## 2 Establishment of the Fluid-Solid Coupling Structure for DD-PMSG
### Assumptions and Boundary Condition Settings  
DD-PMSG is a large-scale model, and simulating full-scale models is time-consuming. In order to improve the efficiency of computer simulation, the generator model is simplified by utilizing its circumferential symmetry. As shown in Table 2, the simplified and original models are compared in terms of simulation accuracy and computation time. The results showed that the simulation error was within 1.5%, but the computation time of the 1/48 scale model was reduced by 93.75%. Therefore, the 1/48-scale model is adopted as the simplified one. Figure 3a,b presents the 1/48-scale generator model.  
In order to further discuss the sensitivity of results to mesh density and element types, this paper conducts the mesh convergence research on the model and investigates its rules. To ensure computational accuracy and adaptability to complex boundary conditions, the solution domain is meshed with hexahedral grids, maintaining a minimum orthogonal quality of 0.15, as Figure 3c mesh model. The sensitivity of results to mesh indicates that the maximum temperature of the generator increases with the increase of the mesh number,as shown in Figure 4. Once the grid count exceeds 9,734,550, the temperature change is very small (less than 1%). Thus, a grid count of at least 9,734,550 is selected for the analysis.  
Based on heat transfer theory, the following assumptions are made for the solution model [16; 17; 18]:  
* The fluid motion is complex, with a high Reynolds number (Re > 2300). Therefore, the flow field in the generator is calculated using a turbulent flow model (SST-k-omega model);  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & \begin{tabular}{c} **Maximum** \\ **Generator** \\ **Temperature** \\ \end{tabular} & \
\begin{tabular}{c} **Computational** \\ **Error** \\ \end{tabular} &
\begin{tabular}{c} **Simulation Time** \\ **Required** \\ \end{tabular} \\ \hline Full-model & 57.31 \({}^{\circ}\)C & 0 & 160 h \\ Simplified 1/12 model & 56.85 \({}^{\circ}\)C & 0.80\% & 60 h \\ Simplified 1/24 model & 56.62 \({}^{\circ}\)C & 1.3\% & 25 h \\ Simplified 1/48 model & 56.51 \({}^{\circ}\)C & 1.40\% & 10 h \\ \hline \hline \end{tabular}
\end{table}
Table 2: Analysis of results before and after simplification.  
Figure 4: Variation of maximum generator temperature with mesh.  
Figure 3: Simplified structure of the **(a)** solution domain; **(b)** fluid domain; **(c)** mesh generation.  
* Copper losses are uniformly distributed in the stator windings, while iron losses are uniformly distributed in the core;
* Since the air flow velocity is much lower than the speed of sound, air is considered as an incompressible fluid;
* The influence of gravity on fluid flow is neglected.  
The boundary conditions of the model are set as follows:
* Set the cooling air inlet as velocity inlet with an entrance velocity of 3 m/s, and the outlet as pressure outlet.
* Due to the circumferential symmetry of the model, the axial surfaces on both sides are set as periodic boundaries.
* The materials are specified as follows: the fluid is air, the stator is silicon steel, and the windings are copper.