# Study on Two-Phase Mixing Inside Flow Focusing/Blurring Nozzle by Gray Distribution Analysis Method
## 3 Gray Distribution Analysis of Experimental Images
### Feasibility Analysis  
For the flow focusing/blurring nozzle, when the flow parameters and the nozzle structure are different, the two-phase interaction in the mixing zone is different, so the flow pattern will be different. Different flow patterns will lead to different gray distribution of the experimental image. In this part, we will analyze the change of the gray distribution of the experimental image with time and study whether the gray distribution of one experimental image can represent the gray distribution of the experimental images under a certain working condition. Then, we will choose several cases. By comparing the difference of the gas-liquid flow images in mixing zone and the difference of the gray distribution of the experimental images in these cases, we can give the relationship between the gray distribution of the experimental images and the flow patterns (flow characteristics), and verify the feasibility of gray distribution analysis methods to study gas-liquid flow inside the nozzle, to a certain extent. Figure 3 shows the gray distribution curves of the experimental images in a mixing zone at different times when the gas flow rate is 40 L/min, the liquid flow rate is 600 mL/min, the orifice diameter is 5 mm, and the tube hole distance is 1 mm. It can be seen from Figure 3 that the gray distribution of the experimental images of gas-liquid flow inside the nozzle has certain differences at different times. This difference may be caused by the high frequency instability of the turbulent flow. The effect of high frequency turbulence instability can be reduced to a certain extent by averaging the gray distribution of the experimental images at different times under the same condition, but it cannot be completely eliminated. The average value of the experimental image's gray distribution curve is also affected by many parameters (such as the number of the experimental images). When we study the gas-liquid mixing in the nozzle through the gray distribution of the experimental images, we pay more attention to the overall trend of the gray distribution curve and we can see from Figure 3 that the difference of the gray distribution curve caused by high-frequency turbulence instability has little effect on the overall trend of the gray distribution curve. Therefore, for one working condition, it is feasible to use the gray distribution of one experimental image to study the gas-liquid mixing in the nozzle. Figure 3 also shows that the analysis results of the gray distribution analysis method for gas-liquid flow in the nozzle are statistically convergent. Figure 4 shows the images and gray distribution of different flow patterns in the mixing zone obtained by the experiment. The gas-liquid flow images in the mixing zone of the nozzle are marked with a red dotted rectangular box, which is also the area to extract the gray  
Figure 3: The gray distribution curves of two-phase flow images under different times. As can be seen from Figure 4, for case 1, the gas-liquid two-phase fluids in the mixing zone do not mix; we can observe the liquid column in the mixing zone, and the boundary of the gas-liquid two-phase fluids is relatively clear, so the flow pattern in the mixing zone is flow focusing. At this time, the gas-liquid interaction in the mixing zone is weak, the light enters the SLR camera through transmission and the brightness of the pixel points is high and uniform, so the image has a high gray level and a good concentration. For case 3, the boundary of the gas-liquid two-phase fluids in the mixing zone is fuzzy, the gas-liquid flow in the mixing zone is close to fog and the gas-liquid mixing is good, so the flow pattern in the mixing zone is flow blurring. At this time, the liquid in the mixing zone is broken into tiny droplets by gas, and the light enters the SLR camera by scattering. The brightness of the pixels is low but still relatively uniform, which reduces the gray level of the image, but the concentration of gray distribution is still very good.