Numerical Study on the Combustion Properties of Ammonia/DME and Ammonia/DMM Mixtures

Abstract

Ammonia (NH₃) is considered a promising zero-carbon fuel and was extensively studied recently. Mixing high-reactivity oxygenated fuels such as dimethyl ether (DME) or dimethoxymethane (DMM) with ammonia is a realistic approach to overcome the low reactivity of NH₃. To study the combustion characteristics of NH₃/DMM and NH₃/DME mixtures, we constructed a NH₃/DMM chemical mechanism and tested its accuracy using measured laminar burning velocity (LBV) and ignition delay time (IDT) of both NH₃/DMM and NH₃/DME mixtures from the literature. The kinetic analysis of NH₃/DMM flames using this mechanism reveals that the CH₃ radicals generated from the oxidation of DMM substantially affects the oxidation pathway of NH₃ at an early stage of flame propagation. We investigated the formation of nitrogen oxides (NO_x) in NH₃/DMM and NH₃/DME flames and little difference can be found in the NO_x emissions. Using NH₃/DMM flames as an example, the peak NO_x emissions are located at an equivalence ratio ($\phi$) of 0.9 and a DMM fraction of 40% in the conditions studied. Kinetic analysis shows that NO_x emission is dominated by NO, which primarily comes from fuel nitrogen of NH₃. The addition of DMM at 40% significantly promotes the reactive radical pool (e.g., H, O, and OH) while the maintaining a high concentration of NO precursors (e.g., HNO, NO_2, and N₂O), which results in a high reaction rate of NO formation reaction and subsequently generates the highest NO emissions.

1. Introduction

Amidst the persisting global energy crisis and escalating concerns regarding environmental pollution, ammonia (NH₃) received significant attention as a zero-carbon fuel [1,2]. In the 1960s, extensive research was conducted in the United States to explore the feasibility of NH₃ combustion in military equipment such as gas turbines, compression ignition engines, and spark ignition engines [3,4]. However, these studies indicated that the direct utilization of NH₃ in combustion systems is challenging compared to conventional hydrocarbon fuels, such as low heating value, slow combustion rate, high ignition energy, and narrow flammable range. Therefore, it seems inevitable to modify or redesign traditional combustion systems to utilize pure NH₃ reliably to expand the operating range and improve the performance of pure NH₃ burners [3,4]. However, development of an existing combustion system can be costly. Hence, ongoing research is primarily directed towards preserving the integrity of present combustion equipment while harnessing the potential of NH₃ in conjunction with other highly reactive fuels. The incorporation of blended fuels serves as a booster to initiate or enhance the stable combustion of NH₃. In practical investigations concerning the blending of NH₃ with diverse fuels, a comprehensive analysis of the fuel combustion process is of utmost importance. It becomes imperative to comprehend the combustion properties via chemical kinetics to effectively enhance combustion stabilities, fuel efficiency, and curtail the emission of NO_x.

Different hydrocarbon fuels, such as hydrogen (H₂) [5,6], alkanes [7,8], and alcohols [9,10] were tested as combustion enhancer for NH₃. For instance, Wang et al. [5] measured the LBVs of NH₃/H₂ mixtures (0, 10, and 20% vol. H₂) at pressures from 1 to 5 bar, temperature from 360 K, and φ from 0.7 to 1.4 in a constant volume chamber and validated the accuracy of mechanisms developed by Okafor et al. [11], Mei et al. [12], and Shrestha et al. [13]. Dai et al. [6] proposed a combustion model for NH₃/H₂ blends by optimizing the mechanism of Glarborg et al. [14], which shows better performance than the mechanisms from Klippenstein et al. [15], Mathieu et al. [16], and Shrestha et al. [17] based on the IDTs measured (0–10% vol. H₂) at conditions (φ = 0.5, 1.0), pressures (20–75 bar), and temperatures (1040–1210 K) in a rapid compression machine. Wang et al. [18] coupled the skeletal n-heptane mechanism of Chang et al. [19] with the detailed NH₃/n-heptane mechanism of Dong et al. [20] to obtain an NH₃/n-heptane that can predict the IDTs of a NH₃/n-heptane mixture very well. Wang et al. [9] measured the LBVs of a NH₃/methanol (20–100% vol.) and NH₃/ethanol (20–100% vol. ethanol) mixture at 1 atm, temperatures from 298 to 448 K, and φ from 0.7 to 1.8 using the heat flux method and developed a NH₃/ethanol mechanism consisting of 91 species and 444 reactions.

