## 3 Results
### Mesured Frictional Pressure Drop
#### 3.1.2 Rectangular and Triangular Tubes  
Figure 8 shows the relation between the measured frictional pressure drop gradients \(\Delta P_{\rm f}/\Delta L\) and quality x flowing in rectangular and triangular tubes, comparing them with the data of a 1.00 mm circular tube that has a similar hydraulic diameter. As in the case of the circular tube, the measured frictional pressure drop in both the small rectangular and triangular tubes increased with increasing mass flux and quality. Moreover, for the low mass flux condition (50 kg\(\cdot\)m\({}^{-2}\cdot\)s\({}^{-1}\) and 100 kg\(\cdot\)m\({}^{-2}\cdot\)s\({}^{-1}\)), the frictional pressure drop indicated higher values in the low-quality region; after that, it decreased with increasing quality. In this region, the value of the frictional pressure drop was not affected by the different cross-section shape or mass flux. Figure 7: Frictional pressure drop vs. quality in downward flow. (Inner diameter is parameter). The frictional pressure drop in the rectangular tube seems small compared to that of the triangular tube; it is supposed that there was no difference in the frictional pressure drop of both the tubes considering the hydraulic diameter that is 15% larger than that of the triangular tube. On the other hand, comparing the circular tube pressure drops, no differences were observed for the non-circular tubes pressure drop at low mass fluxes of 30 and 50 and high mass flux of 400 kg\(\cdot\)m\({}^{-2}\cdot\)s\({}^{-1}\). However, it became smaller at 50, 100, and 200 kg\(\cdot\)m\({}^{-2}\cdot\)s\({}^{-1}\), especially in downward flow. As shown in Figure 9, I had conducted observation experiments using a high-speed camera for the circular, rectangular, and triangular channels with a hydraulic diameter of about 1 mm under the same refrigerant R410A and saturation temperature 10 \({}^{\circ}\)C condition of this study. Moreover, the pressure drop results will be discussed based on these images [14]. Figures 10-12 are the flow pictures in circular, rectangular, and triangular channels, respectively. Figure 8: Frictional pressure drop vs. quality flowing upward and downward in circular, rectangular, and triangular tubes. Figure 9: Test glass channels [14]. To summarize the differences between upward and downward flow, no effect of flow direction was observed on the frictional pressure drop of the circular tube. Thus, there was no difference in the flow patterns in circular channel. However, the rectangular and triangular non-circular tubes were clearly smaller in the downward flow. This is especially noticeable for the quality above 0.3. According to the visualization experiments, this region coincides with the transition from slug flow to annular flow in both tubes. It is especially interesting to note that the downward flow in Figures 11 and 12 with a mass flux of 50 kg\(\cdot\)m\({}^{-2}\cdot\)s\({}^{-1}\) and a quality of 0.9 showed a completely different flow pattern than the upward flow under the same conditions. In other words, an annular flow without any disturbance was observed at low mass flux regardless of the quality. Since this flow pattern has not been reported before, I named it non-disturbance annular flow and refer to it as NA in the figures. This is because gravity (buoyancy) and surface tension have a great impact on the flow pattern. Figure 11: Rectangular channel visualization with pylex glass [14]. Figure 12: Triangular channel visualization with pylex glass [14]. influence on the downward flow, and since the upward flow is in the opposite direction of gravity, the liquid held in the corner of the non-circular tube will always have a velocity distribution due to the shear force of the vapor and gravity, and the shear force from the tube surface will cause the velocity of the liquid to become unstable as it flows downstream.