# Effects of Bulk Flow Pulsations on Film Cooling with Two Sister Holes
## 4 Results & Discussion
### Time-averaged Velocity Magnitude in the Hole  
Figure 15 illustrates time-averaged velocity magnitude contours at the hole exit for 0 and 32 Hz, obtained by an LES, and Figure 16 depicts contours of the time-averaged velocity magnitude in the hole in the z = 0 plane. The ratio of \(L\) to \(D\) in the single-hole configuration was set as 1.6, and the ratios of \(L\) to \(D\) for the primary and sister hole in the triple hole were 1.8 and 3.6, respectively. Therefore, in the triple hole, the mean velocity magnitude at the main hole exit shows distinct high and low momentum regions because of the small \(L/D\) value, while that at the sister hole exit indicates a more developed and uniform flow velocity [3]. The cooling jet with more uniform velocity is better for \(\eta\) due to less injectant lift off. Therefore, small hole in the triple-hole system improve \(\eta\) through the generation of an anti-CRVP and by increasing the \(L/D\) ratios. The same concept holds for 32 Hz pulsation. When the flow oscillates at 32 Hz, the contours of time-averaged velocity magnitude at the hole exit of the single-hole system show more uniform injectant velocity magnitude than those at 0 Hz since the amplitude of the coolant velocity at the hole exit varies periodically and thereby generates large disturbances and mixing. However, the contours of the mean velocity magnitude in the sister holes show flow that is more developed than that in the main hole, even at 32 Hz pulsation. Thus, the small holes increase \(\eta\) through the formation of anti-Counter Rotating Vortex Pair and by increasing the L/\(D\) ratios. In Figure 16d,e, the main flow can be inferred to invade into the windward side of the hole exit because when the flow oscillates at 32 Hz, the hot main flow in the hole reverses periodically, which is detrimental to the hole material.  
Figure 14: Contours of instantaneous \(\eta\) on the wall obtained by an LES: (**a**) Single hole at 0 Hz, (**b**) triple holes at 0 Hz, (**c**) single hole at 32 Hz, and (**d**) triple holes at 32 Hz.  
Figure 17a,b shows profiles of the mean coolant velocity magnitude at the hole exit in the streamwise direction for \(L/D\) ratios around 1.6 and 4, respectively. As stated earlier, the mean velocity magnitude at the hole exit shows large variations for \(L/D\) values of 1.6 or 1.8, while that for \(L/D\) values of 3.6 or 4 is more uniform. Specifically, for the \(L/D\) value of 1.8, the mean velocity magnitude shows smaller variations compared with those for the \(L/D\) value of 1.6. Further, when there is 32 Hz pulsation in the flow, the mean velocity magnitude becomes more uniform than that in the steady state. The difference in the coolant velocity magnitude between the LES results and the experimental data for the leeward side of the hole (\(0<x/D<0.8\)) is attributed to the experimental operating conditions [9]. The experimental data were measured in the absence of the main flow.  
Figure 16: Contours of time-averaged velocity magnitude in the hole at the centerline.  
Figure 17: Profiles of the mean coolant velocity magnitude at the hole exit in the streamwise direction.  
Figure 15: Mean velocity magnitude at the hole exit.