## 4 Results and Discussion  
### The Initial Design  
Figure 10 shows the velocity vector and partial enlargement of the 50% blade height section of the compressor initial design. It can be seen from the diagram that there was no obvious flow separation phenomenon inside the impeller. However, the flow inside the impeller was not uniform. When the fluid flowed along the main blade to 50% of the chord length (the leading edge (LE) of the splitter blade), the flow velocity of the suction side (SS) increased rapidly, while the fluid on the pressure side (PS) still flowed at a lower velocity. This led to a larger pressure gradient between the PS and SS. Thus, the working fluid on the PS would leak through the tip clearance to the SS. It would lead to a significant reduction in compressor performance inevitably. Figure 11 shows the pressure distribution of the impeller blades surface in detail. Generally speaking, the PS pressure was greater than SS pressure. The pressure distribution on the splitter blade surface was basically consistent with that on the corresponding area of the main blade. Under the action of centrifugal force, the pressure of CO\({}_{2}\) increased gradually along the blade profile. There was a larger pressure gradient at the trailing edge (TE). There was no reverse pressure region in the pressure distribution. That means there was no flow separation phenomenon on the blade surface. There was a small low-pressure region at the LE of the impeller blade. It was caused by the local acceleration of the flow impact. When the pressure in the low-pressure region of the LE is lower than the critical point, the transcritical phenomenon will occur. To some extent, it will affect the performance of the compressor. In order to display the cross critical region of the blade surface more clearly, the maximum pressure of the contour was set to 7.38 MPa (CO\({}_{2}\) critical pressure), as shown in Figure 12. The phenomenon was mainly caused by two factors. Firstly, the working fluid entered the compressor along the axial direction, and there was a flow acceleration phenomenon at the rotor LE. The curvature change of the molded lines at the rotor LE was the largest. Thus, the gradient of the velocity increase was correspondingly the largest. At the corner position of the LE on the top of the blade, the accelerating fluid on both sides of the blade would cause an 'ejection' effect. The gradient of the velocity increase was the largest at this position, so the fluid velocity increased sharply. It would produce an obviously  
Figure 10: The velocity vector distribution of the 50% blade height section of the initial design. low pressure and low temperature region. CO\({}_{2}\) entered the two-phase region and was far below the critical state. So, it would result with the possibility of 'condensation'. Secondly, the phenomenon of an 'off vortex at the LE on the top of the blade' near this position would cause an obviously low-pressure area, and the working fluid would enter the two-phase region. This is consistent with the conclusions of other scholars [23; 24]. On the basis of the initial design of the compressor, this paper also contrasted and analyzed Case A and Case B. The calculated performance parameters are shown in Table 5. As can be seen from the table, compared with the initial design, although the total pressure ratio of Case B decreased from 1.67 to 1.65, the total static efficiency increased from 50.3% to 64.56% greatly. The pressure ratio of Case A was 1.67 and the total static efficiency was 63.36%. It was slightly lower than the efficiency of Case B. If the blade number is adjusted, the performance of the compressor may be equivalent to that of Case B, and may even be slightly higher. Compared with the numerical results, it was found that the addition of the splitter blade had little influence on the streamline, pressure and temperature distribution in the whole fluid domain.