## 2 Materials and Methods
### Experimental Verification  
Because the high-speed machine at CHIEF has not yet been built, its experimental verification is currently impossible. Therefore, we employed the same modeling approach to conduct CFD calculations on ZJU400, a supergravity geotechnical centrifuge already  
Figure 4: Results show (**a**) boundary layer number independence and (**b**) grid number independence. Figure 3: Multiple reference frame (MRF) configuration and mesh partition scheme, where (**a**) represents the schematic diagram of MRF division, (**b**) is the grid schematic diagram of A-A cross-section, and (**c**) is the boundary layer grid schematic diagram. constructed at Zhejiang University (Figure 5), under environmental temperatures ranging from 295 to 300 K, and subsequently verified the results experimentally. Table 1 [20] presents the theoretical expression for the windage resistance of a rotating motor, where R is the rotor radius, L denotes the rotor length, \(\rho\) is the density, and \(\mu\) represents the dynamic viscosity. Given the similarities in the processes involved in deriving the windage power for high-speed rotation, the equations in Table 1 hold referential significance for estimating the windage power of supergravity centrifuges. [PERSON] et al. [6] proposed an empirical formula (Equation (12)) for the windage resistance of a supergravity centrifuge, where \(D\) and \(n\) are constants under normal atmospheric pressure conditions. Table 1 shows that the simplified windage formulas listed can be represented by Equation (12). Therefore, in this study, Equation (12) was used as the fitting formula. \[P_{w}=D\rho\omega^{n}. \tag{12}\]  
A comparison chart of the measured motor power versus the simulated windage loss power for ZJU400 at varying accelerations and atmospheric pressures with air as the working fluid is shown in Figure 6. The purple spheres represent the windage power calculated through the CFD simulation, whereas the yellow circles indicate the experimentally \begin{table}
\begin{tabular}{c c} \hline \hline
**Windage Loss** & **Simplified Formula** \\ \hline \(P_{W}=\left[0.074\rho L\pi R^{4}\big{(}\frac{v}{2\pi R^{2}}\big{)}^{0.2}\right] \omega^{2.8}\) & \(C\rho\omega^{2.8}\) \\ \(P_{W}=\frac{[0.45\rho L\pi R^{4}]\omega^{3}}{\log\big{(}\frac{v\pi R^{3}}{2\pi R ^{2}}\big{)}^{3\pi}}\) & \(C\rho\frac{\omega^{3}}{\log(\omega)^{3.88}}\) \\ \(P_{W}=\left[0.030\beta L\pi R^{4}\big{(}\frac{v}{2\pi R^{2}}\big{)}^{0}\right] \omega^{2.86}\) & \(C\rho\omega^{2.86}\) \\ \(P_{W}=\left[0.523\rho L\pi R^{4}\big{]}\frac{\omega^{3}}{\ln\left[0.06\big{(} \frac{v\pi R^{3}}{2\pi R^{2}}\big{)}^{2}\right]}\) & \(C\rho\frac{\omega^{2}}{ln(\omega)^{2}}\) \\ \(P_{W}=\left[1.328\rho L\pi R^{4}\big{(}\frac{v}{2\pi R^{2}}\big{)}^{1}\right] \omega^{2.5}\) & \(C\rho\omega^{2.5}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Available calculation formulas for windage resistance. Figure 5: ZJU400 ultra-gravity centrifuge. measured motor power. The purple curve depicts the fitted curve based on the simulation results, with the fitting formula referenced from Equation (12). The fitting result is given by Equation (13), with a correlation coefficient R\({}^{2}\) of 0.996. \[P_{w}=19.84\rho\omega^{3.11} \tag{13}\]  
The dashed line represents the deviation curve associated with the fitted curve. At rotational speeds below 10 rad/s, the maximum deviation between the fitted curve and the experimental motor power measurement was approximately 35%. When the angular velocity surpassed 14 rad/s, the deviation decreased to within 15%. The triangle symbol represents the wind resistance power obtained by the k-\(\epsilon\) turbulence model simulation, and it is smaller than that obtained by the k-\(\omega\) SST model and deviates more from the experimental value. Therefore, the k-\(\omega\) SST model more accurately simulates the rotation of the supergravity centrifuge, further demonstrating that the k-\(\omega\) SST turbulence model is a more accurate choice.