations recommended for vaporizing droplets in Ref. 8 and 9. Droplet Trajectory for Burning and Vaporimg Droplets c.IcuIated using Two Different Dreg CorreIetiona ] CI 0 c ~.., i5 ).:" 0.06...-------------------, ........ Eisenldam. et al 0 .04 -- Renksizbulut. et al 0 .03 0 .02 0 .01 0 .00 -+---<::::..-....,....--.--....,....-...,.-....,....--.---.---.--,..-......--......---.--~ 0 .0 0 .1 0.2 0 .3 Time (sec) Figure 5. Droplet penetration distance calculated using two different drag correlations for both a vaporizing and a burning droplet . Figure 5 shows the droplet penetration distance as a function of time for both a vaporizing and a burning droplet . The calculations are carried out until the droplet diameter is less than 10Jotm (less than 0.004% of the volume remaining). The total distances predicted for each droplet are compared, and differences are noted as A Y. Results from Fig. 5 show that the two correlations agree within 10% for a vaporizing droplet, (vaporization rate, K~ = 0.3, mass transfer number, B =1.), but as the gasification rate increases, (burning rate, Ke = 0.95, mass transfer number, B=8.), the difference between the correlation becomes significant, A Y= 90%. The primary difference between these correlations is the definition of the Reynolds number. In the Eisenklam et al. correlation8 the viscosity in the Reynolds number is based on free stream conditions (Jot = 4.69&5 kg/m sec), while in the Renksizbulut and Yuen9 correlation, viscosity is the average of the fuel/air mixture viscosity at the surface and the free-stream viscosity, (Jot = 2.71&5 kg/m sec). These results show the strong sensitivity of drag force to differences in calculated parameters. In a problem with such complex 8 |