Exploring Hydrogen–Diesel Dual Fuel Combustion in a Light-Duty Engine: A Numerical Investigation

Abstract

Dual fuel combustion has gained attention as a cost-effective solution for reducing the pollutant emissions of internal combustion engines. The typical approach is combining a conventional high-reactivity fossil fuel (diesel fuel) with a sustainable low-reactivity fuel, such as bio-methane, ethanol, or green hydrogen. The last one is particularly interesting, as in theory it produces only water and NO_x when it burns. However, integrating hydrogen into stock diesel engines is far from trivial due to a number of theoretical and practical challenges, mainly related to the control of combustion at different loads and speeds. The use of 3D-CFD simulation, supported by experimental data, appears to be the most effective way to address these issues. This study investigates the hydrogen-diesel dual fuel concept implemented with minimum modifications in a light-duty diesel engine (2.8 L, 4-cylinder, direct injection with common rail), considering two operating points representing typical partial and full load conditions for a light commercial vehicle or an industrial engine. The numerical analysis explores the effects of progressively replacing diesel fuel with hydrogen, up to 80% of the total energy input. The goal is to assess how this substitution affects engine performance and combustion characteristics. The results show that a moderate hydrogen substitution improves brake thermal efficiency, while higher substitution rates present quite a severe challenge. To address these issues, the diesel fuel injection strategy is optimized under dual fuel operation. The research findings are promising, but they also indicate that further investigations are needed at high hydrogen substitution rates in order to exploit the potential of the concept.

1. Introduction

The environmental impact of fossil fuels burned by internal combustion engines (ICEs) has become a major concern in industrialized countries. Diesel engines, due to their high fuel efficiency and mechanical robustness, represent the mainstream technology for heavy-duty and industrial applications. However, compared to Spark Ignition (SI) gasoline engines, they emit significantly higher levels of nitrogen oxides (NO_x) and particulate matter (PM). These emissions are harmful for the environment and pose serious risks to human health [1,2,3]. As a result, NO_x and PM emissions have been heavily regulated, pushing manufacturers to implement more sophisticated and expensive after-treatment systems.

In order to face environmental regulations and the depletion of fossil fuel reserves, alternative fuels [4,5] and advanced combustion technologies [6,7] have been studied, considering also the fuel production process [8,9,10]. These studies demonstrate benefits in terms of reduced emissions [11] and performance improvement [12,13].

Hydrogen (H₂) produced from renewable sources (often referred to as green H₂) has high potential to address many of the environmental challenges associated with traditional fossil fuels: the absence of CO₂ in the combustion products makes it very attractive for reducing greenhouse gas emissions and improving the overall environmental footprint of ICEs [14,15,16]. Nevertheless, implementing a H₂ combustion system into the current engine technologies presents several technical challenges.

In spark ignition (SI) engines, volumetric efficiency is reduced when the fuel is injected before intake valve closing. Due to its high flammability, even a small amount of H₂ rejected in the intake manifold may induce a backfire [17,18]; the risk of auto-ignition or knock is high for values of equivalence ratio > 0.5 [19,20,21]. Last but not least, the control of NO_x emissions requires ultra-lean mixtures, which are strongly penalizing for the engine power output [22].

H₂ can be used also in compression ignition (CI) engines, in conjunction with diesel fuel [23]: the latter is injected at the end of the compression stroke, in order to ignite a previously prepared lean mixture of H₂ and air. This hydrogen–diesel dual-fuel (H₂-D DF) concept leverages the benefits of hydrogen clean combustion while maintaining the cylinder design of a standard diesel engine (flat cylinder head, bowl in the piston, no spark plug). The advantages in terms of brake thermal efficiency and CO₂ and pollutant emissions are reported in several studies [24,25,26].

Unfortunately, the replacement of diesel fuel with hydrogen can lead to increased combustion temperatures, which may result in higher NO_x emissions and peak of pressure rise rate (PPRR), in comparison to the original diesel engine [27]. NOx and PPRR can be kept very low if an ultra-lean combustion is adopted, but the limits are the combustion stability and the cycle-by-cycle variation.

The support of three-dimensional computational fluid dynamics (3D-CFD) simulations, validated with experimental data, is essential to address the above-mentioned challenges [28]. Some experimental and numerical investigations reported in the literature have identified the diesel injection strategy [29], the substitution rate of H₂, and injection timing [30,31] as the key parameters for matching performance, thermal efficiency, and pollutant emissions.

An interesting aspect of H₂-D DF systems is the potential for retrofitting existing diesel engines and using a relatively small amount of H₂. This approach offers a practical and cost-effective solution for reducing the carbon footprint of current vehicles while awaiting a larger availability of green H₂ that will be possible only after the implementation of a capillary refueling infrastructure [32] and a reduction in H₂ production costs [33,34].

The goal of this article is to improve understanding of H₂-D DF combustion by means of a numerical investigation supported by experimental data, considering a typical light-duty diesel engine, which may be used for industrial applications and/or for light commercial vehicles. In particular, the influence of the H₂ substitution rate and of the diesel injection strategy is deeply analyzed, considering two fundamental operating conditions: medium load/medium speed (2400 rpm–10.5 bar BMEP) and high load/high speed (4000 rpm–13.5 bar BMEP).

2. Materials and Methods

2.1. Engine Characteristics

The engine selected for this study is a high-speed direct injection (HSDI) diesel engine manufactured by FCA–VM Motori in Cento (FE), Italy, and designed for automotive applications. It is a 4-cylinder in-line engine with a total displacement of 2780 cm³, featuring four valves per cylinder. The engine is equipped with a high-pressure common rail fuel injection system and a set of six-hole injectors. Combustion chamber shape is highlighted in Figure 1. The bowl built inside the piston has a standard omega-shaped profile, with a squish height of 0.9 mm and bowl volume of 32.8 cm³. Other main characteristics of the engine are summarized in

Table 1. Main features of the selected engine.

