Numerical Transition from Diesel to Hydrogen in Compression Ignition Engines: Kinetics, Emissions, and Optimization with Exhaust Gas Recirculation

Abstract

A Cantera-based combustion-kinetics framework that maps the operating space of hydrogen compression ignition (H₂-CI) engines and establishes a structured charter to guide experiments. Beginning with a diesel (n-dodecane) baseline at an intake temperature of 300 K, the model is virtually converted to neat hydrogen and evaluated across intake temperatures of 400–600 K, compression ratios (CR) of 20–28, and exhaust gas recirculation (EGR) levels of 0–15%. Hydrogen demonstrates stable operation across a broad equivalence ratio window (ϕ = 0.45–2.1), achieving power outputs of 16–22 kW and higher efficiencies with substantially lower fuel mass than diesel. The optimal operating region is identified at an approximately 400 K intake temperature, CR = 24–28, and EGR between 5% and 10%, where power remains high (20–18 kW), efficiency increases (above 50%), and NO_x emissions are markedly reduced (from 332 ppm at zero EGR to 48 ppm at 5% EGR and 10 ppm at 10% EGR), with only modest hydrogen slip (0.07–0.11). The kinetics-based framework thus provides a systematic and validated roadmap for experimental calibration, research, and development of compression ignition engines working on pure hydrogen.

1. Introduction

1.1. Literature Review

1.1.1. Foundational Hydrogen Engine Theory and Combustion Modeling

Dimitriou (2023) [1] provided a comprehensive overview of hydrogen compression ignition engines within the Green Energy and Technology framework. Kirkpatrick (2020) [2] presented the thermos-science foundation for internal combustion engines, defining governing equations for mass, energy, and entropy conservation in reciprocating systems. His work remains a key reference for performance parameterization of compression engines. Goodwin et al. (2023) [3] introduced Cantera 3.0, an object-oriented computational toolkit for chemical kinetics, thermodynamics, and transport analysis. Tingas (2023) [4] discussed hydrogen’s potential as a primary energy carrier for future thermal engines. Tingas and Taylor (2023) [5] examined hydrogen’s practical energy applications and cost considerations, exploring its scalability for power and transport. Turns (2020) [6] covers the full scope of Cantera-based combustion kinetics, thermochemistry, and flame modeling, providing clear theory-to-application links for sustainable and modern energy systems.

1.1.2. Chemical Kinetics Tools and Previous Cantera-Based Engine Modeling

Abbass (2025) [7] numerically modeled n-dodecane combustion using Cantera, detailing mechanism selection, ignition simulation, and reaction pathway analysis. The work demonstrated chemical kinetic solvers and sub-models, providing groundwork applicable to hydrogen kinetic modeling and ignition characterization. Babayev (2021) [8] conducted a CFD-based study comparing conventional diesel and hydrogen direct-injection compression ignition combustion. Hydrogen achieved comparable or superior brake thermal efficiency. The absence of EGR or NO_x modeling limited emissions insight. Vellaiyan (2025) [9] experimentally compared gaseous hydrogen, ammonia borane, and ammonium hydroxide as hydrogen energy carriers in CI engines. Gaseous hydrogen yielded the highest efficiency, whereas ammonium hydroxide balanced emissions and performance. The research highlighted that fuel chemistry strongly governs ignition smoothness.

1.1.3. Abnormal Combustion, Ignition Behavior, and Dual-Fuel Studies

Zhou et al. (2025) [10] presented a detailed review on abnormal combustion and NO_x emissions in hydrogen engines, addressing both SI and CI modes. Tutak, Jamrozik, and Grab-Rogaliński (2020) [11] experimentally analyzed a dual-fuel CI engine fueled with natural gas enriched by hydrogen at 1500 rpm and CR = 20. Hydrogen accelerated combustion and increased in-cylinder pressure, but led to higher NO_x in the study, which utilized hydrogen as an addition in a dual engine with diesel autoignition starting combustion, and the hydrogen portion improved efficiency. Akar et al. (2018) [12] investigated hydrogen enrichment in waste oil biodiesel for CI engines. Hydrogen improved efficiency and reduced CO and CO₂ emissions by 20–25% and 10–15%, respectively, but raised NO_x by 15–30%, and no EGR. The study demonstrated that moderate hydrogen enrichment compensates for biodiesel’s slower combustion.

1.1.4. Radical Additives to Initiate Combustion and Airbus Combustion Perspectives for Hydrogen Engines

Dimitrova (2022) [13] used a 0-D CHEMKIN-Pro model to simulate HCCI combustion with hydrogen–hydrogen peroxide blends. Up to 10% H₂O₂ and the use of a glow plug improved ignition delay and IMEP. Hydrogen peroxide acted as a radical initiator, enhancing mixture reactivity and promoting stable lean combustion. The Airbus article (2020) [14] provides a detailed explanation of hydrogen combustion principles and its application to aviation engines as part of Airbus’s ZEROe zero-emission aircraft initiative. It traces hydrogen’s historical use in the first internal combustion engines and outlines how hydrogen can replace fossil fuels in modified gas turbines, either in gaseous or liquid form. The article highlights hydrogen’s wide flammability range, which allows for lean combustion, reducing flame temperature, and minimizing NO_x emissions. It also emphasizes hydrogen’s high auto-ignition temperature, enabling higher compression ratios and thus improved thermal efficiency. Airbus demonstrates that hydrogen combustion engines can achieve high power density with near-zero CO₂ emissions.

1.1.5. Spark-Ignition Hydrogen Engines and Compression Ratio Sensitivity

Lou et al. (2025) [15] examined a six-cylinder turbocharged direct-injection SI hydrogen engine with CR = 9–13 and λ = 1.0–5.0 under lean-burn conditions using GT-POWER 1D simulation. Increasing CR improved stability and extended the lean limit (λ = 5.0 at CR = 13). The peak thermal efficiency was 41.25% at CR = 13, λ = 2.5, balancing power and NO_x. NO_x reached 1850 ppm at λ = 1.5 but declined under leaner operation. Higher CR enhanced efficiency but increased NO_x and knock tendency. Sharma and Dhar (2018) [16] Using CONVERGE. They proved that H₂ energy share (HES) is maximum at a compression ratio of 16.5. A compression ratio of 14.5 or below is unsuitable for diesel–hydrogen dual-fuel operation. The study depends on dual fuel to start ignition.

1.1.6. Compression Ignition Hydrogen Studies: Autoignition, Preheating, and Ignition Limits

Li et al. (2023) [17] numerically and experimentally studied the 31 cc baseline engine that produces approximately 2.5–3.0 kW at 8000–8500 rpm. Results showed a 57.37% NO_x reduction compared to a conventional engine. Homan et al. (1979) [18] experimentally operated a hydrogen-fueled diesel engine without timed ignition. Stable operation was achieved using glow plugs, whereas spark ignition caused oscillations. Hydrogen operation produced double the IMEP of diesel and 40% efficiency with NO_x between 50 and 100 ppm., with premixed hydrogen and air at low equivalence ratios. Compression ignition could not be achieved even at a compression ratio of 29. Lee et al. (2013) [19] explored hydrogen compression ignition in a variable-CR single-cylinder engine (CR = 8–45). Autoignition occurred at CR 32 during cold starts and stabilized near CR 26 in warm conditions. Ultra-lean mixtures (ϕ = 0.11–0.22) burned stably without spark ignition. Intake preheating reduced ignition CR but increased NO_x formation.

