## 2 Research Object and Methods
### Numerical Setups
#### 2.4.2 Boundary Conditions and Turbulence Model of the CFD  
The inlet and outlet boundary conditions are set according to the values obtained by experiments. In order to obtain a robust calculation, the inlet boundary condition is set to total pressure, and the outlet boundary condition is set to mass flow rate. All the other walls are treated as non-slip boundaries. The pre-converged steady flow field (based on the SST turbulence model) obtained is accepted as the initial condition followed by the unsteady simulation. In order to acquire accurate acoustic sources, a turbulence model is usually adopted to characterize the unresolved turbulence scales. The Reynolds-averaged Navier-Stokes (RANS) equation is widely used due to the drastic reduction of computational cost for engineering applications on predicting the flow details. However, it only resolves the time-averaged flow-lacking of frequency-related term, which makes it inappropriate for flow-induced acoustics. LES resolves the large eddies and implicitly accounts for the small eddies by using a sub-grid scale model, which is a mainstream turbulence model for simulating the acoustic problems in a fluctuating flow field. The flow field of a high-speed centrifugal pump may exhibit phenomena such as backflow, flow separation, inlet distortion, and rotator-stator interaction, as well as mutual interferences. A sub-grid scale model is used to equalize the flow variables as instantaneous values within the spatial domain, through which the pressure fluctuating phenomenon can be captured from the separated flow. At present, it is impossible to simulate the small-scale eddy due to the wall separation with coarse meshes. Moreover, a near-wall model cannot soundly simulate the near-wall flow structures and the growth-separation phenomena of boundary layers unless it uses micro-sized grids. So far, the computational cost for solving such an engineering problem by using LES is mostly beyond the available computational capabilities. The unsteady RANS model makes it possible to calculate the flow fluctuation by adding an additional time term to the RANS equations. A hybrid method to combine the advantages of LES and RANS models has been popularly developed. SAS is a hybrid turbulence model that introduces the von Karman length scale based on the URANS model. It can dynamically adjust the length scale and does not need to divide the computational domain into the URANS and LES computing regions through the grid-scale, which allows simulating fluctuating flow using a large-eddy model. However, this model may be unstable in solving weak high-wave number dissipation problems, where instability is caused by the mesh when it is not capable of producing small-scale eddies small-scale eddy through the von Karman length scale. Then, the kinetic energy of turbulence flow with high-wave numbers is the absence of dissipation, which in turn poses a negative effect on the simulation results. The SAS turbulence model is not the most suitable model in solving the acoustic problem of a high-speed centrifugal pump. The DES turbulence model included in software Ansys CFX 14.1 is used for the CFD process, which compensates for the demerit of the RANS model in simulating separation. This methodology also helps improve the computation efficiency of the LES model with respect to boundary flow. Moreover, the DES model in the ANSYS CFX is based on the SST formulation. The advantage of this combination is that the accurate prediction of turbulent boundary layers up to separation and in mildly separated regions is carried out using the SST model. In addition, the SST model supports the formulation of a zonal DES formulation, which is less sensitive to mesh resolution restrictions than the standard DES formulation [26]. It switches from the SST-RANS model to the LES model in regions where the turbulent length, \(L_{t}\), predicted by the RANS model is larger than the local mesh spacing.