Engine Type	HSDI 4-Stroke Diesel, EURO IV
Cylinders	4 in-line
Total displacement (L)	2.78
Bore × Stroke (mm)	94 × 100
Connecting rod length (mm)	159
Compression ratio	17.5:1
Swirl ratio	1.8
N. of valves per cylinder	4
Exhaust valve opening (°CA AFTDC)	114
Intake valve opening (°CA AFTDC)	337
Exhaust valve closing (°CA AFTDC)	389
Intake valve closing (°CA AFTDC)	590
Air Metering	Turbocharger with VGT + Intercooler
Injection system	Common rail
Max. Injection press. (MPa)	160
Number of injector holes	6
Injector hole protrusion (mm)	2
Injector hole distance from injector axis (mm)	1.35
Injector hole diameter (mm)	0.153
Max. brake power (kW@rpm)	130@3800
Max. brake torque (Nm@rpm)	440@1750
Max. peak in-cylinder pressure (bar)	150
Max. Engine Speed (rpm)	4600

.

The above-mentioned engine was selected for this study due to its suitability for automotive application, making it an ideal candidate for exploring H₂-D DF combustion in this context. Furthermore, in previous research [35], the same engine was properly modified by the authors to operate in natural gas-diesel DF combustion, further demonstrating its appropriateness for the current study.

The baseline diesel engine was fully characterized at a steady dynamometer test bench, and two operating points with different engine speeds and brake mean effective pressures (BMEP) were considered for this study: a partial load condition (2400 rpm–10.5 bar BMEP) and a full load condition (4000 rpm–13.5 bar BMEP). These experimental conditions, which are summarized in

Table 2. Main engine parameters of the selected operating points.

	Partial Load	Full Load
Engine speed × BMEP (rpm × bar)	2400 × 10.5	4000 × 13.5
Brake Torque (Nm)	232	298
Brake Power (kW)	58.3	124.9
Diesel Fuel Mass (mg/cyl/cycle)	52.0	69.7
Injection strategy	pilot + pre + main	main

, were used to validate the 3D-CFD model.

2.2. 3D-CFD Model Description and Validation

The numerical analysis described in this study was carried out by means of the AVL FIRE M 3D-CFD code, which is widely used in the automotive industry to simulate both cold flows and combustion processes in ICEs. The main models adopted for the simulations are summarized in

Table 3. Main models used for 3D-CFD combustion modelling.

Equation of State	Real Gas/Peng-Robinson
Turbulence model	k-zeta-f
Wall treatment	Hybrid
Wall heat transfer model	Standard
Breakup model	Kelvin-Helmholtz/Rayleigh-Taylor
Wall interaction model	Kuhnke
Turbulent dispersion model	Solved
Drag model	Schiller-Naumann
Wall film model	Solved
Fuel evaporation model	Dukowicz
Diesel surrogate (gas phase)	C7H16
Combustion model	AVL ECFM-3Z
Auto ignition model	Two-Stage
Laminar flame speed	AVL database
Auto ignition delay	AVL database
NOx model	Thermal mechanism

. The Reynolds-averaged Navier–Stokes (RANS) approach was selected and the k-zeta-f model [36] was used to handle turbulence. The Kelvin-Helmholtz/Rayleigh-Taylor (KH–RT) [37] instability model was used for the diesel spray breakup modelling, whose gas phase is modeled with n-heptane (C₇H₁₆). Combustion was modeled thanks to the 3-Zones Extended Coherent Flame Model (ECFM-3Z) [38], which provides a good balance between accuracy and computational cost, in conjunction with the AVL database for laminar flame speeds.

Both diesel and H₂-D DF simulations were carried out from intake valve closing (IVC) to exhaust valve opening (EVO), imposing a swirl ratio of 1.8, based on previous full engine cycle simulations. Therefore, thanks to the axial symmetry of the combustion chamber shape and the homogeneous spatial distribution of the six diesel injector holes, a 60° sector mesh was employed for the analysis (see Figure 2). The authors acknowledge the sector mesh approach approximates the real problem. In fact, the swirl axis may not be perfectly coincident with the cylinder axis and the geometric details of the head are missed. However, this simplification is acceptable, as it does not significantly impact the results of the analysis. The mesh also includes crevices (the gap between the piston skirt and the cylinder liner above the first ring), which were slightly increased to ensure that the compression ratio of the computational fluid domain matched the real one. The main characteristics of the mesh are summarized in

Table 4. Main features of the computational grid.

Volume Cell Size (mm)	1.3 (0.65 from −30 to +30 °CA AFTDC)
Boundary layer thickness (mm)/n. of layers	0.1/2
Number of cells @ TDC	~70,000
Crevices: thickness × height (mm)	0.8 × 12.7

.

Both a mesh size and an angle-step (time-step) sensitivity analysis were conducted, during the injection/combustion process, to ensure that the numerical results were independent of the grid size and of the angle-step. For these analyses, the full load case (4000 rpm–13.5 bar BMEP) was considered.

First of all, three meshes with different average volume cell sizes were built: 1.3 mm, 0.65 mm, and 0.2 mm. Since the results from the last two meshes were in agreement, the 0.65 mm average-cell-size mesh was selected as the best compromise between accuracy and computational cost. The angle-step sensitivity analysis was performed considering three different values during the diesel fuel injection event: 0.01 °CA, 0.1 °CA, and 0.25 °CA. Since 0.1 °CA and 0.01 °CA angle steps guarantee almost the same peak in-cylinder pressure, 0.1 °CA was chosen with the aim to minimize the computational cost.

Outside of the injection phase, the time-step was set at the default values suggested by the software user’s guide.