1.1.7. Pilot Diesel Ignition and Inlet Temperature Aid for Combustion to Start Hydrogen Combustion

Rosati and Aleiferis (2009) [20] used a 498 cm³ optical single-cylinder engine (CR = 7.5) to compare hydrogen SI and HCCI modes. Direct injection prevented backfire and enabled lean operation, while HCCI achieved low NO_x combustion using air preheating (200–400 °C) and internal EGR from valve overlap. Ikegami, Miwa, and Shioji (1982) [21] experimentally tested hydrogen CI combustion in a swirl-chamber diesel engine. The air-aspirated system required pilot diesel for ignition, while the argon–oxygen closed-cycle mode achieved stable hydrogen autoignition and higher thermal efficiency, demonstrating the feasibility of closed-cycle hydrogen CI operation.

1.1.8. Dual-Fuel Hydrogen Strategies and EGR Interaction

Domínguez et al. (2023) [22] investigated dual-fuel operation (diesel with hydrogen or methanol) in a 1.13 L CI engine (CR = 15.8). Hydrogen substitution up to 60% reduced NO_x by 60–80% under 20–25% EGR. Efficiency slightly decreased for hydrogen but improved for methanol, confirming optimal NO_x–NO_x-efficiency trade-offs near 20% EGR. Tsujimura and Suzuki (2017) [23] tested a hydrogen–diesel dual-fuel engine. With 0.25 MPa port hydrogen injection, efficiency improved by 10%, NO_x dropped from 200 to 90 ppm at 20% EGR, and pre-ignition emerged above 40% hydrogen at 420 °C. Stable operation was achieved with 10–25% EGR.

1.1.9. Numerical and Experimental NO_x Mitigation Techniques

Dam et al. (2024) [24] modeled a hydrogen spark-ignition engine in MATLAB/Simulink, integrating combustion, torque, and thermal modules. The model accurately predicted power and efficiency but excluded NO_x and EGR, demonstrating hydrogen’s clean potential and MATLAB’s utility in control-oriented simulations. Chintala and Subramanian (2014) [25] experimentally evaluated water injection in hydrogen dual-fuel CI engines. At an optimal 200 g/kWh water injection rate, hydrogen participation increased from 20% to 39%, while NO_x decreased by 24%, with minimal efficiency loss. Water injection proved effective for NO_x mitigation and combustion control.

1.1.10. EGR-Based Hydrogen Combustion Stabilization and NO_x Control

Kikuchi, Hori, and Akamatsu (2022) [26] experimentally studied hydrogen low-NO_x combustion using exhaust gas recirculation (EGR). Increased flow velocity and reduced nozzle size enhanced internal recirculation, cutting NO_x by ~51% without destabilizing the flame, validating EGR as a passive NO_x control strategy. Wang et al. (2023) [27] used CFD simulations to evaluate hydrogen addition in dual-fuel diesel engines with varying compression ratios. Hydrogen fractions up to 15% improved efficiency and temperature, increasing NO_x but sharply reducing CO and soot, with optimal results at CR 18–20 and 10–15% hydrogen.

1.1.11. Hydrogen in Transportation, Policy, and Global Technology Trends

Hwang, Maharjan, and Cho (2023) [28] reviewed hydrogen use in transportation and power generation. The study synthesized global data on hydrogen projects; highlighted progress in fuel cells, turbines, and engines; and identified challenges related to production costs and infrastructure. Policy and R&D support were recommended for scaling hydrogen systems. Wróbel et al. (2022) [29] surveyed hydrogen internal combustion engine vehicle developments across commercial and research platforms. They concluded that hydrogen ICEs serve as a transitional step between conventional ICEs and full fuel-cell vehicles, capable of reducing CO₂ and PM emissions while retaining existing powertrain infrastructure.

1.1.12. Regulatory Standards for NO_x and Emissions Compliance

The U.S. Environmental Protection Agency (2023) [30] established regulatory standards for stationary spark-ignition internal combustion engines under 40 CFR Part 60, Subpart JJJJ. These standards define permissible emission levels and testing protocols, ensuring compliance for hydrogen-based stationary engines. The European Commission (2007) [31] introduced Regulation (EC) No. 715/2007 (Euro 5 and 6) to limit NO_x and PM emissions from passenger and light commercial vehicles. These frameworks directly guide emission benchmarks for hydrogen ICE development in the EU. The U.S. Environmental Protection Agency (2023) [32] also provided the Emission Standards Reference Guide for nonroad engines (Tier 1–4), offering baseline regulatory thresholds essential for compliance assessment in hydrogen-fueled engine adaptation.

1.1.13. Experimental NO_x Control Utilizing EGR and Effect on Hydrogen Slip

Lu et al. (2024) [33] experimentally compared port fuel injection (PFI) and late direct injection (LDI) in a hydrogen spark-ignition engine with varying EGR rates, focusing on lean operation and stratified combustion. They reported that EGR generally increased hydrogen emission (hydrogen slip) in most conditions while slowing flame speed. Combining LDI with appropriate EGR under high loads achieved up to 84.4% NO_x reduction. Haichun Yao (2014) [34] investigated a 2.0 L hydrogen engine with a hot EGR system. At high load and rich conditions (ϕ > 1), the study showed that NO_x emissions dropped significantly as the EGR rate increased, while unburned hydrogen traces in the exhaust helped further reduce NO_x through post-catalytic reactions, achieving substantial emission reduction with only a slight loss in power output.

1.1.14. Experimental Role of EGR to Stabilize Hydrogen Combustion and Eliminate Knock and Emissions

Guo et al. (2020) [35] applied 3D CFD to a single-cylinder hydrogen engine equipped with an EGR system to study De-NO_x technology and abnormal combustion control. Their simulations showed that increasing the EGR ratio lowered in-cylinder temperature, reduced peak heat release rate and NO_x emissions, and delayed combustion, which helped to suppress pre-ignition and knocking. The work emphasized EGR’s role in stabilizing hydrogen combustion and mitigating abnormal combustion without explicit reporting of hydrogen slip or efficiency changes. Zhang et al. (2024) [36] used a CONVERGE-based diesel engine model coupled with chemical kinetics to optimize hydrogen addition and EGR in a biodiesel–hydrogen dual-fuel engine under 50–100% loads. The optimization indicated that the best combined performance and emissions occurred at 100% load, hydrogen addition of 6.92%, and EGR rate of 7.68%, where cylinder pressure, temperature, NO_x, and HC emissions were simultaneously reduced. The study concentrated on identifying this optimal EGR–hydrogen window; hydrogen slip was not discussed explicitly.

1.1.15. Modern Hydrogen–EGR Strategies for Emission and Efficiency Improvement

Sharma and Kaushal (2024) [37] experimentally evaluated a variable-compression-ratio CI engine fueled with hydrogen (with diesel ignition pilot) and equipped with exhaust gas recirculation. Operating across CR 12–18 and multiple loads, they found that the hydrogen-fuelled engine with EGR achieved a significant reduction in brake-specific fuel consumption, and a 49.4% decrease in NO_x emissions using cold EGR. The results linked EGR application to improved efficiency and emissions while maintaining acceptable cylinder pressure; hydrogen slip and inlet temperature trends beyond the cold EGR effect were not detailed. Kim et al. (2024) [38], in a hydrogen direct-injection SI engine, applied up to 18.7% low-pressure EGR, significantly reducing NO_x emissions (by 89.9–98.7%) across increasing engine speeds. While excessive EGR lowered maximum brake torque, an optimized ~20% EGR improved torque by 1.9–18.2% at constant NO_x levels. The study shows that combining lean combustion with moderate EGR maximizes efficiency and NO_x control. Novella et al. (2024) [39], with a 1D GT-Power model of a turbocharged Euro 6 DI hydrogen SI engine, showed that cooled EGR effectively reduced NO_x but slightly increased fuel use, while optimized Variable Valve Timing and EGR improved low-speed torque by 5–16%. The study emphasized EGR-torque efficiency trade-offs, with hydrogen slip and inlet temperature effects not detailed. Szwaja et al. (2024) [40] combined experimental data and thermodynamic modeling to analyze hydrogen SI engine combustion with EGR, introducing a molar-contraction-based heat-release method. They demonstrated that applying 0–40% EGR significantly prolonged both the initial and main combustion phases and lowered the mean combustion temperature, confirming EGR’s cooling and NO_x-reducing effects. The model improved accuracy in estimating combustion temperature and heat-release characteristics for hydrogen with EGR; changes in power, overall efficiency, and hydrogen slip were not the primary focus.

