## 7 Conclusions  
In this paper, the physical model test and CFD method were used to analyze the flow field and pulsation characteristics in the hump section of a siphon outlet conduit, and the vortex structure in the siphon outlet conduit was analyzed by the isosurface method based on the \(Q\) criterion.  
(1) With the increase of the flow rate, the intensity of the vortices in the cross-section of the hump section of the siphon outlet conduit decreased gradually, the average velocity circulation decreased from 0.056 m\({}^{2}\)/s to 0.008 m\({}^{2}\)/s, and the uniformity of the axial velocity distribution increased from 55.4% to 75.4% and tended to be stable. With the increase of the flow rate, the static distortion index of the cross-section A-A of the hump section decreased gradually, and the small flow condition was seven times higher than that of the large flow condition.  
(2) The equivalent surface method based on the \(Q\) criterion was used to analyze the eddy structure in the siphon outlet conduit. At the threshold Q = 300 s\({}^{-2}\), the vortices with different ranges and shapes existed at the inlet of the siphon outlet conduit, the high-speed zone at the bottom of the hump section, and the outlet of the flow conduit under three characteristic conditions. Under small flow conditions, the vortex structure was mainly distributed at the inlet of the flow conduit in a lamellar shape, while, under the other two characteristic conditions, the vortex structure mostly presented a striped shape.  
(3) Under three characteristic conditions of the siphon outlet conduit without circulation, the overall flow rate was low under the small flow condition, but under the optimum condition and large flow condition, there were obvious swirl zones at the outlet of the downward section of the flow conduit, and there was a large range of shedding. The hydraulic loss of the outlet flow conduit was greater with the circulation flow. The circulation condition under a small flow rate was 6.6 times that without the circulation flow and 1.3 times that under the large flow rate.  
(4) The pressure fluctuation in the hump section of the siphon outlet conduit had obvious periodicity. With the increase of the flow rate, the maximum pressure fluctuation  
Figure 22: Frequency domain of the different measuring points at 2200 r/min.  
amplitude of the hump section decreased gradually; with the decrease of the rotation speed, the pressure amplitude of the same measuring point in the hump section decreased gradually. The main frequency of pulsation at each measuring point in the hump section of the siphon outlet conduit was at two times the frequency.  
Conceptualization, F.Y.; software and writing--original draft preparation, Y.Z.; writing--review and editing, F.Y and A.N.; visualization, Y.Z.; investigation, Z.L. and Y.Y.; supervision, C.L.; project administration, F.Y.; funding acquisition, F.Y.; All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China (grant No. 51609210), major projects of the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (grant No. 20 KJA570001), the open research subject of the Key Laboratory of Fluid and Power Machinery, Ministry of Education (szjj2016-078), the Science and Technology Plan Project of the Yangzhou City (grant No. YZU201901), the Technology Project of the Water Resources Department of the Jiangsu Province (grant No. 2020029), the Scientific Research Program of Jiangsu Hydraulic Research Institute (2020z026),and the Priority Academic Program Development of the Jiangsu Higher Education Institutions (PAPD).  
Not applicable.  
All data necessary to carry out the work in this paper are included in the figures, tables or are available in the cited references.  
The authors declare no conflict of interest.