# Aerodynamic Study of the NASA's X-43A Hypersonic Aircraft
## 4 Results
### CFD Cases  
Case 1 is initially presented with the variation of the pressure field throughout the aircraft at a zero angle of attack in Figure 10a. Since \(AoA<\alpha_{1}\), a shock wave is produced at the beginning of the extrados where, consequently, the pressure is increased and remains approximately constant along the surface. This phenomenon is also present in the aircraft nose (stages 2 and 3); in case of stage 3, the increase of pressure is more significant due to the difference in the design angles (\(\alpha_{3}>>\alpha_{1}\) & \(\alpha_{2}\), see Table 3). Figure 6: Variations of the aerodynamic parameters due to the modifications in \(\alpha_{1}\), (**a**) \(C_{L}\) vs. \(AoA\), (**b**) \(C_{D}\) vs. \(AoA\), (**c**) \(E\) vs. \(AoA\), (**d**) \(C_{M_{C}}\) vs. \(AoA\). Figure 7: Variations of the aerodynamic parameters due to the modifications in \(\alpha_{2}\), (**a**) \(C_{L}\) vs. \(AoA\), (**b**) \(C_{D}\) vs. \(AoA\), (**c**) \(E\) vs. \(AoA\), (**d**) \(C_{M_{C}}\) vs. \(AoA\). Figure 10b shows that shock waves of stages 1 and 2 are completely attached to the sharp leading edge of the wedge. This fact is given because of the high Mach number where X-43A flies and the small wedge angle that presents at the leading edge. X-43A uses the fuselage nose part to form the shock in front of the intake. Theoretically (according to the analytical model), the aircraft should fly with the nose optimised configuration under those conditions of design angles and \(AoA\). Notice that in this case a different colour scale has been used to represent this phenomenon. Focusing on Figure 10c,  
Figure 8: Variations of the aerodynamic parameters due to the modifications in \(\alpha_{3}\), **(a)**\(C_{L}\) vs. \(AoA\), **(b)**\(C_{D}\) vs. \(AoA\), **(c)**\(E\) vs. \(AoA\), **(d)**\(C_{M_{C}}\) vs. \(AoA\). Figure 9: Variations of the aerodynamic parameters due to the modifications in \(\alpha_{4}\), **(a)**\(C_{L}\) vs. \(AoA\), **(b)**\(C_{D}\) vs. \(AoA\), **(c)**\(E\) vs. \(AoA\), **(d)**\(C_{M_{C}}\) vs. \(AoA\). shock 2 (which is the one formed at the beginning of stage 2) is focused on the tip of the lower edge, while shock 3 (the one that corresponds to the shock wave created at the beginning of stage 3) is slightly deflected into the entrance of the throat. Inside the scramjet, different things occur together (see Figure 10d for more detail). On the one hand, the flow expands as a Prandtl-Meyer expansion wave being produced at the end of stage 3. As a result, there is a small region situated in the upper left side in which the pressure decreases from that of the previous stage. On the other hand, shock 3 reflects from the lower edge generating a new shock, which, in turn, reflects from the upper edge forming, once again, another shock wave. In other words, two regular reflections in steady flow inside the engine are created. The first reflection leads to a high pressure region downstream at about 25 kPa, while the pressure after the second reflection is 15 kPa approximately. These differences are caused by the incident pressure of each reflection shock (the one of the first reflection shock is bigger than that of the second reflection shock) which, overall, translates into an energy dissipation of these reflection shock waves along the scramjet. In addition to that, after the first reflection, the flow is theoretically parallel to both wedges. This phenomenon is known as the shock diamond and provides some regions with strong adverse pressure gradients which induce flow separation. Finally, at the end of the upper right side of the scramjet, a Prandtl-Meyer expansion wave is originated. The pressure decreases and remains constant along the surface all the way to the trailing edge; there, the expansion process is so drastically that the pressure goes down to 20 Pa approximately, which enables the creation of some vortex. Overall, all the waves originating along the aircraft are dissipated slowly downstream until the outlet boundary section.