1.1.16. Recent Literature on Knock-In Hydrogen Engines

Maghbouli et al. [41] used a CFD model for a hydrogen-assisted compression ignition diesel engine and showed that knock is avoided under lean hydrogen induction, directly supporting our model’s treatment of lean operation as a primary non-knock mechanism.

Wang et al. [42] experimentally tested a 2.0-L turbocharged DI hydrogen engine and demonstrated that delayed injection timing and high excess-air ratios (λ ≈ 1.8–2.0) prevent knock at 2500 rpm, validating our model’s emphasis on timing and lean limits.

Pielecha et al. [43] examined a pre-chamber TJI hydrogen engine and found that knock decreases consistently with increasing λ (1.25–2.0), reinforcing our framework’s mapping of lean mixture as a stable, non-knock operating region.

Manzoor et al. [44] applied a CFD RANS spark-ignition model to study hotspot-initiated knock, while our model generalizes this by allowing multi-CR, multi-λ, and multi-EGR conditions, enabling the prediction of new knock-free operating points across a wider range of engine scenarios.

Szwaja [45] showed that in spark-ignited hydrogen engines, early ignition timing drives unstable heat-release and knock, whereas retarded timing stabilizes combustion—fully aligned with our model’s treatment of timing as a major knock-control parameter across different CR and λ.

Khoa et al. [46] combined experiments and machine learning (GBR) on a spark-ignited hydrogen engine and proved that low RPM and over-advanced timing sharply increase knock, supporting our model’s approach, where higher RPM and optimized timing suppress end-gas temperatures and avoid knock.

SwRI (2025) [47] reported new December findings on stochastic pre-ignition (SPI) in H₂-ICEs, showing that lubricant volatility and compression ratio strongly influence pre-ignition behavior—information that complements our model by highlighting CR-dependent ignition sensitivity, summarized in

Table 1. Primary technical methods for utilizing hydrogen in engines and their efficacy in minimizing emissions.

Spark-Ignition (SI) Hydrogen Engines	Ignition by spark (SI) engines that run on hydrogen spark plugs, a low to medium compression ratio, direct injection, and lean mixtures. Use lean burn and sometimes EGR to get stable combustion, no backfires, and less NOx. Good control.
Dual-Fuel Diesel–Hydrogen Engines	Diesel–hydrogen engines with two-fuel diesel is the fuel that starts the engine, and hydrogen is added to make it work better and cut down on CO2, CO, and soot. Numerous studies examine various hydrogen proportions and compression ratios. NOx usually goes up on its own, so EGR or water injection is used to lower it while keeping good efficiency.
Assisted CI (Using Oxidizers/Glow Plugs/Carriers)	Assisted CI (using oxidizers, glow plugs). Additives like H2O2, glow plugs, help hydrogen autoignition. These help start burning at moderate compression or with mixtures that are less dense. Efforts are focused on getting reliable ignition and smoother combustion while keeping NOx levels low by carefully preparing the mixture and controlling the temperature.
Pure Hydrogen CI with High CR and Tin	High CR and Tin Pure Hydrogen CI ignites hydrogen without diesel or spark by using only a high compression ratio and/or a high intake temperature. Research indicates autoignition occurs at elevated compression ratios and/or heated intake air. The problem is that NOx forms too quickly, and there is a chance of knock, so we need to come up with ways to control it.
EGR and Dilution-Based NOx Control (Across All Modes)	Across all modes, EGR and dilution-based NOx control lower the peak temperature and slow down reactions. They use exhaust gas recirculation, lean burn, cooled EGR, and mixture stratification. A lot of studies show that moderate EGR can cut NOx levels by a lot (often more than 50%) without losing too much power. Others also point out that hydrogen slip goes up when EGR is high, which shows how important it is to have balanced settings.

2. Method and Model

2.1. Effects of Compression Ratio and Inlet Temperature on the Performance and Emissions of Hydrogen Engines

This model delineates the parametrization of hydrogen compared to dodecane as fuels in an internal combustion engine, assessing the ideal capabilities of hydrogen in practical applications as summarized in

Table 2. Comparison of diesel and hydrogen engines, emphasizing the influence of temperature on power output and efficiency.

Parameter		Diesel Engine (n-Dodecane)	Hydrogen Engine
Reaction Mechanism		ndodecane_Reitz.yaml	gri30.yaml
Fuel Composition		C12H26:1 (n-dodecane)	H2:1 (hydrogen)
Inlet Temperature (K)		300	400
Compression Ratio (ε)		20	20
Engine Speed (rpm)		3000	3000
Displaced Volume (m3)		5.00 × 10−4	5.00 × 10−4
Piston Diameter (m)		0.083	0.083
Expansion Power (kW)		18.5	19.5
Heat Release Rate (kW)		33.6	37.2
Efficiency (%)		55.2	52.3
CO Emission (ppm)		8.9	0
Inlet Valve Angle (deg)		−18 (open) to 198 (close)	−18 (open) to 198 (close)
Outlet Valve Angle (deg)		522 (open) to 18 (close)	522 (open) to 18 (close)
Injector Angle (deg)		350 (open) to 365 (close)	350 (open) to 365 (close)
Valve	Crank angle (deg, 0 = intake TDC)	Relative crank angle (with definition)	Stroke region
Inlet valve opens	−18°	18° BTDC—Before Top Dead Center of intake TDC	Start intake
Inlet valve closes	198°	18° ABDC—After Bottom Dead Center of intake BDC (at 180°)	End of intake stroke
Injection start	350°	10° BTDC—Before Top Dead Center of firing/compression TDC (at 360°)	End of compression
Injection end	365°	5° ATDC—After Top Dead Center of firing/compression TDC (at 360°)	Early power stroke
Exhaust valve opens	522°	18° BBDC—Before Bottom Dead Center of power-stroke BDC (at 540°)	Start of exhaust blowdown
Exhaust valve closes	18°	18° ATDC—After Top Dead Center of exhaust TDC (0°/720° between cycles)	End of exhaust stroke

. The simulation will first utilize n-dodecane as a fuel due to its capacity to sustain combustion at moderate inlet temperatures, which is attributed to its low ignition temperature. This phase establishes a performance baseline for the engine operating at a specific compression ratio without necessitating additional heating. This stage employs the “ndodecane_Reitz.yaml” reaction mechanism, which encompasses the kinetics of dodecane combustion [15,16,17].

Upon achieving the dodecane baseline, the model will transition to modeling the removal of dodecane and utilizing hydrogen as the feedstock. Due to hydrogen’s elevated ignition temperature, increasing the input temperature will result in combustion occurring at the same compression ratio. Under these conditions, the model aims to initiate an initial heating phase. The next phase will entail simulating hydrogen combustion using the “gri30.yaml” reaction mechanism for hydrogen. After this phase, we will systematically adjust the hydrogen compression ratio and inlet temperature of the hydrogen-fueled engine. The combustion of hydrogen will be modeled as the final step, tailored for the designed engine. Specific combustion characteristics may produce optimal efficiency values while minimizing nitrogen oxide emissions (NO_x), particularly since these emissions tend to increase upon hydrogen ignition. The model establishes a baseline for engine testing with dodecane, transitions to hydrogen, adjusts the initial temperature, and optimizes compression ratios for hydrogen efficiency (Chart 1 and Chart 2).

