## 2 Materials and Methods
### Hydraulic Performance Test  
The hydraulic performance test of the HFI was carried out in accordance with the national water-saving irrigation engineering technology research center (Beijing Daxing). the water source was 23 \(\pm\) 2 \({}^{\circ}\)C tap water and the temperature was 25 \({}^{\circ}\)C. Water was used instead of liquid fertilizer [40]. After the HFI composed of T333 and F3434 AFTs, as shown in Table 1, was connected to the test platform, the centrifugal pump was started and the control valve and outlet valve were adjusted such that the inlet pressure (\(H\)) ranged from 0.12 to 0.18 MPa, with a pressure change gradient (\(\Delta H\)) of 0.01 MPa, and the outlet pressure (\(H_{\text{out}}\)) was 0.1 MPa. After the system had been running stably for 5 min, the actual outlet flow rate (\(Q_{\text{m}}\)) of the HFI was measured via an ultrasonic flowmeter (Figure 3). \(Q_{\text{m}}\) was used to verify the accuracy of the numerical simulation. For the optimized HFI, the optimized AFT was fabricated using a photopolymerization 3D printer. After the AFT was assembled with a diaphragm pump to form the HFI, it was installed on the test platform. By adjusting the control and outlet valves, \(H_{\text{out}}\) was set to 0.1 MPa and \(H\) was gradually increased from 0 MPa to 0.12 MPa. The pressure at which the HFI began to inject fertilizer was recorded as \(H_{\text{min}}\). \(H\) was then set to 0.12-0.18 MPa, with \(\Delta H\) = 0.01 MPa. After the system operated stably for 5 min, a mass of water (\(M\), in kg) was added to the injection bucket and the suction pipe was placed in the bucket. A stopwatch was started to measure the time (\(t\), in s) required to completely empty the bucket. Figure 3: Schematic of the HFI hydraulic performance test platform. 1—Water storage barrel; 2—inlet valve; 3—centrifugal pump; 4—pressure relief valve; 5—ultrasonic flowmeter; 6—control valve; 7—inlet pressure gauge; 8—HFI device; 9—fertilization barrel; 10— suction tube; 11—outlet pressure gauge; 12—return valve. (L/h) was calculated as \(Q_{\rm inj}=3600\,M/t\). At each \(H\), \(Q_{\rm m}\) was measured using an ultrasonic flowmeter. The precision of the photopolymerization 3D printer is 0.02 mm; the centrifugal pump head and flow rate are 0.5 MPa and 75 m\({}^{3}\)/h, respectively; the pressure gauge range is 0-0.6 MPa with a precision of 0.4; and the ultrasonic flow meter range is 1.25\(\sim\)170 m\({}^{3}\)/h with a precision of \(\pm\)2%. CFD Numerical Simulation of Hydraulic Turbines  
(1) _3D model construction_  
The AFT blades are parametrically modeled via CFturbo 2022 (CFturbo GMBH, Dresden, Germany), whereas the AFT shaft, K-shaped pipeline, and other components are drawn using UG 12.0 (Unigraphics NX 12.0, Plano, TX, USA). To obtain stable outlet flow simulation results, the inlet and outlet of the K-shaped pipeline are extended to four times the pipe diameter. (2) _Grid division and independence verification_  
Using the Mesh module in ANSYS Workbench 22R2 (Ansys Inc., Canonsburg, WA, USA), the fluid domain was meshed, with the fluid domain controlled by the impeller group set as a rotating domain and the other regions set as stationary domains (Figure 4). The entire fluid domain was meshed with a structured tetrahedral grid configuration. For the mesh independence verification, \(H\) was 0.16 MPa, the outlet was set to a free outflow, with \(H_{\rm out}=0\) MPa, and \(n\) was 1500 rpm. The variation in the AFT outlet flow rate (\(Q_{\rm s}\)) was calculated via Equation (1), and the corresponding change rate (\(E\)) was obtained. The variation in \(E\) with the number of mesh elements (N) showed that when \(N\) reached 1 million, corresponding to a grid size of 5-10 mm, with the impeller surface mesh refined to 1.5 mm and a growth rate of 1.1, \(E\) was less than 0.5% (Figure 5), which meets the requirements for turbine numerical simulation [41].