## 1 Introduction  
With the continuous development of gas turbine technology, the turbine inlet temperature has now surpassed 2000 K [1, 2], far exceeding the high-temperature tolerance limit of conventional materials. This urgently requires innovation and optimization in turbine blade cooling technologies [3, 4, 5, 6]. Blade cooling, especially film cooling, has become a critical method to ensure the stable operation of turbine blades in high-temperature gas environments. The film cooling, first proposed by [PERSON] [7, 8, 9]; is important in this context. Many studies have been conducted to enhance film cooling efficiency, with a focus on geometric parameters of film holes and aerodynamic parameters of the cooling jet. Several experimental and numerical studies [10, 11, 12] have focused on optimizing the shape and dimensions of film holes, resulting in significant findings. Techniques such as using cavities [13], upstream ramp [14], and embedding film holes [15] into grooves have shown promise in improving film cooling efficiency. Additionally, researchers have explored the impact of parameters such as blowing ratio, mass flow ratio, and mainstream Reynolds number on film cooling efficiency, leading to the identification of optimal parameter combinations. [PERSON] et al. [16] studied the interaction between endwall channels and blade showerhead cooling flows, finding that the showerhead cooling flow significantly influences the secondary cooling effect on the endwall and the distribution of cooling airflow. [PERSON] et al. [17] experimentally evaluated novel bean-shaped cooling holes for turbine endwalls, revealing that bean-shaped cooling holes provided superior cooling performance, especially in the pressure-side region. Further studies [18] investigated the effect of pulsating flows in endwall channels on film cooling, providing new correlations for predicting cooling performance. Research by [PERSON] et al. [19] showed that increasing the blowing ratio significantly improved film cooling efficiency and enhanced heat transfer distribution. Numerical simulations by [PERSON] et al. [20] demonstrated that the cooling airflow is affected by secondary flows and upstream structures, and adjusting the position and shape of cooling holes can improve cooling effectiveness. [PERSON] et al. [21] performed a numerical evaluation of film cooling performance at different Reynolds numbers and blowing ratios, showing that film effectiveness and net heat flux reduction vary with these parameters, and proposed new methods for evaluating film cooling performance. [PERSON] et al. [22] proposed a cooling hole layout strategy based on conjugate temperature gradient lines, studying how different temperature gradient distributions in cooling hole layouts affect endwall cooling performance. The results showed that adjusting the hole layout could achieve a more uniform film coverage and temperature distribution, with the temperature gradient line layout demonstrating significant advantages in cooling performance. Despite these methods effectively improving cooling performance, the use of cooling air still reduces the adequate airflow, lowering the turbine's thermal efficiency. In high-performance turbine engines, cooling air consumption can result in a thermal efficiency loss of 20% to 25% [23]. Recent research has focused on pulsating jet cooling technology to reduce cooling air consumption. Pulsating jets reduce the amount of cooling air used and significantly enhance film cooling efficiency [24; 25; 26; 27]. The complex flow phenomena inside gas turbines, including periodic wakes, turbulence, and vortices, profoundly affect film cooling performance [28; 29; 30]. Therefore, a deeper understanding of how these factors impact film cooling performance is crucial for optimizing turbine cooling system design, thereby improving thermal efficiency and reliability. Experiments conducted by [PERSON] et al.