# Optimizing the Auxiliary Air Channels of a Vortex Atomizer by 3D Printing Using the Taguchi Method
## 4 Results and Discussion  
### Spraying Patterns  
Typical jet spraying patterns of the twenty-five experimental cases are shown in Table 3 where the color mark denotes the location of the droplets collection cups. The jets are from right to left. Qualitatively, the spraying patterns can be categorized into two groups, one with a larger axial spray distance as that of Case 6 (hole number of 6, inclination angle of 5\({}^{\circ}\), area of 12 mm\({}^{2}\), and length of 8 mm), the other smaller as that of Case 1 (hole number of 5, inclination angle of 5\({}^{\circ}\), area of 9 mm\({}^{2}\), and length of 6 mm). In other words, the control parameters do affect the spraying pattern noticeably. It is also clear that the surrounding air swirl in the same direction as that of the water jet can considerably delay the breakup of the water jet due to a reduced relative speed between the air and water jet. It is also clear that the sprays are all affected by gravity, thus leading to the asymmetric spraying patterns for all of the cases investigated.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Cases** & **Spray Distribution** & **Cases** & **Spray Distribution** \\ \hline
11 & & 12 & \\
13 & & 14 & \\
15 & & 16 & \\
17 & & 18 & \\
19 & & 20 & \\
21 & & 22 & \\
23 & & 24 & \\
25 & & 24 & \\ \hline \end{tabular}
\end{table}
Table 3: _Cont._Quantitatively, the average droplet weight distributions along the nozzle centerline for the 25 experimental cases (three experiments per case for the average) are shown in Figure 7. The droplet weights along the centerline oscillate considerably due to the 10 cm pitch of the measurement cups. However, a clear trend, irrespective of the cases, shows that the droplet weights decrease as the distance from the nozzle exit increases as expected. Moreover, the curves in Figure 7 can be roughly categorized into two clusters; one consists of Cases 4 and 6; the other consists of the rest of the cases.  
From the droplet weight distribution of each experiment, the individual slope of each curve was calculated by linear regression as illustrated previously in Figure 6. By the computed slopes, the signal to noise ratios and the quality characteristic were determined. The results are tabulated in Table 4 where y\({}_{1}\), y\({}_{2}\), and y\({}_{3}\) represent the droplet weight distribution slope of the three experiments of each case, respectively, and S/N is the signal to noise ratio. It is clear that the S/N ratios of Cases 4 and 6 are 19.23 dB and 19.46 dB, respectively. They are larger than those of the rest cases; namely, these two nozzles perform better than the rest, similar to the results shown in Figure 7. Additionally, the S/N value for Case 1 is 16.38 dB, smaller than that of Case 6; the result is consistent with the corresponding smaller and larger axial spraying distances.  
A similar trend can also be observed from the quality characteristic drawn in Figure 9. The quality characteristic is the average slope of the three repeated experiments of each of the twenty-five cases given in Table 2. The optimum condition is identical to that of the S/N response of the control factors, namely, A2, C4, B4, and D3 for their minimum values of achieving the smaller-the-better goal.