# Effects of Bulk Flow Pulsations on Film Cooling with Two Sister Holes
## 1 Introduction  
The efficiency of the gas turbine can be improved by raising the inlet temperature [1]. However, the turbine blade temperature should remain below the acceptable limit [2]. Film cooling is a widely used in gas turbines [3]. The physics of film cooling under a steady main flow has been widely investigated. Especially, intended vortex interactions could be induced between cooling jets by using specific cooling hole arrangements instead of the single hole. [PERSON] et al. [4] numerically showed that compared with a one-hole system, the use of three holes (a primary hole and two side holes) increased the film cooling effectiveness at \(M=1.0\). They also reported that manufacturing triple cylindrical holes was more economical than manufacturing holes with other shapes. Using square sister holes, [PERSON] et al. [5] controlled the vortex interactions between injectant and main flow at the blowing ratio, \(M\) of 0.5. They numerically found that two sister holes reduced the mixing between the coolant injectant and the crossflow, thereby increasing \(\eta\). [PERSON] et al. [6] numerically investigated the increase in \(\eta\) after forming two sister holes [3]. They varied the blowing ratio among the values 0.2, 0.5, 1.0, and 1.5 and reported an obvious improvement in \(\eta\) at high \(M\). [PERSON] et al. [7] numerically investigated performance of the film cooling for double holes by changing design variables such as the lateral ejection angles and streamwise and lateral distances between the holes. They found that the lateral distanceand lateral ejection angles significantly influenced the film cooling performance while the effect of the streamwise distance on the film cooling effectiveness was considerably less. [PERSON] et al. [8] determined the cooling performance of three types of sister hole configurations by using experimental and numerical methods. They stated that the effectiveness of the film cooling was considerably higher for the triple-hole configurations compared with that for a single-hole configuration under steady flow conditions. However, in real flow fields, the mainstream flow could be unsteady. It could be disturbed by many reasons such as potential flow interactions, and freestream turbulence generated in the combustor or passing wakes [9]. The effect of flow instabilities on the film cooling performance for the triple hole system has not been studied. Understanding the effect of main flow pulsation on the film cooling for the triple holes would help for making better cooling design of the gas turbine engines. [PERSON] et al. [10] observed that most previous computational fluid dynamics (CFD) studies on film cooling had been conducted under steady flow conditions. Few studies have considered the effect of pulsations, caused by flow instabilities, in the main flow. [PERSON] et al. [11] experimentally studied the effect of swirling flow in mainstream flow on \(\eta\). They showed that if the swirling number, which represents the axial flux of the swirl momentum, is increased, \(\eta\) decreases due to improved mixing between the main flow and cooling jet. [PERSON] et al. [12] studied the film cooling effect of a pulsating injectant by using experimental method, and they reported that steady coolant injection maximized \(\eta\)[2]. When the coolant injection was pulsed, \(\eta\) reduced with increase of Strouhal number at \(M=0.5\). [PERSON] et al. [13] reported that coolant pulsation can control the film cooling performance. To understand the physics in the pulsed film-cooling flow field, researchers have investigated the optimal parameter range of coolant pulsation. [PERSON] et al. [14] experimentally studied the effect of cooling jet pulsation on the film cooling in a turbine blade model. They found that jet propulsion weakened the jet liftoff at high blowing ratios, increasing the spread of the coolant on the wall.