## 3 Results and Discussion
### Blowing Ratio M = 0.3
At a phase lag of \(\psi\) = 0.5, the lifted jet is in the d-e stage. During this stage, the blowing ratio increases from its minimum value within the cycle yet remains below the average, leading to inadequate coverage by the end of this interval. When the phase lag reaches 0.75, the lifted jet occupies the a-b stage. Atthis juncture, the jet blowing ratio increases from the average value, resulting in a more effective film coverage. Figure 5: Cont. The changes in turbulence and vorticity represented in these figures are primarily attributable to the interaction among the wake, the pulsating jet, and the separation of the boundary layer. As the wake traverses the plate, it generates a reverse pressure gradient that induces boundary layer separation. This separation leads to an increase in flow disorder, consequently elevating vorticity levels. The separated flow subsequently interacts with the pulsating jet. In the context of turbulence, at a low blowing ratio of M = 0.3, the flow velocity remains comparatively low, enabling viscous forces to exert a significant influence. The periodic motion of the wake, coupled with the pulsation of the jet, destabilizes the flow. In regions where the wake and jet interact, the intensity of turbulence is heightened due to improved mixing among fluids with differing velocities. These modifications in turbulence and vorticity have substantial implications for film cooling efficiency. Increased vorticity may enhance or diminish this efficiency; if it facilitates improved coolant coverage across the plate's surface, the overall efficiency will be elevated. In contrast, efficiency may decline if it causes the coolant to mix and dissipate too rapidly. While turbulence typically enhances heat transfer and is advantageous for cooling, excessive turbulence may disrupt the film, thus impairing the cooling effect. Therefore, thoroughly comprehending these phenomena is crucial for optimizing the film cooling system. This analysis is further supported by the data shown in Figure 8.  
Figure 5: Contours of temperature in one period for different phase lags in \(Z=0\) at M = 0.3. Figure 6: _Cont._  
Figure 7: _Cont._  
When the phase lag between the wake and the pulsating jet is 0.25, the jet attains lift at the film hole at 1/2 T of the period. Although the blowing ratio is declining at this stage, it remains above the average level. In subsequent periods, the blowing ratio decreases, enhancing the coverage effect on the plate surface. At 1/4 T, the wake's sweep over the flat plate ensures effective film coverage during this phase. In scenarios where the phase lag equals 0.5, the jet lift occurs at the film hole at 3/4 T, coinciding with the lowest blowing ratio observed within the cycle. This results in diminished coverage around the filmhole on the plate surface. However, during the interval when the jet is anticipated to be close to the plate surface, the lift induced by the wake moves away from the surface, thereby reducing the overall cooling effect of the cooling film throughout the cycle. At 1/2 T, the wake sweeps across the flat plate, generating a relatively substantial blowing effect; despite this, the film lift during this phase is inferior to that observed during the lower blowing ratio stage. When the phase lag is 0.75, the jet's lifting phase occurs before time T, and the lift generated by the wake remains within the lower blowing ratio range. The wake  
Figure 8: Streamwise distribution of time-mean span averaged film cooling efficiency at M = 0.3. Figure 7: Contours of temperature on the bottom wall in one period for different phase lags at M = 0.3.  
crosses the flat plate at 3/4 T, during which the blowing ratio of the jet is approximately at its average value. Figure 9: Cont. The instantaneous temperature contours presented at various time intervals in Figure 11 provide valuable insights regarding the effects of a blowing ratio (M) of 0.5.