Large-eddy simulation of hydrogen ignition and NO x formation in diesel-pilot dual-fuel combustion

Abstract

This study examines the dynamics of diesel/hydrogen dual-fuel combustion in a constant-volume vessel under compression ignition engine conditions, where a small pilot n-heptane (a surrogate of diesel) injection precedes a long-duration hydrogen main injection containing 93.6% of the energy share. We investigate how pilot n-heptane flame and hydrogen injection affect emissions and combustion by systematically varying the dwell time ( $Δ$ t between the end of n-heptane injection and the start of hydrogen injection) while keeping the injection rate profile fixed. Large eddy simulations with detailed chemistry are performed at vessel conditions of 890 K, 52 bar, and 21 vol.% O $_{2}$ , and compared against Schlieren and apparent heat-release rate derived from measurements. The simulations show a good agreement with experimental results regarding ignition onset and flame propagation. The pilot n-heptane ignites rapidly at the spray tip, $\sim$ 0.5 ms after injection; thereafter, the flame propagates upstream toward the injector nozzle. The hydrogen jet ignites nearly immediately upon its intersection with the n-heptane flame. Varying the dwell time between the end of n-heptane injection and the start of hydrogen injection significantly affects hydrogen ignition timing, peak heat release rates, and NO $_{x}$ emissions. Notably, while longer dwell times lead to delayed hydrogen ignition and lower NO $_{x}$ formation, medium dwell times result in higher NO $_{x}$ emissions, showing a complex non-linear relationship between hydrogen-diesel combustion and NO $_{x}$ emissions.

Keywords

Hydrogen direct injection internal combustion engine compression ignition

Highlights

Ignition consistently initiates near $ϕ \approx$ 0.6 at the pilot–hydrogen interface.

Dwell-time strongly influences ignition delay and flame development pathways.

Large eddy simulation reveals mixing-controlled ignition propagation into hydrogen-richer zones.

NO $_{x}$ accumulation is the highest in the mixing region between the hydrogen jet and the pilot.

Introduction

Hydrogen (H $_{2}$ ) emerges as a promising energy carrier for future energy systems, offering notable benefits for electrochemical and combustion-based energy conversion processes. In internal combustion engines (ICEs), hydrogen is particularly valued for its zero-carbon emission, positioning it as an environmentally friendly alternative to conventional fossil fuels.^1–5 Additionally, hydrogen’s high laminar flame speed enhances combustion efficiency. This leads to higher overall engine efficiencies than those achievable with diesel.⁶ The capability of stable hydrogen combustion in fuel-lean mixtures, due to its wide flammability limits and low ignition energy,² further supports high fuel economy and reduced combustion temperatures.

However, the advantages of using hydrogen in ICE come with several technical challenges that hinder its widespread adoption. Hydrogen’s high auto-ignition temperature allows for the use of higher compression ratios, potentially improving thermal efficiency. At the same time, its low ignition energy, while beneficial for lean combustion, also increases the risk of premature ignition caused by hot spots or residual gases in the combustion chamber.⁷ Moreover, the relatively high auto-ignition temperature of hydrogen (858 K) often requires the use of ignition aids if increasing the compression ratio is not a feasible solution. Additionally, the physical properties of hydrogen, particularly its low density, pose significant challenges for storage and injection into the combustion chamber. Addressing these challenges requires further technological advancements and research to realize hydrogen’s potential as a fuel for ICEs.

Internal combustion engines predominantly utilize two methods of fuel injection: port fuel injection (PFI) and direct injection (DI). PFI involves injecting fuel into the intake port and mixing it with air before entering the combustion chamber. This method allows for significant air–fuel mixing early in the compression cycle, resulting in homogeneous fuel/air mixtures with controlled equivalence ratios. However, when hydrogen is injected using PFI, its low density displaces a considerable air volume during the intake valve opening period, reducing volumetric efficiency.⁸ Additionally, PFI increases the risk of knocking or premature ignition in a premixed or partially premixed hydrogen/air mixture due to exposure to hot spots within the chamber.

In contrast, DI techniques inject fuel directly into the combustion chamber and avoid the drawbacks associated with volumetric efficiency loss and premature ignition. DI is subdivided into high-pressure direct injection (HPDI) and low-pressure direct injection (LPDI) strategies based on the rail pressure used. Injection pressure below 50 bar classify an injection system as LPDI, which typically necessitates to inject the fuel early in the cycle, before cylinder pressure becomes too high to overcome, and thus favors premixed combustion mode. On the other hand, HPDI systems, operating above 50 bar, permit fuel injection at various stages throughout the cycle, including late injection near the top dead center, offering greater flexibility and efficiency.⁹

In HPDI systems, hydrogen’s low density combined with high injection pressures can lead to complex fluid dynamic phenomena such as the formation of shock-waves at the injector nozzle outlet. The presence and characteristics of these shock-waves are greatly influenced by the ratio of injection pressure to back pressure within the combustion chamber.¹⁰ Experimental investigations have shown that these dynamics are critical for understanding how hydrogen behaves under actual engine conditions. For instance, previous studies have detailed how shock-waves can significantly affect the dispersion and hydrogen mixture in the chamber,¹¹ which could impact efficiency and emission profiles. Dauptain et al.¹² explored the behavior of supersonic hydrogen flows, demonstrating how shockwave patterns change with varying pressure ratios. These phenomena have been extensively studied through numerical simulations, particularly employing large eddy simulation (LES).^13,14

