Abstract: Internal and external properties of fluid machinery are affected by the vortices generated in the machine. Traditional methods such as speed and pressure fail to reveal the true flow of the flow field. The vortex identification method succeeds in characterizing the internal vortex structure of the mixed-flow pump and identifying the size and position of the vortex and evolution. Large eddy simulations are used to obtain the vortex structures of different vortex identification methods (vorticity, helicity method, λ₂ criterion, and Q criterion) in the flow field of a mixed-flow pump. The results show that the second generation vortex identification method can obtain the detailed vortex structure inside the mixed-flow pump more than the vorticity criterion method. Among them, the Q criterion eliminates most of the influence of the shear layer, and presents the obvious superiority in capturing the vortex structure inside the mixed flow pump, and accurately displaying the vortex size. Through the identification of the Q criterion, the regular channel vortices in the impeller flow channel of the mixed-flow pump are extracted and evenly distributed in each flow channel. The structure of the vortex leakage at the blade tip is clear, and the interference of the shear layer on the wall is eliminated. In order to form a regular channel vortex, the blade trailing edge vortex sheds the interference of the wall shear layer, and a clear vortex structure can be seen. The Q criterion is more appropriate for vortex identification of the flow field in a mixed-flow pump. It offers advantages in displaying the vortex structure and the size of the vortex，which can be used to analyze the internal flow field of rotating machinery.

Key words: mixed-flow pump, large eddy simulation, vortex recognition, Q criterion, helicity method, λ₂ criterion