## 3 Results and Discussion
### Sealing Performance  
Under the ambient-temperature gradient condition, the sealing performance of the supercritical helium spiral-grooved face seal under a wide range of working conditions was evaluated, including the sealing pressure, sealing temperature, rotational speed, and basic film thickness. The relationship between the sealing performance and the sealing pressure is presented in Figure 9. According to Figure 9a, the pressure at the inlet of the seal was lower than the inlet ambient pressure, showing a pressure loss. However, the pressure loss was not significant when the sealing pressure was lower than 1.1 MPa. As the sealing pressure continued to increase, the pressure loss increased. Additionally, the pressure at the outlet of the seal was larger than the outlet ambient pressure, illustrating a choked-flow effect. As the sealing pressure increased, the pressure rise increased from 0.01 MPa to 0.27 MPa, which was much larger than the outlet ambient pressure of 0.1 MPa. Under the influence of the inertial effect, choked-flow effect, and dynamic pressure effect, the opening force and leakage of the sealing-medium helium with respect to the sealing pressure were calculated. According to Figure 9b, both the opening force and leakage showed an upward trend with the increase of the sealing pressure from 0.1 MPa to 4.6 MPa. While the opening force increased at a high rate initially, before slowing down, the leakage displayed an opposite trend, the result of the changes in variations of dynamic pressure effect, temperature rise, and thermal deformation of the gas film. As the sealing pressure increased to 4.6 MPa, the opening force increased to 6968 N, multiplying by a factor of 29 compared with the sealing pressure of 0.1 MPa. Meanwhile, the leakage was 1.28 g\(\cdot\)min\({}^{-1}\) at the sealing pressure of 4.6 MPa, which was much larger than 0.00167 g\(\cdot\)min\({}^{-1}\) at 0.1 MPa. Compared with the results without considering a temperature gradient in Ref. [35], although the opening force and leakage showed similar trends to the sealing pressure, the value of the leakage was almost half of that in the reference on the base of little difference in the opening force values. Therefore, the ambient-temperature gradient tended to improve the sealing performance. Figure 8: Variations of the pressure increase, temperature rise, and film thickness deformation with respect to the sealing temperature. (\(P_{\text{in}}\) = 5.0 MPa, \(P_{\text{out}}\) = 0.1 MPa, \(T_{\text{out}}\) = 350 K, \(n\) = 50,000 rpm, \(h_{0}\) = 3 \(\upmu\)m). The relationship between the sealing performance and the sealing temperature is presented in Figure 10. Owing to the fixed ambient temperature of 350 K at the outlet of the seal, the temperature gradient along the radius direction decreased with the increase of the sealing temperature at the inlet of the seal. According to Figure 10a, at the sealing temperature of 100 K, the pressure loss induced by the inertial force and the pressure increase induced by the choked-flow effect were both remarkable. As the sealing temperature increased from 100 K to 350 K, the pressure loss at the seal inlet decreased gradually from 8.2% to 3.0%, and the choked-flow effect was weakened at the same time, with a decrease in pressure rise from 0.44 MPa to 0.23 MPa. Figure 9: Relationship between the sealing performance and the sealing pressure. (**a**) Pressure boundaries between the seal rings; (**b**) Opening force and leakage. (\(P_{\text{out}}\) = 0.1 MPa, \(T_{\text{in}}\) = 200 K, \(T_{\text{out}}\) = 350 K, \(n\) = 50,000 rpm, \(h_{0}\) = 3 \(\upmu\)m). Additionally, the opening force of the sealing medium displayed a complicated variation as the sealing temperature increased from 100 K to 350 K. As seen in Figure 10b, although the general trend of the opening force was downward, a mutational increase occurred at 250 K, which was consistent with the variations of the temperature rise and dynamic pressure effect of the gas film.