## 4 Experiment  
To study the practical effect of applying the IM-WIDIM-DPIV algorithm to the measurement of vertical upward oil-water two-phase immiscible flow, an experimental verification was conducted in \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Algorithm** & \multicolumn{2}{c}{**Synthesized Image**} & \multicolumn{2}{c}{**Grayscale Image**} \\ \hline  & Run-Time & Measurement Accuracy & Run-Time & Measurement Accuracy \\ \hline WIDIM-DPIV & 51.25 s & 86.7\% & 2.34 s & 92.8\% \\ IM-WIDIM-DPIV & 143.27 s & 93.8\% & 8.27 s & 96.5\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The run-time and measurement accuracy of WIDIM-DPIV algorithm and IM-WIDIM-DPIV algorithm. Figure 6: IM-WIDIM-DPIV algorithm verification. **(a)** The synthesized image generated by MATLAB. **(b)** The image produced by moving the particles in Figure 6a according to a given displacement field. **(c,d)** The grayscale image pair of local oil–water two-phase immiscible flow. **(e)** The given displacement field in Figure 6a,b. **(f)** The displacement field of Figure 6a,b calculated by the WIDIM-DPIV algorithm. **(g)** The displacement field of Figure 6a,b calculated by the IM-WIDIM-DPIV algorithm. **(h)** The WIDIM-DPIV algorithm error plot of synthesized image. **(i)** The IM-WIDIM-DPIV algorithm error plot of synthesized image. **(j)** The flow velocity field of Figure 6c,d calculated by the WIDIM-DPIV algorithm. **(k)** The flow velocity field of Figure 6c,d calculated by the IM-WIDIM-DPIV algorithm. the oil-gas-water three-phase flow laboratory of the testing service branch of Daqing Oilfield Co., Ltd. in China. The experimental schematic diagram and experiment platform are shown in Figure 7.  
The area to be measured was illuminated with an LED backlight source. The led array lamps are designed by our team, and the parameters are as follows. (1) Light color: no-flicker white; (2) size: 20 cm \(\times\) 20 cm, and evenly distributed with 19 \(\times\) 4 LED lights; (3) input voltage: 220 V; (4) luminous flux: \(\sim\)2400 lm. To make the lighting more uniform, the LED lights are assembled into a rectangular box without top lid, and cover the top of the box with an oil paper. The oil bubble in the vertical upward two-phase flow was used as the tracer in the experiment. A high-speed camera was adjusted to make flow velocity field imaging clear. As shown in Figure 7, Multiphase flow control system controls the flow velocity of oil phase and water phase according to the given velocity and holding rate. When the velocity table of oil phase and water phase has stable numerical value, the flow in pipe reaches the predetermined velocity and water up. The control errors of velocity and holding rate are less than 0.1%. After the oil and water phases are mixed and flowing about 6 m in the pipe, the flow state is steady. The high-speed camera is used to collect the image of oil-water two-phase immiscible flow, and then the DPIV image recorded by the high-speed camera was transmitted to a computer in real time for preservation and processing. Six iterations were carried out in the process of implementing the algorithm to calculate the flow velocity field, and the interrogation window was reduced to a quarter of the original size every two iterations. Interrogation window size changes from 128 pixel \(\times\) 128 pixel to 32 pixel \(\times\) 32 pixel. DPIV measurement experiment under different working conditions was conducted by changing different components of the multiphase flow through control system. The flow velocity in this experiment ranged from 9.4 \(\times\) 10\({}^{-3}\) m/s to 51.9 \(\times\) 10\({}^{-3}\) m/s, with intergroup interval of 4.7 \(\times\) 10\({}^{-3}\) m/s. The water cut ranged from 70% to 90%, with a step rate of 10%. The experimental parameters are of DPIV measurement experiment shown in Table 3.  
Figure 7: Experiment schematic diagram. As shown in Figure 8, there is optical distortion during the experiment as a result of the transparent curved surface of the vertical pipe.