# Reduced chemistry for numerical combustion of NH3/H2 fuel blend

Giovanni Grassi, Luc Vervisch, Pascale Domingo

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Giovanni Grassi, Luc Vervisch, Pascale Domingo. Reduced chemistry for numerical combustion of NH3/H2 fuel blend. Combustion and Flame, 2025, 279, pp.114287. 10.1016/j.combustflame.2025.114287. hal-05326664

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# Reduced chemistry for numerical combustion of NH<sub>3</sub>/H<sub>2</sub> fuel blend

Giovanni Grassi<sup>●</sup>, Luc Vervisch<sup>●</sup>,*, Pascale Domingo<sup>●</sup>

CORIA-CNRS, INSA Rouen Normandie, Saint-Etienne-du-Rouvray, 76800, France

## ARTICLE INFO

**Keywords:**

Ammonia–hydrogen

Combustion

Reduced chemical kinetics

Reactant vitiation

Computational fluid mechanics

Numerical simulations

## ABSTRACT

Ammonia is increasingly recognized worldwide as a promising carrier for hydrogen and energy. One effective strategy is blending ammonia with hydrogen to achieve combustion characteristics comparable to those of natural gas, including stable flame anchoring, controlled flame length, and sufficient heat release for energy production. The design and optimization of ammonia combustion systems rely heavily on computational fluid dynamics (CFD). Accurate CFD simulations of furnaces and gas turbines require chemical kinetic models that strike a balance between simplicity and fidelity, minimizing computational complexity (typically less than 20 species to be transported with the flow) while effectively capturing the essential thermochemistry of hydrogen-enriched ammonia combustion. This study begins with a detailed ammonia/air combustion mechanism and combines various canonical problems to derive two reduced chemical schemes. The methodology employs automated analyses to identify the most influential chemical species and elementary reactions. Five key reactive scenarios representative of premixed and non-premixed burners with eventual dilution by burnt gases are explored: auto-ignition, chemistry interacting with turbulent micro-mixing, freely propagating laminar premixed flames, strained counterflow diffusion flames, and mixing layers. This comprehensive approach facilitates the development of reduced kinetic models specifically tailored to ammonia/hydrogen-air combustion under a set of given operating conditions.

**Novelty and Significance Statement**

Novel reduced chemical schemes are proposed from a reference detailed mechanism for simulating ammonia–hydrogen-enriched combustion. To ensure their applicability in turbulent flame simulations, the reduction methodology incorporates a specific combination of various canonical test cases, including turbulent micro-mixing, for validation and performance assessment. These schemes achieve a significant reduction in stiffness and the number of degrees of freedom to be solved. To demonstrate their feasibility in computational fluid dynamics, a reactive mixing layer is simulated, and the results obtained with the reduced schemes are compared against those from the reference detailed mechanism.

## 1. Introduction

The growing emphasis on reducing carbon dioxide emissions has amplified scientific interest in carbon-free fuels, particularly hydrogen and ammonia [1–4]. However, ammonia combustion poses challenges, including a narrow flammability range and elevated NOₓ emissions [5–7]. For example, ammonia demonstrates significantly lower combustion reactivity compared to natural gas: under stoichiometric conditions, its laminar flame speed is approximately five times lower, and its thermal flame thickness is about 6.5 times greater. Blending ammonia with a certain amount of hydrogen emerges as a promising approach to enhance flame stabilization and ensure adequate heat release in boilers.

Computational Fluid Dynamics (CFD) has become an essential tool for optimizing configurations and operating conditions to minimize pollutant emissions. However, the number of degrees of freedom that

simulations can handle to represent chemical reactions remains limited. The combustion kinetics of ammonia, especially when blended with hydrogen, is particularly complex due to the broad range of time scales involved: oxidation occurs on the order of 0.1 ms, while non-catalytic DeNOx processes in the fumes can extend up to several seconds in large furnaces. The optimal temperature window for such non-catalytic ammonia-based DeNOx is 1100–1300 K. In this process, NH₃ is either directly injected into the exhaust stream or introduced via a fuel-rich burner operation (overall equivalence ratio above unity), allowing the excess ammonia to act as a reducing agent that converts NOₓ into N₂ and H₂O [8–11]. This complexity presents significant challenges in developing reduced kinetic models capable of accurately representing both reactive pathways, i.e., oxidation and subsequent NOₓ evolution.

Since the pioneering work on chemistry reduction [12,13], numerous strategies have been proposed to automatically simplify chemical

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: luc.vervisch@coria.fr (L. Vervisch).</footnote>
schemes [14] while preserving the accurate prediction of key com-
bustion properties, such as ignition delay time, premixed flame speed,
and diffusion flame quenching strain rate. The analysis of species
and elementary reaction interdependencies using oriented graph tech-
niques [15,16] has proven to be highly effective. Once the chemical
system is reduced to capture the evolution of targeted species relevant
to the studied system, the parameters of the reaction rates can be
further refined, for example, through optimization techniques such as
genetic algorithms [17,18].

Skeletal and reduced chemistries for ammonia/hydrogen fuels have
been discussed in the literature [19–22] (not an exhaustive list). Fo-
cussing on premixed flames, a thorough analysis of the chemical
paths has been conducted to propose a two-step chemistry descrip-
tion in [23]. Additionally, automated reduction methods were applied
in [24] to develop a skeletal mechanism, which was validated against
various experimental measurements. These reduced mechanisms were
derived from various detailed mechanisms; however, non-premixed
systems, including diffusion flame quenching, were largely not consid-
ered. The responses of some of these mechanisms are presented in the
supplementary material.

In this study, a strategy is employed to replicate, within a reduced-
order model incorporating detailed chemistry, the behavior of fluid
particles traveling through a turbulent combustion system, includ-
ing reactant dilution by burnt gases. This approach is used to con-
struct a database for chemistry reduction under specific operating
conditions. Starting from a fully detailed chemical mechanism [25,26]
and integrating various additional canonical problems, two reduced
schemes comprising 19 species and 75 reactions are developed and
evaluated. To demonstrate their applicability to CFD, these reduced
mechanisms are applied to direct numerical simulations of a 2D non-
premixed ammonia–hydrogen flame stabilized by a splitter plate, with
results compared against those obtained using the detailed chemical
mechanism.

2. Chemistry reduction methodology

2.1. Reference detailed chemistry and operating conditions

The detailed model used is C3MECHV3.5, developed by merging
various high-fidelity mechanisms, with NUIGMech1.1 as the core and
NOₓ chemistry from NUI Galway [25–27]. This detailed mechanism has
been experimentally validated for ammonia combustion across a wide
range of conditions, and it includes 33 species and 243 reactions.

2.2. Canonical problems

The reduction in the number of species and reactions is achieved by
combining chemistry with stochastic turbulent micro-mixing, enabling
the full range of operating conditions in the composition–temperature
space to be captured. This approach simulates scenarios with three
injection zones (fuel, air, and burnt gases) mimicking a boiler environ-
ment where recirculated burnt gases dilute the reactants, thereby facil-
itating both ignition and flame stabilization. A reduced scheme com-
prising 19 species and 75 reactions is then derived from the stochastic
turbulent micro-mixing problem.

Building on this reduced scheme, minor adjustments to the chemical
rate parameters are made to develop two optimized reduced models.
The optimization process targets both the stochastic turbulent micro-
mixing problem and one-dimensional freely propagating flames, evalu-
ated at various fuel/air equivalence ratios. The species profiles across
these premixed flames, along with their laminar burning velocities,
are analyzed. The two reduced schemes differ based on the emphasis
placed on the optimization targets, either prioritizing micro-mixing or
premixed flames.

Then, these reduced schemes are evaluated in configurations for
which they have not been specifically optimized, such as autoignition

<figure><img src="image_3.png" /><figcaption>**Fig. 1.** Scatter plot of temperature of stochastic particle versus mixture fraction (passive scalar Z = 0 in pure air and Z = 1 in pure fuel). Green: particles from Air-inlet. Blue: Fuel. Red: Burnt gases. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

of homogeneous mixture (i.e., without micro-mixing) and opposed-jet
diffusion flames strained up to their quenching point at low Damköhler
numbers.