Reacting hydrogen jets under high-pressure conditions introduce additional complexities, particularly regarding ignition and flame stabilization. These processes are highly sensitive to variations in ambient conditions, such as oxygen concentration and temperature, which directly influence flame dynamics and ignition characteristics. While less extensively studied compared to non-reactive jet behavior, reacting cases present unique challenges and phenomena that are critical for practical applications. Roy et al.¹⁵ explored the ignition processes by directly injecting a hydrogen jet and igniting it with a spark in a constant volume chamber. Subsequently, more advanced ignition methods have been employed, such as using a laser to initiate combustion under engine-like conditions. It was revealed that the key phenomenon governing flame regression towards the nozzle is the edge-flame deflagration, which is highly dependent on the concentration of ambient oxygen.¹⁶ Naber and Siebers¹⁷ reported that the combustion rate appeared insensitive to changes in oxygen concentration during the mixing-controlled phase of hydrogen jet combustion. Further studies, such as those by Yip et al.,¹⁸ focused on the auto-ignition of hydrogen in constant volume vessels resembling compression ignition engine conditions, where ignition typically starts at a single kernel and subsequently engulfs the jet. These studies show that the lift-off length varies with oxygen concentration, extending significantly at lower levels (10 vol.% O $_{2}$ ).

The hydrogen’s high auto-ignition temperature necessitates innovative strategies for efficient ignition in compression ignition (CI) engines. Dual-fuel strategies, which utilize a fuel with a higher cetane number, like diesel in a pilot injection to initiate the combustion process, offer a practical solution to this problem. Such strategies enhance ignition reliability and overall engine efficiency.^19–23 For example, White²¹ investigated diesel-natural gas dual-fuel configurations using both experimental and numerical methods, finding that converging injector configurations offer better combustion characteristics than parallel configurations. This finding was further supported by experiments conducted in a rapid compression machine, which showed that diesel-natural gas mixtures benefited from converging injector configurations.^22,23 Specifically, stronger interaction between the hydrogen jet and the pilot plume enhances local mixing and thermal coupling, which accelerates the onset of ignition in the hydrogen-rich region and minimizes the extent of premixing. Additionally, these studies observed that the strong interaction between the two fuels could occasionally result in flame quenching, underscoring the delicate balance required in dual-fuel combustion dynamics.

A recent publication experimentally investigated diesel-hydrogen dual-fuel strategies in a constant volume vessel, focusing on varying the injection order between diesel-pilot and hydrogen-main, alongside modifications in ambient conditions and dwell times.²⁴ Unlike experiments with natural gas, these studies did not report quenching effects with hydrogen, indicating a more stable interaction between hydrogen and diesel. It was also observed that increasing the dwell time required prolonged exposure to the diesel flame to achieve successful hydrogen ignition. In related research,²⁵ adjustments to the energy share of diesel and hydrogen were explored, with hydrogen injected first to ensure thorough mixing with air before ignition by diesel. They reported a significant reduction in the hydrogen flame lift-off length, approaching near-zero except in cases of low ambient oxygen concentration.

These studies suggest that the understanding of the interplay between fuel interaction dynamics, mixture heterogeneity, and flame behavior under various operational settings can significantly guide the development of more efficient and cleaner dual-fuel combustion systems. However, at low temperatures, the variability of hydrogen ignition—owing to flammability limits, ignition energy requirements, and mixing quality—remains a key challenge, showing the importance of injection sequence and dwell time in dual-fuel CI strategies. A well-timed injection sequence that promotes adequate mixing while preventing excessive cooling or dilution of the combustion zone can lead to more efficient combustion and better fuel utilization.

LESs of pure hydrogen jets have been reported in the literature. The work of Hamzehloo and Aleiferis¹⁴ investigated the effect of the nozzle pressure ratio on under-expanded hydrogen jets in internal combustion engine applications, studying the interplay between compressibility effects and near-nozzle mixing. Ali et al.²⁶ examined the oscillation modes of Mach disks and their influence on turbulent transition using a density-based, low-dissipation finite-volume solver. Ballatore and van Oijen²⁷ performed LES with a pressure-based solver and a WALE subgrid-scale model combined with fourth-order cubic convective schemes, successfully capturing the mixing behavior of under-expanded hydrogen jets in a constant-volume combustion chamber (CVCC). In a subsequent study, Ballatore et al.²⁸ developed an HR-FGM chemistry tabulation approach capable of accurately predicting ignition delay, kernel location, and flame stabilization. Their results suggested that hydrogen flame recession toward the nozzle may be driven by a sequence of auto-ignition events. The HR-FGM framework was further extended to hydrogen–argon–oxygen mixtures under systematically varied ambient pressure and temperature conditions.²⁹

A related numerical study on dual-fuel heptane-hydrogen HPDI in a CVCC was conducted by Lucchini et al.³⁰ Using the same experimental configuration considered in the present work,²⁴ they performed RANS simulations aimed at calibrating an FGM approach for subsequent application in engine simulations and accelerated optimization. To the authors’ knowledge, no LES studies of dual-fuel heptane-hydrogen combustion in a CVCC configuration have been reported to date.

The primary objective of this work is to use high-fidelity LESs to enhance understanding of the interaction dynamics between diesel flame and hydrogen jet under dual-fuel HPDI CI engine conditions. This study builds upon the experimental findings of Rorimpandey et al.,²⁴ specifically examining scenarios where diesel pilot injections precede hydrogen injections. The focus will be on three distinct cases, differentiated solely by their dwell times, as documented in the referenced experiments.²⁴ Through the use of LES, this research aims to deepen the understanding of the mixing and ignition processes of these two fuels, providing detailed insights into the complex mechanisms of hydrogen jet ignition that are not evident from experimental observations alone.

