Unsteady RANS simulations of under-expanded hydrogen jets for internal combustion engines

Hydrogen can be considered a suitable fuel for heavy-duty reciprocating internal combustion engines (ICEs) in order to limit carbon dioxide emissions. The low volumetric power density of hydrogen and the backfire problem suggest to employing the direct injection technology with relatively high nozzle pressure ratios (NPRs). This paper provides the analysis of under-expanded hydrogen jet dynamics using an open-source high-fidelity simulation tool based on the OpenFOAM framework. The unsteady Reynolds-averaged Navier–Stokes (URANS) equations are solved by an efficient pressure-based solver for compressible flow. URANS equations are attractive for fast engineering analysis of 3D engine cycle and optimization, where large eddy simulation (LES) is too computationally expensive. The accuracy of the simulations is enhanced by employing the weighted essentially non-oscillatory (WENO) approach for the spatial discretization, considering schemes from second-order to fourth-order accuracy. Those schemes are embedded in a pressure-implicit with splitting of operators (PISO) algorithm, obtaining a very robust and accurate numerical method for compressible multi-species flows, which can be shared in an open access framework. Hydrogen injection in air is simulated, with several values of the NPR typical of direct injection ICE in the low-medium range, $8.5\le NPR\le 30$. The main features of the developing jet are analyzed, such as barrel shock dimensions, cone angle and hydrogen–air mixing. The results are validated with respect to experimental and LES data available in the recent literature, demonstrating the efficiency and the accuracy of the employed URANS approach and evaluating its limits.