LES and RANS modelling of under-expanded jets with application to gaseous fuel direct injection for advanced propulsion systems

Abstract

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.

Modelling of liquid oxygen nozzle flows under subcritical and supercritical pressure conditions

“…towards the wall in the flow regions in the vicinity of M=1 iso-lines (annotated as regions 1-3 in the plots). This flow behaviour is also similar to the velocity field of expanding supersonic gas jets [62]. Finally, as shown in Fig.…”

“…9a, upper panel). The presence of this series of shock cells, which will be thoroughly discussed in section 3.4, is a clear characteristic of an under-expanded jet and confirms the resemblance in expansion dynamics between two-phase flashing and supersonic gas jets [62]. Comparison between the upper and lower panels of Fig.…”

Flow Feature in Supersonic Non-Isobaric Jet near the Nozzle Edge

“…In the LES method, the conservation equations are obtained by filtering the unsteady Navier-Stokes equations, while large-scale eddies are calculated explicitly, and the effects that are caused by smaller eddies are modeled using a subgrid turbulence model. The method, in comparison with RANS, allows the improvement of the modeling quality of turbulent mixing layers, but it requires significantly more computational resources [5,8,[17][18][19].…”

CFD simulations of under-expanded hydrogen jets under high-pressure injection conditions

“…Nevertheless, hydrogen injection has to be operated at high pressure due to the low density of the hydrogen, in order to achieve a proper mixing in the available time, which leads to the formation of highly under-expanded fuel jets downstream [2]. Thus, it is fundamental to have an accurate understanding of supersonic jet formation and mixing that are of great importance for a clean and efficient combustion process [3]. Indeed, many parameters can influence the jet formation.…”

“…For NPR greater than about 4, the jet is said to be under highly under-expanded conditions and is characterised by the formation ofa Mach Disk due to the recompression of the flow during the transition from supersonic to subsonic conditions. Besides, with small nozzle diameters (D ≤ 2 mm), highly under-expanded jets are also formed [3].…”