# Numerical Study on Cooling Performance of a Steam-Cooled Blade Based on Response Surface Method
## 3 Effect of Working Parameters on the Cooling Performance of the Blade
### Influence of Flow Ratio of Steam to Mainstream  
Figure 16 provides the effect of the flow ratio of steam to mainstream multiplied by 100, i.e., \(M_{\rm r}\) on the cooling efficiency of the steam-cooled blade, as shown in Figure 16a-c, when \(M_{\rm r}\) is 3, the cooling efficiency distribution on the surface of the steam-cooled blade is in the range of 0.22-0.53; when \(M_{\rm r}\) is 5.5, the cooling efficiency distribution on the surface of the blade is in the range of 0.24-0.62; when \(M_{\rm r}\) is 8, the cooling efficiency distribution on the surface of the blade is in the range of 0.26-0.67. The minimum cooling efficiency of the steam-cooled blade surface increases from 0.22 to 0.26, and the maximum cooling efficiency increases from 0.53 to 0.67, which indicates that the increase of flow ratio of steam to mainstream will greatly improve the cooling efficiency of the steam-cooled blade, which is due to the cooling airflow will carry more heat with the increase of steam flow. At the same time, this will make the temperature distribution of the blade surface more uneven. When the flow ratio of steam and mainstream increases, the cooling efficiency of the steam-cooled blade surface increases, and the increase of the flow ratio of steam and mainstream has the greatest effect on the cooling efficiency of the leading edge of the blade, followed by the mid-chord area and trailing edge of the blade. After calculation, it can be seen that when \(M_{\rm r}\) increases from 3 to 8, the average cooling efficiency of the steam-cooled blade increases by 26.51%, and the temperature non-uniformity increases by 37.99%. From Figure 16d, it can be seen that the average cooling efficiency of the steam-cooled blade is about 14.12-17.72% higher than that of air-cooled blade under different flow ratios of steam to mainstream, which is about 15.68% higher on average; the temperature non-uniformity of the former is about 18.47-29.01% higher than that of the latter, which is about 22.91% higher on average. Figure 15: Influence of mainstream inlet temperature on dimensionless temperature distribution: (a) \(T_{\rm r}\) = 0.6; (b) \(T_{\rm r}\) = 0.65; (c) \(T_{\rm r}\) = 0.7; (d) Variation law of the mean value. Figure 17 provides the effect of steam-cooled blade dimensionless temperature distribution under different flow ratio of steam to mainstream. It can be seen from Figure 17a-c that when the flow ratio of steam to mainstream is multiplied by 100, i.e., \(M_{\rm r}\) is 3, the dimensionless temperature distribution on the blade surface is 0.81-0.93; when \(M_{\rm r}\) is 5.5, the dimensionless temperature distribution on the blade surface is 0.76-0.92; when \(M_{\rm r}\) is 8, the dimensionless temperature distribution on the blade surface is 0.76-0.91. This indicates that the increase of the flow ratio will greatly reduce the dimensionless temperature on the surface of the steam-cooled blade, and when \(M_{\rm r}\) increases, the dimensionless temperature on the surface of the steam-cooled blade has a large reduction. In the relative axial chord lengths of 0.55, 0.05, and 0.9, the dimensionless temperature of the steam-cooled blade decreases by about 4.7%, 4.2%, and 1.5%, respectively. This indicates that the increase in \(M_{\rm r}\) has the greatest effect on the dimensionless temperature in the chord region of the steam-cooled blade, followed by the leading and trailing edge of the blade. After calculation, it can be found that when \(M_{\rm r}\) increases from 3 to 8, the average dimensionless temperature of the steam-cooled blade decreases by 3.71%. From Figure 17d, it can be noted that the increase of flow ratio of steam to mainstream decreases the average dimensionless temperature of both air-cooled and steam-cooled blades, but the former is lower than the latter by about 2.12-2.19% at the same flow ratio, and the average is about 2.16% lower.