## 3 Experiment and Model Validation  
### Experimental Details  
The crossing position of the T-junctions and pipes was 1.5 m away from the water inlet. In the design of the pipeline experimental system and working conditions, the scale effects need to be considered to simulate the real engineering conditions. In the experimental process, the flow of liquid was mainly affected by gravity and pressure, so the gravity similarity criterion and pressure similarity criterion were mainly considered to control the scale effects and design the model test, where the similarity ratios were 1. As shown in Table 1, the working conditions were designed according to the scale effects and test conditions in combination with the design flow and pipe diameter in the relevant design specifications of the sewer. For the flow in the pipe, the flow state is turbulent when the value of \(R_{e}\) is more than 2300. In turbulent conditions, the particles are mixed with each other, the motion is disordered, and it has energy dissipation capability and diffusivity, so they have remarkable influence on the mixing of solutions in the pipes. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**No.** & \(\delta\) & \(Q\) **(m\({}^{3}\)/h)** & \(\varphi\) **(mm)** & \(\theta\) (\({}^{\circ}\)) & **No.** & \(\delta\) & \(Q\) **(m\({}^{3}\)/h)** & \(\varphi\) **(mm)** & \(\theta\) (\({}^{\circ}\)) \\ \hline
1 & & & & 30 & 31 & & & 30 \\
2 & & & & 60 & 32 & & & 60 \\
3 & & & 51.4 & 90 & 33 & & & 51.4 & 90 \\
4 & & & & 120 & 34 & & & & 120 \\
5 & & & & 150 & 35 & & & & 150 \\
6 & & & & 30 & 36 & & & & 30 \\
7 & & & & 60 & 37 & & & & 60 \\
8 & 8 & 61.4 & 90 & 38 & & 8 & 61.4 & 90 \\
9 & & & & 120 & 39 & & & & 120 \\
10 & & & & 150 & 40 & & & & 150 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Working conditions of the proposed design. The \(R_{e}\) values of some typical working conditions are listed in Table 2, which indicated the flow in the test main pipe was turbulent. \(R_{e}\) in the main pipe rose with the increase of the flow rate and decreased with the increase of the main pipe diameter under the same other conditions. In addition, the numbers of \(R_{e}\) in the table were large indicating obvious turbulent characteristics. As seen in Figure 3, the experiments were conducted in a single channel flow facility, consisting of one 2000-L water tank, a 100-mm caliber electromagnetic flowmeter, several triangular supports, pumps, and different kinds of experimental pipes, valves, and so on. In this experiment, the experimental reagent was the salt solution, and the main component was sodium chloride (NaCl), which entered the experimental system from the salt solution inlet. The water tank was used to supply a water source to the experiment, the water from the tank was pumped through the single channel at a constant flow rate, and the salt solution entered from the salt solution inlet. As the aforementioned descriptions, different branch injection angles of the T-junction were considered in the present study. The different incident angles of 30\({}^{\circ}\), 60\({}^{\circ}\), 90\({}^{\circ}\), 120\({}^{\circ}\), and 150\({}^{\circ}\) were designed in the test facilities. The acrylic pipes of about 2 m were used at the T-junction test section to observe the injection of salt solution, while PE pipes were used at the rest place, including the connection part. The absolute roughness of PE pipes is 0.01 mm according to the query of relevant data, and that of the test system was set during the numerical simulation to approach the material characteristics. The pipe on the front end of experimental pipes was sufficiently long to provide fully developed turbulent flow before entering the experimental pipe, at the same time the backwater pipe was designed to adjust flow rate and prevent pump damage. The inner diameter of the connection part as well as the backwater pipe was 51.4 mm, and the inner diameter of the pipe on the front end of experimental pipes was 99.4 mm.