In recent years, artificially synthesized polyoxymethylene dimethyl ethers (CH₃O-(CH₂O)_n-CH₃, PODE_n) attracted attention in that it can be used as fuel directly or as a fuel additive due to its high reactivity and low soot emission [21,22]. As a result, PODE_n has great potential to be used as a promoter for NH₃ combustion in internal combustion engines. DME, as the simplest PODE_n, was investigated as a NH₃ combustion enhancer. Experimental results of the LBVs [23,24] and IDTs [25,26] of NH₃/DME mixtures indicate that DME performs well in enhancing the reactivity of NH₃. Xiao et al. [24] coupled the DME mechanism of Zhao et al. [27] with the NH₃ mechanism of Han et al. [28] and incorporated C–N interaction reactions from Shrestha et al. [29], Dai et al. [25], Konnov et al. [30], and others to develop an NH₃/DME mixed fuel mechanism consisting of 102 species and 594 reactions. Validation based on experimental data and literature confirms that the mechanism proposed by Xiao et al. [24], compared to the mechanisms of Dai et al. [25] and Issayev et al. [26], is not only more simplified, but also more accurate in predicting LBV and IDT. Meng et al. [31] focused on the variation in NO_x emissions during NH₃/DME combustion. They simulated the post combustion NO_x emissions of NH₃/DME using a detailed mechanism consisting of 221 species and 1597 reactions. The results show that the NO_x emissions did not decrease, but increase after DME was blended with NH₃. This phenomenon was also observed in the experiments of Gross et al. [32] on direct injection NH₃/DME compression ignition engines. Meng et al. [31] inferred that the generation of NO_x might be influenced by highly reactive radicals. Recently, Elbaz et al. [33] conducted further research on the blended combustion of DMM with NH₃. They measured the LBVs and Markstein length of NH₃/DMM using spherical freely propagating flames and developed a NH₃/DMM combustion mechanism by coupling the nitromethane mechanism of Shrestha et al. [34] and the DMM mechanism of Sun et al. [35], whereas the mechanism underestimates the measured LBVs for matures containing 20–60% DMM at lean conditions.

At present, there is no mechanism currently available that can simultaneously predict the combustion characteristics of NH₃/DME and NH₃/DMM. An accurate NH₃/DMM mechanism is vital to develop a combustion mechanism of NH₃ with heavier PODE_n. In this study, we developed a combustion mechanism for NH₃/DMM based on the work of Xiao et al. [24] and Li et al. [36]. The accuracy of the mechanism was validated using experimental data of NH₃/DMM [17,33] and NH₃/DME mixtures [24,25] from literature. We performed reaction path analysis, sensitivity analysis, and NO_x formation analysis of NH₃/DME and NH₃/DMM based on the present mechanism. Compared to previous studies [24,31,33], we presented a more comprehensive reaction pathway and provided further explanation for the peculiar phenomenon of NO_x emissions observed at different DMM fractions.

2. Kinetic Modeling

2.1. Numerical Approach

This study employs the one-dimensional (1D) free flame model and zero-dimensional (0D) ideal gas reactor model from Cantera [37] for the calculation of LBV and IDT.