A description of each problem is reported as follows:

(1) **Stochastic micro-mixing:** ignition in an adiabatic constant pressure reactor of stochastic particles, each carrying species concentration and enthalpy (Fig. 1), with a micro-mixing closure to mimick molecular diffusion at the smallest scales of turbulence. The latter is designed to replicate turbulent mixing and, based on the Euclidean Minimum Spanning Tree model (EMST) [28,29] is aimed to simulate the progressive interaction of the different streams injected in the reactor as it would happen in a non-premixed turbulent reaction zone. The number of particles introduced at each inlet is proportional to the inlet's contribution to the total mass flow rate of a representative combustion system. In this study, the mass flow rates of the fuel inlet, $\dot{Q}_m^F$, and the air inlet, $\dot{Q}_m^{Air}$, are in stoichiometric proportion, with the fuel consisting of NH$_3$ enriched with 15% H$_2$ by volume. In practical systems, hydrogen is typically added in the range of 10%–30% by volume. The 15% used in this study ensures that the chemical kinetics remain predominantly governed by ammonia, while still allowing hydrogen to contribute through its own reaction pathways. The third inlet contains burnt gases derived from the chemical equilibrium of the fuel and air mixture. The mass flow rate of these burnt gases at a temperature of 2111 K is defined as $\dot{Q}_m^{BG} = 0.25\dot{Q}_m^T$, where $\dot{Q}_m^T = \dot{Q}_m^F + \dot{Q}_m^{Air} + \dot{Q}_m^{BG}$ is the total mass flow rate, thus corresponding to a dilution ratio of 25% with burnt gases. This level of dilution is representative of conditions expected in furnaces, primarily due to the recirculation of burnt gases. It also corresponds to the threshold at which the Damköhler number becomes sufficiently high to ensure ignition, given the characteristic micro-mixing time considered, representative of real combustion systems. 999 stochastic particles are injected through these inlets, 651 of air, 98 of fuel, and 250 of burnt gases. The equation representing the problem is for the kth particle:

$$
\frac{d\phi^k}{dt} = M I X^k(\tau_T) + \dot{\omega}_\phi^k, \qquad (1)
$$

where $\phi$ represents generic properties (concentration of each
species and the enthalpy in the single particle), “MIX” is the
EMST [28,29] micro-mixing closure used for the diffusion term
depending on the mixing time $\tau_T$ and $\dot{\omega}_\phi$ stands for the chem-
istry related source term, computed with Cantera 2.4.0 [30]. For
tracking the global evolution of the system, a single deterministic
particle $\phi^d$ is added starting from each inlet, it follows:

$$
\frac{d\phi^d}{dt} = \frac{\langle\phi\rangle - \phi^d}{\tau_T} + \dot{\omega}_\phi^d, \qquad (2)
$$
where $\langle\phi\rangle = (1/N_p) \sum_{k=1}^{N_p} \phi^k$ is the mean overall stochastic particles inside the reactor at a given instant in time, to calibrate the diffusive term here modeled with the LMSE/IEM model [31] (For more details, readers are referred to [17].)

The evolution of particles spans the entire range of equivalence ratios, from pure fuel to pure air, with varying degrees of dilution by burnt gases based on the time history of the stochastic particles. After ignition has occurred and as the system progresses toward chemical equilibrium, the characteristic mixing time, $\tau_T$, does not significantly influence subsequent chemistry reduction or optimization. In this paper context, $\tau_T = 1.5$ ms was applied.

(2) **1D premixed flame:** Freely propagating unstrained premixed flames at atmospheric pressure are simulated using Cantera 2.4.0 [30]. To focus specifically on the propagation characteristics in fresh reaction zones, the fresh gases are not diluted with burnt gases in these configurations. The temperature of the fresh gases is 300 K. The equivalence ratio varies within flammability limits for fuel blends composed of NH₃ enriched with 10%, 15%, and 20% H₂ by volume. The simulation employs an adaptive grid to ensure a complete evolution from fresh to burnt gases. Once the temperature and concentration profiles are computed, they are interpolated onto a consistent flame grid for comparing all the chemical reduced schemes studied.

(3) **1D opposed-jet diffusion flame:** Counterflow diffusion flames at atmospheric pressure are simulated using Cantera 2.6.0 [32] to investigate the chemical behavior within diffusive and reactive layers under varying strain rates. The setup comprises two opposing jets, supplying fuel blends: ammonia (NH₃) enriched with 10%, 15%, and 20% hydrogen (H₂) by volume and preheated air at temperatures of 800 K, 900 K, and 1000 K. The flames are subjected to progressively increasing strain rates until extinction occurs, with the evolution of maximum flame temperature monitored as a function of the maximum strain rate.

(4) **Zero-dimensional autoignition:** Auto-ignition of preheated fuel-blend/air mixtures at various equivalence ratios is also considered to verify the accuracy of the predicted ignition delay times.

The four canonical problems previously described are strongly interdependent and cannot be treated in isolation when ensuring the reduced kinetic scheme's accuracy in predicting flame properties. Their interconnected nature makes their combined consideration, particularly during the optimization procedure, essential for developing an effective reduced chemical scheme. The optimization procedure is implemented within the ORCh package [17,18].

## 2.3. Reduction method

The generation of reduced/optimized models is based on the coupling of two different procedures. The reduction of the number of reactions and species using Directed Relation Graph with error propagation (DRGEP) [15,16] is applied to the turbulent micro-mixing problem described above. Then, the optimization of the reaction rate constants using Genetic Algorithm is applied to both micro-mixing and premixed flames [17,33].

### 2.3.1. Directed relation graph with error propagation (DRGEP)

After selecting a set of target species that must be accurately reproduced by the reduced scheme, DRGEP [15,16] evaluates the influence of each species on the net chemical rate of these targets, ranking the species according to their relative importance. The same process is applied to rank the elementary reactions. DRGEP is used on the deterministic trajectories (Eq. (2)), which are influenced by the time-evolving mean values of all stochastic particles. The target species retained here are H₂, NH₃, O₂, N₂, H₂O, OH, NO, NO₂, and N₂O.

The thermochemical evolution is then recomputed, progressively eliminating species and reactions, starting with the least influential

ones. A measure of the discrepancy between the response of the detailed scheme and that of a reduced one is constructed by accumulating the error across all thermochemical variables and trajectory points (for details, see Eq. (10) in [17]). In this study, schemes with a global error exceeding 10% are discarded. Further details on DRGEP can be found in [15,16], and for the current implementation, refer to [17].

In addition to the nine target species listed above, H, O, HO₂, N, NH, NH₂, NNH, N₂H₂, and HNO are retained, along with Ar. Table 1 presents the reduced scheme, which includes 19 species and 75 reactions.

### 2.3.2. Optimization based on genetic algorithm (GA)

To maximize the removal of species and reactions, it is beneficial to combine DRGEP with a slight optimization of chemical rate parameters. This optimization is achieved using a Genetic Algorithm. The stages of the algorithm are summarized as follows:

1. **Definition of Karyotype:** Reaction rate constants are randomly varied within a limited range to generate *M* different optimized schemes that form generation 0. Variations are constrained to 10%–15% for the pre-exponential factors *A* (in logarithmic scale) and the temperature exponents *b*, and up to 8% for the activation energies *E*. The parameter values are converted into binary sequences for easier manipulation. Each mechanism corresponds to a chromosome, and the entire set of chromosomes constitutes the population.

2. **Computation of Trajectories:** Simulations are performed for all schemes based on the selected configuration, such as a turbulent micro-mixing with reaction or freely propagating premixed flames.

3. **Ranking:** A fitness function is defined based on the error between the predictions of the detailed scheme [17] and the optimized scheme. This function ranks all kinetic schemes from best to worst, with the deterministic trajectories (Eq. (2)) serving as input to the fitness evaluation, which compares the detailed and reduced schemes responses averaged over the trajectories [17].

4. **Evolution to the Next Generation:** A new population of *M* chromosomes is generated from the current generation using the following methods:

(a) **Crossover:** *M*/2 pairs of chromosomes are randomly selected, and each pair has a 70% chance of undergoing crossover, where segments of their binary sequences are exchanged.

(b) **Mutation:** Each digit of every chromosome has a 0.2% chance of being altered.

(c) **Elitism:** The best solution (the scheme with the highest fitness) is preserved as the “elite” and carried forward to subsequent generations.

After generating the new population, trajectories are recalculated, and the process is repeated. The algorithm is considered converged when the fitness variation between two iterations is below a few percents, indicating that no further improvement is possible.

