Appendix A
Comparison of droplet distribution in swirling non-swirling kerosene spray
Droplet mean properties (i.e. size, number density and velocity) are presented to describe the global features of kerosene spray. The effect of combustion on droplets transport are emphasized by comparing the spray under swirling conditions (S=0.53) to the non-swirling case (S=0).
For a hollow cone spray it is reasonable to define the location of the spray boundary at the radial position where most of the fuel mass resides. This is accomplished by presenting the droplet volume flux, which is defined as the volume of the droplets passing a unit cross-sectional area per unit of time. Thus the radial profiles of the volume flux are presented in figure 1 at different axial location. The solid boxes along the abscissa indicate the position of the burner passage walls, with the fuel nozzle located at the axis of the burner (r=0). Coflowing air is introduced through the outer coaxial passage. The profiles indicate that radial positions exist at each axial position where the volume flux exhibits a maximum or a peak and
thus are used to define the spray boundary. The results show that the presence of a swirl redistributes the droplets to much larger radial positions (by a factor 2-3 at z=10mm) and the peaks that are farther apart than in the nonswirling case are an order of magnitude higher than in the swirling case. This result indicates that the swirl promotes spray uniformity closer to the nozzle than in the nonswirling case where shear-induced drag disperses the droplets farther downstream.
The figure 2 shows the variation of the Sauter mean diameter D32. The vertical bars identify the nominal spray boundary, which is defined as the radial location where the volume flux exhibits a peak. The spray boundary also becomes ambiguous with increasing axial
Hybrid rocket engine and injection systems. 2011
distance because of droplet dispersion. The peaks in the different case are not coincident because the droplet mean size increases monotonically with increasing radial position. the radial position of the peaks for S=0 are closer to the spray centreline than for S=0.53. the difference is attributed to the centrifugal forces displacing to bulk the droplets radially outward from the spray centreline. Without swirl, the value of D32 tends to increase monotonically with increasing radial position toward the edge of the spray at downstream axial positions. The results indicate that the swirling case, enhancing mixing would result in larger mean sizes near the center of the spray and smaller sizes toward the periphery. the weak radial variation of D32 for S=0.53 occurred at all of the measured axial positions, emphasizing the penetrating influence of swirl that is experienced by the surrounding stream.
The variation of droplet mean size with axial position along the centreline and spray boundary is shown in fig. 3. Compared to the swirling case, the droplet mean diameter is smaller near the spray centreline and larger near the spray boundary in the nonswirling case. The gradual increase in the value of D32 along the spray boundary is again attributed to the entrainment and transport of smaller droplets by the swirling flowfield, and the associated shear layer mixing that occurs between the spray and the surrounding air stream. This mixing promotes the depletion of smaller droplets in the spray boundary by means of such possible mechanisms as coalescence between droplets, droplets vaporization, and radial dispersion away from the spray boundary.
The results for the droplet number density (N) are shown in fig. 4 and fig. 5. The data indicate an increase in radial spread of the spray with axial position for both. In the swirling spray, the maximum value of N occurred near the spray boundary where the larger droplets exist. In contrast, the maximum value of N for the nonswirling case is in the center of the spray despite the hollow-cone nature of the fuel nozzle.
On axial position the values of N are larger for the nonswirling spray near the centreline but are significantly smaller toward the spray boundary. Near the spray boundary the number density is similar to that near the centreline for S=0.53, but significantly lower for S=0 at downstream position. These differences between the nonswirling cases are attributed to the presence of significant air swirl in the latter case that promotes the radial dispersion and spatial uniformity of the fuel droplets. For S=0 the bulk of the mass does not reside in the
Figure 1: Variation of volume flux with radial position r measured at different axial positions
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Figure 2: Variation of Sauter mean diameter D32 with radial position r measured at axial
Figure 3: Variation of Sauter mean diameter D32 with a) axial position along the center line
for the nonswirling and swirling sprays, b) axial position along the nominal spray boundary for the nonswirling and swirling sprays.
Hybrid rocket engine and injection systems. 2011
Figure 4: Variation of number density N with radial position r measured at different axial
Figure 5: Variation of number density N with axial position a) along the centerline for the
non swirling and swirling case; b) along the nominal spray boundary for the nonswirling and swirling case.
