# Large Eddy Simulation of Film Cooling with Bulk Flow Pulsation: Comparative Study of LES and RANS
## 2 Geometry and Boundary Conditions  
The CFD simulations were performed with a three-dimensional mesh. The orange dashed lines in Figure 1a show the computational domain. The geometry of real turbine blades is more complex than that represented by the computational domain. However, the results obtained for a flat plate could be applied to real turbine blades with some corrections [16]. The geometry was adopted from [PERSON], [PERSON], and [PERSON] [12]. In their experimental facility, five cooling holes were created on the plate in a row. To reduce computation time, in the present study, the computational domain was created with a single hole by applying the periodic boundary condition to the sides of the domain. The hole shape was cylindrical without a compound angle. The hole diameter (D) was 0.025 m, the ratio of hole length (L) to hole diameter (D) was 1.6, the ratio of pitch to hole diameter (P/D) was 3, and the injection angle (\(\alpha\)) was 35\({}^{\circ}\). The turbulence intensity of the mainstream at the main inlet was 0.2%, and the velocity of the main flow was 10 m/s. The temperatures at the main inlet and plenum inlet were 293 K and 313 K, respectively, as in the study of [PERSON], [PERSON], and [PERSON] [12]. As illustrated in Figure 1a, the computational domain was extended to 24 times the hole diameter downstream and upstream of the hole center. Figure 1b shows the CFD mesh in the \(z=0\) plane. For the LES calculation in the steady state (0 Hz), a mesh extended to only four times the hole diameter upstream of the hole center was used to reduce computational cost (Figure 1c). The velocity profiles due to which  
Figure 1: Computational domain and grid system. (**a**) Schematic of the computational domain (orange dashed line). (**b**) CFD mesh in the z/D = 0 plane. (**c**) CFD mesh for simulation without bulk flow pulsation. (**d**) Close-up of the mesh around the jet injection region. the boundary layer thickness at the hole center was 1.02D, as stated in [PERSON], [PERSON], and [PERSON] [12], and the turbulence quantities were determined using a separate flat plate mesh and applied at the main inlet of the computational mesh. Figure 1d shows the CFD mesh in the \(yz\) plane and a close-up of the mesh around the jet injection region. In total, 2.04 million hexahedral cells were used in the mesh, as shown in Figure 1b. The mesh spacing values ranged from 6 near the hole to approximately 35 at \(x\) = 24D in \(x^{+}\) units in the \(x\)-streamwise direction. The \(y^{+}\) value of the first cell above the test plate was less than 1 to ensure that the gradient of the wall-normal velocity in the viscous sublayer could be captured accurately, and there were 25 cell layers up to \(y^{+}\) = 30. The mesh spacing value in the \(z\)-spanwise direction was 20 throughout the domain in z\({}^{+}\) units. If h was assumed as the hole wall-normal coordinate, the h\({}^{+}\) value of the first cell was set to less than 2 to accurately capture the gradient of the wall-normal velocity in the viscous sublayer. There were 15 cell layers up to h\({}^{+}\) = 40. Figure 1c illustrates a close-up of the mesh around the jet injection region. The black regions in the figure show that the fine cells were concentrated around the boundary layer and in the region where complex flow structures were induced by the interactions between the mainstream and the jet. Table 1 summarizes the boundary conditions of the domain. As summarized in Table 1, the boundary conditions at the main inlet and plenum inlet were set as the velocity inlet. Except for the LES calculation in the steady state (0 Hz), the velocity profile at the main inlet of the mesh in Figure 1b was spatially uniform, and can be expressed as follows:  
\[V_{min}=A\sin(2\pi\text{f}t)+10\text{ m/s}. \tag{1}\]  
\(A\) values, that is, the main flow velocity oscillation amplitudes, were taken from [PERSON], [PERSON], and [PERSON] [12].