## 2.4. Optimization pathway

The DRGEP approach is first applied to the stochastic mixing problem under the specified conditions—namely, a blend of NH₃ enriched with 15% H₂ by volume, burning in the air under stoichiometric conditions with 25% dilution by adiabatic burnt gases by mass. This process yields a baseline reduced mechanism comprising 18 species plus argon and 75 reactions. Argon is retained because it contributes to the calculation of Chaperon efficiencies (third-body reactions) in the detailed mechanism. These efficiencies are preserved without modification in the reduced mechanisms.
<table><caption>**Table 1**
Reactions and Arrhenius constants for both mechanisms: RmAH-1 and RmAH-2. The Chaperon efficiencies of the detailed scheme [26] are preserved.</caption><thead><tr><th rowspan="2">Reaction</th><th colspan="3">RmAH-1</th><th colspan="3">RmAH-2</th></tr><tr><th>A</th><th>b</th><th>E (J/mol)</th><th>A</th><th>b</th><th>E (J/mol)</th></tr></thead><tbody><tr><td>H<sub>2</sub> + O ⇌ H + OH</td><td>2.64e+09</td><td>0.00</td><td>3.27e+07</td><td>8.52e+09</td><td>0.00</td><td>3.30e+07</td></tr><tr><td>H<sub>2</sub> + O ⇌ H + OH</td><td>1.17e+12</td><td>0.00</td><td>8.09e+07</td><td>9.37e+11</td><td>0.00</td><td>8.30e+07</td></tr><tr><td>H<sub>2</sub> + OH ⇌ H + H<sub>2</sub>O</td><td>2.15e+05</td><td>1.52</td><td>1.45e+07</td><td>1.50e+05</td><td>1.53</td><td>1.41e+07</td></tr><tr><td>H + O<sub>2</sub> ⇌ O + OH</td><td>1.04e+11</td><td>0.00</td><td>6.31e+07</td><td>1.26e+11</td><td>0.00</td><td>6.50e+07</td></tr><tr><td>H + OH (T<sup>+</sup>M) ⇌ H<sub>2</sub>O (T<sup>+</sup>M)</td><td>3.28e+10</td><td>0.23</td><td>-4.64e+05</td><td>2.39e+10</td><td>0.23</td><td>-4.48e+05</td></tr><tr><td>2OH ⇌ H<sub>2</sub>O + O</td><td>2.65e+03</td><td>1.79</td><td>-6.92e+06</td><td>2.71e+03</td><td>1.76</td><td>-7.00e+06</td></tr><tr><td>H + HO<sub>2</sub> ⇌ H<sub>2</sub> + O<sub>2</sub></td><td>2.69e+03</td><td>2.08</td><td>-5.75e+06</td><td>3.75e+03</td><td>2.11</td><td>-5.73e+06</td></tr><tr><td>H + HO<sub>2</sub> ⇌ 2OH</td><td>1.07e+11</td><td>0.00</td><td>1.24e+06</td><td>1.05e+11</td><td>0.00</td><td>1.24e+06</td></tr><tr><td>HO<sub>2</sub> + O ⇌ O<sub>2</sub> + OH</td><td>3.04e+10</td><td>0.00</td><td>0.00e+00</td><td>2.05e+10</td><td>0.00</td><td>0.00e+00</td></tr><tr><td>HO<sub>2</sub> + OH ⇌ H<sub>2</sub>O + O<sub>2</sub></td><td>6.57e+16</td><td>-2.47</td><td>2.46e+06</td><td>1.87e+17</td><td>-2.47</td><td>2.46e+06</td></tr><tr><td>HO<sub>2</sub> + OH ⇌ H<sub>2</sub>O + O<sub>2</sub></td><td>1.02e+06</td><td>1.24</td><td>-5.23e+06</td><td>1.54e+06</td><td>1.25</td><td>-5.20e+06</td></tr><tr><td>H + O<sub>2</sub> (T<sup>+</sup>M) ⇌ HO<sub>2</sub> (T<sup>+</sup>M)</td><td>3.48e+09</td><td>0.44</td><td>0.00e+00</td><td>3.41e+09</td><td>0.43</td><td>0.00e+00</td></tr><tr><td>NH<sub>3</sub> + M ⇌ H + NH<sub>2</sub> + M</td><td>3.90e+13</td><td>0.00</td><td>3.85e+08</td><td>1.01e+14</td><td>0.00</td><td>3.85e+08</td></tr><tr><td>H + NH<sub>3</sub> ⇌ H<sub>2</sub> + NH<sub>2</sub></td><td>2.38e+03</td><td>2.24</td><td>4.32e+07</td><td>1.90e+03</td><td>2.25</td><td>4.37e+07</td></tr><tr><td>NH<sub>3</sub> + O ⇌ NH<sub>2</sub> + OH</td><td>9.33e-02</td><td>3.27</td><td>1.53e+07</td><td>9.33e-02</td><td>3.34</td><td>1.51e+07</td></tr><tr><td>NH<sub>3</sub> + OH ⇌ H<sub>2</sub>O + NH<sub>2</sub></td><td>1.00e+02</td><td>2.37</td><td>-7.11e+05</td><td>1.40e+02</td><td>2.40</td><td>-7.20e+05</td></tr><tr><td>NH<sub>2</sub> + M ⇌ H + NH + M</td><td>1.35e+12</td><td>0.00</td><td>3.21e+08</td><td>2.40e+11</td><td>0.00</td><td>3.18e+08</td></tr><tr><td>H + NH<sub>2</sub> ⇌ H<sub>2</sub> + NH</td><td>1.20e+03</td><td>2.19</td><td>6.80e+06</td><td>1.56e+03</td><td>2.15</td><td>7.02e+06</td></tr><tr><td>NH<sub>2</sub> + O ⇌ NH + OH</td><td>1.13e+10</td><td>0.00</td><td>0.00e+00</td><td>8.64e+09</td><td>0.00</td><td>6.83e+06</td></tr><tr><td>NH<sub>2</sub> + O ⇌ NH + OH</td><td>8.60e-04</td><td>3.97</td><td>6.99e+06</td><td>8.60e-04</td><td>4.09</td><td>6.83e+06</td></tr><tr><td>NH<sub>2</sub> + OH ⇌ H<sub>2</sub>O + NH</td><td>3.87e+03</td><td>1.95</td><td>-8.58e+05</td><td>3.39e+03</td><td>1.91</td><td>-8.58e+05</td></tr><tr><td>2NH<sub>2</sub> ⇌ NH + NH<sub>3</sub></td><td>5.64e-03</td><td>3.54</td><td>2.31e+06</td><td>5.64e-03</td><td>3.50</td><td>2.30e+06</td></tr><tr><td>NH<sub>2</sub> + O ⇌ H + HNO</td><td>1.47e+12</td><td>-0.50</td><td>3.53e+06</td><td>1.22e+12</td><td>-0.50</td><td>3.43e+06</td></tr><tr><td>NH<sub>2</sub> + O ⇌ H + HNO</td><td>1.58e+11</td><td>-0.24</td><td>2.74e+06</td><td>4.33e+10</td><td>-0.25</td><td>2.74e+06</td></tr><tr><td>HO<sub>2</sub> + NH<sub>2</sub> ⇌ NH<sub>3</sub> + O<sub>2</sub></td><td>4.46e+15</td><td>-1.87</td><td>1.30e+06</td><td>2.07e+15</td><td>-1.90</td><td>1.28e+06</td></tr><tr><td>HO<sub>2</sub> + NH<sub>2</sub> ⇌ NH<sub>3</sub> + O<sub>2</sub></td><td>5.32e+04</td><td>1.60</td><td>-5.44e+06</td><td>4.37e+04</td><td>1.61</td><td>-5.43e+06</td></tr><tr><td>HO<sub>2</sub> + NH<sub>2</sub> ⇌ H<sub>2</sub>O + HNO</td><td>2.13e+06</td><td>0.78</td><td>-5.65e+06</td><td>2.74e+06</td><td>0.77</td><td>-5.69e+06</td></tr><tr><td>NH<sub>2</sub> + NO ⇌ NH + OH</td><td>4.35e+07</td><td>0.29</td><td>-3.52e+06</td><td>2.98e+07</td><td>0.29</td><td>-3.53e+06</td></tr><tr><td>NH<sub>2</sub> + NO ⇌ H<sub>2</sub>O + N<sub>2</sub></td><td>2.80e+16</td><td>-2.35</td><td>3.61e+06</td><td>1.29e+16</td><td>-2.36</td><td>3.62e+06</td></tr><tr><td>NH<sub>2</sub> + NO<sub>2</sub> ⇌ H<sub>2</sub>O + N<sub>2</sub>O</td><td>3.17e+15</td><td>-2.16</td><td>1.91e+06</td><td>2.64e+15</td><td>-2.21</td><td>1.95e+06</td></tr><tr><td>NH + NH<sub>2</sub> ⇌ H + N<sub>2</sub>H<sub>2</sub></td><td>1.32e+12</td><td>-0.47</td><td>0.00e+00</td><td>2.19e+12</td><td>-0.47</td><td>0.00e+00</td></tr><tr><td>H + NH ⇌ H<sub>2</sub> + N</td><td>1.58e+08</td><td>0.71</td><td>3.87e+06</td><td>3.87e+08</td><td>0.70</td><td>3.92e+06</td></tr><tr><td>NH + OH ⇌ H<sub>2</sub>O + N</td><td>6.87e+03</td><td>1.73</td><td>-2.29e+06</td><td>7.55e+03</td><td>1.74</td><td>-2.29e+06</td></tr><tr><td>NH + NH<sub>2</sub> ⇌ N + NH<sub>3</sub></td><td>9.39e+00</td><td>2.48</td><td>4.52e+05</td><td>9.97e+00</td><td>2.50</td><td>4.39e+05</td></tr><tr><td>NH + O ⇌ H + NO</td><td>3.46e+10</td><td>0.02</td><td>3.93e+05</td><td>8.77e+10</td><td>0.02</td><td>3.89e+05</td></tr><tr><td>NH + OH ⇌ H + HNO</td><td>2.71e+11</td><td>-0.34</td><td>-1.86e+05</td><td>2.80e+11</td><td>-0.35</td><td>-1.88e+05</td></tr><tr><td>NH + O<sub>2</sub> ⇌ HNO + O</td><td>2.31e+06</td><td>1.03</td><td>4.77e+07</td><td>1.43e+06</td><td>1.03</td><td>4.90e+07</td></tr><tr><td>NH + O<sub>2</sub> ⇌ NO + OH</td><td>4.28e+05</td><td>0.79</td><td>5.04e+06</td><td>3.95e+05</td><td>0.79</td><td>5.01e+06</td></tr><tr><td>2NH ⇌ H<sub>2</sub> + N<sub>2</sub></td><td>9.59e+09</td><td>-0.03</td><td>-6.23e+05</td><td>1.93e+10</td><td>-0.03</td><td>-6.36e+05</td></tr><tr><td>2NH ⇌ 2H + N<sub>2</sub></td><td>9.06e+10</td><td>-0.03</td><td>-6.23e+05</td><td>2.00e+10</td><td>-0.03</td><td>-6.28e+05</td></tr><tr><td>N + NH ⇌ H + N<sub>2</sub></td><td>4.97e+08</td><td>0.51</td><td>7.95e+04</td><td>4.48e+08</td><td>0.51</td><td>7.95e+04</td></tr><tr><td>NH + NO ⇌ H + N<sub>2</sub>O</td><td>2.24e+11</td><td>-0.52</td><td>-2.85e+06</td><td>2.20e+11</td><td>-0.50</td><td>-2.85e+06</td></tr><tr><td>NH + NO ⇌ N<sub>2</sub> + OH</td><td>4.89e+11</td><td>-0.76</td><td>8.37e+04</td><td>8.54e+11</td><td>-0.72</td><td>8.37e+04</td></tr><tr><td>NH + NO<sub>2</sub> ⇌ HNO + NO</td><td>6.14e+09</td><td>0.00</td><td>0.00e+00</td><td>9.88e+09</td><td>0.00</td><td>0.00e+00</td></tr><tr><td>N + OH ⇌ H + NO</td><td>3.65e+10</td><td>0.00</td><td>0.00e+00</td><td>1.77e+10</td><td>0.00</td><td>0.00e+00</td></tr><tr><td>N + O<sub>2</sub> ⇌ NO + O</td><td>1.09e+07</td><td>1.00</td><td>2.68e+07</td><td>1.97e+07</td><td>1.01</td><td>2.68e+07</td></tr><tr><td>N + NO ⇌ N<sub>2</sub> + O</td><td>1.22e+07</td><td>0.93</td><td>-5.36e+06</td><td>1.03e+07</td><td>0.91</td><td>-5.42e+06</td></tr><tr><td>N<sub>2</sub>H<sub>2</sub> + M ⇌ H + NNH + M</td><td>3.38e+40</td><td>-7.58</td><td>3.10e+08</td><td>4.99e+40</td><td>-7.62</td><td>3.04e+08</td></tr><tr><td>H + N<sub>2</sub>H<sub>2</sub> ⇌ H<sub>2</sub> + NNH</td><td>5.04e+05</td><td>1.78</td><td>3.08e+06</td><td>4.20e+05</td><td>1.81</td><td>3.08e+06</td></tr><tr><td>N<sub>2</sub>H<sub>2</sub> + OH ⇌ H<sub>2</sub>O + NNH</td><td>6.70e+00</td><td>2.81</td><td>-2.00e+06</td><td>6.91e+00</td><td>2.85</td><td>-2.01e+06</td></tr><tr><td>N<sub>2</sub>H<sub>2</sub> + NH<sub>2</sub> ⇌ NH<sub>3</sub> + NNH</td><td>2.48e+02</td><td>2.25</td><td>-4.08e+06</td><td>3.32e+02</td><td>2.26</td><td>-4.09e+06</td></tr><tr><td>N<sub>2</sub>H<sub>2</sub> + NO ⇌ N<sub>2</sub>O + NH<sub>2</sub></td><td>4.74e+09</td><td>0.00</td><td>4.95e+07</td><td>2.46e+09</td><td>0.00</td><td>5.00e+07</td></tr><tr><td>NNH ⇌ H + N<sub>2</sub></td><td>2.87e+08</td><td>0.00</td><td>0.00e+00</td><td>3.99e+08</td><td>0.00</td><td>0.00e+00</td></tr><tr><td>NNH + O<sub>2</sub> ⇌ HO<sub>2</sub> + N<sub>2</sub></td><td>7.11e+11</td><td>-0.34</td><td>-5.10e+04</td><td>2.91e+11</td><td>-0.37</td><td>-5.44e+04</td></tr><tr><td>NNH + OH ⇌ H<sub>2</sub>O + N<sub>2</sub></td><td>3.59e+10</td><td>0.00</td><td>0.00e+00</td><td>2.91e+10</td><td>0.00</td><td>0.00e+00</td></tr><tr><td>NNH + NO ⇌ HNO + N<sub>2</sub></td><td>3.63e+10</td><td>0.00</td><td>0.00e+00</td><td>1.51e+11</td><td>0.00</td><td>0.00e+00</td></tr><tr><td>NNH + O ⇌ NH + NO</td><td>3.63e+08</td><td>0.38</td><td>-1.62e+06</td><td>2.22e+08</td><td>0.37</td><td>-1.63e+06</td></tr><tr><td>NNH + O ⇌ H + N<sub>2</sub>O</td><td>1.50e+11</td><td>-0.23</td><td>-8.87e+04</td><td>5.05e+10</td><td>-0.24</td><td>-9.20e+04</td></tr><tr><td>HO<sub>2</sub> + NO ⇌ NO<sub>2</sub> + OH</td><td>2.36e+09</td><td>0.00</td><td>-1.97e+06</td><td>1.49e+09</td><td>0.00</td><td>-1.97e+06</td></tr><tr><td>NO + O (T<sup>+</sup>M) ⇌ NO<sub>2</sub> (T<sup>+</sup>M)</td><td>1.10e+12</td><td>-0.73</td><td>0.00e+00</td><td>1.53e+12</td><td>-0.68</td><td>0.00e+00</td></tr><tr><td>H + NO<sub>2</sub> ⇌ NO + OH</td><td>2.92e+08</td><td>0.85</td><td>-4.44e+06</td><td>2.45e+08</td><td>0.83</td><td>-4.39e+06</td></tr><tr><td>N<sub>2</sub>O + O ⇌ NO + O<sub>2</sub></td><td>4.72e+12</td><td>-0.99</td><td>2.26e+05</td><td>1.42e+12</td><td>-0.94</td><td>2.30e+05</td></tr><tr><td>N<sub>2</sub>O + O ⇌ NO + O<sub>2</sub></td><td>7.33e+13</td><td>-0.82</td><td>5.11e+07</td><td>9.14e+12</td><td>-0.83</td><td>5.20e+07</td></tr><tr><td>N<sub>2</sub>O (T<sup>+</sup>M) ⇌ N<sub>2</sub> + O (T<sup>+</sup>M)</td><td>1.09e+11</td><td>0.00</td><td>2.41e+08</td><td>1.77e+11</td><td>0.00</td><td>2.40e+08</td></tr><tr><td>H + N<sub>2</sub>O ⇌ N<sub>2</sub> + OH</td><td>7.55e+04</td><td>1.82</td><td>5.58e+07</td><td>6.12e+04</td><td>1.82</td><td>5.54e+07</td></tr><tr><td>N<sub>2</sub>O + O ⇌ 2NO</td><td>9.81e+12</td><td>-0.54</td><td>1.17e+08</td><td>6.06e+12</td><td>-0.50</td><td>1.15e+08</td></tr><tr><td>N<sub>2</sub>O + O ⇌ N<sub>2</sub> + O<sub>2</sub></td><td>4.06e+09</td><td>0.00</td><td>6.73e+07</td><td>8.99e+09</td><td>0.00</td><td>6.56e+07</td></tr><tr><td>N<sub>2</sub>O + OH ⇌ HO<sub>2</sub> + N<sub>2</sub></td><td>1.30e-05</td><td>4.75</td><td>1.53e+08</td><td>1.30e-05</td><td>4.73</td><td>1.50e+08</td></tr><tr><td>N<sub>2</sub>O + NO ⇌ N<sub>2</sub> + NO<sub>2</sub></td><td>5.20e+02</td><td>2.26</td><td>1.91e+08</td><td>5.94e+02</td><td>2.30</td><td>1.95e+08</td></tr><tr><td>H + HNO ⇌ H<sub>2</sub> + NO</td><td>8.04e+07</td><td>0.94</td><td>2.06e+06</td><td>9.43e+07</td><td>0.92</td><td>2.03e+06</td></tr><tr><td>NH<sub>2</sub> + NO ⇌ HNO + NH<sub>2</sub></td><td>1.45e+00</td><td>3.15</td><td>2.27e+08</td><td>1.45e+00</td><td>3.09</td><td>2.30e+08</td></tr><tr><td>HNO + O ⇌ NO + OH</td><td>1.98e+10</td><td>0.00</td><td>0.00e+00</td><td>5.35e+09</td><td>0.00</td><td>0.00e+00</td></tr><tr><td>HNO + OH ⇌ H<sub>2</sub>O + NO</td><td>1.07e+06</td><td>1.18</td><td>1.39e+06</td><td>8.98e+05</td><td>1.15</td><td>1.41e+06</td></tr><tr><td>HNO + O<sub>2</sub> ⇌ HO<sub>2</sub> + NO</td><td>1.39e+10</td><td>0.00</td><td>5.91e+07</td><td>9.62e+09</td><td>0.00</td><td>5.92e+07</td></tr><tr><td>H<sub>2</sub> + N<sub>2</sub>O ⇌ H<sub>2</sub>O + N<sub>2</sub></td><td>6.27e+09</td><td>0.00</td><td>1.36e+08</td><td>9.16e+09</td><td>0.00</td><td>1.38e+08</td></tr></tbody></table>