Experiment specifications

In the experiments carried out at UNSW,²⁴ an n-heptane “pilot” (C $_{7}$ H₁₆) and a hydrogen “main” injection occur inside a cubic constant volume combustion vessel with a side length of 114 mm. The chamber is equipped with optical windows measuring 108 mm in diameter, allowing high-speed Schlieren imaging to capture the outline of the fuel jet and flames. The high-speed camera operates at 30,000 frames per second and has a shutter speed of 1.9 $μ$ s, providing an image resolution of $\sim$ 0.15 mm per pixel.

Additionally, chamber pressure is measured with a pressure transducer, and temperature is acquired at the geometrical center of the chamber with a thin-wire K-type thermocouple. To recreate the relevant conditions for CI engines, an initial mixture of air, acetylene (C $_{2}$ H $_{2}$ ), and hydrogen is spark ignited in the chamber. The post-burn mixture composition is listed in Table 1. During the cool-down phase, pressure and temperature measurements are used to trigger fuel injection as soon as they reach the wanted values of 5.2 MPa and 890 K, respectively. Pressure is acquired until the end of hydrogen injection and used to derive the apparent heat release rate (aHRR) diagrams.

Table 1.

Initial conditions and after-burn ambient gas composition.²⁴

Initial ambient gas composition (mole fraction)
O $_{2}$ (%)	0.2063
N $_{2}$ (%)	0.6812
CO $_{2}$ (%)	0.06
H $_{2}$ O (%)	0.035
Initial conditions
Temperature (K)	890
Pressure (MPa)	5.2

The injection parameters, including fuel mass, injection pressure, and duration, are kept constant in each condition. In this work, we only consider three “pilot first” cases, varying in time between the injections. Specifically 0.93, 1.93, and 2.93 ms have been selected. Time t = 0 denotes the start of n-heptane injection. For clarity, throughout, after start of injection (aSOI) refers to the time after the diesel start of injection (SOI). Table 2 shows the injection parameters and the three cases studied. The wall temperature was kept at a constant value of 403 K, to prevent water condensation during the experiment.

Table 2.

Injection details for both fuels and case setup extracted from the experimental measurement.²⁴

Parameter	n-Heptane	Hydrogen
Injector nozzle diameter (mm)	0.105	0.58
Reservoir pressure (bar)	700	200
Injection duration (ms)	0.74	3.52
Injected mass (mg)	0.99	5.22
Energy share (%)	6.4	93.6
Lower heating value (MJ/kg)	43.2	120

Cases	Dwell time (ms)	SOI hydrogen (ms)
I	0.93	1.67
II	1.93	2.67
III	2.93	3.67

SOI: start of injection.

A total of 0.99 mg of n-heptane and 5.28 mg of hydrogen are injected through individual single hole injectors with a converging layout as shown in Figure 1(a) and hole diameter of 0.105 mm for the n-heptane and 0.58 mm for the hydrogen. Total injected energy is 676.8 J, 6.4% of which is accounted by the n-heptane pilot.

Figure 1.

(a) Hydrogen and diesel injector configuration used in the experiments.²⁴ (b) The flow rate profiles imposed as boundary conditions of the n-heptane and hydrogen injections for Case I.

Numerical setup

The simulations solved the fully compressible Navier–Stokes equations with detailed species and internal energy transport, coupled to spray and combustion sub-models, in the CONVERGE computational fluid dynamics (CFD)³¹ software framework. The pressure-implicit with splitting of operators algorithm was selected for pressure–velocity coupling, with a density-based convergence criterion. Second-order spatial accuracy was achieved using a blended Monotone Upstream-centered Scheme for Conservation Laws scheme with total variation diminishing flux limiting, while time integration used a variable time-step constrained by Courant-Friedrichs-Lewy (CFL), chemical source terms, and parcel motion. The maximum velocity-based CFL number was limited to 1, with additional constraints imposed by chemical heat release and parcel dynamics. All governing equations were solved in conservative form with strict conservation enforced for all transported quantities. Turbulence was modeled using LES with a dynamic Smagorinsky-type sub-grid scale model. The SGS kinetic-energy formulation was enabled, together with the Werner–Wengle³² wall model for near-wall treatment. A time interval of 0–8 ms was simulated. The numerical domain is a cube with a side length of 114 mm, as per the experimental study. The geometry of the hydrogen injector nozzle is also part of the mesh, and it is modeled as a cylindrical pipe having 0.58 mm of diameter and 1 mm of length, centered with respect to one of the walls of the chamber, as by Rorimpandey et al.²⁴

The n-heptane pilot injection was modeled using Lagrangian particle tracking with KH-RT breakup³³ and dynamic drag. Liquid n-heptane (C $_{7}$ H₁₆) was injected at 320 K through a single nozzle model with a diameter of 105 $μ$ m and a solid cone angle of 26°, located 12.3 mm above the hydrogen pipe and angled at 12°, as shown in Figure 1(a). A total of 0.99 mg of n-heptane are injected over a duration of 0.74 ms, following a prescribed rate-shape profile in Figure 1(b). Droplet evaporation was modeled using the Frossling correlation,³⁴ and parcel wall interaction followed the Naber-Reitz rebound–slide model.³⁵ The discharge coefficient for the n-heptane injector, which quantifies the extent of cavitation in the nozzle, was set to 1.

Hydrogen was introduced through a dedicated mass-flow inlet boundary, supplying pure H $_{2}$ at 403 K with imposed turbulent inflow fluctuations. A Fourier-based synthetic turbulence method³⁶ was applied at the inlet with an intensity of 6% and a prescribed integral length scale of 0.174 mm, promoting realistic turbulence–chemistry interaction in the jet region. Inlet pressure was treated with a Neumann condition. The H $_{2}$ mass flow rate is a trapezoidal shape with a ramp-up time of 0.3 ms and a ramp-down time of 0.05 ms, as shown in Figure 1(b). The profile in this figure is the same for all cases except that the hydrogen flow rate profile is shifted along the time axis for different dwell time cases. The steady-state peak flow rate is measured in the experiments to be 1.56 mg/ms.²⁴ A total mass of 5.28 mg of H $_{2}$ fuel was injected.

