# Numerical Study on Cooling Performance of a Steam-Cooled Blade Based on Response Surface Method
## 1 Introduction  
Gas turbines are widely used in energy and defense fields such as power generation and mechanical drives, representing high-end core technology power equipment for national security and overall economic development [1]. With the increasing requirements for gas turbine performance in various industries, improving the performance of gas turbines has become an urgent problem at this stage, and one of the most effective methods is to increase the turbine rotor inlet temperature. The increasing turbine inlet temperature will pose a greater challenge to the life and safety of turbine blades [2]. Therefore, many experts and scholars have conducted comprehensive research on the cooling technology of high temperature turbine blades of advanced gas turbines [3; 4; 5]. At present, with the development of computational fluid dynamics and computer technology, the conjugate heat transfer numerical analysis method has been able to satisfy mostof the heat transfer studies [6]. The blade experiments face difficulties such as expensive cost and difficult to guarantee the measurement accuracy, so the use of numerical methods to supplement the blade experiments and the investigation of the cooling mechanism will be one of the effective ways for the development of turbine blade cooling technology in the future. Many domestic and foreign experts and scholars have carried out numerical research on the cooling performance of the blade. [PERSON] et al. [7] used the conjugate heat transfer method to predict the flow and heat transfer characteristics of NASA turbine blades under three operating conditions, and the results showed that the conjugate heat transfer method can be a feasible tool for turbine blade heat transfer analysis and cooling structure design. [PERSON] et al. [8] showed that the calculation results of conjugate heat transfer analysis are more accurate than those of un-conjugate heat transfer because the conjugate heat transfer fully takes into account the effect of the distribution of solid surface temperature on the fluid thermal boundary layer. [PERSON] et al. [9] investigated the cooling performance of turbine blade coated with thermal barrier using the conjugate heat transfer numerical method, and the results showed that the conjugate heat transfer numerical method can better predict the heat transfer coefficient of the blade surface and its internal temperature, etc. The results of [PERSON] et al. showed that the conjugate heat transfer numerical method predicted the blade temperature field very well [10]. [PERSON] et al. [11] used the conjugate heat transfer method to analyze the temperature and flow field distribution on the surface of turbine blades with thermal barrier coating for various turbulence models, and the results showed that the calculated results obtained by the conjugate heat transfer numerical method were in good agreement with the experimental results. In recent years, machine learning methods have been gradually applied to cooling performance prediction of blades and cooling structure optimization of blades due to their excellent performance [12; 13]. [PERSON] et al. [14] numerically investigated the effects of injection angle, mass flow rate, diameter and position on the cooling efficiency of a gas turbine using the response surface method, and explored the sensitivity of the input parameters. [PERSON] et al. [15] used response surface model to investigate the optimal width and location of air film holes in a turbine blade and analyzed the significance of the effects of eight design variables on blade performance. [PERSON] et al. [16] used the response surface method to determine the optimal location of a solar collector when a gas turbine system was at maximum net power, minimum CO\({}_{2}\) emissions, and maximum energy efficiency. [PERSON] et al.