# CFD and Energy Loss Model Analysis of High-Speed Centrifugal Pump with Low Specific Speed
## 1 Introduction  
The pump is the \"heart\" of modern industry. The centrifugal pump accounts for more than 70% of the market share for its advantages of the stable flow, simple structure, small volume, and low cost [1]. The high-speed centrifugal pump with a specific speed between 30-80 has the characteristics of the high head, small flow, and high speed. It plays an irreplaceable role in the aerospace, biomedicine, petrochemical, transportation, and other industries [2]. However, its characteristics of small flow and high head also lead to the different structure and hydraulic characteristics between the low specific speed pump and the ordinary centrifugal pump. The impeller diameter of the low specific speed pump is larger and the outlet width is smaller, resulting in larger friction loss in the impeller channel. Meanwhile, both the large hydraulic loss and the shock loss are caused by the reflux at the inlet, the secondary flow in the channel, and the jet wake flow at the outlet. The empirical correlations of the ordinary centrifugal pump cannot predict the power loss of the low specific speed pump correctly, resulting in the low efficiency and poor working stability of the low specific speed centrifugal pump that is designed by the empirical correlation method [3,4]. A high-speed satellite propulsion pump designed by NASA has been tested, the results of which are different from the prediction based on the similarity theory of large pumps with a deviation more than 25%, indicating that the design method of the ordinarycentrifugal pump is not applicable to the low specific speed and high-speed centrifugal pump. As a result, the development of the low specific speed pump has critical problems due to the high cost and the long period that includes theoretical design and multiple prototype tests [5]. Many performance prediction methods have been proposed, including the empirical correlation method, computational fluid dynamics (CFD), and the energy loss model (ELM). [PERSON] et al., calculated the performance of various low specific speed pumps by the empirical correlation method, which were compared with the test results. Their study illustrated that the impeller structure has a great influence on the error of pump performance predicted by the empirical correlation method [6; 7]. [PERSON] et al., predicted the performance of the low specific speed pump based on the pressure, speed, and torque in the FLUENT numerical simulation results [8; 9; 10]. [PERSON] et al., used CFX to simulate a low specific speed pump and obtained the predicted performance of the pump in the post-processing [11; 12]. [PERSON] et al., conducted three-dimensional turbulent flow numerical simulations of four different low specific speed centrifugal pumps through FINE/TURBOTM 6.2 and predicted the performance of the pump [13]. [PERSON] and [PERSON] proposed a method to calculate the optimum flow, the head, and the specific speed coefficient of the low specific speed centrifugal pump, and the effectiveness of the theoretical method was verified by experiments [14]. The National Engineering Laboratory (NELB) had successfully applied ELM optimization to the design of centrifugal pumps [15]. [PERSON] et al., investigated the energy loss and performance of the pump by the numerical analysis using the entropy generation method [16; 17]. [PERSON] established the energy loss model with the energy loss equation based on the existing theory and the experience, and a program for predicting the performance of centrifugal pump was designed and verified by experiments [18]. [PERSON] et al., improved the full Reynolds stress model by CFD to improve the accuracy of performance prediction of the low specific speed pump [19]. Most of the existing numerical calculations can only predict the overall performance without the detailed analysis of various energy losses. Moreover, the energy loss of the low specific speed pump with a fully sealed structure is more complex.