The pre-combustion process used in the experiments is not simulated. The domain was initialized as a homogeneous mixture at 5.2 MPa and 890 K, representative of the constant-volume experimental conditions. The initial gas composition corresponded to an oxidized, vitiated mixture containing O $_{2}$ , N $_{2}$ , CO $_{2}$ , and H $_{2}$ O. The wall temperature is prescribed at 403 K, with wall heat transfer modeled using the O’Rourke formulation.³⁷ Gas-phase thermodynamics were modeled using a real-gas Redlich–Kwong equation of state. Combustion modeling was enabled with a detailed chemical mechanism from Seidel et al.,³⁸ with 58 species and 128 reactions. Species transport used mixture-averaged diffusion, and energy was solved in terms of specific internal energy. Gas-phase combustion was modeled using the SAGE detailed chemistry solver in constant-volume mode. NO $_{x}$ species were transported, using a 16-step mechanism from Yoshikawa and Reitz³⁹ All heat release was governed directly by detailed chemistry.

Converge CFD implements a Cartesian grid of a specified base size of 4 mm, locally refined at the injection locations, where the jet have the highest Mach number. These fixed refinements are aligned with the axis of injection of each fuel, so that each jet is orthogonal to the upstream cell face. The cell size of the refined regions is 0.125 mm for the heptane and 0.0625 mm for the hydrogen, and extends for 15 mm along the injection direction. Additionally, automatic mesh refinement (AMR) was dynamically triggered based on sub-grid scale (SGS) criteria on velocity, temperature and species mass fraction, refined down to a minimum cell size of 0.125 mm. This ensured adequate resolution of both the premixed hydrogen regions and the liquid-fuel vaporization zones. Refinement was further enforced near fixed refinement interfaces to avoid resolution discontinuities. The total number of computational cells was capped at 50 million to control computational cost.

Figure 2(a) shows the resulting mesh in the center of the domain before hydrogen ignition. Figure 2(b) shows the growing number of cells throughout the simulation, due AMR. In the picture, a substantial change of slope closely follows the instant of hydrogen SOI in each case.

Figure 2.

(a) The mesh through the center of the domain before hydrogen ignition. (b) The cell count for all three cases against time.

It is important to note that shock-resolved accuracy is not claimed in the present simulations. This limitation may influence the prediction of near-nozzle jet development and flame lift-off stabilization. However, the current mesh resolution is considered sufficient for capturing the macroscopic mixing and combustion characteristics focused on in this work.

Results and discussion

Validation of LES results

Figure 3(a) compares mid-plane temperature contours from LES with Schlieren images from the experiment for the short-dwell and long-dwell cases. The first row corresponds to the experimentally derived pilot ignition delay, obtained from pressure traces and reported in Table 3. In the simulations, ignition occurs at 0.57 ms in both cases. Between 0.57 and 0.70 ms, the LES indicates further development of the n-heptane flame, reflected by the broader flame structure at the later time.

Figure 3.

A comparison of the Schlieren imaging from (black and white) the experiments and the simulation²⁴ (temperature contour) for (a) the dwell time of 0.93 ms (Case I) and (b) the dwell time of 2.93 ms (Case III). In the post-processed Schlieren images, the red, blue, and green contours denote the heptane jet, the hydrogen jet, and the flame, respectively.

Table 3.

Experimental versus simulated IDT (derived from aHRR).²⁴

Case	Pilot IDT [ms]	Main IDT [ms]	Main IDT [ms]
Case	Pilot IDT [ms]	after pilot SOI	after main SOI
D-0.93 ms-H exp.	0.58 $\pm$ 0.09	1.19 $\pm$ 0.09	0.26 $\pm$ 0.09
D-0.93 ms-H sim.	0.56	1.20	0.27
D-1.93 ms-H exp.	0.69 $\pm$ 0.03	2.30 $\pm$ 0.05	0.37 $\pm$ 0.05
D-1.93 ms-H sim.	0.53	2.28	0.35
D-2.93 ms-H exp.	0.66 $\pm$ 0.03	3.43 $\pm$ 0.14	0.50 $\pm$ 0.14
D-2.93 ms-H sim.	0.54	3.32	0.39

IDT: ignition delay time; aHRR: apparent heat release rate; SOI: start of injection.

The second row shows snapshots acquired 0.4 ms after pilot ignition for the short-dwell case and 2.37 ms after pilot ignition for the long-dwell case. In the long-dwell configuration, the LES predicts a pronounced cooling of the heptane flame, indicating decay of the pilot radical pool before hydrogen ignition. The third and fourth rows illustrate the subsequent kernel development in the main fuel, highlighting the transfer of ignition from the n-heptane radical pool to the hydrogen mixture. The third column of Table 3 reports the main-fuel ignition delay measured after hydrogen SOI, which provides an approximate measure of the degree of hydrogen premixing before ignition. The longer hydrogen ignition delay observed in the long-dwell case is consistent with the reduced reactivity caused by the cooling of the pilot flame. In both experiment and simulation, the main hydrogen flame initially ignites near the jet tip. However, in the long-dwell experimental case, an additional upstream ignition kernel is observed at 3.57 ms, which merges with the tip kernel by 3.63 ms. The last two rows show the flame stabilization behavior. The LES consistently predicts flame lift-off, whereas the experimental flames remain anchored at the nozzle. This discrepancy is likely related to an under-prediction of radial jet spreading and shear-layer mixing in the simulations, leading to elevated axial velocities and scalar dissipation rates near the nozzle. Comparing the two simulated cases, the predicted lift-off distance is smaller in the short-dwell configuration, which may be attributed to the higher temperature of the residual pilot flame, promoting reactions closer to the hydrogen injector.

