# Research of Modal Analysis for Impeller of Reactor Coolant Pump
## 3 Resonance Analysis of the RCP Impeller  
### Flow Simulation of the RCP  
In the researches above, the accuracy of the modal simulation scheme in water has been verified. The modal analysis of a full-scale RCP impeller was conducted on the simulation platform described in Section 2.2, which includes flow and modal simulation. The fluid model is artificially divided into four domains, namely, inlet fluid, impeller fluid, vane diffuser fluid and volute fluid. Software ANSYS-ICEM was used to construct the unstructured mesh of the model pump, which is shown in Figure 3. Grid cells near the wall were encrypted in order to ensure \(y+z1\) in the wall-adjacent cells, and the maximum number of layers in the boundary layer is set to 20. The total number of mesh elements is 9,597,689. The preliminary flow simulation model of the RCP has been verified by grid independence verification [3] and performance test in our previous researches [19]. During normal operation, the temperature of the liquid in RCP is about 280 \({}^{\circ}\)C. Ignoring the influence of trace boric acid [20] and referring to the look-up table, it can be found that the physical property parameters of the liquid are a density of 750 kg/m\({}^{3}\) and a viscosity of \(9.6\times 10^{-5}\) kg/m\(\cdot\)s. The RNG (Renormalization-group) k-epsilon turbulence model was used in the flow simulation. A second-order scheme of the spatial discretization was adopted by software FLUENT. The boundary conditions are as follows: Mass flow inlet is set at the inlet of pipe. Pressure outlet is set at the outlet of the solute. No slip walls are set at blade walls. The detailed flow simulation settings are shown in Table 2. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Nodal** & **A. Static Impeller** & **B. Static Impeller** & \multicolumn{2}{c}{**C. Rotating**} & \multicolumn{2}{c}{**D. Rotating**} \\
**Diameters** & **in the Air [Hz]** & **in Water [Hz]** & **Impeller in Water** & **Impeller in Water** & **Impeller in the Air** \\  & & & & **[Hz] (100 \%/min)** & **[Hz] (1800 \%/min)** \\ \hline
0 & 3942 & 3152.6 & \(-\)20.0\% & 3363.6 & \(-\)14.7\% & 3942 & 0\% \\
1 & 2520.3 & 1974.2 & \(-\)21.7\% & 2045.8 & \(-\)18.8\% & 2517.7 & +0.001\% \\
2 & 5817.7 & 5003.4 & \(-\)14.0\% & 5604.2 & \(-\)3.7\% & 5812.7 & +0.001\% \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Natural frequencies of the impeller by simulation. When the computation stopped, the steady-state static pressure on the impeller boundaries was recorded, which is shown in Figure 4. The static pressure on the outside of the hub is greater than that on the inside. Due to the seal of the wear ring, the static pressure on the outside is close to the outlet static pressure of the impeller. Figure 5 shows the static pressure on both sides of the blade. It indicates that the pressure difference between the two surfaces gradually decreases along the flow direction, which means that inlet edges of blades bear more load than outlet edges. Applying the pressure distribution to boundary surfaces of the RCP impeller solid, natural vibration modes of the rotating impeller in high-temperature liquid (the speed of sound is 1020 m/s) were simulated. The modal results are shown in Figure 6; and it can be seen that the impeller vibrates in mode shapes with some uniformly distributed nodal diameters in the radial direction. Vibration modes with different radial nodal diameters have different motion directions, such as vibration modes with one nodal diameter coupled to b \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Turbulence model & K-epsilon \\ Convergence precision & \(<\)1 \(\times\) 10\({}^{-5}\) \\ Rated speed of impeller & 1800 r/min \\ Inlet volume flowrate & 17,886 m\({}^{3}\)/h \\ Outlet static pressure & 15.5 MPa \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Impeller simulation settings. Figure 4: The map of static pressure distribution on the impeller surface.