## 1 Introduction  
Axial flow pump devices with low head are widely used in flood control, irrigation, and regional water diversion projects [1, 2]. Tubular axial flow pump devices are mounted with the motor inside a passage, which has the advantages of a straight passage profile and small civil work. According to the motor installation model and passage type, the tubular axial flow pump device can be divided into bulb tubular pump devices, vertical shaft tubular pump devices, and full tubular pump devices [3]. To reduce installation space and obtain a compact structure, the impeller of full tubular pump device is placed inside the motor and the impeller blade is connected with motor rotor. The impeller rotates with the motor rotor as a whole, so there is inevitably a backflow clearance between the motor rotor and the motor shell. Under the action of pressure difference between the impeller inlet and outlet, part of the impeller outflow returns to the impeller inlet through the backflow clearance. The backflow converges with the impeller inflow and produce a clearance backflow vortex (CBV), which leads to disorderly internal flow pattern region and a significant decrease in the energy characteristics. The unsteady flow caused by CBV increases internal vibration inside the impeller, and even endangers safe operation in serious cases. At present, there is a few studies on the backflow clearance in the full tubular pump. [PERSON] [4, 5] compared the hydraulic characteristics and pressure characteristics of a full tubular pump and traditional axial flow pump. The results shown that the hydraulic performance of the full tubular pump is lower than the traditional axial flow pump, but the pressure pulsation amplitude of the full tubular pump is smaller than that of the traditional axial flow pump under the design and over-load condition. Driven by the pressure difference between the pressure side and the suction side of impeller, the tip leakage vortex (TLV) and induced cavitation [6] can be found near the blade tip clearance (BTC). Thus, the BTC of the traditional pump is similar to the backflow clearance of full tubular pump, and the research on BTC can provide some references. Many scholars used numerical simulation and test measurement (high-speed photography and particle image velocimetry) to study the TLV in axial flow pump [7], mixed flow pump [8], pump jet [9; 10], and multiphase pump [11]. The research found that the evolution of TLV includes splitting stage, developing stage and merging stage [12]. The cavitation pattern induced by TLV consists of TLV cavitation, tip corner vortex cavitation, shear layer cavitation, jetting shear layer cavitation, and suction-side-perpendicular cavitating vortices [13; 14]. In addition, the increase of tip clearance radius can intensify TLV and result in a decrease of hydraulic performance [15], but the appropriate tip clearance shape can suppress TLV and induced cavitation [16; 17]. Most of the research focuses on the influence of backflow clearance and BTC on the hydraulic performance and internal velocity field, but the energy losses caused by CBV and TLV have not been made fully clear to date. In 2003, [PERSON] [18; 19] proposed an entropy production theory and, therefore, the spatial distribution of energy losses in hydro-turbine [20], centrifugal pump [21; 22], and axial flow pump [23] can be evaluated from computational fluid dynamics (CFD) post-processing. Furthermore, the effect of geometric parameters on the energy transfer characteristics can also be obtained by using entropy generation theory [24; 25; 26; 27], which can provide reference for optimal design. In the research field of BTC, entropy production theory can better reveal the mechanism of energy losses due to TLV. For instance, [PERSON] [28] and [PERSON] [29] used the entropy production theory to analyze the energy characteristics under different BTC of a mixed flow pump and axial flow pump, respectively.