## 2 Materials and Methods
### Pressurized Tube Structure Design  
The pressurized tube, a critical component connecting the seed-airflow mixing chamber and the distributor, plays a central role in improving the uniformity of seed distribution in the distributor. In this study, a corrugated pressurized tube was employed, as depicted in Figure 2. The main geometric parameters of this pressurized tube include the pressurized tube diameter (\(D\)), corrugation depth (\(S\)), corrugation width (\(K\)), and pressurized tube length (\(L\)). The pressurized tube is divided into two sections: a corrugated section (\(L_{1}\)) with corrugations and a straight section (\(L_{2}\)) without corrugations. By altering the geometric parameters of the pressurized tube, it is possible to modify the seed flow velocity and distribution within the pressurized tube. The use of numerical simulation techniques is an effective means to conserve processing costs and analyze seed migration trajectories. The inner diameter of the pressurized tube is calculated using the following formula:  
\[D=18.8\bigg{(}\frac{V_{f}}{u}\bigg{)}^{0.5} \tag{1}\]  
where \(D\) is the pressurized tube diameter (m); \(V_{f}\) is the fluid volumetric flow rate (m\({}^{3}\)/h), with a maximum incoming airflow of 540 m\({}^{3}\)/h in the experimental setup; and \(u\) is the average fluid velocity (m/s), with an experimental value of 54 m/s at the inlet. Calculating \(D\) results in \(D\) = 99.13 mm, which is rounded to 100 mm. The movement of seeds in the pressurized tube involves turbulent motion. The surface structure of the pressurized tube disturbs the airflow, affecting the friction factor along the path and the distribution of the airflow within the pressurized tube. Pressure loss is a typical characteristic of the airflow movement within the pressurized tube. To determine the pressure loss within the pressurized tube, the Darcy friction factor is used and can be described as follows [24]:  
\[\lambda=\frac{2\Delta p}{\rho v_{i}{}^{2}}\frac{D_{h}}{L_{z}} \tag{2}\]  
where \(\lambda\) is the Darcy friction factor; \(\Delta p\) is the pressure loss between two sections (Pa); \(D_{h}\) is the relative diameter of the pressurized tube (mm); \(\rho\) is the density of air at working conditions (20 \({}^{\circ}\)C), 1.205 kg/m\({}^{3}\); \(u\) is the airflow velocity (m/s); and \(L_{z}\) is the distance between two sections (mm). As the airflow and seeds enter the pressurized tube after passing through the seed-airflow mixing chamber, their direction changes from horizontal to vertical. Seeds unavoid  
Figure 1: Pneumatic conveying seed system. 1. Fan; 2. seed–air mixing chamber; 3. centralized seed; 4. seed box; 5. sensor 6. distributor; 7. pressurized tube; 8. seed conduit. Figure 2: Pressurized tube structure diagram. ably collide with the inner wall of the pressurized tube, causing a decrease in seed velocity. Subsequently, seeds accelerate within the pressurized tube. Some seeds may collide with the corrugated surface, causing another reduction in seed velocity before resuming acceleration. This continues until seeds reach the distribution head. Throughout this motion process, it results in various pressure losses, including acceleration pressure loss within the pressurized tube, pure air pressure loss, gravity-induced pressure loss, pressure loss due to collision and friction among seeds, and pressure loss due to collision and friction between seeds and the pressurized tube wall [25]. (1) Acceleration pressure loss:  
\[\Delta p_{sa}=\frac{1}{2}\lambda_{sa}\mu\rho v^{2} \tag{3}\]  
where:  
\[\lambda_{sa}=2\frac{u}{v} \tag{4}\]  
where \(\Delta p_{sa}\) is the acceleration pressure loss (Pa); \(\lambda_{sa}\) is the acceleration pressure loss coefficient within the pressurized tube; \(\mu\) is the material-to-air transport ratio, taken as 1.5; \(u\) is the critical velocity of wheat seeds (m/s); and \(v\) is the airflow velocity (m/s).