# Effects of Bulk Flow Pulsations on Film Cooling with Two Sister Holes
## 4 Results & Discussion
### Time-Averaged Effectiveness  
When the mainstream flow and injectant oscillated in the single and triple-hole configuration, the spanwise-averaged effectiveness showed identical trends. As shown in Figure 11, increasing the flow frequency reduced \(\eta_{m}\). For the single hole, when the frequency was increased from 0 to 2, 16, and 32 Hz and the Strouhal number (Sr) from 0 to 0.1005, 0.8043, and 1.6085, the spanwise-averaged film cooling effectiveness decreased by approximately 11%, 12%, and 45%, respectively. For the triple-hole system, identical increases in the frequency and Strouhal number decreased the spanwise-averaged effectiveness by approximately 4%, 5%, and 39%, respectively. When the frequency was increased from 16 to 32 Hz, the sharp decrease in \(\eta_{m}\) was because when the Strouhal number is greater than 1, the trajectory of the injectant is considerably different from that in the steady state and the B value in Equation (2) at 32 Hz sharply increases compared with that at 2 and 16 Hz. Nevertheless, the triple-hole system showed higher effectiveness than the single-hole system, regardless of the frequency and Strouhal number, as shown in Figure 12. Experimental data [9] were available only for the single-hole system, and \(\eta_{m}\) obtained by the LES matched well with the experimental data, even though the LES results were slightly underestimated. Figure 13 depicts the ratios of \(\eta_{m}\) in the triple-hole configuration to \(\eta_{m}\) in the single-hole, for various Strouhal numbers; the ratios were obtained through LES analyses.  
Figure 10: Contours of time-averaged dimensionless temperature and velocity vectors at \(x/D=2\) for the triple-hole system (**a**) 0 Hz, Sr = 0; (**b**) 2 Hz, Sr = 0.1005; (**c**) 16 Hz, Sr = 0.8043; and (**d**) 32 Hz, Sr = 1.6085.  
Figure 11: \(\eta_{m}\) under unsteady conditions.  
Figure 12: Laterally-averaged effectiveness under unsteady conditions: (**a**) 0 Hz, Sr = 0; (**b**) 2 Hz, Sr = 0.1005; (**c**) 16 Hz, Sr = 0.8043; and (**d**) 32 Hz, Sr = 1.6085.  
Increasing the pulsation frequency and Strouhal number increased the ratio of the spanwise-averaged effectiveness. While the increase was small between 0 Hz (Sr = 0) and 16 Hz (Sr = 0.8043), it was sharp from 16 Hz (Sr = 0.8043) to 32 Hz (Sr = 1.6085). This indicated that under unsteady main flows and higher pulsation frequencies and Strouhal numbers, configuring a primary hole and two small holes is better than configuring a single hole for film cooling. The coolant injection generated large disturbances in the main flow at 32 Hz because under these conditions, the amplitude of the cooling air velocity pulsation increased remarkably at the inlet of the plenum, as evident in Table 3, and a high jet liftoff was generated as mentioned earlier. Anti-CRVPs reduce the intensity of the main CRVP more effectively when high disturbances are generated in the main flow. Additionally, the ratio of the spanwise-averaged effectiveness was almost independent of the Strouhal number at \(x/D>13\) because the disturbances induced by the coolant jet pulsation weakened in this \(x/D\) range, reducing the film cooling effectiveness of the anti-CRVPs.