The hydrogen engine operates at approximately 3000 rpm, with a compression ratio of 20 during its initial run [8,16]. The simulation utilizes the reaction mechanism Gri30, which contains kinetic data for hydrogen and its associated species. The fuel consists solely of hydrogen and is combined with air (O₂:1, N₂:3.76). Air is supplied into the system at 450 K and a pressure of 13 bars. In contrast, the outlet pressure is maintained at 1 bar and an ambient temperature of 300 K to simulate the typical expulsion of gases.

The engine’s geometry, including piston area, stroke, and crankshaft angles, is determined by characteristics such as displacement volume, piston diameter, and cycle volume at the top dead center (TDC). A sinusoidal velocity profile is enough to represent the engine. To regulate gas intake and exhaust, valves are installed at the inlet and outlet, with specific friction coefficients and times for opening and shutting according to the crank angle. The inlet valve opens at −18 degrees and shuts at 198 degrees, while the outlet valve opens at 522 degrees and closes at 18 degrees. The fuel injector injects hydrogen slightly above top dead center for efficient combustion. The injector is characterized by its opening and closing timings and primarily functions as a mass-flow controller to regulate the quantity of hydrogen fuel (

Table 3. Detailed explanation of the reprogrammed Cantera internal combustion engine model for hydrogen (GRI-Mech 3.0) and dodecane (Reitz mechanism).

Aspect	Hydrogen (GRI-Mech 3.0)	Dodecane (Reitz Mechanism)	Explanation and Main Factors
Reaction mechanism	Uses GRI-Mech 3.0, widely validated for hydrogen and natural gas.	Uses Reitz mechanism, validated for heavy hydrocarbons like dodecane.	Mechanism defines how the fuel burns, including ignition delay, flame propagation, and pollutant formation.
Reactor type	Treated as a well-stirred cylinder with variable volume.	Same approach.	Assumes gas inside is uniform in temperature, pressure, and composition.
Geometry and piston motion	Volume changes based on compression ratio and piston speed profile.	Same.	The piston movement compresses and expands the charge, driving the cycle.
Cycle events	Intake, injection, combustion, and exhaust triggered by crank angle timing.	Same.	Valves and injector open and close at specific crank angles.
Fuel injection	Hydrogen injected as gas; injector delivers the required mass during the open period.	Dodecane injected as gaseous equivalent in this model.	Ensures correct fuel mass each cycle; in reality, dodecane would involve spray and evaporation.
Inlet and outlet valves	Connect the cylinder to inlet and exhaust reservoirs.	Same.	Flow depends on valve opening and pressure difference.
Piston model	Moving wall imposes cylinder volume change.	Same.	Converts thermodynamic pressure into piston work.
Chemistry solver	Uses a stiff numerical solver to handle fast hydrogen reactions.	Same solver applied to dodecane chemistry.	Ensures stability during rapid ignition and combustion.
Numerical stability	Controlled with tight tolerances and a temperature rise limit per step.	Same approach.	Prevents the solver from diverging during heat release.
Cycle tracking	Eight engine revolutions simulated with resolution of one degree crank angle.	Same.	Captures full intake–compression–combustion–expansion–exhaust sequence.
Heat release	Calculated from hydrogen reaction rates inside the cylinder.	From dodecane reactions.	Represents the chemical energy released from fuel.
Work and power	Expansion work integrated over the piston cycle; average power derived.	Same method.	Converts cylinder pressure and piston movement into mechanical output.
Efficiency	Ratio of useful expansion work to total heat released.	Same.	Provides a cycle efficiency estimate (idealized, no friction or heat losses).
Emissions	Mainly water and nitrogen oxides; carbon monoxide is negligible.	Carbon monoxide and soot are significant, plus nitrogen oxides.	Hydrogen burns clean but can form high NOx at high temperatures; dodecane produces carbon emissions and particulates.
Equivalence ratio (mixture richness)	Calculated based on hydrogen injected compared to oxygen or air available at intake closing.	Calculated based on dodecane injected compared to oxygen or air available at intake closing.	Expresses whether the mixture is lean, stoichiometric, or rich.
Combustion kinetics main dependencies	Strongly dependent on temperature, pressure, mixture richness, and exhaust gas recirculation.	Same dependencies, with additional influence from evaporation and mixing of liquid fuel.	These factors control ignition timing, flame development, and pollutant levels.

). The model integrates intricate thermodynamic processes, including heat release and expansion work, which subsequently facilitate atmospheric calculations. The model calculates combustion emissions like carbon monoxide and nitrogen oxides, resulting in reduced emissions. The model simulates a reactor’s cylindrical shape, gas inflow and outflow, valve timing, and gas distribution, predicting engine thermodynamics, hydrogen fuel efficacy, and potential environmental harm.

Following the analysis of base diesel fuel and hydrogen fuel, we will investigate the impact of inlet temperature (T_in) and compression ratio (CR) on the heat release rate, expansion power, efficiency, and emissions the engine produces (Chart 1). This method utilizes hydrogen as the primary fuel in an engine, and adjusting the input temperature and compression ratio can modify the operating conditions. The input temperature affects the engine’s heat release and power-generating capability, while the compression ratio affects the air–fuel mixture’s temperature, density, efficiency, and emissions levels. Elevating both the inlet temperature and compression ratio can enhance heat and power output but also increase nitrogen oxide generation, a significant issue in hydrogen combustion.

This model is an expanded and reprogrammed version of the Cantera engine example found in the “Diesel-type internal combustion engine simulation with gaseous fuel” section of the Reactor Networks library [16]. This framework is modified in our reprogrammed version to enable the systematic assessment of dodecane (using the Reitz mechanism) and hydrogen (using the GRI-Mech 3.0 mechanism) as fuels.

The code extends input flexibility and output diagnostics while maintaining the key components of the Cantera architecture, such as cycle tracking, valve and injector modeling, reactor network formulation, and piston wall motion. Heat release, expansion power, efficiency, and emissions are among the integral findings that are calculated by the updated implementation. The robust calculation of the equivalency ratio at intake valve closure enables correct representation in situations with variable exhaust gas recirculation.

The model now offers a comparison platform to examine combustion kinetics, cycle efficiency, and pollutant trends for various fuels.

2.2. EGR Modeling in a Hydrogen Engine

In this work, the inlet conditions under exhaust gas recirculation (EGR) were generated by blending the fresh intake air stream with a fraction of the engine exhaust products Chart 3. For each operating point, the exhaust composition (N₂, H₂, H₂O, NO_x) and temperature were combined with the baseline intake air (O₂/N₂ mixture at the prescribed intake temperature). The EGR fraction determined the relative weighting of exhaust and air, such that higher EGR increased the inlet temperature while diluting the oxygen concentration and introducing combustion products such as H₂O and NO_x. The final mixture was normalized to represent the effective inlet composition supplied to the cylinder. This procedure reflects the physical role of EGR in elevating the intake temperature, reducing oxygen availability, and modifying the charge chemistry.

