Dynamics of transient under-expanded hydrogen jets from a solenoid injector with a customized single-hole cap

This paper presents an experimental methodology for quantifying internal jet-forming cap pressure losses in hydrogen direct-injection systems through non-intrusive analysis of external near-nozzle under-expanded jet structures. Based on a customized single-hole gasoline direct injection injector with synchronized high-speed schlieren imaging, microscopic shadowgraphy, and needle lift measurements, we establish empirical correlations between observable Mach disk dimensions and upstream flow conditions across pressure ratios from 10 to 96. Key contributions include: (1) needle lift stabilizes at ∼60 μm, independent of injector driving parameters; (2) a validated momentum-based rate of the injection method achieving nozzle discharge coefficient characterization of ∼0.9, demonstrating excellent agreement with needle-lift-derived theoretical predictions; (3) the finding that Mach disk stabilization time scales universally with needle actuation time, independent of pressure ratio, indicating that shock structure development is governed by the establishment of boundary conditions rather than local acoustic phenomena; (4) non-intrusive quantification of inner cap pressure losses yielded a value range of ξ = 0.729–0.756 using empirical Mach disk scaling laws; (5) identification of self-similarity establishment within 0.2 ms providing critical time scales for mixture formation modeling. These findings resolve a key disconnect between classical jet theory and practical injector performance, providing a systematic framework for diagnosing internal flow restrictions from external optical measurements, a capability essential for hydrogen injector optimization where direct internal instrumentation is impractical.