## 3 The Results of the Plates with Riblets and Grooves
In the range of 0.3 Ma to 0.6 Ma, except for the circular grooves structure, the pressure resistance of other grooves structures is smaller than that of the riblets structures, and the circular grooves structures has the largest pressure resistance coefficient, which is due to the largest part of pressure difference located at the top of the groove or riblet. The angle between the normal wall of the top of the circular groove and the horizontal direction is small, which causes the horizontal component of the wall pressure to increase. When the speed increases to 0.7 Ma and 0.8 Ma, the flow enters transonic flow, and the riblets have a greater disturbance to the incoming flow, and the increase in speed will increase the pressure on the windward side of the riblet. Since the protrusions compress the airflow channel, the airflow is accelerated at the top of the trapezoid, which reduces the pressure on the leeward side, and the pressure difference between the two sides of the trapezoidal riblet increases, resulting in the largest total pressure resistance of the trapezoidal riblets structure among these different geometry models. In general, the geometry \begin{table}
\begin{tabular}{c} **Trapezoidal** \\ **Protrusion** \\ \end{tabular} \\ \hline
**Ma** & \(C_{f}10^{-3}\) & \(C_{f}10^{-3}\) & \(\eta\) & \(C_{f}10^{-3}\) & \(\eta\) & \(C_{f}10^{-3}\) & \(\eta\) & \(C_{f}10^{-3}\) & \(\eta\) & \(C_{f}10^{-3}\) & \(\eta\) \\ \hline
0.3 & 6.83 & 4.95 & 27.62\% & 1.73 & 74.66\% & 2.20 & 67.80\% & 1.64 & 76.02\% & 3.70 & 45.89\% \\ \hline
0.4 & 5.56 & 2.37 & 57.37\% & 1.29 & 76.87\% & 1.85 & 66.68\% & 1.16 & 79.07\% & 2.93 & 47.29\% \\ \hline
0.5 & 4.46 & 3.60 & 19.18\% & 0.99 & 77.79\% & 1.57 & 64.73\% & 0.92 & 79.28\% & 2.40 & 46.25\% \\ \hline
0.6 & 3.97 & 3.47 & 12.41\% & 0.77 & 80.59\% & 1.32 & 66.60\% & 0.71 & 82.02\% & 2.57 & 35.19\% \\ \hline
0.7 & 3.49 & 2.86 & 18.10\% & 0.62 & 82.24\% & 0.82 & 76.63\% & 0.59 & 82.98\% & 1.84 & 47.24\% \\ \hline
0.8 & 3.14 & 2.60 & 17.00\% & 0.53 & 83.21\% & 0.68 & 78.18\% & 0.46 & 85.16\% & 1.62 & 48.42\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Friction coefficient and drag reduction rate of different riblets and grooves with different Mach number. speed has a greater influence on the pressure resistance at subsonic, and the speed has a greater influence at transonic. In order to further analyze the mechanism of the reduction of the frictional resistance of the lateral riblets and grooves, the shear stress at the wall surface of each riblet plate at different speeds was analyzed, as shown in Figure 4. In general, the shear stress increases with the increase of the flow velocity. The change of the shear stress in each riblet or groove is very similar, so the shear stress changes periodically in the direction of the incoming flow in the riblets and the grooves. The shear stress in the riblets and grooves is negative, which indicates that the direction of the shear stress has changed, and the direction of flow has changed in the grooves. It can be seen that the location of high shear stress is located on the windward side of the riblets and grooves. Among these different shaped riblets and grooves, there is a high shear stress at the windward edge of the first convex of the triangular protrusion riblets and trapezoidal protrusion riblets, and the shear stress at the subsequent windward edge gradually increased along the flow direction. A large shear stress will be applied between the windward side and the leeward side in the plate with trapezoidal protrusion riblets. This is because the incoming flow on the upper bottom of the trapezoidal protrusion acts similarly to the effect of the smooth flat plate. The change of the shear stress of the plate with circular concave grooves in the grooves is smoother, and the shear stress of the riblets and grooves on the windward side is very small. The variation of the shear stress in the trapezoidal depression is more sufficient than that of the triangular depression, and the negative direction value of the shear stress is also larger.