## 3 Results and Discussion
### Backflow Field  
The swirl flow in the draft tube generates an adverse pressure gradient at the axis, which reverses the flow, leads to backflow, disturbs the flow pattern in the draft tube, and produces hydraulic loss.  
There is an obvious spiral interactive form of swirling flow in the draft tube, including the swirling mainstream that gradually decelerates from the inlet to the outlet, and the swirling backflow that develops and gradually disappears from the inlet near the axis, as shown in Figure 16. The swirling mainstream includes the internal swirling mainstream with a smaller velocity, smaller radius of rotation, and smaller pitch near the axis, as well as the outer swirling mainstream with a larger velocity, larger radius of rotation, and larger pitch near the wall.  
Figure 15: Pressure gradient of draft tube cross-section along the flow direction.  
For NLN, the apparent change in the rotational radius of the swirling mainstream begins near the RSS inlet, and the vortex return extends into the first half of the RSS with a smaller rotational radius. For SLN, the apparent change in the rotational radius of the swirling mainstream begins near the RSS inlet, and the flow velocity of the outer swirling mainstream at the inlet is slightly less than that of NLN, while the pitch entering RSS is greater than that of NLN. The swirling backflow basically disappears until MES. For ELN, the obvious change in the rotational radius of the internal swirling mainstream begins in the second half of RSS, and the obvious change in the rotational radius of the outer swirling mainstream begins near the RSS inlet. The swirling mainstream has a higher flow velocity before RSS, and the internal swirling mainstream enters RSS with a larger pitch. The swirling backflow extends to the second half of RSS, and the rotation radius is slightly larger.  
The backflow velocity of NLN and SLN at the draft tube inlet is small, and the backflow rate is high, while the backflow velocity of ELN at the draft tube inlet is large, and the backflow rate is low, as shown in Figures 17 and 18. For NLN, the backflow velocity increases slightly in FSS and then continues to decrease. The backflow rate has maintained a downward trend, from the rapid decline in FSS to the slow decline in MES, and then to the rapid decline in RSS. The backflow zone gradually develops from the irregular shape near the axis in FSS to the elliptical shape near the wall of RSS, and finally disappears in the first half of RSS, as shown in Figure 19. For SLN, the increase rate of backflow velocity in FSS is less than that of NLN, and it begins to decrease in the first half of MES with a decrease rate greater than that of NLN. The backflow rate increases slowly in the first half of MES and then begins to decrease, with a faster rate of decrease than NLN. The backflow zone is smaller than that of the NLN. It gradually develops from an irregular shape around the locking nut in FSS to an elliptical shape near the wall of RSS. Finally, the backflow disappears in the first half of RSS, and the disappearance position was earlier than that of NLN. For ELN, the backflow rate develops into a slow decline after the rapid decline in FSS. The backflow rate keeps rising rapidly before RSS. After reaching RSS, it first experiences a slow decline and then a sharp decline. The backflow zone gradually increases from a small  
Figure 16: Main flow and backflow in the draft tube (\(V_{\rm m}\) is the main flow velocity, \(V_{\rm b}\) is the backflow velocity): (**a**) NLN; (**b**) SLN; (**c**) ELN.  
zone around the locking nut in FSS, with a zone much smaller than that of SLN and NLN, to an elliptical shape near the wall of RSS, with a zone larger than that of SLN and NLN, and then gradually decreases. Finally, the backflow disappears in the second half of RSS.  
Figure 19: Backflow zone of draft tube cross-section along the flow direction.  
Figure 17: Backflow velocities in draft tube.