## 4 Experimental Verification  
In order to ensure the reliability and accuracy of the numerical simulation study, the external characteristic experiment is carried out on the comprehensive performance experimental bench of the vortex pump. The experimental bench consists of the following two parts: the hardware system and the software system, with the system principle and physical composition shown in Figures 9 and 10, respectively. Figure 8: Distribution of velocity vector in the circumferential section of the vortex pump. Figure 9: System principle of the experiment bench. In the hardware system, the output frequency of the frequency converter can be adjusted to change the output speed of the motor (ABB, YVF5.5 KW, Shanghai, China), which in turn drives the vortex pump to flow the liquid from the inlet to the outlet back to the water tank at different speeds. In which, the ball valve (BEST, H14W-25 RN D25, Wuxi, China) in the inlet and outlet pipelines of the vortex pump plays a throttling role, and the solenoid valve (BEST, Z291/292-25 RII24-16, Wuxi, China) on the outlet pipeline exerts pressure on the water. In the software system, the signal acquisition device converts the analog signals of the pressure sensor (WIKA, A-10, Suzhou, China), flow sensor (BEST, C8004-25 RIIII24-CG05, Wuxi, China), and speed torque sensor (ETH, DRBK-I-50 NM, Shanghai, China) into digital signals and sends them to the industrial computer (ADVANTECH, PCI610L, Shaanxi, China) to achieve overall control of the hydraulic circuit. The experiment bench measurement and control program developed by LabVIEW 2019 software on the industrial computer can adjust the output digital signal through the signal control device, so as to precisely control the opening of the solenoid valve and then adjust the flow in the water hydraulic circuit. The pressure sensor collects pressure data at the inlet and outlet of the vortex pump, the flowmeter collects real-time flow data of the measured water hydraulic circuit, and the signal acquisition device collects and converts the above analog signals into digital signals and transmits them to the industrial computer to obtain the experimental data. In order to verify the accuracy of the test results, 10 repeated tests of the vortex pump were carried out on the comprehensive performance test bench. During the test, the error of flow rate is \(\pm 2\%\), the error of head is \(\pm 0.7\%\), the error of shaft power is \(\pm 1.5\%\), and the error of speed is \(\pm 0.2\%\). At the flow rate of \(0.6\mathrm{Q}_{d}\), external characteristic tests were conducted on the vortex pump under four different operating conditions of 2700, 3000, 3300, and 3600 r/min. The results are shown in Figure 11. It can be seen that under the fixed impeller structure parameters and working conditions of the vortex pump, the numerical simulation results are generally higher than the experimental results, and there are certain deviations between the two results. If the error between numerical simulation and experimental results exceeds 10%, the potential sources of error mainly include grid dependence and experimental setup limitations. Unevenness in mesh processing, different element types  
Figure 10: Physical composition of the bench. and sizes, as well as complex geometry and heterogeneous material properties, will significantly affect the accuracy of the calculation. In the experiment setup, the boundary and initial conditions do not match the simulation assumptions, the measurement equipment accuracy is insufficient, and the influence of the test environment factors may lead to errors. These errors reduce the credibility of the theoretical model, limit its scope of application, weaken the reliability of the research conclusions, increase the risk of drawing wrong conclusions, and may lead to the waste of computing resources.