Burning hydrogen in conventional internal combustion (IC) engines is associated with zero carbon-based tailpipe exhaust emissions. In order to obtain high volumetric efficiency and eliminate abnormal combustion modes such as preignition and backfire, in-cylinder direct injection (DI) of hydrogen is considered preferable for a future generation of hydrogen IC engines. However, hydrogen's low density requires high injection pressures for fast hydrogen penetration and sufficient in-cylinder mixing. Such pressures lead to chocked flow conditions during the injection process which result in the formation of turbulent under-expanded hydrogen jets. In this context, fundamental understanding of the under-expansion process and turbulent mixing just after the nozzle exit is necessary for the successful design of an efficient hydrogen injection system and associated injection strategies. The current study used large-eddy simulation (LES) to investigate the characteristics of hydrogen under-expanded jets with different nozzle pressure ratios (NPR), namely 8.5, 10, 30 and 70. A test case of methane injection with NPR=8.5 was also simulated for direct comparison with the hydrogen jetting under the same NPR. The near-nozzle shock structure, the geometry of the Mach disk and reflected shock angle, as well as the turbulent shear layer were all captured in very good agreement with data available in the literature. Direct comparison between hydrogen and methane fuelling showed that the ratio of the specific heats had a noticeable effect on the near-nozzle shock structure and dimensions of the Mach disk. It was observed that with methane, mixing did not occur before the Mach disk, whereas with hydrogen high levels of momentum exchange and mixing appeared at the boundary of the jet. This was believed to be the effect of the high turbulence fluctuations at the nozzle exit of the hydrogen jet which triggered Gortler vortices. Generally, the primary mixing was observed to occur after the location of the Mach disk and particularly close to the jet boundaries where large-scale turbulence played a dominant role. It was also found that NPR had significant effect on the mixture's local fuel richness. Finally, it was noted that applying higher injection pressure did not essentially increase the penetration length of the hydrogen jets and that there could be an optimum NPR that would introduce more enhanced mixing whilst delivering sufficient fuel in less time. Such an optimum NPR could be in the region of 100 based on the geometry and observations of the current study.3

The current study used large eddy simulations to investigate the sonic and mixing characteristics of turbulent under-expanded hydrogen and methane jets with various nozzle pressure ratios issued into various ambient pressures including elevated conditions relevant to applications in direct injection gaseous-fuelled internal combustion engines. Due to the relatively low density of most gaseous fuels such as hydrogen and methane, DI requires high injection pressures to achieve suitable mass flow rates for fast in-cylinder fuel delivery and rapid fuel-air mixing. Such pressures typically form an under-expanded fuel jet past the nozzle exit. Test cases of hydrogen injection with nozzle pressure ratio (NPR) of 10 issued into quiescent air with pressure P ∞ ≈1, 5 and 10 bar were simulated. Direct comparison between hydrogen and methane jets with NPR=8.5 and P ∞ ≈1 was also made. The effect of ambient pressure on features of transient development of the nearnozzle shock structure and tip vortices (vortex ring) was investigated. It was observed that at constant NPR, higher ambient pressure resulted in slightly faster formation of the Mach reflection and shorter Mach disk settlement time. Different mechanisms were observed between hydrogen and methane with regards to transient formation of their initial tip vortex rings. It was found that the initial transient tip vortices of hydrogen jets may also contribute to the flow instabilities at the boundary of the intercepting shock and, unlike for methane, promote fuel-air mixing before the Mach reflection. It was also shown that the nearnozzle shock structure was only affected by NPR regardless of the ambient pressure. Furthermore, no flow recirculation zone was found just downstream of the Mach disk, a finding comparable to all previous experimental investigations. Also, it was observed that a locally richer mixture was created for jets with higher NPR or with higher ambient pressure at constant NPR. Based on the results of the current study, correlations were proposed for the shock cell spacing and jet tip penetration of highly under-expanded jets issued from millimetre-size circular nozzles.

Hydrogen has been largely proposed as a possible fuel for internal combustion engines. The main advantage of burning hydrogen is the absence of carbon-based tailpipe emissions. Hydrogen's wide flammability also offers the advantage of very lean combustion and higher engine efficiency than conventional carbon-based fuels. In order to avoid abnormal combustion modes like pre-ignition and backfiring, as well as air displacement from hydrogen's large injected volume per cycle, direct injection of hydrogen after intake valve closure is the preferred mixture preparation method for hydrogen engines. The current work focused on computational studies of hydrogen injection and mixture formation for direct-injection spark-ignition engines. Hydrogen conditions at the injector's nozzle exit are typically sonic. Initially the characteristics of under-expanded sonic hydrogen jets were investigated in a quiescent environment using both Reynolds-Averaged NavierStokes (RANS) and Large-Eddy Simulation (LES) techniques. Various injection conditions were studied, including a reference case from the literature. Different nozzle geometries were investigated, including a straight nozzle with fixed cross section and a stepped nozzle design. LES captured details of the expansion shocks better than RANS and demonstrated several aspects of hydrogen's injection and mixing. Incylinder simulations were also performed with a side 6-hole injector using 70 and 100 bar injection pressure. Injection timing was set to just after inlet valve closure with duration of 6 μs and 8 μs, leading to global air-to-fuel equivalence ratios  typically in the region of 0.2-0.4. The engine intake air pressure was set to 1.5 bar absolute to mimic boosted operation. It was observed that hydrogen jet wall impingement was always prominent. Comparison with non-fuelled engine conditions demonstrated the degree of momentum exchange between in-cylinder hydrogen injection and air motion. LES highlighted details of hydrogen's spatial distribution throughout the injection duration and up to ignition timing. Higher peak velocities were predicted by LES, especially on the tumble plane. With the employed injection strategy, the areas closer to the cylinder wall were richer in fuel than the centre of the chamber close to the end of compression.

