# Aerodynamic Characteristics of Supersonic Rocket-Sled Involving Waverider Geometry
## 3 Results and Discussion
### The Flow Field Characteristics
The pressure contours of the area A in Figure 8d are similar to several \"crescent\" shapes due to the change in pressure. Then there is a large area of low pressure in the right of area B in Figure 8b; the lowest pressure drops below 0.5 atm, and this area looks like a \"triangle\". There may be two reasons for this special phenomenon: one is the reason mentioned above (the expansion of air flow), the other is that there are raised shapes on both sides of the waverider configuration, which will hinder the flow of air. This special shape causes the air flow to be compressed in the middle and to expand backward. Such a special flow pattern leads to the formation of a triangular low-pressure area. It is of note that the most important phenomenon occurs in Figure 8f, where the pressure on the lower surface is almost homogeneously distributed. This pressure distribution indicates that there is almost no shockwave oscillation on the lower surface of the RWRS. Therefore, no pressure fluctuation can be observed. This is the most intuitive representation of the waverider configuration controlling shock oscillations. In general, the friction of the bluff body comes from the attached flow before the boundary layer separation, while the friction behind the separation point is relatively small. The distribution of friction can be obtained by analyzing the surface friction coefficient \(C_{f}\), which is defined as follows:  
\[C_{f}=\frac{2\tau_{w}}{\rho_{\infty}U_{\infty}^{2}S_{ref}} \tag{19}\]  
where \(\tau_{w}\) is the frictional stress on the wall, \(\rho_{\infty}\) and \(U_{\infty}\) are the free-stream density and velocity, respectively. \(S_{ref}\) is the reference area; the projected area in the vertical direction is taken in this paper. Figure 9 shows the \(C_{f}\) distribution of the two configurations. It can be seen that the distribution on the upper and lower surfaces of ASRS is almost identical, except for a small increase in the A region of Figure 9c. This phenomenon indicates that  
Figure 8: Pressure \(p/p_{\infty}\) distributions on two rocket-sleds surface from different view: (**a**) side view of ASRS, (**b**) side view of RWRS, (**c**) top view of ASRS, (**d**) top view of RWRS, (**e**) upward view of ASRS, (**f**) upward view of RWRS. the \(C_{f}\) value will be affected when the reflected shockwave collides on the wall [55]. The distribution of RWRRS is quite different due to its special configuration. Near the leading edge line, the \(C_{f}\) value is very large, which is caused by the properties of the waverider. The leading edge of the waverider is extremely sharp and will split the air above and below. In region A of Figure 9b, a more prominent triangular region is observed which is seen in Figure 8d. However, the \(C_{f}\) distribution under RWRRS is more uniform, which is different from the upper side. These results reveal the ability of the waverider to split flow above and below, which can also be applied to control flow through ground effects. Limiting streamlines are often used to describe flow trends near a wall and to identify the location of flow separation [56; 57; 58]. Figure 10 compares the surface limiting streamlines on two rocket-sleds. It is observed that the air flow at the bottom of the ASRS flows outward due to the influence of reflected shockwaves, as shown in Figure 10c. However, the limiting streamlines on RWRRS are different. The limiting streamlines do not bypass the sides, but continue to flow streamwise, which suggests that the flow below RWRRS is less disturbed. To observe the shockwave evolution process in the flow field more directly, we output the partial derivative of the density of air along the direction of the coming flow, namely \(\partial\rho/\partial y\). In Figure 11a, we see that, in the initial stage of shockwave formation, the cross section of the shockwave looks like an annulus. Since the shockwave had not moved to the ground at this time, it can develop freely in all directions.