From this baseline, two optimization pathways are explored using the genetic algorithm. The first optimized chemical scheme, RmAH-1 (Table 1), is developed for the same mixing problem by progressively tightening the allowable variation in reaction rate parameters (from 6.5% to 2.5%). The optimization of RmAH-1 then continues by incorporating NH<sub>3</sub>-H<sub>2</sub>-Air premixed flames (fuel enriched with H<sub>2</sub> at 15%)

at equivalence ratios of $\phi = 0.5$ (fuel-lean), $\phi = 1.0$ (stoichiometric), and $\phi = 1.5$ (fuel-rich), further reducing the parameter variation limit to 0.25% of their nominal value in the detailed scheme. Finally, a stoichiometric premixed flame enriched with 10% H<sub>2</sub> is considered. As a result, RmAH-1 emerges from a combined optimization approach that accounts for both stochastic mixing with burnt gases and premixed
<figure><img src="image_4.png" /><figcaption>**Fig. 2.** Ignition delay time (ms) vs equivalence ratio. Symbol: Detailed scheme [26]. Red: RmAH-1, blue: RmAH-2 (Table 1), black: no-optimization. Initial condition: 1300 K, atmospheric pressure. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>**Fig. 3.** Laminar burning velocity vs equivalence ratio. Blue: Hydrogen fraction of 10% by volume; black: 15%; red: 20%. Symbol: Detailed scheme [26]. Dashed line: reduced (no optimization). Solid line: reduced + optimized, (a): RmAH-1, (b): RmAH-2 (Table 1). Fresh gases at 300 K under atmospheric pressure. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>**Fig. 4.** Stoichiometric premixed flame, 15% H₂ in fuel. Temperature and species mass fractions. Symbol: Detailed scheme [26]. Red: RmAH-1, blue: RmAH-2 (Table 1), black: no-optimization. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

flames at various equivalence ratios and hydrogen enrichment. In the end, the deviations of the rate parameters from the detailed scheme are within a few percent.

The second reduced and optimized scheme, RmAH-2 (Table 1), is derived from the same baseline reduced scheme obtained using DRGEP for the stochastic mixing problem. The optimization then primarily focuses on premixed flames laminar burning velocities (with the same fresh gas composition as RmAH-1) at equivalence ratios $\phi = 0.5, 1.0,$

and 1.5, allowing parameter variations as small as 0.5% in the final optimization stage.

The key changes in terms of critical species and reaction steps that were removed are now discussed. Among the species eliminated, H₂NO, NH₂OH, HNO₂, H₂NN, OH⁻, HNOH, N₂H₄, and H₂O₂ have been demonstrated to play a negligible role in the consumption (particularly through HONO) or production of H₂. Even if H₂NO can be regarded as fundamental for accurately reproducing the ignition delay time [35] in
<figure><img src="image_7.png" /><figcaption>Fig. 5. Stoichiometric premixed flame, 15% H₂ in fuel. NO mass fraction. Symbol: Detailed scheme [26]. Red: RmAH-1, blue: RmAH-2 (Table 1), black: no-optimization. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

ammonia oxidation, it has been demonstrated to exert a very limited influence on the peak concentrations of radicals NH₂ and NH, which are the principal species driving ammonia decomposition and are critical for predicting the laminar burning velocity. As discussed in [36], indeed, following hydrogen addition, the reaction

$$H + O_2 \rightleftharpoons O + OH$$

emerges as the rate-controlling step in the ignition process of the blend. This observation underscores the importance of radicals H and, notably, the highly reactive O to be defined as target species in the DRGEP reduction procedure. Accurate reproduction of their concentration profiles was found essential to reliably estimate ignition delay time and flame speed.

Consequent to the removal of H₂NO, the main reactions involving this species:

$$ \begin{aligned} & \mathrm{NH_2} + \mathrm{OH} \rightleftharpoons \mathrm{H} + \mathrm{H_2NO} \\ & \mathrm{NH_2} + \mathrm{HO_2} \rightleftharpoons \mathrm{H_2NO} + \mathrm{OH} \\ & \mathrm{NH_2} + \mathrm{NO_2} \rightleftharpoons \mathrm{H_2NO} + \mathrm{NO} \\ & \mathrm{NH_2} + \mathrm{O_2} \rightleftharpoons \mathrm{H_2NO} + \mathrm{O} \end{aligned} $$

were eliminated without significantly impacting NOₓ concentrations.

Regarding NO formation and depletion, two key species have been identified: HNO and NNH. Despite their very low concentrations and extremely short lifetimes [37], these species cannot be removed without compromising the accuracy of NO predictions. In particular, HNO serves as a precursor to NOₓ formation via

$$H + \mathrm{HNO} \rightleftharpoons \mathrm{NO} + \mathrm{H_2}$$

favored in fuel-rich conditions due to the abundance of H radicals, and

$$\mathrm{HNO} + \mathrm{OH} \rightleftharpoons \mathrm{NO} + \mathrm{H_2O}$$

predominant in fuel-lean environments owing to the higher concentration of OH radicals [38].

Conversely, removal of NNH results in a significant overestimation of NO concentration, highlighting the pivotal role this radical plays in the DeNOx mechanism, as corroborated by relevant literature. The reaction

$$\mathrm{NH_2} + \mathrm{NO} \rightleftharpoons \mathrm{NNH} + \mathrm{OH}$$

constitutes the principal pathway for NO consumption in the burned gas region of premixed flames, alongside

$$\mathrm{NH_2} + \mathrm{NO} \rightleftharpoons \mathrm{N_2} + \mathrm{H_2O}$$

These observations also emphasize the importance of the radical NH₂, the initial product of ammonia thermal decomposition, within the DeNOx reaction network. Nevertheless, the reactions

$$\mathrm{NH_2} + \mathrm{H} \rightleftharpoons \mathrm{NH} + \mathrm{H_2}$$

$$2\mathrm{NH} \rightleftharpoons \mathrm{N_2H_2} + \mathrm{H_2}$$

were deemed of marginal significance to the formation or consumption of involved species and thus were removed during the DRGEP applied to reactions.