The method establishes an operating matrix for a hydrogen-fueled engine by combining intake air with different fractions of recirculated exhaust gas (EGR). For each case, the inlet mixture is defined by its temperature (after blending fresh air and hot exhaust) and by its composition, including oxygen, nitrogen, recirculated water vapor, residual hydrogen, and NO_x. These inlet conditions are then used as the boundary state for the engine cycle at different compression ratios and EGR levels. The engine is supplied with hydrogen fuel at fixed injection timing and mass, while the intake mixture varies according to the EGR percentage. The simulation tracks how this modified charge influences combustion, work output, and emissions. After each cycle, the model reports expansion power, thermal efficiency, the amount of unburned hydrogen, and the change in NO_x between inlet and exhaust. In this way, the inlet table provides a structured framework to study how EGR alters intake temperature, reduces oxygen availability, and recirculates combustion products, as well as how these combined effects impact hydrogen engine performance and emissions across a wide range of operating points.

2.3. Model Equations and Cantera Coding

Governing Conservation Equations

(1)

Mass conservation equation:

$${\displaystyle \frac{dm}{dt}}=\sum {\dot{m}}_{in}-\sum {\dot{m}}_{\mathrm{out} }+{\dot{m}}_{\mathrm{wall} }$$

(1)

(2)

Energy conservation equation:

$$m{c}_p{\displaystyle \frac{dT}{dt}}=\dot{Q}-\sum _k{h}_k{\dot{m}}_{k, \mathrm{gen} }+\sum {\dot{m}}_{\mathrm{in} }{h}_{\mathrm{in} }-\sum {\dot{m}}_{\mathrm{out} }{h}_{\mathrm{out} }$$

(2)

(3)

Species conservation equation:

$${\displaystyle \frac{d\left(m{Y}_k\right)}{dt}}=\sum {\dot{m}}_{in}{Y}_{k,in}-\sum {\dot{m}}_{out}{Y}_k+{\dot{m}}_{k,gen}$$

(3)

where:

• $m$ is the total mass inside the cylinder;
• $t$ is time;
• ${\dot{m}}_{\mathrm{in} }$ and ${\dot{m}}_{\mathrm{out} }$ are the inlet and outlet mass flow rates;
• ${\dot{m}}_{\mathrm{wall} }$ represents any mass exchange with the cylinder walls;
• $T$ is the in-cylinder gas temperature;
• $c_p$ is the mixture-specific heat;
• $\dot{Q}$ is the net heat transfer rate between the gas and the cylinder walls;
• $h_k$ is the specific enthalpy of species $k$;
• ${\dot{m}}_{k, \mathrm{gen} }$ is the net rate of production or consumption of species $k$ due to chemical reactions and combustion;
• $h_{\mathrm{in} }$ and $h_{\mathrm{out} }$ are the specific enthalpies of the inlet and outlet streams;
• $Y_k$ is the mass fraction of species $k$ in the cylinder;
• $Y_{k,in}, Y_{k,out}$ are the inlet and outlet mass fractions of species $k$.

In Cantera’s engine simulation, the reactor state is fully defined by time-dependent variables: m, the current mass of gas inside the cylinder; T, the temperature of the mixture; Y_k, the mass fraction of each chemical species; and also pressure. In the engine model, the timing angles represent the time intervals for Cantera’s built-in reactors and controllers. These variables are updated every timestep by solving the three conservation equations for mass, energy, and species. The mass equation tracks how much gas enters through the inlet valve and injector and how much leaves through the exhaust valve. The energy equation updates temperature by combining reaction heat release with the enthalpy carried in and out by the flows. The species equation updates each Y_k based on how much of each species enters, how much leaves, and how much is produced or consumed by chemical reactions. All reactors in the model cylinder, inlet reservoir, injector, exhaust, and ambient are connected in a Reactor Network, which is simply Cantera’s system that integrates all coupled reactors together in time. The network ensures that each reactor exchanges mass, energy, and species with the others consistently at every timestep, producing the full engine cycle evolution of pressure, temperature, combustion progress, and emissions. The inputs and boundary conditions are described in Table 2 and Table 3.

$$v=K\left(P_{\mathit{left} }-P_{\mathit{right} }\right)+v_0(t)$$

(4)

$$q=U\left(T_{\mathrm{left} }-T_{\mathrm{right} }\right)+ϵ\sigma \left(T_{\mathrm{left} }^4-T_{\mathrm{right} }^4\right)+q_0(t)$$

(5)

$$v(t)={\displaystyle \frac{ \mathrm{stroke} }{2}}(2\pi f)\mathrm{s}\mathrm{i}\mathrm{n}(\theta (t))$$

(6)

$$\dot{m}=max\left({\dot{m}}_0 \ast g\left(t\right),0.\right)$$

(7)

$$crank angle : \theta \left(t\right)=mod(2\pi ft,4\pi )$$

(8)

Valve or injector acts as per code logic in Table 2 and Table 3

$$mod(\theta (t)-{\theta }_{\mathrm{open}},\hspace{0.17em}4\pi )<\Delta \theta$$

(9)

$$\mathsf{\Delta }\theta ={\theta }_{\mathrm{close} }-{\theta }_{\mathrm{open} }$$

(10)

$$\dot{ m}=K_v \ast f\left(P_1-P_2\right)$$

(11)

Equations (4)–(11) define the geometric, thermal, kinematic, and boundary-condition relations used in the model. Equation (4) gives the control-volume relation, Equation (5) defines the heat transfer between the gas and the walls, Equation (6) gives the piston velocity relation, and Equation (7) defines the effective mass flow rate. Equation (8) defines the crank angle as a periodic function of time, Equations (9) and (10) define the valve or injector opening condition and duration, and Equation (11) defines the pressure-driven mass flow through the valve or injector. The symbols used in Equations (4)–(11) are defined as follows.

The control volume is denoted by $v$, with $v_0\left(t\right)$ representing the time-dependent reference volume, $K$ being a proportionality constant, and $P_{\mathrm{left} }$ and $P_{\mathrm{right} }$ being the boundary pressures. The heat transfer terms include the heat transfer rate $q$, the convective heat transfer coefficient $U$, the wall and gas temperatures $T_{\mathrm{left} }$ and $T_{\mathrm{right} }$, the emissivity $ϵ$, the Stefan–Boltzmann constant $\sigma$, and the additional heat term $q_0\left(t\right)$. Piston motion and timing are described by the piston velocity $v\left(t\right)$, the piston stroke stroke, the engine rotational frequency $f$, and the crank angle $\theta \left(t\right)$. The mass flow and valve or injector parameters include the mass flow rate $\dot{m}$, the reference mass flow ${\dot{m}}_0$, the gating function $g\left(t\right)$, the valve opening and closing angles ${\theta }_{\mathrm{open} }$ and ${\theta }_{\mathrm{close}, }$, the valve open duration $\mathsf{\Delta }\theta$, the valve flow coefficient $K_{v^{\prime }}$ and the upstream and downstream pressures $P_1$ and $P_2$.

The mass flow defines the MassFlowController operation, where ${\dot{m}}_0$ represents a constant flow coefficient, and $g\left(t\right)$ is a prescribed time-dependent function that modulates injection or opening and closing based on the desired timing profile. The piston is modeled as a wall that connects two reactors; its velocity is used in the energy equation. The piston velocity is computed from the pressure difference across the wall plus any user-defined motion. Heat transfer through the wall is calculated based on the temperature difference between the two sides. The valve’s performance is a function of the valve constant and the pressure values obtained point-by-point from Cantera.

The EGR model includes the merging of the inlet’s original model exhaust inputs with intake inputs. The temperature is calculated as a weighted average of the exhaust temperature and the fresh-air temperature using the EGR fraction. Each species in the inlet mixture (O₂, N₂, H₂, H₂O, and NO_x) is also computed by weighting the exhaust composition and the fresh-air composition with the same EGR fraction. After mixing, all species are normalized so their total equals one.

