Publications

The urgent need to combat global warming has spurred legislative efforts within the transport sector to transition away from fossil fuels. Hydrogen is increasingly being utilised as a green energy vector, which can aid the decarbonisation of transport, including internal combustion engines. Computational fluid dynamics (CFD) is widely used as a tool to study and optimise combustion systems especially in combination with new fuels like hydrogen. Since the behaviour of the injection event significantly impacts combustion and emissions formation especially in direct injection applications, the accurate modelling of H2 injection is imperative for effective design of hydrogen combustion systems.

This work aims to evaluate unsteady Reynolds-Averaged Navier Stokes (URANS) modelling of the advective transport process and related numerical methods. Measurements of H2 injection forming supersonic jets inside of constant volume chamber carried out at wide range of relevant conditions are utilised for validation. Investigations focused on aspects of simulated jet definition and its compatibility with Schlieren methods, cubic equations of state as well as probability of the relevant conditions inside the jet, use of adaptive mesh refinement (AMR), mesh dependency, convective flux and colocation methods, nozzle pressure ratio (NPR) effects and contribution of individual terms.

The paper recommends applying molar fraction of H2 to define the jet as well as utilising Soave-Redlich-Kwong as equation of state. Mesh dependency is found to be strongly influenced by nozzle kinetic power (NKP), but not by selection of the turbulence model. Advanced convective flux schemes with flux/slope limiters and colocation generalisation can effectively reduce numerical diffusion and dispersion errors. Finally, comparison of the simulations against physical experiments has shown a good agreement across a wide range of NPRs, proving the reliability of modelling the advection.

Hydrogen direct injection involves shock-containing, under-expanded jets for which Unsteady Reynolds–Averaged Navier–Stokes (URANS) predictions of penetration and mixture preparation are difficult to attribute to turbulence closure alone, because experimental, diagnostic, boundary-condition and numerical uncertainties can obscure model-form effects. This study assesses closure-model effects for a non-reacting, engine-representative high-pressure round (Formula presented.) jet through a controlled Large-Eddy Simulation (LES)–URANS numerical experiment with matched geometry, initial and boundary conditions, numerics and meshing strategy. A ten-realisation LES database, filtered within the dissipative range, is ensemble averaged using a Spherical Intersected Volume (SIV) operator to obtain statistically converged axisymmetric reference fields at approximately 3–5 times lower sampling cost than conventional ensemble sampling. Matched a-posteriori URANS calculations with STandarD (STD), Re-Normalisation Group (RNG), Rapid-Distortion RNG (RDRNG) and Generalised RNG (GRNG) k–ε closures quantify the coupled predictive response, while complementary a-priori frozen-field analyses isolate intrinsic momentum- and species-closure behaviour. With non-closure choices controlled, all tested URANS closures reproduce injection-phase penetration with low relative root-mean-square error of 2.56– (Formula presented.), indicating that larger URANS–experiment penetration discrepancies reported for similar configurations may include substantial non-closure contributions. Residual model-form errors are concentrated in mixture preparation: transport budgets identify turbulent scalar flux, rather than turbulent momentum transport, as the primary initiator of mass-fraction error, and error-propagation analysis shows that these scalar errors propagate through density, pressure and velocity coupling. Accordingly, the inferred LES-consistent turbulent diffusivity is space-, time- and model-dependent, with the corresponding (Formula presented.) spanning approximately 0.1–2, showing that a constant value cannot recover scalar transport consistently. The standard k–ε model gives the highest overall accuracy for the isolated round jet, whereas GRNG provides the most balanced RNG-family response and is therefore the more defensible compromise for engine-relevant applications requiring strain suppression. These results support closure-consistent, dynamically varying (Formula presented.) formulations, together with higher-fidelity realisable stress closures, pressure- and density-aware adaptive mesh refinement, and RNG-family extensions for future high-pressure gaseous-injection modelling.