The zero-dimensional (0D) ideal gas reactor model makes it so that the mixture behaves as an ideal gas. It means that the pressure, volume, and temperature of the mixture are related by the ideal gas law. The following is the governing equation for the zero-dimensional (0D) ideal gas reactor model:

$$\frac{d\left(\rho V\right)}{dt}=0$$

(1)

$$\rho V{c}_v\frac{dT}{dt}=-P\frac{dV}{dt}+\dot{q}-\sum {\dot{m}}_k{h}_k$$

(2)

$$\rho V{c}_v\frac{d{Y}_k}{dt}={\dot{\omega }}_{k}V$$

(3)

$$P=\rho RT$$

(4)

where $\rho$ is the density, $V$ is the reactor volume, $c_v$ is the specific heat capacity at constant volume, $T$ is temperature, $P$ is pressure, $\dot{q}$ represents heat sources or losses, ${\dot{m}}_k$ is the mass flow rate of each species, and $h_k$ is the enthalpy of species $k$, $Y_k$ is the mole fraction of species $k$, ${\dot{\omega }}_k$ is the molar production rate of species $k$, and $R$ is the gas constant.

The one-dimensional (1D) free flame model is stabilized in an axisymmetric stagnation flow and computes the solution along the stagnation streamline, using a similarity solution to reduce the three-dimensional governing equations to a single dimension. The following is the governing equation for the one-dimensional (1D) free flame model:

$$\frac{\mathsf{\partial }\rho u}{\mathsf{\partial }z}+2\rho v=0$$

(5)

$$\rho u\frac{\mathsf{\partial }v}{\mathsf{\partial }z}+\rho V^2=-\mathsf{\Lambda }+\frac{\mathsf{\partial }}{\mathsf{\partial }z}\left(\mu \frac{\mathsf{\partial }v}{\mathsf{\partial }z}\right)$$

(6)

$$\rho c_{p}u\frac{\mathsf{\partial }T}{\mathsf{\partial }z}=\frac{\mathsf{\partial }}{\mathsf{\partial }z}\left(\lambda \frac{\mathsf{\partial }T}{\mathsf{\partial }z}\right)-\sum j_k\frac{\mathsf{\partial }{h}_k}{\mathsf{\partial }z}-\sum h_k{W}_k{\dot{\omega }}_k$$

(7)

$$\rho u\frac{d{Y}_k}{dz}=-\frac{\mathsf{\partial }{j}_k}{\mathsf{\partial }z}+W_k{\dot{\omega }}_k$$

(8)

where $\rho$ is the density, $u$ is the axial velocity, $v$ is the scaled radial velocity, $\mathsf{\Lambda }$ is the pressure eigenvalue (independent of $z$), $\mu$ is the dynamic viscosity, $c_p$ is the heat capacity at constant pressure, $T$ is the temperature, $\lambda$ is the thermal conductivity, $Y_k$ is the mass fraction of species $k$, $j_k$ is the diffusive mass flux of species $k$, $h_k$ is the enthalpy of species $k$, $W_k$ is the molecular weight of species $k$, and ${\dot{\omega }}_k$ is the molar production rate of species $k$.

To ensure the post flame reaches equilibrium, the computational domain was set as a uniform spatial grid of 10 cm width. Additional points were automatically added in regions with steep gradients based on predefined ratios, slopes, and curves [38].

Sensitivity analysis of the LBV for NH₃/DME/air and NH₃/DMM/air mixtures was performed using a ‘Brute force’ method:

$$S_i=\frac{k_i}{S_l}\times \frac{\mathsf{\partial }{S}_l}{\mathsf{\partial }{k}_i}$$

(9)

where $k_i$ represents the rate constant of the i-th reaction (1/s), and $S_l$ is the LBV (cm/s). By varying $k_i$ and calculating the resulting changes in $S_l$, normalized sensitivity coefficients $S_i$ can be obtained. Each rate constant is increased by a factor of 2 by doubling the preexponential A factor while keeping those of the other reactions constant. A positive sensitivity coefficient indicates that the reaction promotes the flame propagation, while a negative coefficient indicates that the reaction inhibits the flame propagation. An element flux analysis was performed to study the reaction path of the fuels under the experimental conditions. Rate of production (ROP) analysis was also performed to assist the interpretation of the results.

