# Study on Two-Phase Mixing Inside Flow Focusing/Blurring Nozzle by Gray Distribution Analysis Method
## 4 Results and Discussions
### Local Analysis of Two-Phase Flow Field in Mixing Zone  
Although we have studied two-phase flow and mixing in the mixing zone under different nozzle structures and flow parameters by using the gray distribution curve, as the gray distribution curve is a frequency statistical result, we do not know much about the two-phase local flow field in the mixing zone. The local flow field information is important to understand the two-phase interaction in the mixing zone. Therefore, we used Matlab software to analyze the local flow field in the mixing zone with different flow patterns. Figure 14 shows the radial and axial gray scale distribution of the local flow field under different flow patterns in the mixing zone. Figure 14a shows the gray scale distribution of the radial flow field in the center of the mixing zone under different flow patterns. Figure 14b shows the gray scale distribution of the axial flow field in the center of the mixing zone under different flow patterns. Figure 13: The gray distribution curves of the two-phase flow images under different air flow rate and orifice diameter: the water flow rate and tube hole distance are 100 mL/min and 1 mm. Based on case 1, the air flow rate and orifice diameter in cases 1 to 3 can be dimensionless into (In the form of air flow rate/orifice diameter):1/1, 1.5/1.66 and 2/2.33. As can be seen from Figure 14a, the gray scale level of the radial flow field is larger, and the gray distribution is more uniform during flow focusing. The obvious gas-liquid interface makes the gray scale level of the flow field lower when the radial position is smaller or larger. When the flow pattern is flow blurring, the gray scale level of the radial flow field in the mixing zone is low, but the gray distribution is still relatively uniform. The thickness of the two-phase mixture center region is relatively large, which results in the lower gray scale level of the flow image in the radial center region but actually the radial gray scale distribution is relatively uniform. In the transition mode, the gray scale level of the radial flow field is close to that of the flow blurring, but the gray distribution curve is very nonuniform. This is due to the instability caused by the strong radial inertia force of the gas acting on the liquid. In general, the gas-liquid flow or mixing in the mixing zone is stable in the radial direction when the flow pattern is flow focusing or flow blurring, while the interaction of the gas-liquid two-phase radial inertia force in the transition mode makes the gas-liquid two-phase mixing radially unstable. As shown in Figure 14b, for different flow patterns, when the axial distance is small, the gray scale level of the two-phase flow images will increase with the increase of the axial position. This is because the liquid column or liquid mist in this area will reflect the inner tube wall, thus affecting the gray scale level of the flow images. In the flow focusing mode, the gray scale level of the axial flow field is high and uniform. In the flow blurring mode, the gray scale level of the axial flow field is lower, and the gray scale level distribution curve has small pulsation. In the transition mode, the gray scale level of the axial flow field is close to the flow blurring mode and the gray scale level distribution curve decreases in pulsation. The analysis shows that the gas-liquid flow in the mixing zone is axially stable when in flow focusing mode, while the gas-liquid two-phase flow in the mixing zone is axially unstable when transition mode or flow blurring mode, and the gas-liquid flow characteristics are similar in these two modes. The analysis of the local flow field in the mixing zone shows that the gas-liquid flow in the mixing zone is completely stable in the flow focusing mode. In the flow blurring mode, the gas-liquid flow in the mixing zone is stable in the radial direction, but there are small pulsations in the axial direction.