# Effect of Vaneless Diffuser Shape on Performance of Centrifugal Compressor
## 3 Result and Discussion
### Flow Field Analysis
#### 3.2.3 Span Cross-Section Radial Velocity  
The radial velocity distribution was analyzed by taking 70% of the span cross-section locations with a large return flow zone near the shroud side to display the circumferential flow characteristics of the vaneless diffusers.  
Figures 8-10 show the radial velocity distribution inside vaneless diffusers at 70% span height under three flow conditions. As can be seen from Figure 8 that when the relative mass flow is 1.125, the backflow phenomenon at the exit of the impeller is aggravated by the convergence of the vaneless diffuser width, and the value of the high-speed area of the circumferential flow is increased, which may be the reason why the pinch of diffuser width will lead to the decline of the compressor pressure ratio under the condition of near choking. The most negative impact investigated from Figure 8 is the case that converges the width of the diffuser from the hub side. What causes this is the flow high-speed area that near the hub side. Convergence of the diffuser width from the hub side under the condition of large mass flow tends to increase the radial speed value of the overall high-speed area and reduce the conversion process of velocity to pressure in the case of large mass flow.  
Figure 7: Radial velocity distribution on the meridional surface at 0.6 relative mass flow: (**a**) parallel; (**b**) convergence from shroud; (**c**) convergence from hub; (**d**) equal convergence from shroud and hub.  
The three convergent forms of vaneless diffuser can improve the backflow area at the outlet of the impeller and decrease the value of the high-speed flow area under the design flow condition, as shown in Figure 9. Among the three shapes, the width of the diffuser can be pinched from the shroud side to the best effect. Compared with the relative mass flow of 1.125, the width of the three convergent diffusers can effectively reduce the backflow area on this section, and the vaneless diffuser that converged from the shroud of the wall under this flow condition makes the backflow area shrink most significantly.  
For the 0.6 relative mass flow operation condition, the jet wake structure located at the impeller outlet in the parallel wall diffuser is suppressed by the downstream backflow area, and distortion acted on jet wake structure occurs follow on, as shown in Figure 10. After converging the diffuser width, the backflow zone disappears and the jet wake structure recovers, indicating that the convergence of the width improves the flow characteristics at the diffuser inlet, and besides these the three convergence forms have little difference in effect on the backflow area.  
Figure 8: Seventy percent span height radial velocity distribution at 1.125 relative mass flow: (**a**) parallel; (**b**) convergence from shroud; (**c**) convergence from hub; (**d**) equal convergence from shroud and hub.  
Through combining the radial velocity profile of the diffuser meridian and the 70% span height cross section contours, it can be seen that the convergence of the vaneless diffuser width can significantly improve the backflow phenomenon on the shroud side and reduce the high speed flow area on the hub side when the relative mass flow is 1.125 and 1. At 0.6 flow coefficient, there is no significant difference in the effect of the three convergent forms of the vaneless diffuser on the backflow area on the meridian near the shroud side, but the size of the this area where the impeller is connected to the diffuser can be reduced. Therefore, the efficiency improved by the convergence of the diffuser width is summarized as suppressing the internal backflow area of centrifugal compressor.  
Figure 9: Seventy percent span height radial velocity distribution at 1 relative mass flow: (**a**) parallel; (**b**) convergence from shroud; (**c**) convergence from hub; (**d**) equal convergence from shroud and hub.