This study employs computational simulations to investigate film cooling using fan-shaped injection holes, with a focus on analyzing the distribution of turbulent kinetic energy (TKE) over a flat surface. The research utilizes the \(k-\epsilon \) turbulence model to examine the impact of cooling fluid velocity at the injector exit on TKE and film cooling effectiveness at blowing ratios of 1.0, 1.4, and 2.0. The results demonstrate that increasing the outlet velocity enhances coolant dispersion and improves cooling effectiveness, particularly up to a blowing ratio of 1.4. Visualization of TKE highlights significant turbulence and thorough mixing between the coolant jet and mainstream gas. This study offers significant findings in optimizing outlet injection velocity and TKE distribution, thereby enhancing film cooling performance through diffuser-type injection. Given the practical implementation of fan-shaped injection holes in turbine engines, a comprehensive TKE analysis for cooling turbine components becomes crucial. Understanding the optimal outlet velocity and TKE distribution holds substantial significance in developing efficient cooling strategies for gas turbine applications. The implications of this research extend to various domains, including thermal management, electronics cooling, and power generation systems, all of which can benefit from improved cooling approaches. Notably, our study reveals that a 40% increase in blowing ratio could result in a 100% increase in TKE, facilitating the mixing of coolant gas with hot gas.