The 3D-CFD model was then validated against the selected diesel experimental data (2400 rpm–10.5 bar BMEP and 4000 rpm–13.5 bar BMEP), whose main engine parameters are listed in

Table 5. Diesel validation cases: main parameters for experiments and numerical simulations.

Engine Parameters	2400 rpm–10.5 bar BMEP		4000 rpm–13.5 bar BMEP
	Exp.	Num.	Exp.	Num.
Pressure @ IVC (bar)	2.5	2.5	1.5	1.5
Trapped mass (mg/cycle/cyl)	1283.5	1283.5	1640.2	1639.1
Diesel mass (mg/cycle/cyl)	52.00	52.00	69.70	69.60
Diesel SOI pilot (°CA AFTDC)	−14.7	−14.7	-	-
Diesel in pilot injection (mass%)	1.1	1.1	-	-
Diesel SOI pre (°CA AFTDC)	−0.6	−0.6	-	-
Diesel in pre injection (mass%)	2	2	-	-
Diesel SOI main (°CA AFTDC)	10.5	10.5	−12.0	−9.0
Diesel in main injection (mass%)	96.8	96.8	100.00	100.00
Residuals * (mass%)	7	7	5	5
EGR (mass%)	0	0	0	0
Swirl ratio (-)	1.8	1.8	1.8	1.8
Head temperature (K)	-	500	-	500
Liner temperature (K)	-	480	-	480
Piston temperature (K)	-	520	-	520

* based on the results of a validated GT-Power model of the full engine.

. Figure 3 shows the comparison between the measured and predicted in-cylinder pressure and apparent heat release rate (AHRR; Equation (1)), which are in good agreement. The main difference is represented by the underestimation of the maximum AHRR by the numerical model, both at partial and full load. The capability of the 3D-CFD model to correctly predict the combustion characteristics is confirmed by the comparison between the experimental and numerical results in terms of the gross indicated mean effective pressure (IMEP*; Equation (2)), peak in-cylinder pressure, and combustion phasing parameters reported in

Table 6. Comparison between experimental and numerical IMEP*; peak in-cylinder pressure and combustion phasing parameters: 2400 rpm–10.5 bar BMEP.

Engine Parameter	Exp.	Num.	Absolute Error
IMEP* (bar)	11.30	10.61	0.69
Peak in-cylinder pressure (bar)	93.74	93.97	0.23
CA10 (°CA AFTDC)	17.5	17.8	0.3
CA50 (°CA AFTDC)	24.5	27.0	2.5
CA90 (°CA AFTDC)	38.5	43	4.5
Δθ10–90 (°CA)	21.0	25.2	4.2

and

Table 7. Comparison between experimental and numerical IMEP*; peak in-cylinder pressure and combustion phasing parameters: 4000 rpm–13.5 bar BMEP.

	Exp.	Num.	Absolute Error
IMEP* (bar)	21.70	21.25	0.27
Peak in-cylinder pressure (bar)	138.00	139.70	1.6
CA10 (°CA AFTDC)	2.8	2.9	-
CA50 (°CA AFTDC)	17.8	18.8	1
CA90 (°CA AFTDC)	42.8	46.0	3.2
Δθ10–90 (°CA)	40.0	43.1	3.1

.

$$\mathrm{A}\mathrm{H}\mathrm{R}\mathrm{R}={\displaystyle \frac{\mathrm{k}}{\mathrm{k}-1}}\mathrm{p}{\displaystyle \frac{\mathrm{d}\mathrm{V}}{\mathrm{d}\mathsf{\theta }}}+{\displaystyle \frac{1}{\mathrm{k}-1}}\mathrm{V}{\displaystyle \frac{\mathrm{d}\mathrm{p}}{\mathrm{d}\mathsf{\theta }}}$$

(1)

$${\mathrm{I}\mathrm{M}\mathrm{E}\mathrm{P}}^{\ast }={\displaystyle \frac{1}{V_d}}{\int }_{\mathrm{I}\mathrm{V}\mathrm{C}}^{\mathrm{E}\mathrm{V}\mathrm{O}}\mathrm{p}\mathrm{d}\mathrm{V}$$

(2)

It should be noted that the H₂-D DF experimental data of the selected engine are not yet available. Therefore, experimental data of a comparable diesel engine (

Table 8. Main features of the selected engine.

Engine Type	4-Stroke, Single Cylinder, Optically Accessible
Stroke (mm)	92
Bore (mm)	85
Cylinder volume displacement (cm3)	522
Combustion bowl volume (cm3)	19.7
Compression ratio	16.5:1
Number of valves	4
EVO (°CA AFTDC)	116
IVO (°CA AFTDC)	344
EVC (°CA AFTDC)	380
IVC (°CA AFTDC)	588
Diesel injection system, common rail
Number of holes	7
Cone angle of fuel jet axis (deg)	148
Hole diameter (mm)	0.141
Hydrogen PFI injection system
Number of holes	1
Maximum injection pressure (bar)	5

), properly modified by the CNR-STEMS research center to operate in H₂-D DF combustion [39,40], were used to validate a 3D-CFD model of the latter engine. The new set of parameters was then used to update the numerical model of the VM engine. This approach ensured that the H₂-D DF combustion simulations for the VM engine were based on a reliable framework.

Table 9. Comparison between experimental data and numerical results of the CNR-STEMS H₂-D DF single-cylinder research engine.

