## 3 Calculation Setup and Results Analysis
### Steady-State Calculation
This effect is particularly pronounced in the case of a 2.5 mm deviation. In contrast to static pressure, total pressure accounts for dynamic pressure effects. Consequently, we observe that the impact arising from circumferential non-uniformity in the clearance is significantly mitigated. Differences in total pressure distributions among the five deviation values are only discernible at the location with the smallest clearance. This clarifies why deviations have minimal overall effects on the pressure distribution and hydraulic performance of the unit. Proceed by examining the static pressure distribution on the inner surface of the upper crown cavity in Figure 10.  
Figure 9: Radial deviation-induced total 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**). Proceed by examining the total pressure distribution on the inner surface of the upper crown cavity in Figure 11.  
Combining the static pressure and total pressure distributions from Figures 10 and 11, it can be observed that, in terms of the overall pressure distribution, whether it is on the inner surface or the outer surface, whether it is static pressure or total pressure, the pressure distribution characteristics are nearly identical: they exhibit distinct features at the maximum and minimum points within the clearance compared to other areas. For the outer surface, static pressure better reflects its characteristics. It shows that, before 0.5 mm, a reduction in clearance leads to the generation of a high-pressure zone, while after 0.5 mm, due to the extremely narrow clearance, it transitions into a low-pressure zone. This aligns with the results of [31]. Meanwhile, the total pressure also exhibits similar features but is less pronounced than static pressure. On the other hand, for the inner surface, due to the application of wall velocity, the pressure distribution is more evident under total pressure conditions. This better illustrates the pressure distribution, and it is also noticeable how the pressure changes significantly as the fluid passes through the sealing area before and after. Figure 5:0 Radial deviation-induced static pressure distribution on the upper crown chamber inner 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**). Regarding the lower ring section, since the distribution patterns on the inner and outer surfaces align with those of the upper crown, we focus our analysis solely on the inner surface. As for the pressure distribution in the bottom ring chamber, it is illustrated in Figure 5:1 Upon comparing the five radial deviations, it becomes evident that there is no significant alteration in their pressure distribution. The only notable difference is observed in the low-pressure region at the minimum clearance, where the pressure is slightly higher than at the maximum clearance. This discrepancy arises because the clearance in the bottom ring chamber is approximately 0.2 mm smaller than that in the upper crown chamber. Consequently, the bottom ring chamber does not exhibit a transition from a high-pressure region to a low-pressure region as seen in the upper crown chamber at its minimum clearance. Figure 5:2 Radial deviation-induced total pressure distribution on the upper crown chamber inner 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**). Moving forward, we analyze the numerical values of pressure and radial forces for components under various deviations to further investigate how these deviations affect the magnitude and direction of pressure and radial forces.