## 3 Results and Discussion
### Effect of Impingement Hole  
#### 3.3.1 Effect of Impingement Hole Diameter  
5 kinds of impingement hole diameters including 4.8 mm, 6.0 mm, 7.2 mm, 8.4 mm and 9.6 mm are investigated in this part. Figure 7 shows the average Nusselt number of the upper and lower surfaces with various impingement hole diameters at \(Re=2\times 10^{3}\)-6 \(\times\) 10\({}^{4}\). When the impingement hole diameter is constant, the average Nusselt number of the upper and lower surfaces increases with the increase in the \(Re\). The increase in the \(Re\) indicates that the air jet velocity at the inlet of the impingement holes increases, the impact is more intense, and the \(Nu\) of the surfaces increases accordingly. Figure 5: Comparison of numerical simulation results of the average Nusselt number with experimental ones for the lower surface. (\(\overline{Nu}\) is the average Nusselt number of surface). Figure 6: Streamlines and \(Nu\) distribution with and without pin fins on the lower surface at \(Re=2\times 10^{3}\). In the range of 4.8 mm\(\sim\)9.6 mm, the larger the impingement hole diameter, the larger the average Nusselt number of the upper and lower surfaces. Among the five kinds of hole diameters studied, the impingement cooling effect with 9.6 mm is the best. When the impingement hole diameters are 6.0 mm, 7.2 mm, 8.4 mm and 9.6 mm, the average Nusselt number of the upper surface is increased by 22.3%, 24.2%, 86.6% and 123.6% compared with 4.8 mm. The average Nusselt number of the lower surface is increased by 19.3%, 46.2%, 79.6% and 104.3%, respectively. The increase in the impingement hole diameter leads to the reduction in the jet velocity, which makes the Nu decrease. However, when the impingement hole diameter increases, the coverage area of the impingement flow increases and the turbulence intensity in the impingement superposition region increases, which will improve the impingement cooling of the cavity. From the results, the influence of increasing the coverage area is greater than that of reducing the jet velocity. In addition, it is found that when \(Re\) and the impingement hole diameter are constant, the average Nusselt number of the lower surface is higher than that of the upper surface by comparing Figure 7a,b. Because the pin fins on the lower surface can directly improve the impingement cooling, while the upper surface is mainly cooled by air reflux. Figure 8A,B are \(Nu\) distribution of the upper and lower surfaces at \(Re=2\times 10^{4}\) under different impingement hole diameters. At the same \(Re\), the larger the impingement hole diameter, the larger the high \(Nu\) area, that is, the impingement cooling improves obviously. With the increase in the hole diameter, the maximum \(Nu\) on the lower surface increases, but the minimum decreases. When the hole diameter is 9.6 mm, the maximum \(Nu\) is 84.403 and the minimum \(Nu\) is 0.095. That is, there is almost no cooling and heat transfer in the local area, which may occur ablation. With the increase in the impingement hole diameter, \(Nu\) on the upper surface near the impingement holes increases significantly, while it is evenly distributed on the lower surface. Pin fins on the lower surface make the heat transfer more uniform, and the upper surface is smooth and unobstructed. The \(Nu\) of the cavity boundary area is small and the temperature is relatively high, where may produce local ablation. Figure 9a,b show the Nu distribution curves of the upper and lower surfaces along the proposed geometry at \(Re=2\times 10^{3}\) under the impingement hole diameter of 7.2 mm. In Figure 9a, on the upper surface, the air flow is reflected and diffused, the upstream region is directly impacted by the cooling air flow, the Nu in this region is high. Near the step and outlet, the turbulence intensity of air flow increases and the heat transfer is strengthened. In Figure 9b, on the lower surface, the heat transfer is more uniform on the lower surface than that on the upper surface because of the pin fins.