I. Introduction mproving the aero engine efficiency requires higher turbine inlet temperature which has reached greater values than blade and vane materials can withstand. In response to this problem, cooling schemes such as jet impingement, ribs, pin fins and film cooling have been employed to help increase the engine component life and overall efficiency. Film cooling is a topic that has been used extensively in modern aero engines for cooling hot section components. With film cooling, relatively cooler air forms a thin protective film on the outer surface of the blade, creating an additional layer of resistance between the hot gas and the blade. Bunker [1] provided a comprehensive introduction on the development and importance of the film cooling. It has been demonstrated that film cooling is an effective means for maintaining acceptable airfoil metal temperature and providing prolonged turbine life. There have been numerous studies that focus on film cooling over flat surfaces and turbine blade. Although the film cooling technology has been fully developed in recent years, complex engine conditions still require engineers to get more cooling knowledge.

One of the earliest studies on film cooling is that by Wieghardt [2]. In that study, film cooling was used on airfoil to anti icing so that the secondary gas was actually hotter than the primary gas. Then this technique was applied in the combustor of turbine engine. The geometric parameter of the film hole is the key factor affecting the film cooling characteristics. In the 60s, Goldstein [3] researched the ideal forms of 2D layer film cooling. Then the louvered and shingled combustor film cooling was considered to be useful because they are close to the ideal slot. In an effort to obtain higher cooling performance, the shape of film cooling evolved from slot to single hole and then shaped hole [4]. Different film-cooling hole shapes are used to keep the jet attached to the surface over a range of blowing ratios. Most of the shaped hole outlets are expanded in the spanwise direction or flow direction which can lead to a better attachment on the surface. Guo et al.[5] investigated the cooling characteristics on a fully cooled guide vane with fan-shaped holes in a transonic annular cascade. They found that fan-shaped holes had a higher level of film-cooling effectiveness than cylindrical holes on the suction side. Furthermore, for the initially downstream of the hole on the pressure side, the fan-shaped hole had a better cooling characteristic than the cylindrical hole. But the fan-shaped hole had a much faster decay of film-cooling effectiveness than the cylindrical hole on the pressure side. Liu [6] utilized thermochromic liquid crystal technique to measure the leading edge film cooling effectiveness between cylindrical and laid-back holes. The aerodynamic parameters such as the blow ratio, turbulence intensity, pressure gradient and momentum ratio are also the main factors affecting the film cooling characteristics. Dittmar et al.[7] made comparisons about the film cooling effectiveness between the double-row cylindrical holes and single-row fan-shaped holes on a turbine blade pressure side. Their results showed that the cooling effect was equivalent in low blowing ratio. But in high blow ratio, the single-row fan-shaped holes had a better cooling effect than the double-row cylindrical holes. Thole et al.[8] investigated the effect of momentum ratio on the film cooling efficiency, and found that momentum ratio best scaled the characteristics of the thermal field. In the experiments, the film cooling jets were found to remain attached to the surface when I< 0.4; to detach and then reattached to the surface when 0.4< I< 0.8; to detach and …