# Investigation on Unsteady Flow Characteristics of a SCO\({}_{2}\) Centrifugal Compressor
## 4 Results and Discussion
### Unsteady Flow Phenomen in the Centrifugal Compressor  
The rotational condition resulted in an extremely unsteady flow state in the centrifugal compressor. In this section, streamlines, pressure, Mach number distribution at different time steps in one period are covered to analyze the unsteady flow in the designed SCO\({}_{2}\) centrifugal compressor. Temperature distribution on the impeller blade and diffuser blade is also exhibited to show the influence of LE and TE towards SCO\({}_{2}\) flow. We chose a period of revolution after the convergence of unsteady computation to conduct the following discussion. The results of four key moments in a rotational period T are compared to illuminate the unsteady flow phenomenon. In the SCO\({}_{2}\) centrifugal compressor, the SCO\({}_{2}\) fluid first flows past the impeller passage. The input power drives the impeller to rotate. On account of rotation, the centrifugal force acts on SCO\({}_{2}\) fluid, resulting in the increase of pressure. Afterwards, the working fluid flows into the diffuser passage, in which its kinetic energy transforms into the static pressure energy. Hence, the static pressure further enlarges until the SCO\({}_{2}\) fluid flows out of diffuser. Figure 8 gives the streamline in the whole passage of the SCO\({}_{2}\) centrifugal compressor. As shown in Figure 8, due to the influence of rotation, the diffusers are situated at different locations towards the impeller in each time step. The inlet of centrifugal compressor first serves as an intake of SCO\({}_{2}\) fluid. In the impeller passage, the working fluid rotates along with the impeller, thus resulting in vortices in the passages. In the meantime, the relative velocity remains almost constant. Then, SCO\({}_{2}\) enters into the diffuser passage. The absolute velocity increases with rotational speed taken into account. At the LE of diffuser blade, a velocity stagnation point appears. Afterwards, the working fluid passed through the diffuser passage with the increasing pressure and the decrease in velocity. Comparing the four moments in a period of revolution, the distribution of velocity streamlines are roughly identical while the distribution of vortices vary in different time steps of a period, respectively, as shown in Figure 8a-d. To be exact, at 0.5T and 0.75T, the diffuser blades hold back the wake flow from impeller, thus resulting in more vortices in the rotor passages. Especially at 0.75T, the diffuser blade locates at the middle of rotor passage. Due to the obstacle influence of diffuser blade, the maximum velocity locates near the LE of diffuser blade. Hence, the streamlines at 0.75T are the most disorganized. Figure 9 shows the pressure contours at mid-span of impeller and diffuser blades at different time steps. As Figure 9 indicates, the pressure achieves the minimum value at the inlet of compress. On account of rotation, the centrifugal force acts on \(\text{SCO}_{2}\) fluid, resulting in the increase of pressure in the rotor passage. Afterwards, the working fluid flows into the diffuser passage, in which its kinetic energy transforms into the static pressure energy. Hence, the static pressure further enlarges until the \(\text{SCO}_{2}\) fluid flows out of diffuser. Comparing the four moments in a period of revolution, the distribution of pressure at the mid-span of blades varies. When the TE of impeller blade is close to the LE of diffuser blade, the pressure of the outlet reaches its maximum, as shown in Figure 9a. Moreover, there exists a stagnation point at the LE of diffuser blade, respectively shown in Figure 9a-d. To be exact, at 0.75T, the diffuser blade is located at the middle of rotor passage and the diffuser blades hold back the wake flow from the impeller, thus resulting in a maximum stagnation pressure of 23.29 MPa. Figure 10 provides the Mach number contours at the mid-span of the impeller and diffuser blades at different time steps. Figure 10: _Cont._  
Figure 9: Pressure contours at mid- span of blades: (**a**) 0.25T; (**b**) 0.5T; (**c**) 0.75T; (**d**) 1T.