Overall, the topology of the n-heptane and hydrogen experimental flame, the timing of the interaction between the jets, as well as the progression of the hydrogen flame toward the hydrogen injector nozzle, are well captured by the simulation.

The aHRR for each case is shown in Figure 4. The LES results were compared with multiple realizations of the experimental data. The ignition delay time (IDT) of both fuels reported in the experiments shows variations not only for different dwell time cases but also for runs of the same dwell time. This scattering in aHRR and IDT can result from fluctuations in the turbulent flow and the thermodynamic variables in the combustion chamber, such as random hot spots. All experimental and simulation profiles have undergone the same filtering procedure to eliminate high-frequency fluctuations in the data. The aHRR in both the experiments and simulation is calculated from the pressure trace using the following equation:⁴⁰

\frac{d Q}{d t} = \frac{1}{γ - 1} V \frac{d P}{d t}

(1)

where

γ

is the specific heat ratio, P is the pressure in the chamber, and V is the chamber volume.

Figure 4.

The aHRR from LES and several experimental runs for different dwell times of (a) 0.93 ms (Case I); (b) 1.93 ms (Case II); and (c) 2.93 ms (Case III).

For all cases, the first aHRR peak, around 1 ms, shows the onset of ignition of n-heptane, which occurred shortly after the end of the n-heptane injection. The heat release from hydrogen combustion can be divided into two phases: partially premixed flame propagation upstream toward the jet nozzle and diffusion-controlled combustion. Considering Case I, aHRR starts raising again, after the pilot bump, at 1.20 ms, and reaches its peak at around 1.7 ms, denoting partially premixed combustion along this time span. aHRR then flattens at 2.07 ms, indicating a quasi-steady-state hydrogen jet diffusion flame. In this phase, combustion is controlled by the rate at which fuel and oxidizer are supplied to the reaction zone of the hydrogen jet. The aHRR from the diffusion flame shows good agreement between the experiment and simulation for the short and long dwell time cases. However, in the medium dwell-time case, quasi-steady-state aHRR is under-predicted. The cause of this miss-prediction could be found in slightly different hydrogen mass flow rates between the experiments and simulations. Constant steady-state hydrogen injection profiles are used in the simulations, whereas some variations may be present in the experiments.

Counterflow diffusion flame extinction analysis

To better understand the lift-off discrepancy, it is essential to consider the established mechanisms for flame lift-off in non-premixed jet flames, which include (a) high-scalar dissipation rates near the nozzle, leading to local flame extinction,⁴¹ (b) edge flame propagation speeds being slower than the local flow speeds in the mixing layer, preventing the flame from reaching the nozzle,⁴² and (c) the flow residence time being shorter than the ignition delay time of the mixture.^43,44

Figure 5(a) shows the hydrogen jet velocity and Mach number radial profiles at 4 ms after pilot SOI, at different distances from the nozzle, for the medium dwell case. The flow is primarily subsonic, except for the jet-core close to the nozzle. At 4 mm and 8 mm from the nozzle, the high velocity gradient in the radial direction increases local scalar dissipation, which implies flame extinction in the near nozzle region.⁴¹ Moreover, jet velocity is very high also at the periphery, before the sharp drop, possibly higher than flame regression speed.⁴² Thus, the over-prediction of the lift-off of the hydrogen flame is due to the under-prediction of the hydrogen jet’s radial spreading, which could result from the low mesh resolution in the injector pipe and in the proximity of the nozzle region. Downstream of the jet core region, the flow residence time increases, the velocity drops, and the jet spreads significantly in the radial direction, leading to increased mixing and a low scalar dissipation rate, which enables the flame to sustain itself downstream of the jet core.

Figure 5.

(a) Velocity and Mach number profile along the radial direction of the H $_{2}$ jet at 4 ms. The black, red, and green lines refer to a distance from the nozzle of 12, 8, and 4 mm, respectively. Solid lines are velocity and dashed lines are Mach numbers and (b) Mach number of hydrogen injection at 4 ms.

To provide a canonical reference for flame extinction under the thermochemical conditions relevant to the present simulations, a series of laminar opposed-flow (non-premixed) hydrogen–air flames was computed using the CounterflowDiffusionFlame solver in Cantera.⁴⁵ The configuration consists of axis-symmetric, opposed fuel, and oxidizer jets, which generate a quasi-one-dimensional strained diffusion flame. The extinction point was determined following the scaling-based batch continuation procedure proposed by Fiala and Sattelmayer.⁴⁶ Starting from a low-strain, steady-burning solution, the imposed strain rate was systematically increased. At each step, an initial guess for the new solution was constructed by scaling the grid spacing, inlet mass fluxes, velocity field, and pressure curvature according to analytical scaling relations derived for counter-flow diffusion flames.

For each strain-rate level, the flame was solved to steady state, and the maximum temperature $T_{max}$ was recorded. Extinction was identified when the flame could no longer sustain a temperature rise above the inlet temperature, and the extinction strain rate was defined as the strain rate of the last stable burning solution. Figure 6 shows the evolution of $T_{max}$ as a function of the maximum axial strain rate $a_{max}$ , showing the characteristic gradual temperature decrease followed by a sharp collapse near extinction.

Figure 6.

Evolution of $T_{max}$ as a function of the maximum axial strain rate $a_{max}$ .

