# Effect of Vaneless Diffuser Shape on Performance of Centrifugal Compressor
## 1 Introduction  
Centrifugal compressors are widely used in the energy, power, aerospace, and petrochemical industries and in other fields. Improving its efficiency is still one of the difficulties and hot spots in the research of aerodynamics of turbomachinery. Optimizing the design of the components of a centrifugal compressor is an effective method that can be used to improve its performance. [PERSON] [1] studied the influence of the volute design on the global performance of the volute, and compared ten kinds of volute design schemes by CFD (computational fluid dynamics) simulation. The final results show that, compared with the forward or symmetrical volute, the backward volute has a more reasonable and uniform velocity field and better comprehensive performance under different working conditions. [PERSON] [2] conducted numerical simulations and experiments on a transonic centrifugal compressor and explored the unsteady physical mechanisms that affect compressor performance, such as impellers and diffusers coupling loss and the periodic changes of shock waves, and proposed an analytical model for loss correction in steady-state calculation. The instability of the rotating stall and surge under low flow conditions also greatly affects the performance of compressor [3; 4; 5]. [PERSON] [6] carried out numerical simulations studying the rotating stall and surge conditions of centrifugal compressors with and without vanes respectively, and compared the flow characteristics of the two compressors. The results showed that the static pressure fluctuation in the vaneless diffuser was higher than that in the vaned diffuser when surge occurs, but the rate of pressure drop in the vaned diffuser is faster than that in the vaneless diffuser. [PERSON] [7] and [PERSON] [8] also discussed the mechanism of the rotary stall and its influence on the aerodynamic performance of the compressor through numerical simulation. At present, the research on the centrifugal compressor impeller has been perfected, so efforts should be made to improve the performance of the centrifugal compressor from the perspective of optimizing the diffuser [9]. Vaneless diffusers [10,11] can be divided into parallel wall-types, convergent types and expansion types according to the different ratios of the diffuser outlet width to the impeller outlet width. Due to the large internal cross section of the expansion type vaneless diffuser, a large reversed pressure gradient can be generated, and secondary flows and backflows are easily generated during the flow process, so the expansion type vaneless diffuser is rarely used in practical applications. [PERSON], [PERSON] et al. [12,13] conducted experimental studies on parallel wall type vaneless diffusers with different width ratios, and the results showed that appropriate pinches of the width of vaneless diffusers at the outlet of the impeller could improve the isentropic efficiency and pressure ratio of the centrifugal compressor. The secondary flow at the shroud could be inhibited and the flow field of the diffuser could also be stabilized. A vaneless diffuser with a pinch of width led to higher performance of the centrifugal compressor stage and impeller but lower performance of the vaneless diffuser itself [14]. [PERSON] [15] carried out a theoretical analysis of the stability of centrifugal compressors, and compared the prediction results with the experimental results of centrifugal compressors matched with three different width vaneless diffusers. Reduced width of the diffusers could make the unstable conditions appear in a smaller flow condition and reduce the number of stall cells in the rotating stall. [PERSON], [PERSON] [16, 17, 18] carried out experimental studies on the stability of the final stage of a high-pressure centrifugal compressor and the performance of the compressor on the vaneless diffusers with two radius ratios, multiple width ratios, and different contraction shapes.