## 1 Introduction  
In order to improve thermal efficiency, the gas inlet temperature of a gas turbine is continuously improved. However, the super-high temperature resistance of the material is limited, and the research on advanced cooling methods has lower cost and is less time-consuming than the development of vane materials with ultra-high temperature resistance, therefore, turbine vane cooling technology has become one of the hot spots in the field of gas turbine research. Jet impingement cooling is one of the most effective heat transfer enhancement technology, which is commonly used in gas turbine vane cooling, especially for the pressure side of turbine vane [1]. There are many factors affecting the flow and heat transfer of impingement cooling. In order to meet the different requirements, the heat transfer capacity can be further enhanced by changing the parameters of the impingement hole, increasing the vortex and other methods to improve the jet intensity [2]. The methods to study the flow and heat transfer of impingement cooling include numerical simulation, experiment and the combination of the above two. [PERSON] et al. [3] introduced the research progress of numerical simulation for impingement cooling. At present, Reynolds-averaged Navier-Stokes model is mostly used to analyze the flow and heat transfer of gas turbine vane cooling, because its computational effort is little. [PERSON] et al. [4] found that the average surface heat transfer coefficient of concave and convex target plates is significantly larger than that of flat target plate, but in the stagnation region of the impinging jet, the average surface heat transfer coefficient of flat target plate is better than concave one. [PERSON] et al. [5] studied the effect of the plate thermal conductivity on the heat transfer coefficient of the impingement cooling system. There is a weak relationship between the heat transfer coefficient and the plate thermal conductivity. During the heating process, the heat transfer coefficient remains almost constant. [PERSON] et al. [6] simulated the flow and heat transfer of turbine vane leading edge by array jet impingement cooling, and found that increasing the hole diameter ratio and reducing the hole spacing ratio can effectively improve the comprehensive heat transfer coefficient of vane leading edge impingement cooling. [PERSON] et al. [7] investigated the effect of the jet diameter on the impingement cooling flow and heat transfer at the leading edge of the turbine vane. At a fixed Reynolds number, the wall heat transfer coefficient increases as the jet diameter increases. [PERSON] et al. found that the Nusselt number \(Nu\) of the effective cooling zone first increases and then decreases with the increase in jet hole diameter [8], and staggered arrangement of jet holes and film holes can improve the heat transfer of the effective cooling zone [9]. [PERSON] et al. [10] studied the influence of the relative position of impingement holes and effusion holes on the impingement cooling, and staggered rows of holes have larger overall cooling efficiency than stacked rows of holes. [PERSON] et al. [11] simulated the different heat transfer patterns of the jet impingement on the semicircular surface. The average temperature of the center jet surface is lower than that of the side jet, but the \(Nu\) distribution of the center jet surface is smoother, and the maximum \(Nu\) is near the impingement point. [PERSON] et al. [12] found that the \(Re\) of jet and nozzle diameter determine the thermal convection resistance, and the plate material and thickness determine the transverse heat conduction resistance, thus affecting the cooling effect. [PERSON] et al. [13] simulated the flow and heat transfer of jet impingement cooling system under different jet \(Re\), velocity ratio and channel height. The results show that when the \(Re\) and velocity ratio increases and the channel height decreases, the \(Nu\) and total entropy production increase. [PERSON] et al.