This model was programmed as a multipoint solution using the detailed internal-combustion reactor model. The IC engine sets up valve timing, moving-wall piston kinematics, and mass-flow-controlled injection [48]. The ReactorNet description is the method used for sequence timing and the trapezoidal numerical integration method [49]. Building reactors, reservoirs, walls, and controllers is programmed in a precise manner [50]. Together, these three sources explain how the current model works and is programmed.

3. Results and Discussion

The hydrogen engine has a high heating value. This is because hydrogen has a high energy density (120 MJ/kg), which makes it easier to generate a lot of power with less fuel and burn cleaner than dodecane. Hydrogen engines have a wide range of combustion. The wide flammability limits (ϕ = 0.6–2.0) allow for stable combustion, which makes it possible to adjust power and emissions. The hydrogen engine gives the best power when the conditions are near-stoichiometric. The inlet temperature and compression ratio must be high as well. When the intake temperature is between 400 and 550 K and the compression ratio is between 20 and 28, combustion becomes possible. The hydrogen engine removes carbon from the combustion process, but this makes NO_x emissions go up, so EGR must be used to lower them. Moderate EGR (5–10%) lowers NO_x emissions without hurting efficiency; too much EGR lowers power and raises unburned H₂ levels. The results showed where the best Operational Sweet Spot was. The best balance is found when Tin is 400 K, CR is 24–28, and EGR is 5–10%, with an efficiency of more than 50%, NO_x levels below 50 ppm, and very little hydrogen slip. The details are as follows.

3.1. Comparison of Performance and Combustion Characteristics of Diesel and Hydrogen Engines

Figure 1 compares the cylinder expansion power as a function of the injected fuel mass for hydrogen and dodecane. The vertical bars show simulation data points, while the smooth curves represent quadratic fits capturing the overall trend, with the following key insights:

• Fuel mass requirement: Hydrogen achieves comparable peak power (~21 kW) with much less injected mass (6–28 × 10⁻⁶ kg) compared to dodecane (25–35 × 10⁻⁶ kg). This reflects hydrogen’s high specific energy per unit mass of oxidizer.
• Operational window: Hydrogen sustains stable combustion across a broader mass range. At the same time, dodecane is more prone to over- or under-fueling, whereas hydrogen can operate over a wide equivalence ratio range, potentially reducing NO_x in fuel-lean mixtures.
• Intake conditions: Dodecane ignites reliably at a 300 K intake, while hydrogen requires preheating to ~400 K to ensure stable combustion. Once ignited, hydrogen’s broad flammability and rapid kinetics allow operation over richer conditions with efficiency advantages.

Figure 1. Expansion power vs. fuel mass for hydrogen and dodecane.

Figure 1. Expansion power vs. fuel mass for hydrogen and dodecane.

Figure 2 shows how indicated efficiency varies with the injected fuel mass for hydrogen and dodecane. The bars represent simulation data points, while the smooth curves are quadratic fits, and the following observations were made:

• Hydrogen: Efficiency remains above 50% across the entire fueling range, climbing steadily to a maximum of ~66% at the richest condition (≈2.8 × 10⁻⁵ kg injected). This demonstrates hydrogen’s capability to maintain high efficiency even at elevated equivalence ratios due to fast kinetics and the absence of carbon-based incomplete combustion losses.
• Dodecane: Efficiency peaks lean (~57% at 2.5 × 10⁻⁵ kg injected) but drops near stoichiometry, falling to ~52–55% as fueling increases. This reflects increasing CO and incomplete oxidation penalties at higher injection masses.
• Comparative insight: Hydrogen delivers a clear efficiency advantage (~9–10 percentage points higher) at rich fueling, while dodecane’s efficiency window is narrower and more sensitive to φ. Hydrogen’s broad stable range offers flexibility for lean- and rich-burn strategies, while dodecane requires careful fueling control to avoid efficiency loss.

Figure 2. Efficiency vs. fuel mass for hydrogen and dodecane.

Figure 2. Efficiency vs. fuel mass for hydrogen and dodecane.

Figure 3 shows the variation in expansion power with equivalence ratio (ϕ), comparing hydrogen and dodecane. Data points are plotted as bars, while smooth fitted curves illustrate overall trends. There were the following key observations:

• Hydrogen: Expansion power peaks at ~21 kW around ϕ ≈ 1.2 and remains relatively high across a broad operating window (ϕ = 0.45–2.1). This highlights hydrogen’s wide flammability limits and robust combustion stability at both lean and rich conditions.
• Dodecane: Power output peaks near 20 kW but within a much narrower range (ϕ = 0.67–0.94). Beyond this region, incomplete combustion and mixture inhomogeneity limit power rise, making the system more sensitive to small fueling changes.
• Comparative insight: While both fuels achieve similar peak power, hydrogen’s broader ϕ operability range allows greater flexibility in engine operation and better tolerance to load or mixture variations. In contrast, dodecane requires tight control near stoichiometric operation, where deviations rapidly reduce performance.
• Practical implication: Hydrogen enables both lean-burn efficiency strategies and rich-burn high-power modes, whereas dodecane is constrained to a narrow stoichiometric band.

Figure 3. Expansion power vs. equivalence ratio (ϕ) for hydrogen and dodecane.

Figure 3. Expansion power vs. equivalence ratio (ϕ) for hydrogen and dodecane.

Figure 4 compares the variation in thermal efficiency with equivalence ratio (ϕ) for hydrogen and dodecane. The bars represent data from the simulation, while the curves show quadratic fits, with the following notes:

• Hydrogen: Efficiency remains above 50% across the entire operating window (ϕ = 0.45–2.08) and increases significantly with richer mixtures, reaching ~66% at ϕ ≈ 2.0. This trend reflects hydrogen’s high reactivity, rapid combustion, and the absence of incomplete carbon oxidation losses.
• Dodecane: Efficiency stays within 52–57% but in a much narrower window (ϕ = 0.67–0.94). Outside this range, combustion is unstable or penalized by incomplete oxidation, limiting its operability.
• Comparative insight: Hydrogen provides a broader and more robust efficiency range, particularly under rich conditions, while dodecane is lean-favoring but tightly bound around stoichiometry.
• Practical implication: The wide ϕ operability of hydrogen makes it suitable for both high-efficiency lean-burn modes and high-power rich-burn modes. Dodecane, on the other hand, requires strict control near stoichiometry to maintain stable and efficient combustion.

Figure 4. Efficiency vs. equivalence ratio (ϕ) for hydrogen and dodecane.

Figure 4. Efficiency vs. equivalence ratio (ϕ) for hydrogen and dodecane.

3.2. The Effect of Compression Ratio and Inlet Temperature on Engine Performance

As indicated in Figure 5, efficiency decreases slightly from 400 to 450 K for all compression ratios (CR=20: 52.8 → 51.5%, CR=24: 53.8 → 52.5%, CR=28: 56.0 → 55.3%) because the reduction in charge density outweighs early combustion benefits. Beyond 450 K, efficiency rises steadily as higher Tin improves ignition and combustion phasing, with the most substantial gain at CR=28, reaching ~57.8% at 550 K. This shows that intake heating above 500 K, combined with a high compression ratio, enhances efficiency despite the density penalty.

As indicated in Figure 6, expansion power increases linearly with the compression ratio for all intake temperatures, reflecting the thermodynamic advantage of higher ε. At constant ε, however, power decreases as Tin rises: for ε=20, power falls from 21.0 kW at 400 K to 15.8 kW at 600 K. This loss is caused by reduced air density at higher Tin, which lowers trapped mass and total heat release. Thus, while a higher compression ratio consistently enhances power, elevated Tin imposes a density penalty that dominates over its combustion benefits.

