# Dynamic Instability Analysis of a Double-Blade Centrifugal Pump
## 2 Computational Modeling and Experimental Test
### Simulation Setup  
The ANSYS CFX 19.0 was used as a simulation tool. In the simulation, the inlet boundary condition was set at total pressure (1 atm), and the outlet boundary condition was set as mass-flow. Impeller is the rotating part, and other parts are the stationary parts. Both steady simulation and transient simulation strategies were undertaken in the research. In the steady calculation, the interface between the rotating impeller and the volute was set as the frozen rotor, and in the transient calculation, it was set as the transient rotor-stator interface. The spatial discretization of the governing equation is based on the finite volume method, and the transient calculation time step is 1.72414 \(\times\) 10\({}^{-4}\) s, which is 1/120 of the rotation period. The high resolution is selected for advection scheme, transient scheme is second order backward Euler, turbulence numeric is high resolution, the convergence target is set to 10\({}^{-5}\), and the maximum number of iteration steps in each time step is 15. Standard wall function was used to process the near wall surface, and the solid wall surface was set to be no slip. In addition, the impeller, gas-liquid separation chamber, suction, and volute wall surface were set to rough wall surfaces with a roughness of 0.04 mm, and the remaining solid walls were set to smooth wall surface. The quality of the grid directly affects the accuracy and time of numerical calculation. In the CFD calculation, the structured meshes were constructed using Gridpro software, as shown in Figure 2. The grid sensitivity analysis was carried out to determine the appropriate number of grids. Figure 3 shows that as the number of cells exceeds about 3 million, the head and torque basically remain constant and their values are about 16.7 m and 19.4 N\(\cdot\)m under designed flow rate condition. In order to balance the calculation accuracy and calculation time, the total mesh number of the final model was set at 4.4 million, in which the number of cells of impeller, volute, gas-liquid separation chamber and suction channel are 680,000, 460,000, 215,000, 170,000, respectively; and the remaining parts of the computational domain consists of 940,000 cells. Table 2 shows the verification results of the independence of turbulence models under designed flow rate condition. It can be seen that the influence of different turbulence models on the calculation results is small, and the relative error is lower than 3%, which satisfies the precise requirements of the relevant calculation. In this study, SST \(k\)-\(\omega\) was selected as the turbulent model for subsequent calculation, because it can obtain the wall separation flow and shear flow under the off-design condition well [22; 23; 24]. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline \multicolumn{2}{c}{Design operation condition} \\ Flow rate \(Q_{\mathrm{d}}/(\mathrm{m}^{3}\mathrm{\cdot h}^{-1})\) & 100 \\ Total head \(H_{\mathrm{d}}/(\mathrm{m})\) & 15 \\ Rotation speed \(n/(r\cdot\mathrm{min}^{-1})\) & 2900 \\ Rotation frequency \(f_{n}/(\mathrm{Hz})\) & 48.33 \\ Specific speed \(n_{\mathrm{d}}\) & 231.5 \\ Reynolds number \(\mathrm{Re}\ (\mu_{2}{}^{2}{D_{2}}^{2}/v)\) & \(3.06\times 10^{6}\) \\ \multicolumn{2}{c}{Pump geometrical parameters} \\ Impeller inlet diameter \(D_{1}/(\mathrm{mm})\) & 100 \\ Impeller outlet diameter \(D_{2}/(\mathrm{mm})\) & 142 \\ Blade outlet width \(b_{2}/(\mathrm{mm})\) & 68 \\ Blade outlet angle \(\beta_{2}/(^{\circ})\) & 21 \\ Number of blades \(z\) & 2 \\ Basic circle diameter \(D_{3}/(\mathrm{mm})\) & 150 \\ Volute inlet width \(b_{3}/(\mathrm{mm})\) & 80 \\ Tongue placement angle \(\varphi_{0}/(^{\circ})\) & 25 \\ Tongue flow angle \(\omega_{0}/(^{\circ})\) & 20 \\ Throat area \(A_{8}/(\mathrm{mm}^{2})\) & 5000 \\ Tongue radius \(R_{\mathrm{t}}/(\mathrm{mm})\) & 6 \\ Pump discharge diameter \(D_{\mathrm{o}}/(\mathrm{mm})\) & 80 \\ Pump suction diameter \(D_{1}/(\mathrm{mm})\) & 100 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Main data of the pump.