## 2 Geometric Models and Numerical Methods  
### Geometric Model and Meshing  
This study uses a centrifugal pump with low-specific speed \(n_{\text{s}}\) of 13 as the research object. The rated speed of the pump is 2900 rpm, design flow \(Q_{\text{d}}\) is 4 m\({}^{3}\)/h, and design head \(H_{\text{d}}\) is 80 m. The main geometric parameters of the centrifugal pump are described as follows: Number of impeller blades \(Z\) is 8, pump inlet diameter \(D_{\text{s}}\) is 40 mm, pump outlet diameter \(D_{\text{o}}\) is 32 mm, impeller inlet diameter \(D_{1}\) is 50 mm, impeller outlet diameter \(D_{2}\) is 220 mm, inlet width of blade \(b_{1}\) is 15 mm, and outlet width of blade \(b_{2}\) is 7 mm. [PERSON] and [PERSON] [25] indicated that different blade trailing edge shapes can effectively change the wake structure of the impeller. Blade trailing edge has three types, namely, one-sided arc, two-sided oblique and concave cutting. The effects of different trailing edge shapes on the unstable vortex structure of a single turbine blade outlet in a nonrotating state were experimentally studied. The results show that different cutting angles will have significantly different effects on the unstable vortex structure at the outlet of stationary turbine impeller when the two sides of blade trailing edge are bevelled. This study applies two-sided cutting to the centrifugal pump's rotating state for studying the effects of different cutting angles of blade trailing edge on the unstable flow inside the centrifugal pump under off-design conditions. This study presents three types of centrifugal pump impeller with different trailing edge cutting cone angles, namely, the original impeller (OTE), where its blade pressure surface and suction surface are bevelled, 15\({}^{\circ}\) cutting cone angle of blade trailing edge (OBS15) and 30\({}^{\circ}\) cutting cone angle of blade trailing edge (OBS30). Their specific structures are shown in Figure 1.  
Figure 2 shows the mesh of full-flow field fluid calculation domain of a centrifugal pump. Structured hexahedral meshes are used in the relatively regular fluid domains, such as the inlet section, impeller and tip clearance. Complicated calculation domains, such as the volu  
Figure 1: Geometry of different blade trailing edges: (**a**) original trailing edge (OTE) impeller; (**b**) 15\({}^{\circ}\) cutting angle of blade trailing edge (OBS15) impeller; (**c**) 30\({}^{\circ}\) cutting angle of blade trailing edge (OBS30) impeller.  
mesh. In particular, an unstructured hexahedral core mesh is used in the main area of the volute calculation domain except the near-wall area, and the near-wall area of the volute is encrypted using a prism layer. Considering the influence of wall y+ value on the accuracy of shear stress transport (SST) \(k\)-\(\omega\) turbulence model and LES numerical calculation, boundary layer encryption is performed on each wall surface of the impeller. Grid-independent verification is conducted on the performance of the original pump. For different grid numbers (\(0.54\times 10^{6}\), \(2.35\times 10^{6}\), \(4.11\times 10^{6}\), \(6.27\times 10^{6}\), \(8.39\times 10^{6}\), \(10.42\times 10^{6}\)), head coefficients \(\psi\) are 1.494, 1.458, 1.418, 1.417, 1.419 and 1.420, respectively. The performance of the centrifugal pump is basically stable when the number of grids in the flow field calculation domain exceeds \(2.35\times 10^{6}\). Considering the influence of the number of grids on performance and y+ value, the total number of grids in the flow field calculation domain is set to \(10.42\times 10^{6}\), the number of grids of the impeller is set to \(7.38\times 10^{6}\), and the average y+ value of the pump surface is 10.53. The average y+ value of impeller is 5.13.