## 3 Results and Analysis
### Internal Flow Field of AFT
#### 3.2.2. Blade Surface Pressure Curve  
For the AFT with \(P_{\max}\) (M\({}_{1}\) = 2), the \(BP\) curves show a similar trend across the four AFTs when \(H\) = 0.18 MPa and \(n\) = 2500 rpm. The \(BP\) curve on the pressure surface, when \(x/L\) is 0-0.1, increases sharply and then decreases sharply, whereas the \(BP\) curve on the suction surface, with the exception of D44, decreases sharply and then increases sharply. When \(x/L\) is 0.1-0.8, the \(BP\) curve on the pressure surface decreases slowly, whereas the \(BP\) curve on the suction surface increases slowly. When \(x/L\) is 0.8-1.0, both the pressure and suction surface \(BP\) curves decrease sharply and then increase sharply, reaching a minimum value at \(x/L\) = 0.93 (Figure 12).  
The difference in \(BP\) (\(\Delta BP\)) was calculated on the basis of the pressure and suction surfaces at different positions on each blade. The average values (\(\overline{\Delta BP}\)) for impellers D33, D34, D43, and D44 were 36.2 kPa, 27.6 kPa, 31.7 kPa, and 26.1 kPa, respectively. \(\overline{\Delta BP}\) decreased with increasing M\({}_{2}\). Compared with those of D33, the \(\overline{\Delta BP}\) values of D34, D43, and D44 were 23.7%, 12.4%, and 27.9% lower, respectively. When M\({}_{2}\) = 3.5, the \(\overline{\Delta BP}\)  
Figure 11: Internal flow velocity contours of D33 at \(H\) = 0.18 MPa with \(n\) = 2000 rpm (**a**), 2500 rpm (**b**), and 3000 rpm (**c**) and at \(H\) = 0.14 (**d**), at \(H\) = 0.16 MPa (**e**), and at \(H\) = 0.18 MPa (**b**) with \(n\) = 2500 rpm.  
Figure 12: The blade surface pressure curves of the first impeller (**a**) and the second impeller (**b**) along the inlet direction of four kinds of axial-flow turbines with M\({}_{1}\) = 2 at an inlet pressure (\(H\)) of 0.18 MPa and a rotational speed (\(n\)) of 2500 rpm are plotted.  
of the \"more-less\" AFT (based on M\({}_{3}\)) was 14.8% greater than that of the \"fewer\" AFT. Additionally, \(\overline{\Delta BP}\) exhibited a positive correlation with \(P_{\max}\).  
When \(x/L\) is in the range of 0-0.1 or 0.8-1.0, the \(BP\) values on the suction surface of the AFT are less than zero (\(BP<0\)). In these regions, \(\mid\)\(BP\)\(\mid\) is defined as the \(NP\), where a larger \(NP\) value indicates a greater likelihood of cavitation at that position, potentially resulting in erosion. The \(NP\) values at \(x/L\) = 0-0.1 are, on average, 23.6% higher than those at \(x/L\) = 0.8-1.0. For the first impeller along the water flow direction, the \(NP\) values for D33, D34, D43, and D44 are 26.9, 4.2, 15.8, and 18.5 kPa, respectively. D33 has the highest \(NP\) value, which is 84.3%, 41.2%, and 80.8% higher than those of D34, D43, and D44, respectively. For the second impeller along the water flow direction, the \(NP\) values for D33, D34, D43, and D44 are 55.9 kPa, 42.1 kPa, 50.5 kPa, and 34.7 kPa, respectively. Compared with D34, D43, and D44, D33 still has the highest \(NP\) value but is 24.7%, 9.6%, and 37.9% lower, respectively.  
For D33, when \(n\) increases from 2000 rpm to 3000 rpm, the \(BP\) curves of the two blades exhibit minimal changes (Figure 13). When the pressure (\(H\)) is between 0.14 MPa and 0.18 MPa, as \(H\) increases, the \(BP\) values on the pressure surface and \(\overline{\Delta BP}\) of the AFT gradually increase, whereas the change in \(BP\) values on the suction surface is relatively small (Figure 14).