At the extinction point, several commonly used strain-rate definitions were evaluated, including the mean axial strain rate, the maximum axial strain rate, the inlet potential-flow strain rates, and the axial strain rate at the stoichiometric surface. The latter,

a_{stoich, ext} = 2.71 \times 10^{5} s^{- 1}

is particularly relevant, as non-premixed flames are anchored near the stoichiometric mixture-fraction surface and their stability is governed by the local balance between chemical time scales and scalar dissipation.

The counter-flow extinction analysis provides a quantitative reference for the maximum strain (or, equivalently, scalar dissipation rate) that a diffusion flame can sustain under the present thermochemical conditions. To establish a quantitative extinction threshold in terms of scalar dissipation rate, the stoichiometric scalar dissipation rate at extinction, $χ_{st, ext}$ , was extracted from the counter-flow diffusion flame simulations. For the last stable burning solution prior to extinction, the mixture fraction profile $Z (x)$ was computed using the Bilger⁴⁷ formulation, which provides a conserved scalar for non-premixed combustion. The stoichiometric mixture fraction $Z_{st}$ was determined directly from the inlet compositions based on elemental mass conservation for hydrogen-air combustion. The local scalar dissipation rate was then evaluated as follows:

χ (x) = 2 D {(\frac{d Z}{d x})}^{2}

where

D

is a constant molecular diffusivity, chosen to be identical to the value used in the CFD post-processing in order to ensure consistency between the canonical and turbulent configurations. Finally, the extinction scalar dissipation rate

χ_{st, ext}

was obtained by interpolating

χ (x)

Z = Z_{st}

Figure 7 shows an instantaneous snapshot of the near-nozzle region, where contours of the mixture fraction in a narrow band around the stoichiometric value ( $0.03 \leq Z \leq 0.034$ ) are superimposed on the temperature field and colored by the local scalar dissipation rate. Near the nozzle exit, the computed scalar dissipation rates exceed the extinction limit inferred from the counter-flow flame analysis, indicating that flame stabilization is not possible in this region. Further downstream, turbulent mixing rates decrease, and the local scalar dissipation rate falls below the extinction threshold, allowing the flame to stabilize and resulting in the observed lift-off behavior.

Figure 7.

Instantaneous temperature field with the stoichiometric mixture-fraction surface ( $0.03 \leq Z \leq 0.034$ ) colored by scalar dissipation rate at $t = 4.0$ ms, for the medium dwell case.

The stoichiometric surface forms a thin, highly convoluted layer that follows the jet shear region. In the immediate vicinity of the nozzle exit, this surface is exposed to very large scalar dissipation rates, with values exceeding the extinction threshold $χ_{st, ext} = 1.37 \times 10^{4} s^{- 1}$ obtained from the counter-flow diffusion flame analysis. Consistently, no sustained temperature rise is observed at the nozzle exit, indicating that local mixing rates are too high to allow stable flame anchoring. Further downstream, the scalar dissipation rate along the stoichiometric surface decreases below $χ_{st, ext}$ , coinciding with the appearance of a persistent high-temperature region and the establishment of a stabilized flame.

Beyond mixing and scalar-dissipation effects, unsteady flame–flow interaction mechanisms (e.g. TFUP-type stabilization regimes⁴⁸) may also influence flame reattachment behavior in hydrogen flames, but their assessment requires dedicated diagnostics and is left for future work.

Overall combustion process

Figure 8 shows instantaneous mid-plane snapshots at four representative times ( $t = 1.5$ , $2.5$ , $3.5$ , and $5.5$ ms). Each snapshot reports (top row) equivalence ratio $ϕ$ , temperature $T$ , and OH mass fraction $Y_{OH}$ , and (bottom row) REAC_RATIO, flame index FLAME_INDEX, and oxygen mass fraction $Y_{O_{2}}$ .

Figure 8.

Instantaneous mid-plane snapshots at $t = 1.5$ , $2.5$ , $3.5$ , and $5.5$ ms. Top row: equivalence ratio $ϕ$ , temperature $T$ , and OH mass fraction $Y_{OH}$ . Bottom row: REAC_RATIO, flame index FLAME_INDEX, and oxygen mass fraction $Y_{O_{2}}$ for medium dwell case.

The equivalence ratio reported is an element-based quantity and it can be written as follows:

ϕ = \frac{2 \sum_{k} N_{k} n_{C, k} + 0.5 \sum_{k} N_{k} n_{H, k}}{\sum_{k} N_{k} n_{O, k}}

(2)

where

N_{k}

is the local number of moles of species

k

, and

n_{C, k}

n_{H, k}

, and

n_{O, k}

are the number of C, H, and O atoms in species

k

, respectively. With this definition,

ϕ

is governed primarily by mixing (neglecting differential diffusion effects) rather than reaction progress.

The quantity REAC_RATIO is a post-processing diagnostic intended to indicate the presence and intensity of chemical activity (reaction progress). It is defined as the cell equivalence ratio that does not include H $_{2}$ O and CO $_{2}$ in the calculation. We use REAC_RATIO here strictly as a qualitative reacting/non-reacting indicator, and we do not interpret it as a conserved scalar or a stoichiometric marker.

The flame topology is assessed using a Takeno-type flame index.⁴⁹ The (normalized) flame index is based on the alignment of fuel and oxidizer gradients,

FI = \frac{\nabla Y_{F} \cdot \nabla Y_{O_{2}}}{| \nabla Y_{F} | | \nabla Y_{O_{2}} |}, - 1 \leq FI \leq 1

(3)

where

Y_{F}

denotes a fuel mass fraction (or an effective fuel scalar) and

Y_{O_{2}}

is the oxygen mass fraction. Positive values indicate premixed-like burning (aligned gradients), while negative values indicate non-premixed (mixing-controlled) burning (opposed gradients). In multi-fuel configurations,

Y_{F}

should be interpreted as an effective fuel scalar as implemented in the post-processing, and the flame index is therefore used to classify local burning mode rather than to attribute a given reaction zone to a specific fuel stream.

