# Effects of Bulk Flow Pulsations on Film Cooling with Two Sister Holes
## 4 Results & Discussion  
### Contours of Time-Averaged \(\eta\) and Dimensionless Temperature  
Figures 6 and 7 show contours of time-averaged \(\eta\) on the wall for the ordinary and triple hole, respectively, at various frequencies and Strouhal numbers. The contours for the single-hole system at 0 and 32 Hz are compared to the contours with the experimental data of [PERSON] [30]. The effectiveness is slightly over-predicted by LES, however, the contours obtained in the experiment were similar to those predicted by the LES. The coolant's contact with the plate is hardly affected by an increase in the frequency from 0 to 16 Hz. However, it is significantly reduced by the 32 Hz pulsation owing to increased mixing. The Strouhal number for the 32 Hz pulsation is 1.6085, and as stated earlier, if the Strouhal number is greater than 1, the coolant is significantly affected by the pulsation during its passage through the hole. For each frequency of the pulsation, coolant spreading and contact with the test plate is considerably better in the triple-hole system compared with the ordinary hole system, as shown in Figures 6 and 7. The improvement is attributable to the anti-CRVPs generated by the sister holes, leading to weak main CRVP and weak entrainment of hot gas under the injectant. Figure 5: Close-up view of the grid near the injection region [3]. Figure 8 illustrates the cross-sectional dimensionless mean temperature contours at \(x\)/\(D\) = 2.5, 5, and 10 for 0 and 32 Hz pulsations and a comparison of the contours with the experimental data of [PERSON] [30]. If there is 32 Hz pulsation in the flow, a smaller injectant comes in contact with the wall compared with at the case of 0 Hz. However, as shown in the mean effectiveness contours of the film cooling on the wall in Figures 6 and 7, the coolant spreading and contact with the test plate is considerably better in the triple-hole compared with the single-hole system. Figure 6: Contours of time-averaged \(\eta\) on the wall for single-hole system for 0 (Sr = 0), 2 (Sr = 0.1005), 16 (Sr = 0.8043) and 32 Hz (Sr = 1.6085). Figure 7: Contours of time-averaged \(\eta\) on the wall for the triple hole for 0 (Sr = 0), 2 (Sr = 0.1005), 16 (Sr = 0.8043) and 32 Hz (Sr = 1.6085). As shown in the contours of the experimental data in Figure 8, there is no data for the dimensionless temperature near the test plate because it could not be measured through cold-wire measurement. However, except near the test plate, the contours obtained in the experiment were similar to those predicted by the LES. The small difference between the LES results and the experimental data is because the experimental data were measured using an apparatus with a single hole with \(L/D=4\) while the LES results were obtained with a single hole with \(L/D=1.6\). The dimensionless temperature near the plate decreased as the mainstream flow travelled downstream, and \(x/D\) increased because of the intense  
Figure 8: Cross-sectional time-averaged dimensionless temperature distributions at \(M=0.5\). mixing of the mainstream flow and coolant jet by the turbulence. Thus, at \(x/D=10\), the temperatures near the wall in the triple hole configuration and the single cooling hole configuration becomes similar because of the strong mixing. Figures 9 and 10 show the contours for the time-averaged dimensionless temperature at \(x/D=2\) for the single-hole and triple-hole systems for 0, 2, 16, and 32 Hz pulsations. The anti-Counter Rotating Vortex Pairs weakened the main Counter Rotating Vortex Pair and reduced the lift off of the coolant jet, decreasing the entrainment of the hot gas of main flow under the injectant [3]. Therefore, the temperature near the test plate remained similar to the temperature of the coolant-core part and the film cooling effectiveness increased. Figures 9 and 10 display cross-sectional contours of the mean dimensionless temperature and the mean velocity vectors at \(x/D=2\) for the single-hole and triple-hole systems, respectively.