Development and validation of a versatile simulation model for extremely under-expanded hydrogen jets

Direct injection of hydrogen in internal combustion engines generates extremely under-expanded jets characterized by complex shock structures, necessitating the use of high-resolution computational fluid dynamics (CFD) simulations for accurate prediction. However, such simulations are computationally prohibitive for model-based development. This study developed and validated a versatile and computationally efficient inflow boundary model for jets from an inward-opening injector with a straight cylindrical orifice. In this methodology, the upstream flow—including the intricate shock-wave structures up to the Mach disk—is represented by flow quantities at the Mach disk, which are then applied as inlet boundary conditions for downstream simulations. High-resolution CFD simulations were first validated against shadowgraph imaging to accurately capture jet structure, which subsequently informed the boundary conditions for the inflow boundary model. The inflow boundary was divided into three concentric regions: a stagnant core, a uniform jet, and an outer edge region. To accurately represent shear-layer development without empirical calibration, a radially decreasing velocity profile and an initial turbulence distribution were prescribed in the outer edge region. The model was validated across a broad range of operating conditions. Simulation results demonstrated strong agreement with the macroscopic jet characteristics observed via shadowgraph imaging and with hydrogen distributions measured by negative laser-induced fluorescence. Compared with high-resolution simulations, model-based simulations decreased the computational load by approximately 400-fold while maintaining practical accuracy. This demonstrates their suitability for efficient model-based development and optimization of hydrogen internal combustion engines.