# Aerodynamic Study of the NASA's X-43A Hypersonic Aircraft
## 4 Results
### CFD Cases
Finally, the increase of the \(AoA\) also produces an increase of the pressure gradients inside the scramjet in addition to a higher curvature of shock 3 and the waves created at the trailing edge. Figure 11: Density field (**a**), temperature field (**b**), Mach field (**c**) and \(y^{+}\) distribution along the walls (**d**) of case 1 for \(AoA=0^{\circ}\). For \(AoA=4^{\circ}\) (Figure 14), the aircraft can be considered to fly with the nose optimised configuration since the oblique shock wave formed at the beginning of stage 3 is focused on the tip of the lower edge of the scramjet. The pressure field of the other two CFD cases studied, case 2 and case 3 defined in Table 3 for \(AoA=0^{\circ}\), is presented in Figure 15. Case 2 was designed to fly with the nose optimised configuration for \(AoA=0^{\circ}\) as seen in Figure 15a. In addition to that, the design angles \(\alpha_{1}\) and \(\alpha_{4}\) were slightly reduced from case 1 in order to have a better aerodynamic performance according to the results obtained of the analytical model, see Figures 6 and 9; the maximum reached pressure (situated in the lower edge of the scramjet) is about 22 kPa instead of the 25 kPa observed in case 1 which, in the end, translates into a higher lift. Case 3 was not only created to improve the aerodynamics of the aircraft by reducing \(\alpha_{1}\) and \(\alpha_{4}\) from case 1, but also to avoid the drastic expansion and, consequently, an extremely low pressure and velocity and a high temperature at the trailing edge by eliminating its surface. In this case, for \(AoA=0^{\circ}\), shock 3 is slightly deflected into the entrance of the throat as seen in Figure 15b. Furthermore, it was seen that the aircraft flew with the nose optimised configuration for \(AoA=4^{\circ}\) (this corresponding simulation is not presented in the study). The maximum pressure  
Figure 14: Tip of the lower edge of the scramjet of case 1 for \(AoA=4^{\circ}\). Figure 12: Pressure field (**a**) and density field (**b**) of case 1 for \(AoA=14^{\circ}\). Figure 13: Temperature field (**a**) and Mach field (**b**) of case 1 for \(AoA=14^{\circ}\). is focused along the scramjet and is about 27 kPa. Furthermore, as the surface of the trailing edge is eliminated, the drastic expansion is not observed as in the other cases. The integral aerodynamic characteristics \(C_{L}\), \(C_{D}\), \(E\) and \(C_{M_{CG}}\) in terms of the angle of attack for the three CFD cases are shown in Figure 7:0 As seen in Figure 16a, case 3 has the highest lift coefficient until \(AoA=6^{\circ}\), where it is approximately the same as that of case 2. Case 1, however, has the lowest lift coefficient with a negative lift coefficient for \(AoA=0^{\circ}\). According to Figure 16b, case 1 has the highest drag coefficient up to \(AoA=2^{\circ}\), where the first place is replaced by case 3, and case 1 has a very similar drag coefficient as case 2. The combination between the lift and drag coefficients leads to the aerodynamic efficiency in terms of the \(AoA\) (Figure 16c). Both cases 2 and 3 have a similar \(E\); the aerodynamic efficiency of case 3 is higher for \(AoA=[-4,\ -2,\ 0,\ 2]^{\circ}\) and lower for the other angles of attack. Therefore, according to this graph, the maximum aerodynamic efficiency of case 2 is the highest one (\(E_{max}=3.52\) for \(AoA=6^{\circ}\)), followed by the one in case 3 (\(E_{max}=3.28\) for \(AoA=6^{\circ}\)) and finally case 1 (\(E_{max}=3.09\) for \(AoA=8^{\circ}\)). In addition, from \(AoA=10^{\circ}\), all cases seem to converge to a certain value. Finally, the behaviour of the pitching moment coefficient through the different angles indicates a longitudinal instability condition with regard to any perturbation of the \(AoA\) (Figure 16d); cases 1 and 2 are mostly similar according to this graph, while case 3 has the highest pitching moment coefficient for \(AoA=[-4,\ -2,\ 0]^{\circ}\) and the lowest one for the other angles of attack.