Engine Parameter	Exp.	Num.	Absolute Error
Engine speed (rpm)	2000		-
IMEP* (bar)	4.38	4.88	0.5
Experimental peak in-cylinder pressure (bar)	60.2	59.8	0.4
CA10 (°CA AFTDC)	−0.8	0.2	1
CA50 (°CA AFTDC)	9.4	9.6	0.2
CA90 (°CA AFTDC)	22.2	24.8	2.6
CA10–90 (°CA)	23	24.6	1.6

reports the main experimental data of the CNR-STEMS H₂-D DF engine and the comparison with the predictions of the corresponding 3D-CFD model, while Figure 4 illustrates the comparison between experimental and numerical in-cylinder pressure and AHRR. Once again, the simulation outcomes closely match the experimental measurements, demonstrating the robustness of the H₂-D DF combustion model.

2.3. Experimental Setup

The experimental investigations presented below were conducted using two distinct engine test benches located at different facilities: the engine test bench at the Department of Engineering “Enzo Ferrari” of the University of Modena and Reggio Emilia and the CNR-STEMS test bench. Both experimental campaigns were carried out to comprehensively evaluate the combustion characteristics and performance of the engines discussed in this work.

The first experimental setup was used to test the 2.8-L turbocharged VM Motori (Cento (FE), Italy) diesel engine outlined in Table 1. Tests took place at the University of Modena and Reggio Emilia’s engine test bench, equipped with an Apicom (Cento (FE), Italy) FR 400 BRV eddy-current dynamometer and Apicom (Cento (FE), Italy) Horus software for system control and data acquisition. Standard sensors for pressure and temperature monitoring were integrated, along with a Coriolis flow meter for precise diesel fuel consumption measurement. In-cylinder pressure traces were recorded using a high-frequency indicating system, which includes a Kistler piezoelectric, a charge amplifier, and an optical encoder. Data acquisition was conducted via a time-based method, with real-time analysis performed using Alma Automotive (Bologna, Italy) software on National Instruments (Austin, (TX, USA)) Compact RIO hardware, achieving an angular resolution with a 0.3° crank angle.

The second setup employs an optical access single-cylinder compression ignition (CI) research engine (Table 8). The engine is equipped with a conventional extended piston, featuring a 46 mm flat sapphire window in the piston crown to enable visualization of the in-cylinder combustion process. A 45° visible-IR mirror within the extended piston reflects combustion images to high-speed cameras, capturing the entire combustion process. The engine maintains its original four-cylinder common rail injection system, controlled by an open electronic control unit (ECU) capable of adjusting injection timing, pressure, and duration. For premixed hydrogen injection, an electronic Port Fuel Injector (PFI) was installed in the intake manifold and connected to a compressed gas supply regulated at 5 bar. The premixed fuel was injected once the exhaust valves were closed to ensure effective mixing with intake air with no short-circuits. The ECU managed synchronization of the direct injection system, while a delay unit aligned the PFI timing with the engine cycle.

Additional features of this setup include the following:

• Air Flow and Pressure Monitoring: Intake air is conditioned (filtered, dehumidified, and temperature- and pressure-controlled) to maintain consistent in-cylinder conditions. The Sensyflow (Göttingen, Germany) FMT500-IG measures air mass flow rate.
• Gaseous Fuel Supply: The hydrogen supply line comprises a pressure regulator, flame arrester, and flame trapper. Gas flow rates are measured using a Brooks thermal mass flow meter.
• Data Acquisition: In-cylinder pressure is monitored using a piezoelectric transducer, and both the diesel and PFI injection signals are captured before it reaches the injector. Signals are digitized and recorded every 0.2° crank angle by means of a multi-channel acquisition system. Pressure data from 200 combustion cycles are averaged, and heat release rates are calculated using thermodynamic principles.

2.4. Methodology

The updated VM engine numerical model was employed to investigate the effects of increasing H₂ energy fraction on engine performance, both at partial and full load (2400 rpm–10.5 bar BMEP and 4000 rpm–13.5 bar BMEP, respectively). In detail, simulations were conducted for H₂ energy shares of 20%, 40%, 60%, and 80% of the energy provided in the corresponding diesel operation. The progressive reduction in diesel fuel energy was produced by lowering the mass injected during the main injection (Figure 5) so as to guarantee a constant energy input for the specific operating point.

Experimentally, H₂ is responsible for a reduction in the volumetric efficiency of the engine when port injected. However, in the numerical investigation presented below, it was assumed that the total mass at IVC remains unchanged. This approach allows for simply considering the variation in H₂ content in the premixed charge, isolating the impact of H₂ substitution on the combustion process. It is important to highlight that the simulated condition can actually be achieved on the real engine by properly regulating the turbocharger.

Once the effects of increasing H₂ fraction on combustion characteristics were analyzed, a start of injection (SOI) sweep was carried out. This analysis was necessary because in DF combustion, as the substitution of diesel fuel with H₂ increases, the combustion shifts from being predominantly diffusion-based to predominantly premixed. Therefore, this requires optimization of the diesel fuel injection strategy. Furthermore, the simplicity of adjusting only the SOI makes this approach particularly well suited for achieving a straightforward and effective conversion, aligning with the objective of enabling dual-fuel conversion with minimal modifications.

The aim of these analyses is to recover the efficiency lost passing from diesel to DF combustion, potentially exceeding that of the corresponding diesel operation.

3. Results and Discussion

The results of the H₂-D DF combustion simulations, carried out with the VM engine numerical model, will be presented below. First, the partial load operating point will be discussed, followed by the full load condition.

