# Large Eddy Simulation of Film Cooling with Bulk Flow Pulsation: Comparative Study of LES and RANS
## 4 Results and Discussion
### Dimensionless Temperature Contours at \(y\)/D = 0 and \(z\)/D = 0  
Figure 6 shows the time-averaged film cooling effectiveness contours on the test plate obtained experimentally [26], as well as by means of LES and RANS. The experimental contours were measured for L/D = 4, having higher film cooling effectiveness than LES results for L/D = 1.6. However, they are included in Figure 6 for reference. In the case of 0 Hz, in the region where \(x\)/\(D\) is less than 3, the experimental and LES results differ because of the L/D effect, but they show similar distributions downstream. At 32 Hz, the effect of L/D decreases, and the experimental and LES results have similar distributions. The RANS result predicted less mixing with the main flow than the experimental result, so the film cooling efficiency was higher at the centerline than that in the experiment, and the film cooling efficiency was lower between the holes.  
Figure 7 illustrates the time-averaged dimensionless temperature contours obtained by LES and RANS on the \(z=0\) plane. A comparison of the LES and RANS temperature fields in the absence of  
Figure 5: Phase-averaged dimensionless temperature contours at \(x\)/\(D\) = 5: (**a**) experiment [12]; (**b**) LES (Smagorinsky–Lilly); (**c**) RANS (realizable k-\(\epsilon\)). Numbers in contours, 1: \(\theta\) = 0.05, 2: \(\theta\) = 0.1, 3: \(\theta\) = 0.15, 4: \(\theta\) = 0.2, 5: \(\theta\) = 0.25, 6: \(\theta\) = 0.3, 7: \(\theta\) = 0.35, 8: \(\theta\) = 0.4, 9: \(\theta\) = 0.45, A: \(\theta\) = 0.5, B: \(\theta\) = 0.55, C: \(\theta\) = 0.6, D: \(\theta\) = 0.65.  
Figure 6: Time-averaged film cooling effectiveness contours on the test plate: (**a**) steady (0 Hz) and (**b**) with flow pulsation (32 Hz).  
pulsation (Figure 7a) shows that, in the RANS result, the region with high dimensionless temperature (red in the contour) is longer along the surface than that in the LES result. The overprediction of the centerline film cooling effectiveness by RANS in Figure 2b can be confirmed from the time-averaged temperature contours shown in Figure 7a. Under the application of 32 Hz (Figure 7b), mixing with the main flow occurs in both the LES and the RANS results, and the red-colored region remains within the hole. In the case of LES, injectant lift-off is clearly shown compared to that in RANS, so a blue contour area can be seen near the wall after \(x/D=5\).  
Figure 8 shows the dimensionless temperature fields obtained by means of LES and URANS at \(y/D=0\) and \(z/D=0\) for each phase with pulsation of the main flow. The figure shows periodic jet lift-off and periodic formation of large coolant vortices. As can be seen in the contours for \(z/D=0\), the locations of the large coolant vortices obtained using LES and URANS are similar to each other. However, the jet shear layer vortices, which are generated due to shear between the main flow and the coolant jet [27], are present within the gray circle in the LES contour at \(z/D=0\) in Figure 8a, whereas these vortices are absent in the URANS contours at \(z/D=0\). The LES contours at \(y/D=0\) show a wider coolant spread along the spanwise z-direction than the URANS contours. Moreover, the horseshoe vortex is clearly visible in the LES contours at \(y/D=0\), as in Figure 8a, whereas this vortex is not clearly visible in the URANS contours at \(z/D=0\), as in Figure 8b.  
Figure 7: Time-averaged dimensionless temperature contours at \(z/D=0\): (**a**) steady (0 Hz) and (**b**) with flow pulsation (32 Hz).