Flash-boiling of sprays may occur when a superheated liquid is discharged into an ambient environment with lower pressure than its saturation pressure. Such conditions normally exist in direct-injection spark-ignition engines operating at low incylinder pressures and/or high fuel temperatures. The addition of novel high volatile additives/fuels may also promote flashboiling. Fuel flashing plays a significant role in mixture formation by promoting faster breakup and higher fuel evaporation rates compared to non-flashing conditions. Therefore, fundamental understanding of the characteristics of flashing sprays is necessary for the development of more efficient mixture formation. The present computational work focuses on modelling flash-boiling of n-Pentane and isoOctane sprays using a Lagrangian particle tracking technique. First an evaporation model for superheated droplets is implemented within the computational framework of STAR-CD, along with a full set of temperature dependent fuel properties. Then the computational tool is used to model the injection of flashing sprays through a six-hole asymmetric injector. The computational results are validated against optical experimental data obtained previously with the same injector by high-speed imaging techniques. The effects of ambient pressure (0.5 and 1.0 bar) and fuel temperature (20-180° C) on the non-flashing and flashing characteristics are examined. Effects of initial droplet size and break-up submodels are also investigated. The computational methodology is able to reproduce important physical characteristics of flashboiling sprays like the onset and extent of spray collapse. Based on the current observations, further improvements to the mathematical methodology used for the flash-boiling model are proposed.

The Poisson equation is commonly encountered in engineering, for instance, in computational fluid dynamics (CFD) where it is needed to compute corrections to the pressure field to ensure the incompressibility of the velocity field. In the present work, we propose a novel fully convolutional neural network (CNN) architecture to infer the solution of the Poisson equation on a 2D Cartesian grid with different resolutions given the right-hand side term, arbitrary boundary conditions, and grid parameters. It provides unprecedented versatility for a CNN approach dealing with partial differential equations. The boundary conditions are handled using a novel approach by decomposing the original Poisson problem into a homogeneous Poisson problem plus four inhomogeneous Laplace subproblems. The model is trained using a novel loss function approximating the continuous $ {L}^p $ norm between the prediction and the target. Even when predicting on grids denser than previously encountered, our model demonstrates encouraging capacity to reproduce the correct solution profile. The proposed model, which outperforms well-known neural network models, can be included in a CFD solver to help with solving the Poisson equation. Analytical test cases indicate that our CNN architecture is capable of predicting the correct solution of a Poisson problem with mean percentage errors below 10%, an improvement by comparison to the first step of conventional iterative methods. Predictions from our model, used as the initial guess to iterative algorithms like Multigrid, can reduce the root mean square error after a single iteration by more than 90% compared to a zero initial guess.

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.

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The mixing characteristics of highly turbulent under-expanded gaseous fuel jets issued from millimeter-size circular nozzles are important for developing advanced direct injection gaseous-fuelled internal combustion engines. In the present study high-resolution large eddy simulation in conjunction with an adaptive mesh refinement technique was used in order to investigate key mixing characteristics of under-expanded hydrogen and methane jets under various ambient thermodynamics. Penetration rate, volumetric growth and initial transient vortex ring behaviour were investigated under near atmospheric and elevated ambient pressures and temperatures, P ∞ ≈1 bar and 10 bar, T ∞ =296 K and 600 K, using a nozzle pressure ratio of 10. The conditions corresponded to injection strategies ranging from late intake stroke around inlet valve closure to late compression. It was observed that increasing the ambient temperature at constant pressure resulted in increase in both tip penetration and volumetric growth of the under-expanded jets. It was also found that the effect of diffusivity, ratio of specific heats and ambient density must be considered when scaling volumetric growth of under-expanded jets of different gases and/or when issued into different ambient temperatures. Moreover, substantial differences were observed between the transient jet formation of hydrogen and methane fuels. It was found that the embedded shock structures and supersonic annular shear layers played a significant role in the formation and evolution of the transient preliminary and secondary vortex rings. It was also noted that the evolution of the vortex ring influenced significantly the volumetric growth and hence mixing quality of under-expanded jets.