The Brayton cycle demonstrates that gas turbine efficiency can be increased by increasing the inlet temperature [
1]. The temperature of the blade surface should be kept below the acceptable limit to prevent excessive thermal stress. The cooling air is injected through small holes on the blade surface, and it protects the wall from hot main flow by reducing the wall temperature. The investigation of the film cooling performance using numerical methods such as Reynolds-averaged Navier–Stokes simulation (RANS), large eddy simulation (LES), or detached eddy simulation (DES) costs less than experiments. The LES predicts the mixing between the cross flow and injectant better than the RANS approach, even though its computation time is significantly longer [
2,
3,
4]. Numerous CFD studies have attempted to understand the film cooling physics when the cross flow is steady.
In a numerical study under the steady state, Walters and Leylek (2000) employed the standard
k–ε model for a three-dimensional (3-D) unstructured mesh to simulate film cooling on a flat plate [
5]. They determined that the model did not well predict the reattachment of the coolant in the narrow field at high blowing ratios. Moreover, they stated that the RANS results overpredicted
ηc and displayed less lateral coolant spreading on the wall. The effectiveness,
η, is defined in Equation (1).
where
Taw is the adiabatic wall temperature,
TG represents the main flow temperature, and
TC is the coolant temperature. Furthermore, Tyagi and Acharya (2003) conducted LES for film cooling simulations [
6]. They employed a dynamic mixed model and applied the velocity profiles obtained by RANS to the hole inlet. They stated that the LES better predicted
η than RANS; this is since LES can predict the coherent structures of the film cooling. Rozati and Tafti (2007) studied the influence of the freestream turbulence on film cooling using LES [
7]. They found the counter rotating vortex pair (CRVP) and showed that the fully turbulent jet decreased
η by increasing the mixing with the cross flow. Na et al. (2007) demonstrated that a ramp installed upstream of the hole can increase
η since the ramp results in the interaction between the cross flow and injectant being further away from the test plate, causing the formation of a weak horseshoe vortex [
8]. In their simulations, they employed the realizable
k–ε model. Johnson et al. (2011) showed the effects of the hole length to hole diameter ratio, momentum ratio on
η using the realizable
k–ε model [
9]. They determined that the mesh refinement around the hole trailing edge was helpful for yielding better
η at high momentum ratios. Moreover, they stated that
η was low when the injectant had high momentum, and the ratio of
L/D was small due to the high injectant lift off. The various CFD studies on film cooling show that LES simulation is superior to RANS simulation for predicting the film cooling performance at 0 Hz. Additionally, the cooling jet can be injected from the hole with a spanwise injection angle to the main flow. When a compound angle is implemented, the film cooling performance improves as the CRVP changes to a single vortex [
10,
11]. Lee et al. studied the film cooling flow variation with
β ranging from 15° to 90° experimentally [
12]. They discovered that the CRVP of the injectant exhibits a strong asymmetry at an orientation angle of 15° and changes to a single vortex at an orientation angle of 30°. Jung and Lee [
13] experimentally measured
η variation with the compound angle. When a compound angle was adopted,
η increased from 20% to 80% depending on the orientation angle and blowing ratio.
However, unsteady main flow could be generated in the film cooling flow fields because of several reasons, such as flow interactions between the stator and rotor [
14]. Thus, understanding the effects of the pulsating main flow on the film cooling performance is important for high efficiency design of the gas turbine. However, little experimental research and few numerical studies have been conducted on the effects of pulsating main flow on film cooling. Coulthard et al. (2000) showed the effects of cooling air pulsation on the film cooling performance experimentally [
15]. They found that
η decreased when the frequency of the pulsation of the coolant injection increased. Moreover, they found that the best cooling performance was obtained at an
M of 0.5. Nikitopoulos and Acharya (2009) showed the effect of the injectant pulsation on film cooling and found that
η can be controlled and improved by the injectant pulsation numerically [
16]. They stated that frequency, duty cycle, and
M affect the film cooling performance. The instability pattern can be approximated by a sinusoidal form, since the instability pattern is more similar to a sinusoidal waveform than a simple pulse. Seo et al. (1998) experimentally showed the effects of sinusoidal pulsations of 2, 16, and 32 Hz on film cooling [
14]. They reported that when the frequencies were increased at
M = 0.5 and short
L/D,
η was decreased and the heat transfer coefficients was increased. Jung et al. (2001) experimentally investigated the effects of sinusoidal pulsations in the mainstream on film cooling [
17]. They reported the flow structures of the film cooling via phase- and time-averaged velocity profiles, with Reynolds stresses at 0, 2, 16, and 32 Hz for
M = 0.5. Moreover, they showed that the influence on the flow structures increased with the pulsation frequencies. Generally, the computational cost of LES is significantly higher than that of RANS. However, RANS has a limitation in the prediction of complex flow structures induced in film cooling flow fields, since all turbulent fluctuations are ensemble-averaged, while LES directly resolves eddies of large scale in the flow, yielding accurate, complex flow predictions [
18,
19].