A nuclear reactor coolant pump (RCP) [1], the device in the reactor core and the steam generator that transfers the heat energy [2], is the "heart" of a nuclear reactor driving the circulation flow of the coolant in the main loop [3]. The nuclear reactor coolant pump is the only rotating part of the nuclear island, so it belongs in a nuclear safety grade one facility. Moreover, it is also the main energy-consuming equipment in the nuclear power plants, which must be guaranteed to operate continuously over a long term and without trouble. An investigation on the internal flow in the mixed-flow nuclear reactor coolant pump is one of the key problems for the development of reactor coolant pumps in large pressurized water reactors. Some investigations have been conducted to study the design of the mixed-flow pump [4] and [5] and flows instabilities [6] and [7]. However, most of them only focus on the unsteady pressure pulsation in impeller [8] and [9] or the performance of the nuclear reactor coolant pump [10] and [11]. The unsteady flow structure of a mixed-flow nuclear reactor coolant pump, especially in certain specific regions, is very important to the safety analysis of a nuclear reactor, as it could generate serious flow-induced vibration, threatening the pump integrity [8]. Therefore, a comprehensive analysis and prediction of pressure pulsation caused by intense rotor-stator interaction are essential for the design of the mixed-flow nuclear reactor coolant pump [12] and [13]. At present, in order to improve the efficiency and stable operation of the nuclear reactor coolant pump, the complicated internal unsteady flow structures should be thoroughly illustrated.The nuclear reactor coolant pump has a special structure equipped with a spherical casing, which determines a typical and complex flow pattern within the pump. Knierim et al.[14] designed a new type of reactor coolant pump for a 1400 MW nuclear power plant. The impeller and diffuser were gradually optimized based on the computational fluid dynamics (CFD). The volute casing is a spherical shape with a discharge nozzle facing the impeller, and the flow structures in the region around the discharge nozzle are uniform. The region of the discharge nozzle itself is characterized by the fact that the flow below the outlet port is divided into two parts. One portion flows out of the casing discharge nozzle, whereas the other portion circulates around the casing once more prior to exiting. Kato et al.[15] and [16] described internal flows of a high-specific-speed mixed-flow pump at low flow rates using large-eddy simulation (LES), and it showed that the head-flow curve exhibited weak • Flow separations and backflows easily occur at the diffuser channels near the discharge nozzle region.• At the left region of the casing, the discharge nozzle is affected significantly by an intense rotor-stator interaction effect.• In the right and middle of the casing nozzle, unsteady flow structures are more complicated.• An unsteady vortex-shedding effect would motivate evid...