Using natural gas in internal combustion engines (ICEs) has been emerging as a promising strategy to improve thermal efficiency and limit exhaust emissions. Major benefits can be had in fact running under lean combustion conditions. However, as the mixture is leaned out beyond the Lean Misfire Limit (LML), some issues may occur in terms of effective and stable engine operation. Thus, different solutions have been proposed over the last decade to overcome those problems. Among them, the stratification of the charge has been shown to successfully extend the LML with respect to conventional lean burn engines. Upon development and optimization of such strategies, Computational Fluid Dynamics (CFD) may be particularly useful to understand thoroughly the phenomena occurring during the mixing and combustion phases and their dynamic coupling. A detailed description of the turbulent properties of the PSC injection process is crucial to reliably represent the stratification effects. The LES approach has been validated as accurate to capture the typical scales of motion of the mixing process due to the PSC injection into a Constant Volume Combustion Chamber (CVCC). This work aims at extending the studies already done into the CVCC toward the analysis of the behavior of a real engine, comparing the current findings with the CVCC data.