Additionally, the second decomposition product of ammonia, NH, plays a critical role in the conversion of NO to N₂O and N₂, through the reactions

$$ \begin{aligned} & \mathrm{NH} + \mathrm{NO} \rightleftharpoons \mathrm{N_2O} + \mathrm{H} \\ & \mathrm{NH} + \mathrm{NO} \rightleftharpoons \mathrm{N_2} + \mathrm{OH} \end{aligned} $$

This aspect warrants careful consideration, given that N₂O is a potent greenhouse gas with a global warming potential approximately 300 times greater than that of CO₂ [39].

The final oxidation product of ammonia, the radical N, was likewise identified as essential for accurately representing the combustion behavior of NH₃ and in particular to properly match the profiles of radicals NH and NH₂. Of the thirteen reactions involving this highly reactive species, only six were removed:

$$ \begin{aligned} & 2\mathrm{NH} \rightleftharpoons \mathrm{N} + \mathrm{NH_2} \\ & \mathrm{N} + \mathrm{N_2H_4} \rightleftharpoons \mathrm{N_2H_3} + \mathrm{NH} \\ & \mathrm{N} + \mathrm{O} + \mathrm{M} \rightleftharpoons \mathrm{NO} + \mathrm{M} \\ & \mathrm{N_2} + \mathrm{M} \rightleftharpoons 2\mathrm{N} + \mathrm{M} \\ & \mathrm{NH} + \mathrm{M} \rightleftharpoons \mathrm{H} + \mathrm{N} + \mathrm{M} \\ & \mathrm{NH} + \mathrm{O} \rightarrow \mathrm{N} + \mathrm{OH} \end{aligned} $$

Ultimately, the reactive pathways involving N₂Hₓ species were condensed to retain only N₂H₂, reflecting the very low reaction rates observed during stochastic mixing. Species N₂H₃ and N₂H₄, which exhibited the lowest DRGEP coefficients, were consequently excluded from the mechanism at an early stage.

### 3. Analysis of the reduced schemes

The predictive capabilities of the two reduced and optimized schemes, RmAH-1 and RmAH-2, are now assessed against the detailed scheme by applying them to both seen and unseen cases from the optimization process. Overall, RmAH-1 demonstrates better performance than RmAH-2. However, when applied to non-premixed problems, both yield valuable results. Analysis of the reduced schemes responses is now provided, based on the pattern followed during their optimization.

#### 3.1. OD-ignition

The reduction and part of the optimization were performed based on the micro-mixing problem featuring a time varying fuel-air equivalence ratio, meaning that the ignition of a homogeneous mixture evolving at a constant equivalence ratio was not explicitly considered. Simulations of an adiabatic constant-pressure reactor were conducted using Cantera 2.6.0 [32], with initial conditions of 1300 K and atmospheric pressure. The ignition delay time (IDT) is defined as the moment when the temperature rises by 300 K.

The IDT response to equivalence ratio for hydrogen molar fractions of 10% and 20% is shown in Fig. 2. A decrease in IDT is observed from lean conditions to stoichiometric, followed by an increase as the equivalence ratio rises further. Among the reduced schemes, considering all equivalence ratios RmAH-2 (blue) demonstrates the best performance, while RmAH-1 (red) performs better under the stoichiometric condition for 10% H₂ enrichment (see zoom inset in Fig. 2(a)). Both schemes do better than the non-optimized reduced scheme (black). Hence, as expected from premixed flame physics, targeting the premixed flame speed in the optimization of RmAH-2 also aids in accurately reproducing the ignition delay time.
<figure><img src="image_8.png" /><figcaption>**Fig. 6.** Maximum temperature vs maximum strain rate $s^{-1}$ in an opposed-jet diffusion flame. Symbols detailed scheme [26], square: preheated air at 800 K, circle: 900 K, star: 1000 K. Red: RmAH-1, blue: RmAH-2 (Table 1), black: no-optimization. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>**Fig. 7.** Strained (400 $s^{-1}$) diffusion flame. Temperature and species mass fractions. Symbol: Detailed scheme [26]. Red: RmAH-1, blue: RmAH-2 (Table 1), black: no-optimization. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>**Fig. 8.** Air turbulent micro-mixing trajectory (Eq. (2)) 15% $H_2$ enrichment in volume. Species mass fractions and temperature. Squares: detailed scheme [26]. Red: RmAH-1, blue: RmAH-2 (Table 1), black: no-optimization. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>
<figure><img src="image_11.png" /><figcaption>**Fig. 9.** Fuel turbulent micro-mixing trajectory (Eq. (2)) 15% H₂ enrichment in volume. Species mass fractions and temperature. Squares: detailed scheme [26]. Red: RmAH-1, blue: RmAH-2 (Table 1), black: no-optimization. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>**Fig. 10.** Burnt gases turbulent micro-mixing trajectory (Eq. (2)) 15% H₂ enrichment in volume. Temperature and species mass fractions. Squares: detailed scheme [26]. Red: RmAH-1, blue: RmAH-2 (Table 1), black: no-optimization. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

## 3.2. Freely propagating premixed flames

Fig. 3 illustrates the flame speed as a function of the equivalence ratio for 10%, 15%, and 20% H₂ enrichment by volume, as obtained with the three schemes: RmAH-1, RmAH-2, and the original non-optimized version. The latter underestimates the laminar burning velocity, whereas RmAH-1 and RmAH-2 offer a good compromise. However, RmAH-2 provides a more accurate prediction on the lean side (Fig. 3(b)), as its optimization sequence was more focused on premixed flames.

The representative species and temperature profiles across a premixed stoichiometric flame with 15% H₂ enrichment are compared to the detailed mechanism in Fig. 4 (zoomed-in view of the reaction zone). Both mechanisms accurately capture the temperature distribution and the mass fractions of H₂, O₂, and NH (Fig. 4(a)). The results for NH₃ are also satisfactory, as shown in Fig. 4(b), which additionally presents minor species such as O, H, OH, and NH₂. Notably, RmAH-1 outperforms RmAH-2 in the burnt gases when reproducing slowly evolving species, as the latter underestimates NO reduction, as seen in Fig. 5. This discrepancy may be attributed to the optimization of RmAH-1, which was primarily conducted over turbulent mixing trajectories. In addition to the thermal decomposition of NO, the stoichiometric post-flame zone lacks NH₃, preventing SNCR-driven NO reduction. However, radicals and trace amounts of NH₂ contribute to the observed NO reduction, highlighting the importance of including these intermediate species in the reduced mechanism.

## 3.3. Strained diffusion flame

Fig. 6 shows the maximum temperature response in an opposed-jet flame as a function of the maximum strain rate measured across the

flame. None of the reduced schemes were specifically optimized for this canonical problem. Nevertheless, RmAH-1 (red in Fig. 6) consistently outperforms the other schemes, regardless of the H₂ enrichment level, accurately capturing the quenching point at higher strain rates. This suggests that exposure to a wide range of equivalence ratios and conditions in the model problem, which involves turbulent micro-mixing of the fuel blend with air and vitiation (Fig. 1), contributes to developing reduced schemes that are well suited for non-premixed applications. Additionally, the internal chemical flame structure is also well predicted, as shown in Fig. 7 for a strain rate of 400 s⁻¹.

## 3.4. Stochastic micro-mixing with vitiation

The turbulent micro-mixing case used for reduction and optimization is now recomputed using the reduced schemes. The evolution of deterministic trajectories (Eq. (2)) originating from a given inlet (fuel blend, air, and burnt gases) is compared to the results obtained with the reduced schemes.

Fig. 8 presents the mean response of particles from the air inlet. Overall, both optimized schemes perform well. The red curve, representing RmAH-1, provides a more accurate prediction of the complex behavior of species that mix before reacting. Fig. 8(b) illustrates the evolution of NH₃, which initially forms due to the mixing of the air stream with the fuel blend and subsequently decreases as combustion progresses. The impact of scheme optimization on NO prediction is also evident in Fig. 8(b), where the non-optimized reduced scheme exhibits significant deviations.