Time $t = 1.5$ ms shows the n-heptane diffusion flame. Between $t = 2.5$ , corresponding to the ignition of the hydrogen jet, and $3.5$ ms, corresponding to the diffusion flame of hydrogen, the high- $T$ and high- $Y_{OH}$ regions expand and convect downstream, with a marked increase in the reacting volume as entrainment of oxidizer into the jet proceeds. The $Y_{O_{2}}$ contours show that oxygen penetration is the strongest along the jet periphery, and over the same interval, the flame index becomes increasingly dominated by negative values along the stabilized reacting interface, indicating a mixing-controlled burning mode as the jet develops.

At $t = 5.5$ ms, the reacting structure occupies a larger fraction of the jet, with sustained high $T$ and $Y_{OH}$ throughout the plume. The oxygen field continues to indicate oxidizer supply primarily from the outer shear layer, and the flame index remains predominantly negative, consistent with a globally mixing-controlled flame. The persistence of regions with weaker or fluctuating flame index near highly strained interfaces suggests localized departures from a purely diffusion-controlled structure, which is expected in a dual-fuel, pilot-assisted configuration with strong turbulence-chemistry interaction.

Impact of dwell time on hydrogen combustion

The temperature contour in Figure 9 shows the combustion behavior of the n-heptane flame. As can be seen, the ignition begins at the tip of the n-heptane spray. Similar to the earlier discussion on the hydrogen jet, this is due to the long residence time, low scalar dissipation rate, and low flow speed in the n-heptane spray tip, all of which favor ignition and flame stabilization. The flame quickly spreads upstream towards the injector due to the edge flame propagation mechanism.^42,44

Figure 9.

Temperature distribution along the center of the domain illustrates the (a) stages of n-heptane combustion for the short dwell time case (Case I) and (b) immediately before hydrogen ignition for the three dwell time cases.

By increasing dwell time, the pilot combustion has more time to evolve, so the state of the ignition source changes, and the effective penetration length of the pilot flame extends further into the chamber. As a result, the location where the hydrogen jet first interacts with the pilot can shift, in addition to the flame being progressively cooled by entrainment. This further clarifies why hydrogen IDT increases as dwell time increases. Figure 10 shows the joint distribution of equivalence ratio and temperature in the combustion chamber, commonly referred to as a $ϕ$ – $T$ diagram. Each marker corresponds to one computational cell of the LES at a given time instant. Specifically, it shows the temperature of the n-heptane flame, right before hydrogen ignition, as the dwell time is delayed. Although the maximum temperature is very similar in each of the cases, when dwell time is increased, mean flame temperature drops, as denoted by the dots moving towards the lower part of the diagram. Longer dwell time also result into a leaner mixture (more dots to the left), due to the entrainment of more fresh oxidizer and combustion products into the flame, before interacting with the hydrogen. Hydrogen is highlighted by the concentration of points below 1000 K because hydrogen has not yet ignited at this point.

Figure 10.

$ϕ$ – $T$ diagram before the hydrogen ignition for all three cases.

Since hydrogen SOI occurs after n-heptane ignition, the n-heptane flame is not affected by the hydrogen injection until the hydrogen jet reaches the n-heptane flame. As explained above, Figure 9(b) shows that as the dwell time increases, the n-heptane flame cools down by the ambient gas. When the hydrogen jet flow reaches the n-heptane flame, the hydrogen/air mixture ignition becomes slower with increasing dwell time. The slower ignition allows more hydrogen mixing with the hot gas in the n-heptane flame, and as such, once ignited, the peak heat release rate is higher in the long dwell time case (e.g. Case III; Figure 4).

Figure 11 shows again a $ϕ$ – $T$ , aiming this time at describing the temporal evolution of the thermochemical state. This is done by showing a sequence of time steps during hydrogen ignition for the short dwell time case (Case I).

Figure 11.

$ϕ$ – $T$ diagram during hydrogen ignition for Case I (short dwell). Each point represents a computational cell. Color indicates the local atomic carbon-to-hydrogen ratio (C/H), with C/H $= 0$ corresponding to pure hydrogen and increasing values indicating carbon-containing mixtures and combustion products.

The points are colored by the local atomic carbon-to-hydrogen ratio (C/H), computed from the major resolved species mass fractions as the ratio of total carbon atoms to total hydrogen atoms present in the mixture. In this representation, pure hydrogen, pure n-heptane and the preheated ambient gas are represented, respectively, from values of C/H =0, C/H $\approx 0.44$ and C/H $\approx 0.86$ . Values close to 0 (dark blue) refer to hydrogen rich zones, while between 0 and 0.44 denote the certain presence of hydrogen (blue to purple). Values above, but close to, 0.44 (purple) might refer either to n-heptane rich or hydrogen lean mixture, while values close to 0.86 (red to orange) denote very lean conditions for both fuels.

Since both the C/H and the equivalence ratio are atom-based, both scalars are conserved throughout reactions. Therefore, the increase in C/H above 0.44 and the shift towards the left part of the diagram, observed in the combustion products of n-heptane, is caused exclusively by mixing with the ambient gas.

