## 3 Results and Discussion  
### Blowing Ratio M = 0.3  
Figures 5 and 6 illustrate the contours of temperature and vorticity during a single period for varying phase lags between the incoming wake and the pulsating jet in the central plane \(Z\) = 0 at a blowing ratio of M = 0.3. The figure demonstrates that after the airflow sweeps over the plate surface in the wake region, the boundary layer separates and progresses downstream due to the reverse pressure gradient. The coolant jet exited from the film hole exhibits a notable lift, with the lift distance extending approximately 10D along the X direction. When the phase lag between the wake and the pulsating jet is equal to 0, as depicted in Figures 5a and 6a, the lift at the film hole is observed at 1/4 T of the cycle. At this point, the pulsating jet is situated near the maximum value of the cycle. As illustrated in Figure 6a, the lift-produced coolant jet leads to insufficient coverage of the flat plate surface by the jet film. Consequently, the uncovered area on the flat plate moves downstream in conjunction with the lift area of the cooling film. At time T, when the wake traverses the surface of the flat plate, the lift area is positioned at 15D, resulting in an enhanced coverage effect of the cold air jet on the plate surface. When the phase difference between the wake and the pulsating jet is 0.25, Figures 5b and 6b indicate that the wake sweeps over the flat plate at 1/4 T. During this phase, the jet blowing ratio at the outlet of the film hole reaches its maximum, though the film coverage at the film hole remains inadequate. The jet lift at the film hole occurs at 1/2 T of the cycle, at which point the jet blowing ratio is in a phase of decline, leading to a diminished coverage effect of the jet on the plate surface in subsequent cycles. When the phase difference between the wake and the pulsating jet is 0.5, Figures 5c and 6c reveal that the wake sweeps over the flat surface at 1/2 T, where the jet blowing ratio continues to decrease. Within the wake's sweeping range, the jet blowing ratio remains relatively high, thereby producing significant film lift. At 3/4 T, jet lift is observed at the film hole, and the jet blowing ratio reaches its lowest value within the cycle, resulting in improved mainstream coverage at the film hole. Lastly, when the phase difference between the wake and the pulsating jet is 0.75, Figures 5d and 6d illustrate that the wake sweeps over the flat plate at 3/4 T. During this period, the jet blowing ratio remains low, leading to minimal coverage of the cold air jet on the surface of the flat plate behind the film hole when the jet lift occurs at the subsequent cycle time T.  
Figure 7 presents the instantaneous temperature distribution on the plate surface at various time intervals under the operating condition of M = 0.3. Following the wake's passage, the lifting area generated by boundary layer separation extends to the film hole, intensifying the jet's departure from the plate surface and propelling it downstream. During this phase, the coolant jet demonstrates a limited protective effect on the plate surface. The coolant jet reestablishes coverage over the plate surface upon traversing the lifting area. The jet assumes a critical cooling role throughout this interval during the subsequent wake sweeping across the plate. The duration of the exit of the jet lifting area of the film hole to the arrival of the subsequent wake at the plate surface is approximately 0.25 T. When the phase lag between the wake and the pulsating jet is zero, this interval corresponds to the b-c stage of the jet, characterized by the highest flow rate and effective coverage over the plate surface. Conversely, at a phase lag of 0.25, the interval corresponds to the c-d stage, during which the jet flow rate descends below the average value. In this context, the elevated flow rate stage precedes the jet lift, disrupting the favorable film that had formed earlier, significantly compromising the cooling effect.