A similar trend is observed in the mass fractions of species originating from the fuel inlet (Fig. 9(a)). Here, O₂ initially increases due to turbulent mixing with the air inlet before decreasing as combustion progresses. The peak of intermediate minor species, such as NH, shown in Fig. 9(a), is well captured by the reduced schemes.
<figure><img src="image_13.png" /><figcaption>**Fig. 11.** Mixing layer DNS (length in m). Top: detailed scheme [26]. Middle: RmAH-1. Bottom: RmAH-2 (Table 1). Left: Temperature distribution. Right: scatter plots of NO mass fractions vs Bilger's mixture fraction [34]. Black: conditional mean.</figcaption></figure>

<figure><img src="image_14.png" /><figcaption>**Fig. 12.** Transverse distribution of time averaged statistics at a streamwise position x = 5 cm. Symbols: detailed scheme [26]. Red: RmAH-1, blue: RmAH-2 (Table 1). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>
<figure><img src="image_15.png" /><figcaption>**Fig. 13.** Transverse distribution of time averaged statistics at a streamwise position *x* = 7.8 cm. Symbols: detailed scheme [26]. Red: RmAH-1, blue: RmAH-2 (Table 1). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

The trajectory of a particle originating from the burnt gases inlet follows a much more complex evolution shown in Fig. 10. Initially in thermochemical equilibrium, these particles mix with the fresh air and fuel-blend inlets, causing their concentrations to change abruptly as they transition to non-equilibrium conditions before eventually returning to equilibrium for a large residence time. The reduced schemes perform reasonably well in capturing these rapid transitions, which are characteristic of real combustion chambers where burnt gases re-circulate and rapidly mix with reactants right after injection. It was also verified that increasing the dilution rate – i.e., injecting a larger amount of burnt gases – dampens the sharp variations observed right after injection, eventually leading to a fully steady equilibrium state where only burnt gases remain in the system.

### 3.5. 2D-mixing layer

To assess the proposed ammonia–hydrogen–air chemistry reduction strategy in a more complex scenario, a two-dimensional mixing layer with heat loss at wall is simulated using both the detailed and reduced schemes of Table 1 with the structured mesh reactive flow solver SiTCom-B [40]. The convective terms are computed with a fourth-order centered skew-symmetric-like scheme [41], the diffusive terms are discretized with a fourth-order centered scheme, time is advanced with a fourth-order Runge–Kutta method [42] and the boundary conditions are prescribed with 3D-NSCBC [43]. The transport coefficients are expressed using the Curtiss and Hirschfelder formulation [44]. The stiffness of the chemical system is reduced with the simplified schemes, allowing for a time step that is four orders of magnitude larger than that required by the detailed scheme. The reduction in stiffness arises from the elimination of $N_2H_4$, a species with a very short chemical timescale of the order of $10^{-11}$ s during the ignition phase. $N_2H_4$ exists in a quasi-steady state: it is produced rapidly but also consumed quickly, favoring the formation of radicals such as NH and $NH_2$. In the optimized mechanism, however, the key species governing ignition becomes NNH, which has a significantly longer chemical timescale of about $10^{-7}$ s. The removal of the reaction pathways involving $N_2H_3$ and $N_2H_4$, which originates from $N_2H_2$, along with the exclusion of recombination reactions involving highly reactive radicals like O and OH, as well as stable species such as $O_2$, has proven essential in achieving the observed reduction in stiffness.

The upper stream consists of preheated air at 1700 K with a mean velocity of 39.6 m s⁻¹ and a cold wall maintained at 600 K. Below an adiabatic splitter plate, the lower stream comprises a mixture of ammonia and hydrogen (15% by volume) at ambient temperature (300 K) with a velocity of 15 m s⁻¹. A symmetry condition is imposed at the bottom. Additionally, 10% velocity fluctuations are introduced as homogeneous turbulence at both inlets. The grid resolution is uniform

and fixed at 50 µm, with a domain length of 12 × 1 cm, discretized into 2400 × 200 cells.

Fig. 11 presents the first 3 cm of the domain, where the flame is stabilized. In this case representative of a real burner, both reduced schemes accurately capture the flame stabilization dynamics. The ignition length, determined by the induction time combined with flame propagation along the stoichiometric line, is similar across all chemical schemes. The global structure of the mixing layer is also well represented by the reduced schemes, and they also capture the instantaneous response of NO in detail, as shown in the scatter plot in Fig. 11, which compares the results with those from the simulation using the detailed mechanism.

Time averaged statistics of the thermochemical quantities were collected over approximately two flow-through times and plotted against the spanwise (transverse) direction of the mixing layer for two streamwise positions, located 5 cm and 7.8 cm downstream of the splitter plate (Figs. 12 and 13). The reactants and minor species closely match the responses of the detailed scheme, with almost no differences between the two reduced schemes. However, a slight deviation is observed for the radical NH at both streamwise locations (Figs. 12(a) and 13(a)) and for OH at 7.8 cm (Fig. 13(b)). This departure from the detailed scheme is visible in the scatter plot of NH versus mixture fraction shown in Fig. 14. These deviations of NH have little impact on the mass fraction of NO, which is well predicted by both schemes (Figs. 12(b) and 13(b)).

### 4. Conclusion

To address the need for reduced kinetic schemes suitable for high-fidelity simulations of hydrogen-blended ammonia combustion, two distinct schemes have been developed to analyze the details and effects of the reduction process. The study demonstrates that a database built from a turbulent micro-mixing problem coupled with detailed chemistry provides a strong foundation for applying systematic reduction methods based on graph analysis. Subsequently, optimization procedures with small variations in chemical parameters can be employed to target specific flame properties, such as the flame speed response to equivalence ratio variations.

The internal structure and quenching point of a one-dimensional strained opposed-jet flame are accurately captured without requiring additional optimization. Since the optimization primarily targeted the premixed flame speed, this outcome aligns with the theoretical relationship between flame speed and quenching strain rate as predicted by asymptotic theory [45].

The application to the simulation of ammonia–hydrogen–air combustion in a two-dimensional mixing layer further confirms these findings from zero- and mono-dimensional canonical problems, as both the flame base position and its downstream development closely match the response of the detailed scheme.
<figure><img src="image_16.png" /><figcaption>**Fig. 14.** Scatter plots of NH mass fractions vs Bilger's mixture fraction [34]. Yellow: conditional mean. Green: stoichiometric iso-line. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

From this development of reduced schemes across various operating conditions involving ammonia enriched hydrogen, it is concluded that

chemistry reduction should ideally be regarded as a preprocessing step for computational fluid dynamics. This approach enables the development, from reference detailed chemical schemes, of a tailored kinetic scheme optimized for the specific operating conditions of the combustion system under investigation.

### CRediT authorship contribution statement

**Giovanni Grassi:** Writing – review & editing, Writing – original draft, Visualization, Validation, Software, Methodology, Investigation, Formal analysis. **Luc Vervisch:** Writing – review & editing, Validation, Project administration, Methodology, Investigation, Formal analysis, Conceptualization. **Pascale Domingo:** Writing – review & editing, Validation, Resources, Project administration, Methodology, Investigation, Funding acquisition, Formal analysis, Conceptualization.

### Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

### Acknowledgments

The first author is funded by the project ENCODING (Enabling Sustainable combustion technologies using hybrid physics-based, data-driven modeling) from the European Union's Horizon Europe research and innovation programme under grant agreement No 101072779. This work was performed using HPC resources from CRIANN (Centre Régional Informatique et d'Applications Numériques de Normandie).

### Appendix A. Supplementary data

Supplementary material related to this article can be found online at https://doi.org/10.1016/j.combustflame.2025.114287.

### References

[1] O. Herbinet, P. Bartocci, A. Grinberg Dana, On the use of ammonia as a fuel: A perspective, JFUECO 11 (2022) 100064.

[2] A. Valera-Medina, H. Xiao, M. Owen-Jones, W.I.F. David, P.J. Bowen, Ammonia for power, Prog. Energ. Combust. Sci. 69 (2018) 63–102.

[3] A. Stagni, S. Arunthanayothin, M. Dehue, O. Herbinet, F. Battin-Leclerc, P. Bréquigny, C. Mounaim-Rousselle, T. Faravelli, Low- and intermediate-temperature ammonia/hydrogen oxidation in a flow reactor: Experiments and a wide-range kinetic modeling, Chem. Eng. J. 471 (2023) 144577.

[4] B. Zhang, M. Rubio, F. Egolfopoulos, S.B. Cronin, Stable combustion of ammonia in an internal combustion engine: A single fuel approach enabled by multi-pulse transient plasma ignition, Fuel 381 (2025) 133502.

