## 3 Process of Design Optimization
### Definition of Design Problems
However, these algorithms are not as accurate as computational fluid dynamic (CFD) simulations and wind tunnel experiments and may have computational errors of up to 10% [6; 22]. As the range of the projectile directly affects its impact on the target, the drag coefficient is a crucial aerodynamic force coefficient in projectile design. This paper considers the engineering calculation error of the drag coefficient during the design process and conducts robust optimization on the pulse correction projectile. Using a combination of CFD simulations and wind tunnel experiments, the error range of the drag coefficient for a projectile was determined based on its original design as shown in Figure 4. The simulation software used is FLUENT V16.2 [34]. To ensure computational accuracy, the time step for solving was initially set at 1 \(\times\) 10\({}^{-6}\) s and eventually determined to be 1 \(\times\) 10\({}^{-5}\) s. Unstructured polyhedral grids were chosen for numerical calculations, and a density-based solver was employed. The far-field inflow was specified using the pressure far-field condition. In order to improve simulation accuracy, grid refinement was applied to regions such as the projectile head and tail where shock waves might occur. The size of the refined grids ranged from 0.5 mm to 4 mm, while the remaining parts of the projectile had a uniform grid size between 5 mm and 50 mm, with larger grid sizes in regions farther away from the projectile. The maximum value of Y+ was set to 0.96. As deterministic CFD simulations do not account for the random variations in the operating environment that can affect the performance of the aircraft, uncertainty quantification methods were employed to provide stochastic solutions for the variables of interest, thereby supporting the fine-tuning of the aircraft's shape, structure, and flight control system [35; 36; 37]. Hence, the uncertainty quantification is used for both the choice of the time step and the residual settings in the CFD simulations. To ensure the reliability of the CFD numerical calculation method, the study first examines grid independence (as shown in Figure 5 and Table 2). The results in Table 2 demonstrate that the simulated values of the drag coefficient \(C_{x}\) under different grid density schemes are highly consistent, confirming the reliability of the CFD numerical method. Additionally, the accuracy of the CFD calculation results is evaluated using wind tunnel experimental data. The experimental model involves a 1/4 scale model of the projectile. The experimental wind tunnel is a downdraft temporary impact closed high-speed wind tunnel, with an experimental section size of 0.3 m \(\times\) 0.3 m and a length of 0.6 m. The available Mach number range is 0.5-4.5. The model is supported and the angle of attack changes through the wind tunnel's angle of attack mechanism. A 6-component strain balance is used to measure the force and torque of the model along the three coordinate axes. The experimental Mach number \(Ma\) is 2, and the angle of attack varies from \(-4^{\circ}\) to \(8^{\circ}\). The experimental model installation diagram is shown in Figure 6. By comparing the CFD simulation values with the wind tunnel experimental values under the grid scheme 1 (\(Ma=2\)), the study evaluates the accuracy of the CFD calculation. As shown in Figure 7, the variation trend of the simulated and experimental values of the drag coefficient is generally consistent. Both increase nonlinearly with an increasing angle of attack, and the error between the two increases with an increasing angle of attack. The maximum relative error is approximately 0.02, indicating that the CFD numerical method can accurately solve the projectile's aerodynamic parameters. Furthermore, it can be used to evaluate the error between accurately calculated aerodynamic parameter values and those calculated using the PRODAS engineering algorithm. Figure 8 presents a comparison between the drag coefficient calculated using PRODAS and CFD at \(\delta\) = 0\({}^{\circ}\) for \(Ma\)\(\in\) 0.4-3.