## 2 Aerodynamic Load and Deformation Analysis of Multi-Stage Telescopic Wings
### Aerodynamic Analysis of Flight Environmental Loads
#### 2.1.2 Aerodynamic Simulation Analysis  
After establishing the flow field model, a systematic mesh convergence analysis is conducted to ensure that the computational results remain independent of mesh size. The primary objective of the mesh convergence analysis is to assess the influence of mesh resolution on aerodynamic force calculations and to determine the optimal mesh size that balances computational accuracy and efficiency. Therefore, all model parameters remain unchanged, with only the mesh size being varied to analyze the convergence behavior of lift and drag forces. In this study, a mesh size of 10\({}^{-2}\) m is selected as the reference medium-resolution grid. Additionally, two finer mesh configurations and two coarser mesh configurations are generated to evaluate the effect of mesh refinement on computational accuracy.  
Figure 5 illustrates the variations in lift and drag forces as a function of mesh size. The results indicate that as the mesh resolution increases, the computed values of lift and drag gradually converge. When the mesh size is further refined below 10\({}^{-2}\) m, the numerical error is reduced to less than 0.2%, indicating that the computational discrepancy is within an acceptable threshold. Considering both numerical accuracy and computational cost, a mesh size of 10\({}^{-2}\) m is deemed optimal, as further refinement has a negligible impact on the results. Thus, this study adopts a mesh size of 10\({}^{-2}\) m to ensure computational accuracy while maintaining efficiency.  
The analysis is performed under the design flight conditions of Mach 5.0 at an altitude of 20 km. The aerodynamic and thermal loads on the wing are evaluated for these conditions. The wing's aerodynamic and thermal load distribution contour maps are shown in  
Figure 5: Grid convergence analysis. (**a**) Lift variation; (**b**) drag variation.  
From the aerodynamic thermal load contour map of the wing surface shown in Figure 6b and the corresponding simulation dataset, the thermal load distribution of the wing is presented in Figure 7. Due to the impact effects of high-speed airflow and aerodynamic heating, the leading edge of the wing exhibits a higher temperature, reaching up to 600 \({}^{\circ}\)C. The temperature across the wing surface varies between 300 \({}^{\circ}\)C and 500 \({}^{\circ}\)C. The majority of the wing surface shows a relatively uniform temperature distribution, with temperatures stabilizing around 500 \({}^{\circ}\)C. This indicates that the aerodynamic heating effects rapidly diminish toward the rear part of the wing surface, and the thermal environment in most areas remains relatively stable. Based on these temperature distribution characteristics, to ensure representativeness and coverage during thermal experiments, the temperature of 500 \({}^{\circ}\)C, representative of the majority of the wing surface area, should be selected as the test criterion.  
Based on the aerodynamic simulation results of the service environment loads for the multi-stage telescopic wing, it is recommended to use an aerodynamic load of 15 kPa and an aerodynamic heating temperature of 500 \({}^{\circ}\)C as the evaluation conditions to simulate extreme flight scenarios. This selection not only simplifies the experimental conditions but also effectively covers the primary heat-affected regions of the wing surface under actual operating conditions, ensuring that the experimental results hold significant engineering relevance and practical guidance value.  
Figure 6: As illustrated in Figure 6a, the wing surface pressure is predominantly within the range of 15 kPa.  
Figure 7: Chordwise distribution of thermal load on wing surface.