# Numerical Study on Cooling Performance of a Steam-Cooled Blade Based on Response Surface Method
## 5 Conclusions  
In this paper, the cooling performance of the steam-cooled blade, including cooling efficiency, temperature non-uniformity and dimensionless temperature, was studied numerically using experimental design and response surface model, and the relevant empirical formulas were fitted. The main conclusions are as follows:  
Figure 21: The factor effect diagram of \(\eta_{\rm ave}\): (**a**) Pareto effect diagram; (**b**) Normal effect diagram.  
Figure 19: The factor effect diagram of \(\varepsilon_{\rm ave}\): (**a**) Pareto effect diagram; (**b**) Normal effect diagram.  
(1) The empirical formulas obtained using the experimental design and response surface model have high accuracy, and the \(RMSE\) of the response surface model are all less than 0.01 and the \(R^{2}\) are all greater than 0.99 when the responses are the average cooling efficiency, temperature non-uniformity and average dimensionless temperature of the blade, respectively.  
(2) The influence of the mainstream inlet temperature on the cooling performance of the steam-cooled blade is not significant, and the influence of the mainstream outlet pressure is also small. When the pressure increases from 120 kPa to 160 kPa, the average cooling efficiency of the steam-cooled blade decreases by 3.29%, the temperature non-uniformity decreases by 1.03%, and the average dimensionless temperature increases by 0.52%.  
(3) When the mainstream inlet to outlet pressure ratio, temperature ratio and flow ratio of steam to mainstream vary from 1.3-1.5, 0.6-0.7 and 3-8, respectively, the average cooling efficiency of the steam cooled blade increases by 5.92%, 7.35% and 26.51%, respectively; the average dimensionless temperature decreases by 0.93%, increases by 3.74% and decreases by 3.71%, respectively; the temperature non-uniformity decreases by 4.09%, 30.08% and improves by 37.99% respectively.  
(4) Under the same working conditions, the steam-cooled blade has higher cooling efficiency and lower dimensionless temperature compared with the air-cooled blade, but at the same time the former has higher temperature non-uniformity than the latter. In the research working condition parameter range, the average cooling efficiency of the former is about 14.06-17.81% higher than that of the latter, the average dimensionless temperature is about 1.86-2.58% lower, and the temperature non-uniformity is about 18.47-29.01% higher.  
Conceptualization, Z.Z. and L.X. ([PERSON]); methodology, Z.Z. and L.X. ([PERSON]); software, Z.Z.; validation, Z.Z., L.X. ([PERSON]).; formal analysis, Z.Z. and J.G.; investigation, Z.Z. and Y.L.; resources, Z.Z., L.X. ([PERSON]) and J.G.; data curation, Z.Z. and Y.L.; writing--original draft preparation, Z.Z. and L.X. ([PERSON]); writing--review and editing, L.X. ([PERSON]), Z.Z. and L.X. ([PERSON]); visualization, L.X. ([PERSON]) and Z.Z.; supervision, L.X. ([PERSON]) and J.G.; project administration, J.G.; funding acquisition, L.X. ([PERSON]). All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Project Supported by Natural Science Basic Research Plan in Shaanxi Province of China (2022)Q-545), the Project funded by China Postdoctoral Science Foundation (2021M702573) and the National Natural Science Foundation of China (51876157).  
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Written informed consent has been obtained from the patient(s) to publish this paper.  
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The authors declare no conflict of interest.