# Effect of Vaneless Diffuser Shape on Performance of Centrifugal Compressor
## 3 Result and Discussion
### Flow Field Analysis
#### 3.2.4 Pressure Distribution Law of Diffusers in Length Direction  
Near the entrance of the vaneless diffusers in Figure 11, the difference between the static pressure values of the three convergent vaneless diffusers and the parallel wall vaneless diffuser has no significant difference. And in Figure 11, the definition of symbols below picture can be find in Appendix A. The static pressure value always shows a convergent type with the extension of the diffuser length. The state pressure of diffusers of reduced width is higher than that of the parallel wall diffuser and the static pressure difference is gradually increased. The variation of static pressure of the three convergent vaneless diffusers is formed a stable law after 15% of the vaneless diffuser length: the highest static pressure can be realized by converging diffuser wall from the shroud side, the lowest one can be realized by converging from the hub side.  
As for the total pressure distribution, the parallel wall diffuser and the three forms of convergent vaneless diffusers have the same total pressure distribution trend along the length of the diffusers, and the total pressure distribution of the three forms of convergent diffusers are always higher than the parallel wall diffuser. Due to the complexity of the flow field in the vaneless diffuser, such as the jet-wake structure at the impeller outlet, the clearance leakage vortex, and the boundary layer separation in the vaneless diffuser, the total pressure of the vaneless diffuser gradually decreased in the radial direction.  
The static pressure rise effect of the three convergent forms of diffusers in Figure 12 is more obvious than that when the relative mass flow is 1.125 in Figure 11. Obviously, the effect of diffuser convergence on static pressure and total pressure distribution tends to be consistent.  
Figure 10: Seventy percent span height radial velocity distribution at 0.6 relative mass flow: (**a**) parallel; (**b**) convergence from shroud; (**c**) convergence from hub; (**d**) equal convergence from shroud and hub.  
Figure 13 shows the mean distribution of static pressure and total pressure along the length direction of vaneless diffusers at 0.6 flow coefficient. The static pressure distribution under these conditions maintains the same trend for the four vaneless diffusers, and the static pressure rise is not as significant as the design conditions. It can be seen that the total pressure value is obviously larger than the other two working conditions. The performance of static pressure and total pressure in these three convergent vaneless diffusers is still consistent with the previous two conditions.  
Figure 11: Mean static pressure and total pressure distribution along the diffuser length direction at 1.125 relative mass flow: (**a**) static pressure distribution; (**b**) total pressure distribution.  
Figure 12: Mean static pressure and total pressure distribution along the diffuser length direction at 1 relative mass flow: (**a**) static pressure distribution; (**b**) total pressure distribution.  
Figure 13: Mean static pressure and total pressure distribution along the diffuser length direction at 0.6 relative mass flow: (**a**) static pressure distribution; (**b**) total pressure distribution.  
The conclusion for the distribution of total pressure and static pressure along the length direction of the vaneless diffuser in three operating conditions can be summarized as follows: the best effect is reached through the pinch from the shroud side, and the advantage of this shape is more obvious under the design operating condition. The improvement of the static pressure of the vaneless diffuser by the convergence of the width is mainly reflected in the second half of the length of the diffuser. The difference in the total pressure is mainly reflected in the pressure value along the vaneless diffusers, especially under 0.6 relative mass flow condition.