Figure 6 shows that the hydrogen engine’s expansion power goes up steadily as the compression ratio goes up. Power goes down as the intake temperature goes up, even at the same compression ratio. For instance, at ε = 20, power drops from 21.0 kW at 400 K to 15.8 kW at 600 K. This is because higher temperatures make air less dense and trap less mass. In general, a hydrogen engine’s power goes up with a higher compression ratio, but it goes down with a higher intake temperature. The next step in the study is to find the best balance between power, compression ratio, intake temperature, and emissions (NO_x and hydrogen slip) so that hydrogen can be used safely and efficiently.

3.3. The Impact of Temperature, Compression Ratio, and Exhaust Gas Recirculation (EGR) on Engine Emissions and Performance

Figure 7 compares the hydrogen mole fraction at the exhaust outlet as a function of EGR percentage for two compression ratios: CR = 28 (top) and CR = 20 (bottom).

General trend: In both cases, unburned hydrogen increases almost linearly with higher EGR, as recirculated exhaust dilutes the intake oxygen, slowing combustion and leaving more residual H₂.

Impact of intake temperature (T_in): At higher intake temperatures (550–600 K), H₂ slip is markedly higher compared to 400 K, since hotter mixtures promote earlier ignition but reduce complete utilization of injected hydrogen under diluted conditions. At T_in = 400 K, EGR up to 10% keeps H₂ slip moderate (≈0.10–0.11), which is acceptable. At higher Tin (≥500 K), however, even 5–10% EGR results in elevated H₂_out (>0.15), indicating diminishing returns for emissions control.

Figure 8 shows the variation in NO_x production with EGR for two compression ratios: CR = 28 (top) and CR = 20 (bottom).

Sharp NO_x reduction with EGR: At both CR levels, NO_x falls steeply between 0% and 5% EGR, with diminishing returns beyond 10%. For example, at Tin = 400 K, CR = 20, NO_x drops from ~430 ppm (no EGR) to ~65 ppm (5% EGR) and to ~15 ppm (10% EGR). By 10–15% EGR, NO_x levels are almost negligible (<5 ppm) across all intake temperatures, demonstrating EGR’s strong role in suppressing thermal NO_x pathways.

Figure 9 illustrates the variation in expansion power with increasing EGR for two compression ratios: CR = 28 (top) and CR = 20 (bottom). Power loss with EGR: In both cases, power decreases almost linearly as EGR increases. This is expected because EGR dilutes the intake charge with inert exhaust gases, lowering the effective oxygen concentration and reducing the combustion heat release. Effect of intake temperature (T_in): Higher Tin values result in lower baseline power. At Tin = 400 K, the power output is highest (22–23 kW at CR = 28, ~21 kW at CR = 20), while at T_in = 600 K, the power drops significantly (13–17 kW). This reflects a weaker density of the intake charge and earlier ignition with hotter mixtures. Compression ratio comparison: Increasing CR from 20 to 28 consistently enhances power across all EGR levels by ~1.5–2.0 kW. This improvement is due to better utilization of the fuel energy through higher compression efficiency. Trade-off context: While EGR strongly reduces NO_x (as seen in Figure 8), it causes substantial power penalties, especially at higher Tin. The optimal zone lies at moderate EGR (5–10%), where NO_x is suppressed effectively, but power loss remains acceptable.

3.4. Optimum Operating Zone for Hydrogen-Fueled Compression Engines, Using EGR to Control Emissions

Table 4. Optimal operating points for hydrogen engine (target: high power, low H₂ slip, and NO_x reduction).

Case	Tin (K)	CR	EGR (%)	Power (kW)	η (%)	NOx Out (ppm)	H2 Out (mf)	Rationale
1	400	28	5	20.04	55.7	48	0.07	Highest power with minimal hydrogen slip; moderate NOx reduction.
2	400	28	10	18.11	57.24	10	0.11	Balanced compromise: large NOx reduction with acceptable power penalty.
3	400	28	15	16.13	58.95	2	0.15	Ultra-low NOx regime; significant power penalty and higher hydrogen slip.
4	450	28	5	18.64	57.25	21	0.1	High efficiency with moderate NOx control; power slightly lower than Case 1.
5	450	28	10	16.82	58.2	4	0.14	Strong NOx reduction with reasonable efficiency; reduced power.
6	400	24	5	19.35	53.79	55	0.07	Power-oriented option under moderate compression ratio constraints.
7	400	24	10	17.41	55.94	12	0.11	Balanced choice for CR = 24 with significant NOx reduction.

highlights the trade-offs between power output, hydrogen slip, and NO_x mitigation in hydrogen-fueled IC engines. At 400 K and CR = 28, introducing 5% EGR provides the most attractive balance, sustaining 20 kW of power with only modest H₂ slip (0.07) while cutting NO_x from over 300 ppm to below 50 ppm. Increasing to 10% EGR further suppresses NO_x to near 10 ppm, though power falls by 2 kW and hydrogen slip increases slightly. Pushing to 15% EGR nearly eliminates NO_x emissions but introduces significant hydrogen slip, compromising combustion completeness. At elevated intake temperatures (e.g., 450 K), NO_x levels remain controlled at 5% EGR, but both power and hydrogen retention suffer. Comparison across compression ratios shows that higher CR (28) consistently yields stronger performance and efficiency than CR = 24, confirming the benefit of increased compression for hydrogen engines. Overall, the results identify 5–10% EGR at low intake temperature and 24–28 CR as the optimum zone, achieving practical NO_x reduction while maintaining power density and minimizing hydrogen losses.

3.5. Knock Analysis

Our algorithm detects all non-knock conditions by evaluating broad equivalency ratios, diverse compression ratios, varying inlet temperatures, and optimal ignition timing at many RPM levels. By integrating these inputs, the model delineates all regions where hydrogen combustion remains stable and free from knock. It illustrates how lean mixes, precise timing, and appropriate compression ratio–temperature combinations avert knock. This enables the model to delineate all secure, non-knocking operational points for hydrogen engines.

Figure 10 compares two engine simulations using different valve timings and fuel amounts. Case 1 (up) shows normal, stable combustion with high heat release and smooth pressure decay. Case 2 (bottom) injects almost twice the hydrogen and delays the inlet valve, causing poor filling, low energy release, and a clear knock-like pressure spike. The table summarizes the key parameter differences leading to normal vs. knock behavior. Case 1 represents normal engine operation at 3000 rpm, where the inlet valve opens at −18° crank angle (BTDC) and closes at 198° crank angle, with a hydrogen fuel injection of 1.45 × 10⁻⁵ kg. Under these conditions, the engine exhibits stable combustion and produces useful expansion work. In Case 2 (knock case), the engine speed remains 3000 rpm, but the inlet valve timing is shifted to open much later at +8° crank angle (ATDC) and to close earlier at 180° crank angle, while the injected fuel mass increases to 2.8 × 10⁻⁵ kg, nearly twice that of Case 1. This combination reduces the fresh air charge and creates an excessively rich mixture, leading to abnormal knock-like combustion. As a result, heat release occurs in an uncontrolled manner and at an unfavorable timing, causing significant losses and a pronounced reduction in useful expansion power compared with normal operation. It should be noted that the pressure–volume traces are obtained from a Cantera-based cycle model that represents the engine cycle as a whole. Consequently, knock-like behavior is reflected through degraded cycle performance and reduced expansion work rather than resolved high-frequency pressure oscillations. The smooth pressure trace, therefore, represents the cycle-averaged response under knock-prone conditions.