At $t = 1.30$ ms aSOI, the mixture of hydrogen and ambient gas (blue to red dots on the bottom left), starts to heat up because it gets closer to the n-heptane flame, which has already partially leaned out by mixing with the ambient gas (see Figure 9). At this stage, the jets are only exchanging heat, but not yet mixing. Between $t = 1.33$ and $1.37$ ms aSOI, a rapid temperature rise first appears at lean conditions near $ϕ \approx 0.5 - 0.7$ , corresponding to the hydrogen–air/pilot interface. This initial ignition manifests itself as a vertical migration of points from the low-temperature branch into the high-temperature branch at an approximately constant equivalence ratio. Following ignition, heat release rapidly spreads into the hydrogen-rich region, as evidenced by the vertical translation of low-C/H population towards a peak temperature of 2700 K. Once ignition takes hold at the interface, the heat-release region spreads into the hydrogen-richer side, and the flame propagates upstream, as seen in a later time instance and as visualized in Figures 3 and 9. We, therefore, refer to $ϕ = 0.6$ as a typical ignition band in these cases rather than a fixed universal value. The same ignition sequence is observed for all investigated cases, although the temporal extent of the process increases with dwell time.

The production rate of NO $_{x}$ for all cases is shown in Figure 12(a). The total mass of NO $_{x}$ in the chamber is shown in Figure 12(b). NO $_{x}$ formation in the pilot n-heptane flame is rather low, as indicated in the $t < 0$ time interval in Figure 12(a) and (b) (before the start of the hydrogen injection). Due to the total energy of hydrogen being 93.6%, NO $_{x}$ formation is mainly in the hydrogen jet flame. The NO $_{x}$ mass before hydrogen injection (Figure 12(b), $t < 0$ ) provides only a lower bound on the contribution n-heptane, because the pilot-generated hot products and radicals continue to influence NO formation after hydrogen arrives. It can be seen that the long dwell time case exhibits the lowest formation rate of NO $_{x}$ and also the lowest mass of NO $_{x}$ in the chamber, with the highest in the medium dwell time. Figure 12(c) shows that the NO $_{x}$ mass fraction is highest in the mixing region between the hydrogen jet and pilot-affected gases, reflecting accumulation in regions of longer product residence time; this should not be interpreted as the location of peak NO formation.

Figure 12.

(a) Temporal evolution of the rate of NO $_{x}$ formation, $t = 0$ indicating the start of injection (SOI) of hydrogen injection, (b) the total mass of NO $_{x}$ in the chamber normalized by the total energy of fuels in the chamber [g/kWh], and (c) the NO $_{x}$ mass fraction, Temperature and ratio of element C to element H at the peak NO $_{x}$ production for the short dwell time.

The NO $_{x}$ formation process can be explained using the Zel’dovich thermal NO reactions: $N_{2} + O \to NO + N$ and $N + O_{2} \to NO + O$ . These reactions are enhanced by high temperatures and elevated concentrations of O $_{2}$ and N $_{2}$ molecules in the flame. In the shortest dwell time case (Case I), the hydrogen jet intersects with the pilot flame earlier, resulting in the lowest ambient gas entrainment into the flame region and, consequently, relatively low NO $_{x}$ production. In contrast, the longest dwell time case (Case III) experiences the highest ambient gas entrainment into the flame. However, the pilot flame is cooled significantly, leading to a lower flame temperature in the hydrogen jet and, thus, the lowest thermal NO formation rate. Case II strikes a balance with moderate ambient gas entrainment and relatively high flame temperatures, resulting in the highest NO $_{x}$ formation.

Conclusions

LESs of hydrogen/n-heptane dual-fuel combustion in a constant-volume vessel were performed to investigate jet–jet interaction, ignition behavior, and NO $_{x}$ trends under engine-relevant conditions. Three cases with identical injection parameters but different dwell times between the pilot and main injections were analyzed and compared with Schlieren imaging and apparent heat-release rates from experiments.

In all cases, hydrogen ignition occurs once the hydrogen jet intersects the n-heptane pilot flame. Short dwell times lead to nearly immediate hydrogen ignition upon intersection, whereas longer dwell times result in delayed ignition due to cooling and dilution of the pilot flame before interaction. These trends are consistently observed in both LES and experiments.

The highest NO $_{x}$ mass fractions are observed in the mixing region between the hydrogen jet and pilot-affected gases, reflecting accumulation in regions of longer residence time, while the overall NO $_{x}$ formation rate is strongly governed by dwell-time-dependent flame temperature and air entrainment. The long dwell time allows more hydrogen/air to mix with the hot gas of the n-heptane flame, resulting in a peak heat release rate at ignition. A cooler n-heptane flame in the long dwell time case results in a lower flame temperature in large regions, which results in a lower NO $_{x}$ formation rate. The medium dwell time case shows the highest NO $_{x}$ formation rate due to the combination of high flame temperature and large entrainment of ambient gas to the flame.

The onset of n-heptane ignition is at the spray tip due to the long residence time and low scalar dissipation rate in the region. The onset of hydrogen ignition is at the jet tip by the n-heptane flames. The flames in both the n-heptane jet and the hydrogen jet propagate upstream toward the nozzle. LES predicted a short lift-off length for the hydrogen flame, but longer than that observed in the Schlieren images. Combustion analysis confirmed that the discrepancy in flame lift-off results from an over-prediction of the local scalar dissipation rate and the under-prediction of the jet spreading in the radial direction.

Footnotes

Acknowledgements

This work is sponsored by the Swedish Energy Agency and Scania CV AB within the HYZERO project. The simulations were performed on resources provided by the National Academic Infrastructure for Supercomputing in Sweden (NAISS). The authors thank Convergent Science for providing the CONVERGE licenses and technical support for this work.

ORCID iD

Hesameddin Fatehi

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The authors received funding from the Swedish Energy Agency.

Declaration of conflicting interests

The authors declare no potential conflicts of interest with respect to research, authorship, and publication of this article.

Data availability statement

Data will be made available on request.

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