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Direct injection of gaseous fuels usually involves the presence of under-expanded jets. Understanding the physics of such process is imperative for developing Direct Injection (DI) internal combustion engines fueled, for example, by methane or hydrogen. An experimental-numerical characterization of the under-expanded jets issued from an innovative multi-hole injector, designed for application in heavy-duty engines, is carried out. The experimental characterization of the jet evolution was recorded by means of schlieren imaging technique and, then, a numerical simulation procedure was validated, allowing a comprehensive injection process analysis. A high-order and density-based solver, capable of reproducing the most relevant features of the under-expanded jets, was developed within OpenFOAM framework. Initially the effects of the upstream-to-downstream pressure ratio, namely Net Pressure Ratios (NPR), on the spray morphology were investigated.