3.1. Partial Load

Starting from the diesel operation at 2400 rpm–10.5 bar BMEP, corresponding to a partial load condition, H₂ energy share was progressively increased, passing from 0% (diesel combustion) to 80% of the energy provided with diesel fuel in diesel operation. The amount of diesel fuel is reduced accordingly, in order to keep the total energy input constant. Figure 6 shows the variation in the equivalence ratio of the H₂–air premixed charge (${\varphi }_{H_2}$; Equation (3)) with increasing H₂ energy share.

$${\mathsf{\varphi }}_{{\mathrm{H}}_2}={\displaystyle \frac{{\mathsf{\alpha }}_{\mathrm{s},{\mathrm{H}}_2}}{\left(\frac{{\mathrm{m}}_{\mathrm{a},\mathrm{T}\mathrm{O}\mathrm{T}}-{\mathrm{m}}_{\mathrm{a},\mathrm{D}}}{{\mathrm{m}}_{{\mathrm{H}}_2}}\right)}}$$

(3)

where ${\varphi }_{H_2}$ is the equivalence ratio of the H₂-air premixed charge; ${\alpha }_{s,H_2}$ is the stoichiometric air to fuel ratio of H₂ (34.0); $m_{a,TOT}$ is the air mass trapped at IVC; $m_{a,D}$ is the air mass that reacts with diesel fuel, supposing diesel fuel combustion occurs in stoichiometric conditions; $m_{H_2}$ is the H₂ mass trapped at IVC.

Figure 7 and Figure 8 report the effects of increasing H₂ mass fraction in the premixed charge on the in-cylinder pressure and rate of heat release (ROHR), peak in-cylinder pressure, peak pressure rise rate (PPRR), IMEP*, combustion efficiency (η_c), crank angles corresponding to 10, 50, and 90% of mass fraction burnt (CA10, CA50, CA90), and turbulent combustion duration (CA10–90). It should be noted that in the following discussion, ROHR will be used instead of AHRR, which represent, respectively, the total rate of heat released by the combustion process and the difference between the total rate of heat released during combustion and the wall heat flux.

As the H₂ energy content increases, the in-cylinder pressure at the end of the compression stroke, which corresponds to the peak in-cylinder pressure (Figure 8a), increases from about 94 to 98.7 bar. This is due to the higher γ (Equation (4)) of H₂ with respect to air.

$$\gamma ={\displaystyle \frac{c_p}{c_v}}$$

(4)

where $c_p$ is the specific heat at constant pressure, while $c_v$ is the specific heat at constant volume.

The PPRR appears slightly affected by the substitution of diesel fuel with H₂ since it increases by only 0.2 bar/°CA (from 2.9 to about 3.1 bar/°CA) passing from diesel combustion to 80% H₂-D DF combustion (Figure 8a). During combustion, the second peak in-cylinder pressure increases until 60% of H₂ energy share, while a lowering of the second peak pressure appears at 80% of diesel fuel energy reduction. This depends on the combustion rate (ROHR), which speeds up until 60% of H₂ energy share then slows down. The reason is probably the progressive reduction in the diesel fuel mass, which, at 80% of energy substitution with H₂, constitutes a weak energy source to start combustion of the lean premixed charge.

IMEP* (Figure 8b) is positively affected by the substitution of the high-reactivity fuel with the low-reactivity one until 40% H₂ energy share, which produces an IMEP* improvement of 2.7% with respect to diesel combustion (from 10.6 to 10.9 bar). Higher energy substitutions result in worsening performance, with a maximum drop of 19.6% at 80% of H₂ energy share (from 10.6 to 8.5 bar). The IMEP* trend can be explained as follows: η_c continuously worsens as the H₂ energy share increases, with a maximum reduction of about 19.2% at 80% diesel fuel energy substitution (Figure 8b). This is probably due to the increase in ${\varphi }_{H_2}$ and, consequently, of the premixed H₂ mass that cannot completely burn because of flame quenching near the combustion chamber walls and the mass of H₂ trapped in the crevices. However, combustion becomes faster up to 40% H₂ energy share, especially in the first part of the combustion process, as demonstrated by the shift of CA50 toward Top Dead Centre (TDC) (Figure 8c). Therefore, for low substitution, thermodynamic efficiency (η_th) increases, outweighing η_c effect. Then, CA10-90 (Figure 8d) increases significantly, and both η_th and η_c decrease, causing a deterioration in IMEP*.

In order to further improve performance in DF operation at low substitutions of diesel fuel with H₂ and to recover the efficiency lost at high substitutions, a design of experiment (DOE) was conducted by varying the SOI of the diesel fuel pilot and the pre and main injections. In particular, the diesel fuel injection strategies were rigidly shifted, advancing the SOI of the three injections from 5 to 30 °CA by steps of 5 °CA compared to the reference injection strategies (Figure 5a). As an example, Figure 9 shows the SOI variation applied to the diesel fuel injection strategy of the diesel case. As can be seen, the same SOI variation is applied to the three injections (pilot, pre, and main). The same approach was used for each of the H₂-D DF cases studied at partial load.

Figure 10 reports the contour maps of peak in-cylinder pressure, PPRR, IMEP*, and η_c as a function of H₂ energy share and SOI variation (ΔSOI). As can be seen from Figure 10c,d, the trends of IMEP* and η_c as a function of the H₂ energy share shown in Figure 8b are confirmed for all the ΔSOI values considered, except for the ΔSOI values of −25 and −30 °CA. For the latter ΔSOI values, IMEP* decreases with an increasing substitution of diesel fuel with H₂. Furthermore, IMEP* generally increases by advancing diesel fuel SOI. Therefore, IMEP* is maximized for small substitutions of diesel fuel with H₂ (20% H₂ energy share) and high diesel fuel injection advances (ΔSOI equal to −25 and −30 °CA), which correspond to an average improvement in IMEP* of about 27% compared to the reference diesel combustion.

However, two important constraints should be considered, namely, the maximum allowable in-cylinder pressure and PPRR. The following thresholds were imposed:

• maximum allowable in-cylinder pressure: 150 bar;
• maximum allowable PPRR: 5 bar/°CA.

The threshold on peak in-cylinder pressure corresponds to the maximum in-cylinder pressure compatible with the mechanical strength of the engine, while the PPRR limit was chosen in order to guarantee low levels of noise and vibrations, comparable to those of the reference diesel engine, that at the same operating point has PPRR = 2.9 bar/°CA. It can be observed that the constraint on PPRR is always stricter compared to the peak in-cylinder pressure constraint.

