## 3 Results and Discussion
### Thermo-Hydrodynamic Characteristics  
Under different sealing pressures, the effect of a large ambient-temperature gradient on thermo-hydrodynamic characteristics was investigated. The distributions of pressure, temperature, and film thickness were calculated between the sealing pressure 0.1 MPa and 4.6 MPa under a large ambient-temperature gradient condition, and the results are presented in Figure 5. In the calculations, the basic film thickness was 3.0 \(\upmu\)m, the rotational speed was 50,000 rpm, and the inlet and outlet ambient-temperature values were 200 K and 350 K, respectively. According to Figure 5a, a local high pressure occurred at the tip of the spiral grooves, illustrating that spiral grooves had a distinct dynamic pressure effect. The dynamic pressure effect was not enhanced continuously with the increase of the sealing pressure, which increased gradually with the increase of sealing pressure to 1.6 MPa, and then started to decrease as the sealing pressure increased continuously. As a result, in Figure 6 the pressure increase on the base of the sealing pressure increased from 0.13 MPa to 1.29 MPa, and then decreased to 0.42 MPa. The turning point of the hydrodynamic pressure effect was owing to the stronger inertial effect and choked-flow effect, with the increase of the sealing pressure. According to Figure 5b, the temperature distribution of the gas film did not change much with respect to the sealing pressure, and the variation of the maximum temperature at the inlet of the seal was controlled within 14.5 K under different sealing pressure conditions. The temperature rise of the entire gas film was obvious, ranging between 194.7 K and 207.1 K for different sealing pressure conditions. As shown in Figure 6, the variation of temperature rise was similar to the variation of the pressure increase, which increased firstly from 204.5 K to 207.1 K as the sealing pressure increased from 0.1 MPa to 1.6 MPa, and then decreased to 194.7 K when the sealing pressure increased continuously to 4.6 MPa. The temperature rise of the gas film was generated by the high-speed shearing, while it was heavily influenced by the gas expansion. An obvious temperature drop at the outlet of the seal occurred due to the gas expansion, and it became more and more obvious as the sealing pressure increased. Under the collective contributions of the pressure and temperature distributions, the deformation of the gas film displayed a transformation from convergent to divergent at the sealing pressure of 1.6 MPa, which is presented in Figure 5c. Here, the film thickness deformation was defined as positive when the film thickness at the inlet of the seal was less than that at the outlet, forming a divergent clearance; otherwise it was negative, forming a convergent clearance. As shown in Figure 6, when the sealing pressure increased from 0.1 MPa to 1.1 MPa, the film thickness at the inlet of the seal was larger than that at the outlet of the seal, and the deformation of the gas film decreased from 0.35 \(\upmu\)m to 0.10 \(\upmu\)m. When the sealing pressure increased continuously from 1.6 MPa to 4.6 MPa, the film thickness at the inlet of the seal was lower than that at the outlet of the seal, and the deformation of the gas film increased from 0.04 \(\upmu\)m to 0.91 \(\upmu\)m.  
These results above were obviously different from those which did not consider the ambient temperature gradient, in Ref. [35], in which the supercritical helium gas face seal with T-grooves showed a divergent clearance, with the sealing pressure growing from 1.0 MPa to 5.0 MPa. Therefore, although the temperature rise of the gas film was large, the existence of the ambient-temperature gradient contributed to achieving a better dynamic pressure effect and lower thermal deformation of the supercritical helium face seal, near the sealing pressure of 1.6 MPa. Furthermore, the distributions of the pressure, temperature, and film thickness of the sealing medium were calculated numerically under different ambient-temperature gradients.