## 3 Results and Discussion
### Effect of Impingement Hole
#### 3.3.2 Effect of Impingement Hole Number  
9 kinds of impingement hole numbers including 1, 2, 4, 6, 8, 10, 12, 14 and 16 are investigated in this part. The average Nusselt number of the lower surface under various impingement hole numbers at \(Re\) = 2 \(\times\) 10\({}^{3}\)-6 \(\times\) 10\({}^{4}\) is shown in Figure 11. In the range of 1-16, the more the impingement hole number, the larger the average Nusselt number of the lower surface. Since the distribution area of the impingement hole is fixed, the range of hole number arranged is limited. The impingement cooling effect with 16 is the best among nine kinds of hole numbers. When the impingement hole number are 2, 4, 6, 8, 10, 12, 14 and 16, the average Nusselt number of the lower surface are increased by 53.1%, 143.7%, 230.8%, 309.8%, 362.7%, 397.4%, 436.5% and 553.9% compared with one impingement hole.  
Because the impingement holes are distributed in the fixed area, the increase in the number of impingement holes increases the coverage area of the cooling jet and makes the heat transfer more uniform, which improves the overall heat transfer effect.  
Figure 12 is \(Nu\) distribution of the lower surface at \(Re\) = 2 \(\times\) 10\({}^{4}\) under different impingement hole numbers.  
Figure 10: Comparison of frictional resistance under various impingement hole diameters.  
At the same \(Re\), the more the impingement hole number, the more uniform the \(Nu\) distribution and the larger the high \(Nu\) area, that is, the impingement cooling improves obviously. The maximum \(Nu\) on the lower surface increases with the increase in the hole number. When the hole number is 16, the maximum \(Nu\) is 68.362. The minimum \(Nu\) is 0.002 when there is one impingement hole, that is, there is basically no cooling and heat transfer in some parts where may produce local ablation. When the number of impingement holes is little, the local temperature is easy to be too high, resulting in local ablation.  
Figure 13 is a comparison of frictional resistance under various impingement hole numbers. The more the impingement hole number, the greater the flow resistance. The \(Re\) has little effect on the flow resistance when the impingement hole number is little. The pressure drop of the impingement cavity with one impingement hole is the smallest. Compared with it, the flow resistance with the hole number of 2, 4, 6, 8, 10, 12, 14 and 16 are increased by 3.95%, 22.9%, 52.4%, 92.7%, 141.5%, 200.8%, 258.9% and 444.2%, respectively.  
Figure 11: Comparison of the average Nusselt number of the lower surface under various impingement hole numbers.  
Figure 12: \(Nu\) distribution of the lower surface under different impingement hole numbers at \(Re=2\times 10^{4}\).  
The average Nusselt number of the lower surface with 14 impingement holes increases by 436.5% compared with one impingement hole. That with 14 impingement holes decreases by 17.9% compared with 16 impingement holes. The flow resistance of the impingement cavity with 14 impingement holes is 258.9% higher than that with one impingement hole. That with 14 impingement holes is 31.9% lower than that with 16 impingement holes. Considering the heat transfer and pressure drop, the number of the impingement hole can be selected as 14.