## 5 Results and Discussion  
### Effects of Dual-Rotor Rotation Direction on Sealing Performance  
The seal between shafts is special because it couples two rotating rotors. To study the effects of rotational direction on the hydrodynamic lubrication of the sealing gap, we analysed the sealing performance of inner and outer rotors rotating in the same direction, inner and outer rotors rotating in counter-rotation and the inner and outer rotors rotating uniaxially. Our results were compared with the four modes listed in Table 4 as examples. Figures 5-8 show the gas film's pressure distribution cloud map with and without sealing differential pressure in the four rotation modes. Figure 9 compares the gas film's force and friction power consumption with and without sealing differential pressure in the four rotation modes. Considering only the effects of the rotation direction on the fluid dynamic pressure effect, we found that when two rotors rotated in the same direction (as shown in Figure 5), there were large pressure peaks in the circumferential and axial directions; the gas film's dynamic pressure effect was best in this condition. However, during counter-rotation (as shown in Figure 7), the dynamic pressure effect of the gas film was the weakest. The gas film's dynamic pressure effects on the dual-rotor movement's \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Rotation Mode**} & **Outer Rotor Speed** & **Inner Rotor Speed** \\  & \(n_{2}\) **(rpm)** & \(n_{1}\) **(rpm)** \\ \hline Mode 1 & 7000 & 10,000 \\ Mode 2 & 7000 & 0 \\ Mode 3 & 7000 & \(-\)10,000 \\ Mode 4 & 0 & 7000 \\ \hline \hline \end{tabular} Note: The signs indicate the same or counter-rotation direction.  
\end{table} 
Table 4: Four inner and outer rotor rotation modes. Figure 4: Comparison of numerical calculation results and test results. static state (as shown in Figures 6 and 8) exist between these two extremes. According to the hydrodynamic pressure principle, the fluid film's pressure distribution relates to fluid viscosity, the sliding velocity of two moving surfaces, fluid film thickness and variations on these factors. If fluid viscosity and film thickness are unchanged, fluid will enter from the large opening of the wedge space and flow out of the small opening when the rotors move in the same direction. These activities enhance the hydrodynamic pressure effect. Thus, the maximum pressure of the gas film is greater than that when only one wall is moving. On the other hand, during counter-rotation, the hydrodynamic pressure effect was weakened to less than that observed when only one wall was moving. Figure 5: Mode 1 (codifection rotation): (**a**) without inlet pressure difference; (**b**) with inlet pressure difference. Figure 6: Mode 2 (only the outer rotor rotates): (**a**) without inlet pressure difference; (**b**) with inlet pressure difference. As shown in Figures 5-8, when there is inlet/outlet differential pressure, \(\Delta P\) = 80 kPa. The gas film's dynamic pressure effects were best when the two rotors rotated in the same direction (as in Figure 5). The gas film's dynamic pressure effects were weakest under counter-rotation (as in Figure 7). Compared with the mode without differential pressure, the gas film's maximum pressure distribution shifted towards the inlet (position 0 of the L coordinate) because of increased inlet pressure. Additionally, the maximum pressure increased. When the rotors ran in the same direction, the gas film's maximum pressure value, without differential pressure, was 0.2143 MPa. Meanwhile, the gas film's maximum pressure value, without differential pressure, was 0.2331 MPa. Under counter-rotation, the gas film's maximum pressure value (without differential pressure) was 0.1296 MPa. Meanwhile, the gas film's maximum pressure, with differential pressure, was 0.18 MPa. The gas film pressure results from hydrostatic pressure and the rotary dynamic pressure effect; these combine to form the between-shaft seal.