2.2. Mechanism Optimization

The mechanisms developed in this study are mainly drawn from Xiao et al. [24] and Li et al. [36], which serve as NH₃/DME and DMM submechanisms, respectively. The mechanism of Xiao et al. [31] coupled the DME mechanism of Zhao et al. [27] with the NH₃ mechanism of Han et al. [28] and incorporated C–N interaction reactions from Shrestha et al. [29], Dai et al. [25], and Konnov et al. [30]. The mechanism of Xiao et al. [24] performs well in predicting the LBVs [24] and IDTs [23] of NH₃/DME mixtures. The mechanism of Li et al. [36] based on the hieratical structure of ‘reaction classes’ was originally proposed by Curran et al. [39]. Validation based on experimental data and literature confirms that the mechanism proposed by Shrestha et al. [29] and Li et al. [36] is not only more simplified, but also more accurate in predicting LBVs and IDTs of DMM/air mixtures. We propose a new NH₃/DMM mechanism by coupling the NH₃/DME submechanism from Xiao et al. [24] and the DMM submechanism from Li et al. [36] and updating the reaction rates of some key reactions. The specific updates of the reaction rates are outlined in

Table 1. Updates in the present mechanism. Units are s, mol, cm, and cal in $\mathrm{k}=\mathrm{A}{T}^n\exp \left(-\frac{E_a}{RT}\right)$.

No.	Reaction	A	n	Ea	Ref.
1	NH + NO = N2O + H	2.7 × 1015	−0.78	20.0	[40]
2	NH2 + OH = NH + H2O	2.04 × 104	2.52	−616.032	[41]
3	NH3 + OH = NH2 + H2O	3.25 × 1012	0.0	2120.0	[42]
4	NNH + O = NH + NO	5.2 × 1011	0.388	−409.0	[15]
5	NH2 + NO = H2O + N2	9.5 × 1016	−1.44	268.0	[25]
6	NH2 + NO2 = H2NO + NO	2.0 × 1019	−2.369	870.0	[14]
7	HNO + O2 = NO + HO2	2.0 × 1013	0.0	14896.0	[25]
8	H2NO + NO2 = HONO + HNO	6.0 × 1012	0.0	2000.0	[25]
9	N2H3 + HO2 = N2H4 + O2	9.2 × 105	1.94	2126.1	[25]
10	H + O2 + M = HO2 + M	4.65 × 1012	0.44	0.0	[43]
11	H + OH + M = H2O + M	3.5 × 1022	−2.0	0.0	[44]
12	O + H2O = OH + OH	6.7 × 107	1.704	14986.8	[45]
13	HO2 + OH = H2O + O2	1.93 × 1020	−2.49	584	[46]
14	HO2 + O = O2 + OH	1.0 × 1013	0.0	−4452	[47]
15	CH2 + O2 = HCO + OH	1.06 × 1013	0.0	1500.0	[44]
16	HCO + O2 = CO + HO2	13.45 × 1012	0.0	400.0	[44]
17	CO + OH = CO2 + H	8.7 × 104	2.053	−355.7	[48]
18	CH3OCH2OCH3 + H = CH3OCH2OCH2 + H2	5.04 × 106	2.3	6453.155	[49]
19	CH3OCH2OCH3 + H = CH3OCHOCH3 + H2	2.18 × 1010	1.155	6548.757	[49]
20	CH3OCH2OCH3 + M = CH3OCH2O + CH3 + M	2.33 × 1019	−0.66	84139.5	[50]
21	CH3OCH2OCH3 + NH2 = CH3OCH2OCH2 + NH3	1.8 × 100	3.61	4353.0	est DME
22	CH3OCH2OCH3 + NH2 = CH3OCHOCH3 + NH3	3.79 × 103	2.426	4475.0	est DME
23	CH3OCH2OCH3 + NO2 = CH3OCH2OCH2 + HONO	5.8 × 101	3.5	23755.0	est DME
24	CH3OCH2OCH3 + NO2 = CH3OCHOCH3 + HONO	9.93 × 102	3.112	22010.0	est DME
25	CH3OCH2OCH3 + NO2 = CH3OCH2OCH2 + HNO2	6.5 × 102	3.0	23176.0	est DME
26	CH3OCH2OCH3 + NO2 = CH3OCHOCH3 + HNO2	1.11 × 104	2.667	21473.0	est DME

.

.

