## 1 Introduction  
An increase in hot gas inlet temperature is helpful for turbine efficiency improvement and energy-saving. The significantly curved leading edge bears the highest thermal load in turbine blades. Jet impingement has the maximum heat transfer rate among all the single-phase heat transfer processes. Therefore, when faced with a much higher cooling standard, a good choice is jet impingement cooling, which is widely used in the leading edge of blades. A lot of studies dealing with experimental and computational methods on fluid flow and heat transfer behavior of impinging jets on a concave surface have been reported in the literature. [PERSON] et al. [1] quantified the heat transfer characteristics of jet plates with different thicknesses for simulating the heat transfer in the leading edge of gas turbine blade. The results showed that the \(Nu\) changed slightly in the stagnation region of the target surface with different thicknesses. The contraction effect of the hole cavity can be minimized when the inlet of the jet is rounded, which causes a more symmetrical jet. Racetrack shaped jets can enhance heat transfer compared with round jets. [PERSON] et al. [2]investigated the heat transfer mechanism of the impinging jet on a concave surface with \(Re\) = 12,000-20,000 and three different nozzle positions (\(E/d\) = 0, 0.5, and 1.0). Their results showed that heat transfer characteristics of tangential jet impact depended on \(Re\) and nozzle position. [PERSON] et al. [3] analyzed heat transfer performance of jets on concave target surfaces with different cooling hole diameters, including 0.4\(D\), 0.6\(D\), 0.8\(D\), and 1.0\(D\) (\(D\) = 10 mm). Through evaluating and comparing moderate \(Re\) and \(Nu\) distribution, they found that heat transfer performance was largely determined by the diameter and location of the cooling holes. [PERSON] et al. [4] investigated the effect of different jet arrangements on a flow and heat transfer at \(Re\)= 10,000-40,000, a jet-to-target spacing of 1 and relative surface curvature of 10. They pointed out that both inline and staggered cases could enhance heat transfer uniformity compared with the array jet. Curved surface-averaged \(Nu\) increased when the jet-to-jet spacing was in an inline arrangement. [PERSON] and [PERSON] [5] applied a new structure of jet cooling in the leading edge of gas turbine blade. They studied the effect of concave target surfaces with different curvature radiuses on cooling performance. In the available reported studies, most of the nozzles used in impinging jets on a concave surface are the conventional smooth circular holes or slots with non-swirling case, while the common features of impinging jets issuing from the conventional holes/slots include very high local convective heat transfer at the stagnation point and a rapid decay of heat transfer along the radial direction on the target wall. That is, conventional impinging jets induce a non-uniform radial heat transfer, leading to a non-uniform temperature distribution along the target surface. At the same time, the curved configuration of the leading edge exacerbates the non-uniform heat transfer. The thermal stress caused by temperature differences is high enough to cause structural damage, which weakens device security. Therefore, it is essential to develop a new cooling method that can not only enhance heat transfer, but also make a more uniform cooling on the target surface. [PERSON] et al. [6] analyzed the cooling performance of the cooling chamber of the leading edge of a gas turbine. They found the swirling flow existing in the cooling chamber could improve the cooling efficiency, and a larger ratio of swirl chamber radius to jet slot height and a larger Reynolds number could enhance the cooling performance on the leading edge of a gas turbine, though the pressure loss of the swirl chamber is increased. [PERSON] et al.