Based on the above considerations, the best compromise between performance improvement and limited mechanical stresses, noise, and vibrations can be achieved by advancing the diesel fuel injection strategies of the DF cases until reaching the PPRR = 5 bar/°CA limit.

Figure 11a depicts the diesel fuel SOI variations, with respect to the baseline diesel fuel injection strategies shown in Figure 5a, for the diesel and H₂-D DF cases that meet the PPRR limit of 5 bar/°CA. As can be seen, the ΔSOI must be gradually reduced as the H₂ energy share increases up to 60% and then starts increasing up to 80% H₂ energy share. As a result, peak in-cylinder pressure is always higher than in the baseline diesel and DF cases, but well below the above-mentioned threshold of 150 bar. As far as the combustion efficiency of the optimized cases is concerned (Figure 11b), it worsens as the H₂ mass fraction in the premixed charge increases. This is due to the increase in ${\varphi }_{H_2}$ and, consequently, of the H₂ mass that cannot burn because of flame quenching near the combustion chamber walls and the mass of H₂ trapped in the crevices. Moreover, both optimized diesel and optimized H₂-D DF cases show lower combustion efficiency compared to the baseline diesel combustion, with the reduction ranging between 0.6% and 14%. However, the IMEP* of the optimized cases is always higher than in the baseline diesel case (IMEP* = 10.6 bar), with a maximum enhancement equal to +22.9% at 40% H₂ energy share. This is due to the optimal combustion phasing produced by the diesel fuel SOI variation (advancement), which shifts CA50 toward TDC to about 10 °CA AFTDC, regardless of the H₂ energy share (Figure 11c). In addition, combustion duration reduces up to 40% H₂ energy share (Figure 11d). The above-mentioned effects overcome the reduction in η_c, enabling a relevant performance (IMEP*) improvement with respect to the baseline diesel case. At 60% H₂ energy share, combustion duration matches that of the baseline diesel case, while η_c further worsens it, reducing the IMEP* enhancement. Finally, if the maximum substitution of diesel fuel with H₂ is considered, both the drop in η_c and the significant increase in CA10-90 counteract the optimal combustion phasing, minimizing the IMEP* improvement with respect to the baseline diesel combustion.

It can therefore be concluded that, in DF operation at partial load, optimizing the diesel fuel SOI can improve engine performance. Advancing the diesel fuel injection timing significantly enhances performance at low H₂ energy shares, while at high H₂ substitution levels, it is possible to recover the drop in IMEP* caused by decreased combustion efficiency, even surpassing the IMEP* of the reference diesel case. However, η_c cannot be fully recovered by varying the SOI and remains lower than that of the reference diesel combustion.

3.2. Full Load

The second condition that was investigated is the full load operating point: 4000 rpm–13.5 bar BMEP. Also, in this case, diesel fuel was progressively substituted with H₂, increasing the H₂ energy share from 0% to 80% of the energy provided with diesel fuel in the full load diesel operation. As in the partial load condition, the total energy input from the two fuels was kept constant, switching from diesel to DF combustion, and the diesel injection law was modified as shown in Figure 5b. Figure 12 shows ${\varphi }_{H_2}$ of the premixed H₂-air charge, as defined in Equation (3), as a function of the H₂ energy share.

The introduction of H₂ leads to a significant increase in peak in-cylinder pressure, which rises from 139.7 bar in the diesel operation to 182.3 bar when 80% of energy is supplied by H₂ (Figure 13 and Figure 14a). This trend aligns with similar studies that demonstrate the effects of H₂ on pressure rise in DF engines at medium-high loads [41]. Peak in-cylinder pressure rise is due to the intensification of the ROHR as the amount of H₂ increases. In fact, passing from diesel to DF H₂-D combustion, the combustion process transitions from diffusive to premixed. Moreover, H₂ is characterized by a laminar flame speed higher than any other fuel and the widest flammability range. It is also interesting to notice that the ignition delay increases with the H₂ energy fraction. This effect is attributable to two causes: in order to guarantee the same mass at IVC as the H₂ fraction increases, temperature at IVC must be reduced, which decreases temperature at the end of the compression stroke; H₂ tends to absorb part of the heat released by diesel fuel during the low temperature heat release, delaying the start of the high temperature heat release.

As far as combustion phasing is concerned (Figure 14c), CA10 is almost unaffected by variation in the H₂ energy share, while CA50 is always decreasing with growing H₂ energy share (from 18.8 °CA AFTDC to 9.2 °CA AFTDC), in accordance with the intensification of the ROHR. CA90 initially decreases, reaching its lowest point at 40% H₂ energy share, then increases. As a result, CA10-90 shortens up to 40% H₂ energy share (CA10-90 = 33 °CA AFTDC; −10 °CA with respect to diesel operation), then turbulent combustion slows down due to the increasing amount of the premixed charge located in the periphery of the combustion chamber that burns slowly and partially (Figure 14d).

IMEP* increases as the H₂ fraction rises, peaking at 60% H₂ energy share (23.1 bar; +9.0% compared to diesel combustion), as depicted in Figure 14b. However, η_c decreases with increasing H₂ substitution until 40% H₂ energy share (92.2%; −1.7% compared to diesel combustion), then starts to increase, reaching a value comparable to that of diesel combustion at 80% H₂ energy share.

Therefore, the trend of IMEP* can be attributed to the faster combustion rate observed with higher H₂ fractions and demonstrated by the shift of CA50 toward TDC (Figure 14c), which leads to a greater η_th that is capable of outweighing the η_c worsening.