The updated reaction rate constants for R1, R2, R3, and R4 are referenced from the literature [15,40,41,42]. By modifying the reaction rate constant of R1, R2, R3, and R4, the accuracy of the mechanism is improved while adjusting the contribution of different elementary reaction pathways in the combustion process of ammonia.

$$\mathrm{NH}+\mathrm{NO}={\mathrm{N}}_2\mathrm{O}+\mathrm{H}$$

(R1)

$${\mathrm{NH}}_2+\mathrm{OH}=\mathrm{NH}+{\mathrm{H}}_2\mathrm{O}$$

(R2)

$${\mathrm{NH}}_3+\mathrm{OH}={\mathrm{NH}}_2+{\mathrm{H}}_2\mathrm{O}$$

(R3)

$$\mathrm{NNH}+\mathrm{O}=\mathrm{NH}+\mathrm{NO}$$

(R4)

The reaction rate constants for reactions R5 and R6 were adjusted based on the literature [14,25]. Additionally, reactions R7, R8, and R9 were introduced to further optimize the reaction pathway of NH₃ during the initial stages of combustion. These adjustments effectively enhanced the accuracy of the mechanism’s predictions for NH₃ IDT.

$${\mathrm{NH}}_2+\mathrm{NO}={\mathrm{H}}_2\mathrm{O}+{\mathrm{N}}_2$$

(R5)

$${\mathrm{NH}}_2+{\mathrm{NO}}_2={\mathrm{H}}_2\mathrm{NO}+\mathrm{NO}$$

(R6)

$$\mathrm{HNO}+{\mathrm{O}}_2=\mathrm{NO}+{\mathrm{HO}}_2$$

(R7)

$${\mathrm{H}}_2\mathrm{NO}+{\mathrm{NO}}_2=\mathrm{HONO}+\mathrm{HNO}$$

(R8)

$${\mathrm{N}}_2{\mathrm{H}}_3+{\mathrm{HO}}_2={\mathrm{N}}_2{\mathrm{H}}_4+{\mathrm{O}}_2$$

(R9)

Reactions R10 and R11 are important pathways for the consumption of H radical and play a suppressive role in the combustion of NH₃/DMM/air and NH₃/DME/air mixtures. In this study, the reaction rate of R10 decreased at low temperatures and increased at high temperatures based on data from Fernandes et al. [43]. The reaction rate of R11 was slightly decreased based on data from GRI 3.0 [44].

$$\mathrm{H}+{\mathrm{O}}_2+\mathrm{M}={\mathrm{HO}}_2+\mathrm{M}$$

(R10)

$$\mathrm{H}+\mathrm{OH}+\mathrm{M}={\mathrm{H}}_2\mathrm{O}+\mathrm{M}$$

(R11)

Under lean conditions with a high fraction of NH₃, O radicals tend to react with H₂ and H₂O, while under rich conditions, O radicals tend to react with H₂ and CH₃, both of which play important promoting roles in NH₃/DMM/air and NH₃/DME/air mixtures. In this study, the reaction rate of R12 is increased based on data from Sutherland et al. [45].

$$\mathrm{O}+{\mathrm{H}}_2\mathrm{O}=\mathrm{OH}+\mathrm{OH}$$

(R12)

Under conditions with a low fraction of NH₃, reactions R13 and R14 suppress the combustion of NH₃/DMM/air and NH₃/DME/air mixtures by consuming radicals. In this study, the reaction rate of R13 is increased and that of R14 is decreased based on data from Burke et al. [46] and Baulch et al. [47], respectively, to adjust the consumption pathway of HO₂.

$${\mathrm{HO}}_2+\mathrm{OH}={\mathrm{H}}_2\mathrm{O}+{\mathrm{O}}_2$$

(R13)

$${\mathrm{HO}}_2+\mathrm{O}={\mathrm{O}}_2+\mathrm{OH}$$

(R14)

