## 5 Conclusions  
An open type system is built in a semi-anechoic room as a test rig to study performance and radiated noise characteristics of a high-speed centrifugal pump under different rotational speed. A CFD/CFA calculation method is proposed to predict the fluid-borne noise and radiated noise characteristics. Experimental and numerical analyses were performed on the model pump for flow-induced noise characteristics. The main conclusions are the following:  
1. In the speed range of 5000-6750 r/min, pump performance conforms to similar laws; the dimensionless head curve is basically the same at different speeds. With decreases of rotational speed, the zone with high value in the efficiency becomes narrow and moves to small flow rate area, and the highest value of efficiency gets continuously reduced. The dimensionless radiated noise also conforms to a similar law, and the highest efficiency point pump presents the lowest noise level.  
2. Based on [PERSON]'s acoustic analogy theory, the proposed CFD/CFA method is proven effective to calculate the fluid-borne noise and flow-induced radiated noise of the model pump. The DES model could give accurate sound-source information. Considering the coupling effect of the structure field, the predicted radiation sound field exhibited dipole characteristics combined with the acoustic finite element method. Consistent with the experimental results, the predicted noise spectrum of pump required flow rate shows broadband characteristics but with obvious discrete peaks, which are not only related to the fluid sound source (\(6f_{0}\)) at the low-frequency region, but also to the natural vibration frequency of the structural mode (3000-6000 Hz region).  
3. The main frequency of the pressure pulsation in the flow field presents blade passing frequency (\(6f_{0}\)), which further causes the radiated noise to show dipole characteristics. Therefore, rotor-stator interaction between the rotating impeller and stationary volute of the pump flow field is the main cause of flow-induced noise. The unstable flow such as the stall vortex in the pump impeller and the flow separation in the tongue area lead to the broadband characteristics of pressure pulsation concentrated at the low-frequency region, which also present in the noise spectrum.  
Conceptualization, Q.S. and J.Y.; methodology, Q.S.; validation, C.S., and X.H.; formal analysis and investigation, K.H.; writing--original draft preparation, Q.S.; writing--review and editing, J.Y.; funding acquisition, H.L. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Key Research and Development Program of China (2018 YFB0606103), the National Natural Foundation of China (51976079), the China Postdoctoral Science Foundation (2019M661745), and the open foundation from the Key Laboratory of Water-Saving Agriculture of Henan Province (FIRI2017-20-01, FIRI2016-19-01).  
The authors gratefully acknowledge the financial support by the National Key Research and Development Program of China, the National Natural Foundation of China, the China Postdoctoral Science Foundation and the open foundation from Key Laboratory of Water-Saving Agriculture of Henan Province.  
The authors declare no conflict of interest.