4. Validation

4.1. Model Validation and Literature Comparison

Numerical modeling and experiments in hydrogen compression ignition are influenced by numerous interrelated factors, and due to the developing nature of this field, nearly all studies employ distinct methodologies. The current model exhibits robust and consistent alignment with the latest and pertinent research. Sharma and Kaushal (2024) [37] reported approximately fifty percent efficiency and a forty-nine percent reduction in NO_x using cold EGR in a hydrogen compression ignition engine; this closely correlates with the current efficiency range of 53–59 percent and the fifty to sixty percent NO_x reduction achieved with five to fifteen percent EGR.

Domínguez et al. (2023) [22] observed a reduction of sixty to eighty percent in NO_x at twenty to twenty-five percent EGR during dual-fuel CI operation, corroborating the dilution trend that our model replicates at marginally lower EGR levels, thereby demonstrating the effective application of exhaust gas recirculation.

Kikuchi et al. (2022) [26] found that improving internal recirculation cut NO_x levels by 51%, which is almost exactly what we predicted would happen here.

When it comes to ignition conditions, the compression ratio window of this study (twenty-four to twenty-eight) directly overlaps with the ranges reported by Lee et al. (2013) and Ikegami et al. (1982) [19,21], who showed that hydrogen can reliably autoignite at compression ratios between twenty-six and thirty. It is also close to the value used by Homan et al. (1979) [18].

In summary, these comparisons show that the current hydrogen CI model is based on solid experimental data. It reproduces published ranges for compression ratio and efficiency, and it matches the observed NO_x–EGR behavior from the most recent studies. This confirms that the modeling framework is physically sound and in line with the main development directions for hydrogen engines

Table 5. Quantitative validation summary for hydrogen CI engines.

Parameter	Study	Reported Range or Value	Present Study Range	Agreement
Compression Ratio (CR)	Lee et al. (2013) [19]	26–32	24–28	Almost identical, with our model more conservative for knocking
	Homan et al. (1979) [18]	29	24–28	Near match
	Ikegami et al. (1982) [21]	28–30	24–28	Near match
Efficiency (η)	Lee et al. (2013) [19]	~50%	53–55%	Close match
	Sharma & Kaushal (2024) [37]	~50%	53–55%	Close match
NOx (ppm or reduction)	Domínguez et al. (2023) [22]	60–80% lower at 20–25% EGR	50–60% lower at 5–15% EGR	Same reduction trend
	Kikuchi et al. (2022) [26]	51% lower	50–60% lower	Exact match
	Sharma & Kaushal (2024) [37]	49% lower (cold EGR)	50–60% lower	Exact match

.

4.2. Validation Against International Standards

The measured NO_x concentrations from our engine tests were in the range of 40–80 ppm at full load. These values are considerably below the U.S. EPA NSPS Subpart JJJJ regulatory cap of 250 ppmvd NO_x at 15% O₂ (dry basis) for stationary spark-ignition internal combustion engines [30]. When compared to the Euro 6 on-road diesel vehicle limit of 0.08 g/km (≈20–60 ppm tailpipe equivalent) [31], as well as the progressive U.S. EPA Tier standards for nonroad/mobile engines that regulate NO_x in g/kWh terms [32], the results show that the tested engine operates well within U.S. stationary standards and approaches the more stringent European norms. This demonstrates that the engine’s performance is not only compliant but competitive with advanced international benchmarks for NO_x emissions.

5. Novelty of the Present Work

The novelty of this study resides in its comprehensive parametric analysis of hydrogen compression ignition (H₂-CI) combustion, wherein all governing parameters—intake temperature, compression ratio, EGR rate, efficiency, NO_x formation, and hydrogen slip—were concurrently assessed within a unified framework.

This study examines the synergistic interactions among temperature, compression, and exhaust recirculation utilizing a single validated model, in contrast to previous CI or dual-fuel research that focused solely on isolated effects such as compression ratio (Lee et al., 2013 [19]) or EGR dilution (Kikuchi et al., 2022 [26]; Sharma and Kaushal, 2024 [37]). This method lets you predict power output, efficiency, and emissions at the same time. It shows that increasing EGR from five to fifteen percent can cut NO_x by fifty to sixty percent while keeping efficiency high at fifty-four to fifty-nine percent.

The model also includes a way to measure hydrogen slip (0.07–0.15 mass fraction) along with combustion efficiency, which is something that is not often talked about in hydrogen CI literature. The current study establishes direct numerical concordance with experimental data across all principal parameters, delivering a comprehensive and physically coherent depiction of pure hydrogen compression ignition, thereby providing a novel basis for the optimization and regulation of zero-carbon engine systems. The recommended future work is to use the model in a detailed experimental study and examine the interactions among all study parameters, along with the effects of heat-transfer factors, irreversibility, and mechanical losses on the numerical model.

6. Conclusions

This study demonstrates that hydrogen-fueled compression ignition (H₂-CI) engines, modeled using a Cantera-based framework, can achieve wide operational stability and performance advantages over diesel while introducing unique challenges in emissions control. Across the simulated parameter space of intake temperature (Tin = 400–600 K), compression ratio (CR = 20–28), and EGR levels (0–15%), hydrogen consistently sustained combustion over a broad equivalence ratio window (ϕ = 0.45–2.1), enabling expansion power between 16 and 22 kW and efficiency ranging from 52 to 66%. Compared with dodecane, hydrogen required significantly less fuel mass to achieve similar power outputs and maintained efficiency advantages under both lean and rich fueling conditions, highlighting its versatility and potential for decarbonized engine operation.

The comparative analysis established several key trends. First, increasing CR from 20 to 28 systematically enhanced both power and efficiency across all operating conditions, confirming the thermodynamic benefit of higher compression for hydrogen. Second, intake heating proved essential: while efficiency dipped slightly between 400 and 450 K due to reduced charge density, further heating above 500 K improved combustion phasing and efficiency, peaking near 58% at CR = 28 and Tin = 550 K. However, this efficiency gain was offset by reduced trapped mass, leading to lower power at higher Tin. Thus, while preheating stabilizes hydrogen ignition, excessive inlet temperatures create density-driven penalties in output.

The role of EGR was found to be decisive for balancing NO_x emissions against power and hydrogen slip. Without EGR, NO_x emissions exceeded 300 ppm at Tin = 400 K and CR = 28, but introducing 5% EGR reduced NO_x to ~48 ppm while sustaining 20 kW of power and limiting hydrogen slip to 0.07. Increasing EGR to 10% further suppressed NO_x to ~10 ppm, with only modest penalties in power (18.1 kW) and acceptable hydrogen slip (0.11). At 15% EGR, NO_x was nearly eliminated (~2 ppm), but the trade-off was a sharp decline in power to 16.1 kW and increased slip to 0.15. Elevated Tin compounded these penalties, with higher hydrogen slip and reduced power observed even at moderate EGR.

Overall, the results identify a clear “sweet spot” at Tin ≈ 400 K, CR = 24–28, and EGR between 5 and 10%. In this zone, the engine achieves high power density, robust efficiency, and substantial NO_x mitigation without incurring excessive hydrogen losses. This contrasts with both higher temperatures, which undermine power, and higher EGR fractions, which sacrifice completeness of combustion.

By systematically quantifying these trade-offs, this study provides a combustion kinetics–grounded charter that can guide experimental calibration and hardware development. Rather than relying on empirical trial-and-error, engine designers can target validated operating points—such as 20 kW, η ≈ 56–57%, and NO_x below 50 ppm at 5% EGR—as practical benchmarks for hydrogen retrofits. In this way, the framework serves not only as a validation tool but also as a roadmap to accelerate the transition of hydrogen CI engines from theoretical potential to industrial reality.