Reactions R15, R16, and R17 are important pathways for CO₂ formation. The promoting effect of reaction R15 on the combustion of NH₃/DMM/air and NH₃/DME/air mixtures becomes more significant with an increase in the fraction of hydrocarbon fuels in the mixture, while reaction R16 starts to inhibit combustion as the fraction of hydrocarbon fuels decreases. Reaction R17 is an important reaction that consumes CO to produce CO₂, playing a promoting role in the combustion of NH₃/DMM/air and NH₃/DME/air mixtures. In this study, the reaction rates of R15 and R16 are updated based on data from GRI 3.0 [44], and the reaction rate of R17 is decreased based on data from Jshi et al. [48], improving the accuracy of the CO₂ generation pathway in the mechanism.

$${\mathrm{CH}}_2+{\mathrm{O}}_2=\mathrm{HCO}+\mathrm{OH}$$

(R15)

$$\mathrm{HCO}+{\mathrm{O}}_2=\mathrm{CO}+{\mathrm{HO}}_2$$

(R16)

$$\mathrm{CO}+\mathrm{OH}={\mathrm{CO}}_2+\mathrm{H}$$

(R17)

Reactions R18, R19, and R20 are important components of the low-temperature oxidation mechanism of DMM. Reactions R18 and R19 inhibit the combustion of the NH₃/DMM/air mixture by consuming H radicals, while reaction R20 promotes the combustion of the mixture by generating CH₃OCH₂O and CH₃ radicals through the decomposition of DMM. The reaction rates of R18 and R19 are increased based on simulation data from Vermeire et al. [49], and reaction R20 is updated based on the molecular collision effects in the DMM decomposition process proposed by Jacobs et al. [50]. Through these updates to the aforementioned reactions, the low-temperature oxidation pathway of DMM in this mechanism is improved.

$${\mathrm{CH}}_3{\mathrm{OCH}}_2{\mathrm{OCH}}_3+\mathrm{H}={\mathrm{CH}}_3{\mathrm{OCH}}_3{\mathrm{OCH}}_2+{\mathrm{H}}_2$$

(R18)

$${\mathrm{CH}}_3{\mathrm{OCH}}_2{\mathrm{OCH}}_3+\mathrm{H}={\mathrm{CH}}_3{\mathrm{OCHOCH}}_3+{\mathrm{H}}_2$$

(R19)

$${\mathrm{CH}}_3{\mathrm{OCH}}_2{\mathrm{OCH}}_3+\mathrm{M}={\mathrm{CH}}_3{\mathrm{OCH}}_2\mathrm{O}+{\mathrm{CH}}_3+\mathrm{M}$$

(R20)

Furthermore, reactions R21–R26 are the interactions between DMM and nitrogen estimated based on the NH₃/DME/air mechanism proposed by Xiao et al. [24] in this study.

$${\mathrm{CH}}_3{\mathrm{OCH}}_2{\mathrm{OCH}}_3+{\mathrm{NH}}_2={\mathrm{CH}}_3{\mathrm{OCH}}_3{\mathrm{OCH}}_2+{\mathrm{NH}}_3$$

(R21)

$${\mathrm{CH}}_3{\mathrm{OCH}}_2{\mathrm{OCH}}_3+{\mathrm{NH}}_2={\mathrm{CH}}_3{\mathrm{OCHOCH}}_3+{\mathrm{NH}}_3$$

(R22)

$${\mathrm{CH}}_3{\mathrm{OCH}}_2{\mathrm{OCH}}_3+{\mathrm{NO}}_2={\mathrm{CH}}_3{\mathrm{OCH}}_3{\mathrm{OCH}}_2+\mathrm{HONO}$$

(R23)

$${\mathrm{CH}}_3{\mathrm{OCH}}_2{\mathrm{OCH}}_3+{\mathrm{NO}}_2={ \mathrm{CH}}_3{\mathrm{OCHOCH}}_3+\mathrm{HONO}$$

(R24)

$${\mathrm{CH}}_3{\mathrm{OCH}}_2{\mathrm{OCH}}_3+{\mathrm{NO}}_2={\mathrm{CH}}_3{\mathrm{OCH}}_3{\mathrm{OCH}}_2+{\mathrm{HNO}}_2$$

(R25)

$${\mathrm{CH}}_3{\mathrm{OCH}}_2{\mathrm{OCH}}_3+{\mathrm{NO}}_2={ \mathrm{CH}}_3{\mathrm{OCHOCH}}_3+{\mathrm{HNO}}_2$$

(R26)

The complete mechanism is composed of 108 species and 615 reversible reactions.

