A density-based solver with the classical fourth-order accurate Runge-Kutta temporal discretization scheme was
developed and applied to study under-expanded jets issued through millimeter-size nozzles for applications in highpressure
direct-injection (DI) gaseous-fuelled propulsion systems. Both large eddy simulation (LES) and Reynoldsaveraged
Navier-Stokes (RANS) turbulence modelling techniques were used to evaluate the performance of the new
code. The computational results were compared both quantitatively and qualitatively against available data from the
literature. After initial evaluation of the code, the computational framework was used in conjunction with RANS
modelling (k-ω SST) to investigate the effect of nozzle exit geometry on the characteristics of gaseous jets issued from
millimeter-size nozzles. Cylindrical nozzles with various length to diameter ratios, namely 5, 10 and 20, in addition to
a diverging conical nozzle, were studied. This study is believed to be the first to provide a direct comparison between
RANS and LES within the context of nozzle exit profiling for advanced high-pressure injection systems with the
formation of under-expanded jets. It was found that reducing the length of the straight section of the nozzle by 50%
resulted in a slightly higher level of under-expansion (~2.6% higher pressure at the nozzle exit) and ~1% higher mass
flow rate. It was also found that a nozzle with 50% shorter length resulted in ~6% longer jet penetration length. At a
constant nozzle pressure ratio (NPR), a lower nozzle length to diameter ratio resulted in a noticeably higher jet
penetration. It was found that with a diverging conical nozzle, a fairly higher penetration length could be achieved if an
under-expanded jet formed downstream of the nozzle exit compared to a jet issued from a straight nozzle with the same
NPR. This was attributed to the radial restriction of the flow and consequently formation of a relatively smaller
reflected shock angle. With the conical nozzle used in this study and a 30 bar injection pressure, an under-expanded
hydrogen jet exhibited ~60% higher penetration length compared to an under-expanded nitrogen jet at 100 μs after start
of injection. Moreover, the former jet exhibited ~22% higher penetration compared to a nitrogen jet issued
through the conical profile with 150 bar injection pressure.