[5] H. Kobayashi, A. Hayakawa, K. Kunkuma, A. Somarathe, E.C. Okafor, Science and technology of ammonia combustion, Proc. Combust. Inst. 37 (2019) 109–133.

[6] M. Aziz, F.B. Juangsa, A.R. Irhamna, A.R. Irsyad, H. Hariana, A. Darmawan, Ammonia utilization technology for thermal power generation: A review, J. Energ. Inst. 111 (2023) 101365.

[7] M. Zhang, X. Wei, Z. An, E.C. Okafor, T.F. Guiberti, J. Wang, Z. Huang, Flame stabilization and emission characteristics of ammonia combustion in lab-scale gas turbine combustors: Recent progress and prospects, Prog. Energ. Combust. Sci. 106 (2025) 101193.

[8] V. Bykov, M. Stein, U. Maas, Study of mechanism of ammonia decomposition and oxidation: From NOx reduction to ammonia auto-ignition problem, Proc. Combust. Inst. 39 (2023) 4267–4275.

[9] T. Cai, D. Zhao, E. Gutmark, Overview of fundamental kinetic mechanisms and emission mitigation in ammonia combustion, Chem. Eng. J. 458 (2023) 141391.

[10] A. Alnasif, S. Mashruk, H. Shi, M. Alnajideen, P. Wang, D. Pugh, A. Valera-Medina, Evolution of ammonia reaction mechanisms and modeling parameters: A review, App. Energ. Combust. Sci. 15 (2023) 100175.

[11] C. Locci, L. Vervisch, B. Farcy, N. Perret, Selective non-catalytic reduction (SNCR) of nitrogen oxide emissions: A perspective from numerical modeling, Flow Turbul. Combust. 100 (2018) 301–340.
[12] N. Peters, Numerical and asymptotic analysis of systematically reduced reaction schemes for hydrocarbon flames, in: T. Roger G. Roland (Ed.), Numerical Simulation of Combustion Phenomena, in: Lecture Notes in Physics, vol. 241, Springer Berlin Heidelberg, 1985, pp. 90–109.

[13] N. Peters, Systematic reduction of flame kinetics: Principles and details, in: A.L. Kulh, J.R. Bowen, J.-C. Leyer, A. Boris (Eds.), in: Dynamics of reactive systems, vol. 113, Washington, DC, 1988, pp. 67–86.

[14] R.B. Brad, A.S. Tomlin, M. Fairweather, J.F. Griffiths, The application of chemical reduction methods to a combustion system exhibiting complex dynamics, Proc. Combust. Inst. 31 (2007) 455–463.

[15] P. Pepiot-Desjardins, H. Pitsch, An efficient error-propagation-based reduction method for large chemical kinetic mechanisms, Combust. Flame 154 (2008) 67–81.

[16] T. Lu, C.K. Law, A directed relation graph method for mechanism reduction, Proc. Combust. Inst. 30 (2005) 1333–1341.

[17] N. Jaouen, L. Vervisch, P. Domingo, G. Ribert, Automatic reduction and optimisation of chemistry for turbulent combustion modelling: Impact of the canonical problem, Combust. Flame 175 (2017) 60–79.

[18] N. Jaouen, H. Nguyen, P. Domingo, L. Vervisch, ORCh: A package to reduce and optimize chemical kinetics. application to tetrafluoromethane oxidation, SoftwareX 27 (2024) 101819.

[19] O. Mathieu, E.L. Petersen, Experimental and modeling study on the high-temperature oxidation of ammonia and related NOx chemistry, Combust. Flame 162 (2015) 554–570.

[20] H. Xiao, M. Howard, A. Valera-Medina, S. Dooley, P.J. Bowen, Study on reduced chemical mechanisms of ammonia/methane combustion under gas turbine conditions, Energy Fuels 30 (2016) 8701–8710.

[21] J. Otomo, M. Koshi, T. Mitsumori, H. Iwasaki, K. Yamada, Chemical kinetic modeling of ammonia oxidation with improved reaction mechanism for ammonia/air and ammonia/hydrogen/air combustion, Int. J. Hydrog. Energy 43 (2018) 3004–3014.

[22] X. Liu, Y. Wang, Y. Bai, W. Yang, Development of reduced and optimized mechanism for ammonia/hydrogen mixture based on genetic algorithm, Energy 270 (2023) 126927.

[23] B. Li, D. Fernández-Galisteo, A.L. Sánchez, F.A. Williams, Systematically derived reduced kinetics for hydrogen+ammonia gas-turbine combustion, Combust. Flame 269 (2024) 113698.

[24] J. Ren, W. Wenyu, Z. Chun, Development of a reduced combustion model for ammonia/hydrogen combustion, Fuel 354 (2023) 129389.

[25] S. Dong, B. Wang, Z. Jiang, Y. Li, W. Gao, Z. Wang, X. Cheng, H.J. Curran, An experimental and kinetic modeling study of ammonia/n-heptane blends, Combust. Flame 246 (2022) 112428.

[26] 2024. https://c3.universityofgalway.ie/combustionchemistrycentre/mechanismdownloads/.

[27] Y. Zhang, O. Mathieu, E.L. Petersen, G. Bourque, H.J. Curran, Assessing the predictions of a NOx kinetic mechanism on recent hydrogen and syngas experimental data, Combust. Flame 182 (2017) 122–141.

[28] S. Subramaniam, S. Pope, A mixing model for turbulent reactive flows based on euclidean minimum spanning trees, Combust. Flame 115 (1998) 487–514.

[29] A.R. Masri, S. Subramaniam, S.B. Pope, A mixing model to improve the pdf simulation of turbulent diffusion flames, Symp. (Int.) Combust. 26 (1996) 49–57.

[30] 2018. https://github.com/Cantera/cantera/releases/tag/v2.4.0.

[31] C. Dopazo, E. O'Brien, Functional formulation of nonisothermal turbulent reactive flows, Phys. Fluids 17 (1974) 1968–1975.

[32] 2021. https://github.com/Cantera/cantera/releases/tag/v2.6.0b2.

[33] J. McCall, Genetic algorithms for modelling and optimisation, J. Comput. Appl. Math. 184 (2005) 205–222.

[34] R.W. Bilger, S.H. Starner, R.J. Kee, On reduced mechanisms for methane/air combustion in nonpremixed flames, Combust. Flame 80 (1990) 135–149.

[35] A. Stagni, C. Cavallotti, S. Arunthanayothin, Y. Song, O. Herbinet, F. Battin-Leclerc, T. Faravelli, An experimental, theoretical and kinetic-modeling study of the gas-phase oxidation of ammonia, React. Chem. Eng. 5 (2020).

[36] J. Chen, X. Jiang, X. Qin, Z. Huang, Effect of hydrogen blending on the high temperature auto-ignition of ammonia at elevated pressure, Fuel 287 (2021) 119563.

[37] S.J. Klippenstein, J.A. Miller, L.B. Harding, B. Ruscic, The role of NNH in NO formation and control, Combust. Flame 158 (2011) 774–789.

[38] J. Otomo, M. Koshi, T. Mitsumori, H. Iwasaki, K. Yamada, Chemical kinetic modeling of ammonia oxidation with improved reaction mechanism for ammonia/air and ammonia/hydrogen/air combustion, Int. J. Hydrog. Energy 43 (2018) 3004–3014.

[39] A.N. Hayhurst, A.D. Lawrence, Emissions of nitrous oxide from combustion sources, Prog. Energy Combust. Sci. 18 (1992) 529–552.

[40] www.coria-cfd.fr/index.php/SiTCom-B, 2020.

[41] F. Ducros, F. Laporte, T. Soulères, V. Guinot, P. Moinat, B. Caruelle, High-order fluxes for conservative skew-symmetric-like schemes in structured meshes: application to compressible flows., J. Comput. Phys. 161 (2000) 114–139.

[42] S. Gottlieb, C. Shu, Total variation diminishing Runge-Kutta schemes, Math. Comp. 67 (1998) 74–85.

[43] G. Lodato, P. Domingo, L. Vervisch, Three-dimensional boundary conditions for direct and large-eddy simulation of compressible viscous flows, J. Comput. Phys. 227 (2008) 5105–5143.

[44] C.F. Curtiss, J.O. Hirschfelder, Transport properties of multicomponent gas mixtures, J. Chem. Phys. 17 (1949) 550.

[45] N. Peters, Turbulent Combustion, Cambridge University Press, 2000.