3. Results and Discussion

3.1. Mechanism Validation

The present mechanism is validated against the measured LBVs of NH₃/DMM/air and NH₃/air mixtures from literature as shown in Figure 1. The calculated LBVs agree very well with the measured LBVs of NH₃/DMM/air mixtures at most conditions, only slight underestimation up to ~2 cm/s is observed for pure DMM/air mixtures. For NH₃/air mixtures, the calculated LBVs lies in the cross-section of the experimental data from literature. The validation of the present mechanism is also performed against the LBV of NH₃/DME/air mixtures under ambient condition as shown in Figure 2. The present mechanism predicts the LBVs precisely for NH₃/DME mixtures except that it slightly underestimates the LBVs of pure DME by 3cm/s from $\phi$ = 0.7 to 1.3. For NH₃ with 50% DME fraction at elevated temperature and pressures, the validation is firstly performed at T_u = 298 K and P_u ranges from 1 to 4 atm as shown in Figure 3a. The present mechanism generally predicts the LBVs well at most conditions, albeit the biggest underestimation up to 5 cm/s is observed at the leanest condition for P_u = 1 atm. The discrepancy mitigates at elevated pressures. The overall performance is further improved for all three pressures at elevated temperature T_u = 373 K as shown in Figure 3b.

Figure 4 illustrates the comparison of calculated IDTs using the present mechanism and the measured IDTs of the NH₃/DME mixture from Issayev et al. [26]. As can be seen, the present mechanism can accurately predict the measurements at all four conditions. Figure 5 and Figure 6 illustrate the comparison between the predictions of the present mechanism and the measured IDTs of pure DME and pure NH₃ from Dai et al. [25]. As shown in the figure, the present mechanism accurately predicts IDTs of pure DME and pure NH₃. In general, the present mechanism can accurately predict the LBVs of NH₃/DMM/air and NH₃/DME/air mixtures and the IDTs of the NH₃/DME/air mixture as well. To our knowledge, there are no IDT measurements of NH₃/DMM available at present, and further validation against the IDTs of NH₃/DMM will be added in our future study. The present mechanism is employed to perform a chemical kinetic analysis of NH₃/DMM flames in the next section.

3.2. Kinetic Analysis

3.2.1. Reaction Pathway and Sensitivity Analysis

To investigate the overall oxidation pathways of NH₃/DME/air mixtures, we conducted a reaction path analysis by tracing nitrogen (Figure 7a) and carbon (Figure 7b), respectively, at T_u = 298 K, P_u = 1 bar, $\phi$ of 0.9, and a DME substitution rate of 40%. Similar to the reaction path of pure ammonia [13,26], the first step for ammonia is dehydrogenation to form NH₂, followed by the generation of N₂ through four key intermediate species: NH, NHO, NNH, and NO. At a flame temperature of 1000 K, NO can be converted to NO₂, but its influence diminishes as the temperature increases. When the flame temperature reaches 2000 K, N₂O can be further converted to N₂. When DMM fraction reaches 40%, NH₂ reacts with CH₃ generated from the thermal decomposition of DMM to produce a significant amount of CH₃NH₂. At a flame temperature of 1500 K, the flux of the ${\mathrm{NH}}_2\to {\mathrm{CH}}_3{\mathrm{NH}}_2$ reaction pathway will exceed 60% in the N element reaction path. This phenomenon was also observed in previous studies on NH₃/DME/air [23,24] and NH₃/CH₄/air [53] mixtures, indicating that the addition of DMM has a significant impact on the early oxidation process of NH₃. From the reaction pathway diagram of ammonia, it can be observed that at a flame temperature of 1500 K, NO is mainly generated through three pathways: $1.{\mathrm{NH}}_3\to {\mathrm{NH}}_2\to \mathrm{NH}\to \mathrm{NO}$, $2.{\mathrm{NH}}_3\to {\mathrm{NH}}_2\to \mathrm{HNO}\to \mathrm{NO}$, and $3.{\mathrm{NH}}_3\to {\mathrm{NH}}_2\to \mathrm{NH}\to \mathrm{NHO}\to \mathrm{NO}$. The fluxes of NO generated through these channels do not exceed 20%. However, as the fuel oxidation process progresses, the DMM component in the fuel is consumed first, and the temperature increases, leading to the oxidation of NH₃. Additionally, the accumulated CH₃NH₂ in the early stage will also be converted to NO. The high temperature will suppress the flux of the $\mathrm{NO}\to {\mathrm{N}}_2$ pathway, resulting in the accumulation of NO.

