## 5 Conclusions  
In this paper, a fluid self-lubricating centrifugal pump utilizing R134a refrigerant was proposed to investigate the distribution regularities of pressure, temperature, relative velocity, and bubble volume under different operating conditions. The main conclusions of this study are as follows:  
1. The numerical model of the centrifugal pump, which utilizes R134a refrigerant and incorporates a self-lubricating mechanism, demonstrates excellent predictive capability for hydraulic performance. By employing a modified Sauer-Schnerr cavitation numerical model, the cavitating performance was accurately predicted. The head coefficient value at design conditions was 0.9981, with a calculation error of 2.6%. The numerical calculations yielded a critical cavitation number of 0.546, which closely matched the experimental value of 0.551, and a breakdown number of 0.347, compared to the experimental value of 0.412.
2. With the cavitation number decreases, a significant change occurs to the pump head, and cavitation clouds originate from the leading edge of the inducer and develop downstream along the suction side of the inducer blades. When the cavitation number falls below the critical value, cavitation clouds begin to emerge at the trailing edge of the inducer. The bubbles gradually expand within the flow passage, leading to a sudden decrease in the impeller blades' pressure capacity and a rapid drop of the pump head.
3. The installation of an inducer at the impeller's upstream reduces effectively the pump's critical and breakdown numbers. After installing the inducer, the critical cavitation number decreases from 0.783 to 0.566, and the breakdown number decreases from 0.718 to 0.372. Different from the pump with an inducer, the pump head curve  
Figure 23: Effect of inlet temperature on bubble volume fractions under the critical cavitation number \(\sigma=0.556\).  
drops more steeply after reaching the critical cavitation number, indicating that the cavitation condition in the flow passages deteriorates rapidly with decreasing inlet pressure.
4. With the occurrence of cavitation, the thermal effect of refrigerant impacts the cavitating process of the pump. In the case of the isothermal model, the bubble fraction and temperature drop were overestimated, reaching 100% and 30 K, respectively. However, in the non-isothermal model, these values were less than 50% and 2 K, respectively. The thermal effect of the refrigerant suppresses the development of cavitation clouds due to the temperature increase.  
As for the refrigerant centrifugal pump, the internal flow characteristics and thermal physical properties of refrigerants are crucial to its performance. The results obtained from this study can provide valuable guidance for the hydraulic design of refrigerant centrifugal pumps.  
Software, X.F.; validation, X.F. and B.Z.; formal analysis, X.F.; investigation, H.Z.; resources, Y.H.; data curation, X.L.; writing--original draft preparation, X.F. and B.Z.; writing--review and editing, S.C.; visualization, R.X.; supervision, Z.Z.; project administration, Z.Z. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the China Postdoctoral Science Foundation (No. 2021M692533) and the Youth Innovation Team of Shaanxi Universities.  
Not applicable.  
The authors declare no conflict of interest.