Lightweight method for injection rate prediction of supersonic gas flow from pintle-type hydrogen injector

Research on hydrogen engines has been actively pursued to achieve carbon neutrality in the transportation sector. To optimize the combustion characteristics of hydrogen engines under various driving conditions, active and precise control of the hydrogen injection flow rate is crucial. Lightweight prediction for hydrogen injection rates from pintle-type injectors, which are widely used in hydrogen engines, is required for the control of the injection rate as well as the model-based engine development. However, lightweight injection rate prediction for gaseous fuel has been conducted solely for hole-type injectors and not for pintle-type injectors that have an annular internal flow path with complex configurations. In this study, a lightweight methodology is introduced to predict the hydrogen injection rate of pintle-type hydrogen injectors based on the compressible flow theory of converging-diverging nozzles with minimum mass flow rate data obtained with a safer surrogate gas. The validity of the method for various injection conditions and gases (nitrogen, helium, and hydrogen) is discussed. The methodology demonstrated prediction accuracy of over 92% for nitrogen and helium injection rates under different injection pressures (1.5–4 MPa) and ambient pressures (0.1–2 MPa). The versatility of the prediction methodology for various gases, including hydrogen, was also confirmed. The error sources were analyzed thoroughly based on the dynamic characteristics of the pintle behavior and differences in gas properties.