# Optimizing the Auxiliary Air Channels of a Vortex Atomizer by 3D Printing Using the Taguchi Method
## 3 Experimental Approach  
A schematic diagram of the experimental setup, consisting of a water pump, a supporting steel table with a fixed bracket, an atomizer, and a water droplet weight measuring cups, is depicted in Figure 4a. Water was adopted as the spraying liquid. It was driven by a water pump to provide a gauge pressure of 33 kg\({}_{\mathrm{f}}\)/cm\({}^{2}\) (approximately 485 psig). The resulting Reynolds number of the liquid jet was about 125,400, namely, a turbulent liquid jet. Water was sprayed continuously for 60 s under the constant gauge pressure of 33 kg\({}_{\mathrm{f}}\)/cm\({}^{2}\). The atomizer was 120 cm above the ground floor. The water droplet weight measuring range was from 300 cm to 700 cm from the atomizer. The pitch of the measuring cups was constant with the value of 10 cm. In addition to the droplet weight measurements, the spraying patterns were also recorded for further analysis. A typical example of the sprayed pattern, as depicted in Figure 4b, shows that the jet is not symmetric due to the influence of gravity. The design parameters of the auxiliary air holes include their numbers, inclination angle, flow areas, and lengths. In order to deduce the optimum air hole configuration under a reasonable cost, the Taguchi method was applied in the design of experiments. The  
Figure 3: Designed and fabricated rings with needed air holes. (**a**) Designed 3D model. (**b**) 3D printing fabricated rings with air holes. Figure 2: Air and water flows in and out of the atomizer. (**a**) Water flow direction of atomizer. (**b**) Air flow direction of atomizer. Taguchi method has been used frequently in reducing experimental tasks. For example, [PERSON] et al. (2019) [PERSON] et al. (2019) proposed three novel designs for enhancing mixing in micro-fluidic devices, namely, passive, active, and a combination of both. Their simulation results showed that the pure active micro-mixer design had superior mixing ability and could be further optimized by using the Taguchi method. In this study, the above four parameters were taken as the control factors in the experimental design. The experimental procedure is illustrated in Figure 5, beginning with the determination of the quality characteristic, followed by determining the noise factors, degree of freedom, and factor levels so that an appropriate orthogonal table could be selected. Afterwards, experiments were carried out while data were acquired and analyzed to determine the optimum experimental condition and subsequent validation. Details are as follows. The total number of the control parameters is four. Five levels for each control factor were considered as illustrated in Table 1. These levels are deduced from the current field design of the nozzle. That is, the numbers of holes are five, six, seven, eight, and nine; the inclination angles are from 5\({}^{\circ}\) to 25\({}^{\circ}\) with an increment of 5\({}^{\circ}\); the flow area of the air hole varies from 9 mm\({}^{2}\) to 21 mm\({}^{2}\) with an increment of 3 mm\({}^{2}\); the lengths of the holes are 6, 7, 8, 9, and 10 mm, respectively. To accommodate the combination of these control factors and levels effectively, the L\({}_{25}\) orthogonal table was chosen for this study. The symbol is  
Figure 4: Experimental setup and typical spraying pattern. (**a**) Schematic diagram of the experimental setup. (**b**) Typical spraying pattern. L\({}_{25}\) (5\({}^{4}\)), representing 25 experimental cases, 4 control factors, and 5 levels for each control factor. Compared to the full factorial experimental design which requires 625 experimental cases, the 25 experimental cases by the Taguchi method dramatically reduced the time and cost of the experiments. Details of the twenty-five experimental cases of the chosen L\({}_{25}\) orthogonal table are illustrated in Table 2 in which the symbols A, B, C, and D denote the control factors, and the numerals 1, 2, 3, 4, and 5 are the levels of the control factors, respectively. The reasons for choosing this L\({}_{25}\) orthogonal table are twofold.