However, it should be noted that the maximum allowable peak in-cylinder pressure for the VM engine is 150 bar (Table 1), while the peak in-cylinder pressure in DF operation at full load is always higher than the above-mentioned limit. Moreover, PPRR rises with the mass fraction of H₂ in the premixed charge, reaching almost 19 bar/°CA (Figure 14a).

Therefore, it is essential to optimize the diesel fuel injection strategy with the aim to achieve efficient DF combustion with acceptable mechanical stresses, noise, and vibrations.

In detail, a DOE was performed, varying SOI of the diesel fuel main injection by an angle between −3 °CA and + 6 °CA by steps of 1 °CA, with respect to the baseline diesel fuel injection strategy. In Figure 15, the effect of the SOI variation on the injection strategy of the diesel case is illustrated. As can be seen, the main injection timing was shifted both forward and backward. The same SOI variation was applied to each of the H₂-D DF cases studied. Linear interpolation was applied to estimate the results for the SOI and H₂ energy share values not directly simulated.

Figure 16 reports the contour maps of peak in-cylinder pressure, PPRR, IMEP*, and η_c. Three lines are also drawn on the maps: the red dashed line represents the maximum allowable peak in-cylinder pressure of the VM engine (150 bar); the red dotted line corresponds to the maximum in-cylinder pressure of the baseline diesel engine (140 bar); and the magenta dashed line is the acceptable limit on PPRR based on the engine application (12 bar/°CA).

Figure 16a confirms the peak in-cylinder pressure trend with H₂ energy share observed for the baseline diesel fuel injection strategy, showing that this trend is observable for all the SOI values considered. It also highlights that the baseline diesel engine operates with some margin, as the peak pressure of 140 bar remains below the maximum allowable limit. This indicates the possibility of advancing the injection timing by approximately 2 °CA without surpassing structural constraints. It is noteworthy that the peak pressure limit is more restrictive than the PPRR constraint. However, unlike the partial load condition, where both limits produced nearly parallel curves on the maps, the behavior here is different. Specifically, while both H₂ substitution and injection timing advance have a similar influence on the peak pressure (with limit curves inclined at approximately 45°), the impact of H₂ substitution on PPRR seems to be more pronounced, resulting in nearly vertical limit curves. Unlike partial load conditions, where H₂ can be substituted across all studied fractions by adjusting the SOI, at full load it is not possible to exceed 78.4% H₂ energy share if the ΔSOI is restricted to a maximum value of 6 °CA. This limitation in H₂ energy share arises due to the PPRR constraint.

From Figure 16c, it appears that IMEP* is more influenced by the H₂ energy share than the diesel fuel SOI and increases as the diesel fuel SOI is advanced and ${\varphi }_{H_2}$ is increased. For the baseline full diesel configuration, advancing the fuel injection by 2 °CA results in a 0.8% increase in IMEP* a reduction of 1.9% in η_c. The figure also shows that η_c is maximized for ΔSOI values between +3 °CA and +6 °CA and for H₂ energy share values below 20%, while advancing the diesel fuel SOI compared to the injection strategy of the reference diesel case is generally disadvantageous.

The IMEP* trend with H₂ energy share and ΔSOI, despite the behavior of η_c, suggests that the overall engine efficiency improves due to the faster combustion associated with the increasing ${\varphi }_{H_2}$ of the premixed charge. In confirmation of this, Figure 16e reports the contour map of CA10-90, which is minimum for negative ΔSOI values and H₂ energy shares between 20% and 60%.

Based on the previous analysis, the SOI value that permitted us to maximize the IMEP* in full diesel and DF operations was selected for each H₂ energy share, considering also the constraints on peak in-cylinder pressure (150 bar) and PPRR (12 bar/°CA). Figure 17 highlights that ΔSOI should be progressively delayed as the H₂ mass fraction increases in order to achieve the above-mentioned targets for peak in-cylinder pressure and PPRR. Additionally, the figure shows that in the baseline DF case the SOI was not modified; for this reason, the engine exceeded its structural limits.

DF cases with optimized ΔSOI are compared with the DF cases with the baseline injection strategy in terms of peak in-cylinder pressure, PPRR, IMEP*, η_c, combustion phasing parameters, and combustion duration (Figure 18).

It can be observed that by optimizing the injection timing of the baseline diesel engine with ΔSOI = −2.2 °CA, a gain of 0.2 bar in BMEP (0.8%) is achieved but results in a reduction of 1.9% in efficiency, as previously mentioned. Figure 18a confirms that the SOI optimization keeps the peak pressure and PPRR within structural limits. Notably, in Figure 18b, all dual fuel configurations employing the optimized injection strategy show higher IMEP* values compared to both the baseline diesel configuration and the diesel engine with optimized injection timing. However, regarding combustion ηc, only the configuration with a 40% H₂ share surpasses the performance of the two full diesel configurations. This 40% H₂ share case, with its optimized injection law (ΔSOI = 2.55 °CA), achieves the highest IMEP* and combustion efficiency among all the optimized cases. Specifically, it increases IMEP* by 1.2 bar (5.6%) and combustion efficiency by 2.1% compared to the optimized diesel case.

Figure 18c,d display the characteristic combustion timing. It can be observed that hydrogen substitution consistently accelerates combustion compared to the diesel case. Figure 18d shows that, even for the optimized cases, the minimum combustion duration is achieved at a 40% H₂ share. For higher hydrogen shares, the combustion duration tends to increase as the hydrogen moves more toward the periphery and farther from the injection zone, slowing down the combustion process.

An additional notable point is observed at the maximum admissible hydrogen energy substitution corresponding to 78.4%. In this case, ΔSOI is set to the maximum value of 6 °CA (Figure 17), IMEP* increases by 0.47 bar (2.2%), and combustion efficiency improves by 1.3% compared to the optimized full diesel case. These results demonstrate that H₂ can effectively substitute diesel while maintaining engine performance, in some cases even improving it, with respect to the baseline engine configuration and while keeping the engine in safe working condition.

