In the context of the clean transport sector, there has been growing interest in the use of hydrogen in internal combustion engines due to its potential to nearly eliminate all engine-out criteria pollutants, while maintaining high thermal efficiency through the use of a lean combustion process. Direct Injection (DI) is widely recognized as a method for enhancing thermal efficiency and minimizing the risk of abnormal combustion. However, a major challenge is the reduced time available for mixture homogenization, making injection timing a critical parameter to optimize. To address this, a comprehensive experimental campaign was conducted in a constant volume vessel to assess the performance of a hydrogen injector using the Schlieren technique. The jet behavior was analyzed by varying injector recess, injection pressure, and back pressure. Subsequently, the case study was replicated in a 3D Computational Fluid Dynamics (CFD) environment, addressing the complexities associated with modeling under-expanded jets. The model was first validated against experimental data, and then a simplified simulation approach was developed to significantly reduce computational effort while maintaining the reliability of the results.