## 2 Materials and Methods
### Numerical Simulation Geometry, Mesh, and Boundary Conditions  
Simcenter STAR-CCM+2402 software was utilized as a CFD simulation tool (a premium multiphysics simulation and CFD analysis software developed by Siemens Digital Industries Software, located in Munich, Germany.). Based on the actual dimensions of CHIEF, a simplified CFD model was constructed, as depicted in Figure 2, where the sidewalls were modeled as water-cooled surfaces. As the thermal resistances of water cooling and wall conduction are much smaller than those of gas-to-wall heat transfer, we assumed that the sidewall temperatures were close to the coolant temperature, which was set to a constant temperature of 300 K, representing stainless-steel walls in contact with cooled water. The heat transfer boundary conditions on the top and bottom walls were configured for natural convection with the surrounding environment at a temperature of 300 K and an associated natural convection heat transfer coefficient of 5 W/m\({}^{2}\)-K. Under the simulated conditions, the maximum Reynolds number reached 10\({}^{9}\), falling within the turbulent regime. [PERSON] et al. (16) and [PERSON] et al. (17) independently employed the k-\(\omega\) SST turbulence model in simulations of electric motors and hydro turbines, respectively, and performed experimental validation. Their findings indicated that the SST model offers high accuracy in computations involving high-Reynolds-number rotation. Hence, the SST model was adopted in this study. The viscous heating option accounts for frictional heating effects. To address the compressibility of the gas owing to high-speed rotation, a pressure-based coupled solver method was used, with second-order accuracy for pressure and third-order accuracy for other variables. Ideal gas laws were employed to account for changes in the properties of helium and air. The roughness height of the inner walls and the outer surfaces of the rotating bodies was set to a common value for stainless steel, which was 0.05 mm.  
Mesh quality is a critical factor that determines whether the simulation results converge. [PERSON] et al. (19) performed comparative simulations of a rotating gear using both sliding mesh and multiple reference frame (MRF) approaches and demonstrated that the MRF method yields higher accuracy with a smaller computational burden. Therefore, this study adopted the MRF method and employed the Simcenter STAR-CCM+2402 software for mesh generation. Unstructured meshes were used because of the irregularity of the arms. As shown in Figure 3, the computational domain was divided into rotating and stationary domains. The MRF zoning is depicted in Figure 3a, where the darker-shaded region represents the rotating domain encompassing the arms and experimental capsule. Figure 3b shows a cross-sectional view of the mesh layout. The rotating parts interface with the stationary parts through a boundary layer, transferring the computation values across them. As shown in Figure 3c, the boundary layer is refined, with the first layer node height near the rotating body and the internal wall set to 0.05 mm to satisfy the requirements for low-Reynolds-number modeling near the wall. Figure 4a illustrates the independence of the simulation results from the number of boundary layers. For a total boundary layer thickness of 0.02 m, the torque due to wind resistance no longer varies significantly (with a change of less than 0.5%) after the boundary layer contains 10 layers. Thus, the number of boundary mesh layers was set at 10 in this study, as indicated by the arrow points. Figure 4b demonstrates the independence of wind resistance torque from the total number of mesh elements. When the mesh count exceeds 17 million (as indicated by the arrow), the torque due to wind resistance stabilizes with a variation of less than 0.5%. To maximize computational cost savings and time efficiency, this study used a mesh count of 17 million elements for the final calculations.