Finally, the two most relevant operating points were selected and analysed in comparison with the baseline diesel case. The selected points are as follows: the 78.4% H₂-D DF case with ΔSOI = 6°, as it represents the highest hydrogen share, and the 40% H₂-D DF case with ΔSOI = 2.55°, as it achieved the highest IMEP. Figure 19 compares the baseline diesel engine (red dashed line) with the two DF cases with optimized ΔSOI (green and blue lines) in terms of pressure trace and ROHR. The figure shows that the 40% H₂ case reaches the highest peak pressure at 150 bar, compared to 139.7 bar for the baseline diesel and 138.9 bar for the 78.4% H₂ case (which is very close to baseline diesel peak pressure). The highest PPRR is obtained in the 78.4% H₂ case, hitting the structural limit as a result of the optimization process. Most significantly, Figure 19 shows that the pressure trends are significantly different across the cases, with the most distinctive pattern observed in the case with the highest H₂ energy share. This case is characterized by a notable double-peak in the pressure curve with a very sharp ROHR trace.

In terms of IMEP*,

Table 10. Comparison between diesel and optimized 80% H2-D DF.

	Diesel	Opt. Diesel	40% H2 H2-D DF	78% H2 H2-D DF
H2 energy share (%)	0	0	40	80
ΔSOI (°CA)	0	−2.18	−2.55	−6.00
Max in-cylinder pressure (bar)	139.7	150.0	150.0	138.9
PPRR (bar/°CA)	3.71	5.01	4.91	12.00
IMEP* (bar)	21.25	21.41	22.61	21.88
ηc (%)	93.82	92.09	94.01	93.25
CA10-90 (°CA)	43.1	42.0	34.3	38.8

shows that the 40% H₂ H₂-D DF case has a gain of 1.36 bar (+6.40%) compared to the baseline diesel (the gain is 1.20 bar (+5.60%) compared to the optimized diesel), while the 78.4% H₂ H₂-D DF case has a lower gain of 0.63 bar (+2.96%) compared to the baseline diesel (the gain is 0.47 bar (+2.20%) compared to the optimized diesel). η_c increases by 0.2% for the 40% H₂ share and decreases by 0.6% for the 78.4% H₂ case. Finally, combustion duration is reduced by 8.8 °CA for the 40% H₂ share and by 4.3 °CA for the 78.4% H₂ share, when compared to the diesel baseline.

From both the general analysis conducted earlier and the examination of these specific operating points, it can be concluded that, at full load, the transition from diesel to H₂-D DF operation invariably requires modifications to the injection timing strategy to maintain mechanical stresses within acceptable thresholds. Furthermore, optimal engine performance, characterized by a significant increase in IMEP* compared to the pure diesel case, is achieved at intermediate H₂ substitution levels (approximately 40%). At higher H₂ shares, the combustion process becomes more abrupt, and the necessary delay in injection timing, required to limit peak in-cylinder pressure and the PPRR, negatively impacts the cycle efficiency, leading to performance levels that struggle to reach those of the reference diesel case.

4. Conclusions

This numerical study investigated the implementation of hydrogen-diesel dual fuel (H₂-D DF) combustion in a light-duty diesel engine, focusing on the effects of increasing H₂ substitution for diesel fuel and on the optimization of the diesel fuel injection strategy. Two operating points were analyzed: a medium load/medium speed (2400 rpm–10.5 bar BMEP) condition and a high load/high speed (4000 rpm–13.5 bar BMEP) condition.

For the first partial load point, based on the analysis presented in this paper, the following conclusions can be drawn:

• Increasing the H₂ energy share up to 40% improves IMEP* thanks to the faster combustion process. Higher energy substitutions determine a reduction in IMEP*, which was observed to drop at 80% H₂ energy share;
• The performance deterioration at high H₂ substitutions is due to the worsening of the combustion efficiency, which reduces as the H₂ mass fraction in the premixed charge increases;
• Advancing the diesel fuel injection strategy of the DF cases further improves performance at low H₂ energy shares, while at high H₂ substitutions it is possible to recover the drop in IMEP*, exceeding the IMEP* of the baseline diesel case. However, combustion efficiency cannot be recovered by advancing the diesel fuel SOI, which remains lower than that of the baseline diesel combustion.
• Under full load conditions, the following observations were made:
• H₂ leads to significant increases in both peak in-cylinder pressure and pressure rise rate (PPRR), exceeding the engine’s structural limits. To mitigate these effects and ensure safe operation, a delay in diesel injection is necessary. In this analysis, an optimal SOI was determined for each H₂ energy share to keep the peak pressure and PPRR within acceptable limits.
• Optimal IMEP* is achieved at around 40% hydrogen substitution; however, higher levels lead to abrupt combustion and reduced efficiency, resulting in performance that falls short of the diesel baseline.
• Two optimal points were then identified: configuration with 40% H₂ energy share and ΔSOI = 2.55° CA (maximizes IMEP*, achieving a 6.4% increase compared to the baseline diesel engine and obtains the highest combustion efficiency); configuration with 78.4% H₂ energy share and ΔSOI = 6° CA (permits the maximum H₂ share and achieves a 2.96% increase in IMEP* compared to the baseline diesel engine, with a slight reduction in combustion efficiency).

These findings demonstrate that injection timing optimization plays a critical role in enabling the conversion of diesel engines to dual fuel operation, enhancing performance while respecting the engine’s structural limits. The conversion of conventional diesel engines to H₂-DF systems is not only feasible in terms of performance but it can also be essential for the future of sustainable transportation. However, several technological challenges remain, including H₂ injection technology, material compatibility, regulatory frameworks, and infrastructure development.