## 3 Calculation Setup and Results Analysis  
### Steady-State Calculation  
The inlet and outlet boundary conditions were set as follows, in accordance with [31]:  
1. Computational fluid dynamics (CFD) simulations were conducted using a mesh comprising five million elements by using ANSYS. Mesh independence verification had been previously performed, and the subsequent deviation model made adjustments to the clearance mesh division and size based on this foundation. 2. Because in the actual operation of the unit, only pressure data can be obtained, the pressure measurement data obtained during the operation of the unit are directly used here, that is, pressure-pressure conditions: inlet, 2459 kPa; outlet, 480 kPa. Due to practical engineering constraints, the inlet boundary was set as the total pressure conditions, while the outlet was set as the static pressure conditions. 3. As in the prior literature, owing to the immense size of the turbine unit and the small clearance dimensions, achieving convergence in calculations posed challenges compared to earlier units. Therefore, a time step of 2000 steps and a convergence criterion of \(10^{-4}\) were employed. Similar to previous studies, wall velocity was included in this analysis, and its validity has also been explained in the literature. Figure 4: Radial installation deviation indication. Figure 5: The radial installation deviation mesh of the upper crown chamber (**top-left**), the bottom ring chamber (**top-right**) and the vaneless zone (**bottom**). Pressure Distribution  
In this section, we take into account the influence of wall velocity on the upper crown, vaneless zone, and lower ring. Thus, it was decided to separately record both the total pressure and static pressure to further assess the impact of the wall velocity. However, prior to this, it is necessary to consider whether the influence of deviations on other components can be neglected. From Figure 6, it can be seen that under these five deviations, the pressure distribution in the runner, vaneless zone, and spiral casing is hardly changed. This further illustrates that the impact of radial deviations is limited to the vicinity of where the deviations occur. Therefore, in the subsequent analysis, only these localized components will be analyzed, and not the entire turbine unit. Furthermore, in terms of hydraulic performance, we extracted the hydraulic efficiency under five different deviations and compared it with data obtained from physical measurements (Figure 7). It is evident that deviations have little influence on the overall performance of the unit. Consequently, as previously mentioned, our subsequent analysis will concentrate on the regions affected by deviations. Figure 6: Cross-sectional full-channel pressure distribution in the XOY plane: 0.1 mm (**top-left**), 0.3 mm (**top-right**), 0.5 mm (**middle-left**), 1.5 mm (**middle-right**), 2.5 mm (**bottom**). Figure 7: Hydro efficiency (**top**) vs. output (**bottom**) comparison chart. Static pressure distribution on the outer surface of the upper crown cavity was extracted for analysis as shown in Figure 8.  
Total pressure distribution on the outer surface of the upper crown cavity was extracted for analysis as shown in Figure 9.  
Figure 8: Radial deviation-induced static pressure distribution on the upper crown chamber outer surface of the runner at different levels, 0.1 mm (**top-left**), 0.3 mm (**top-right**), 0.5 mm (**middle-left**), 1.5 mm (**middle-right**), 2.5 mm (**bottom**). Drawing from Figures 8 and 9, it is evident that, regardless of whether dynamic pressure is considered, a common trend emerges--as the clearance increases, there is a transition from pressure rise to pressure drop occurring at the location with the most significant clearance variation. This implies that when the deviation is less than 0.5 mm, reducing the clearance leads to increased pressure at that point. However, beyond 0.5 mm, due to the extremely small clearance size, fluid ingress becomes difficult, resulting in a shift towards lower pressure.