As shown in Figure 7b and Figure 8, the C–N interaction has a relatively small impact on the oxidation of DME and DMM. DME first reacts with H, OH, O, and CH₃ radicals to undergo dehydrogenation, forming CH₃OCH₂. The CH₃OCH₂ radical primarily undergoes thermal dissociation to produce CH₃ and CH₂O. At lower flame temperature (1000 K), a small amount of CH₃ reacts with NH₂ under the influence of C–N interaction, leading to the formation of CH₃NH₂. As the flame temperature increases to 1500 K, more than 60% of the CH₃ radicals undergo self-recombination and further oxidation to form C₂ species (e.g., C₂H₆ and C₂H₅) or reacts with H, HO₂, and CH₂O radicals to produce CH₄. Meanwhile, CH₂O is further oxidized to CO through the pathway ${\mathrm{CH}}_2\mathrm{O}\to \mathrm{HCO}\to \mathrm{CO}$. When the flame temperature reaches 2000 K, CH₄ and C₂ species are involved in oxidation reactions, and CO is gradually completely oxidized to CO₂ by OH radicals.

The sensitivity analysis of the LBV for pure NH₃, NH₃/DME, and NH₃/DMM mixtures are performed at T_u = 298 K, P_u = 1 bar, and $\phi$ of 0.9 as shown Figure 9. Consistent with the findings of Xiao et al. [24], the reactions involving H radicals, namely H + O₂ = O + OH and H + O₂ (+M) = HO₂ (+M), have the most significant promoting and inhibiting effects on the LBV of pure NH₃. Additionally, the reactions involving NH₂ radicals, NH₂ + NO = NNH + OH and NH₂ + NO = H₂O + N₂, correspond to two reaction pathways (${\mathrm{NH}}_2\to \mathrm{NNH}\to {\mathrm{N}}_2$ and ${\mathrm{NH}}_2\to {\mathrm{N}}_2$) for the oxidation of NH₂ as shown in Figure 7. Furthermore, the reactions NH₃ + O = NH₂ + OH and HO₂ + NH₂ = NH₃ + O₂ are also important in the ${\mathrm{NH}}_3\to {\mathrm{NH}}_2$ reaction pathway. Overall, the concentration variations of highly reactive radicals such as H and key intermediate species such as NH₂ play a crucial role in the combustion process of pure ammonia. Figure 9b represents the sensitivity analysis of the LBVs for NH₃/DME/air and NH₃/DMM/air mixtures with 40% DMM or DME fraction at T_u = 298 K, P_u = 1 bar, and $\phi$ of 0.9. For both flames, the chain branching reaction H + O₂ = O + OH always exhibits the highest sensitivity. Other highly sensitive reactions, such as CO + OH = CO₂ + H and HCO + M = CO + H + M, are crucial for the reaction pathway $\mathrm{HCO}\to \mathrm{CO}\to {\mathrm{CO}}_2$ (as shown in Figure 7 and Figure 8) and achieving complete oxidation of carbon to CO₂. The reaction H + O₂ (+M) = HO₂ (+M) plays the most significant inhibitory role in the combustion of both flames, followed by the key reactions of NH₃ oxidation to NH₂ radicals: HO₂ + NH₂ = NH₃ + O₂ and NH₃ + OH = H₂O + NH₂. Furthermore, CH₃, as a key radical in the oxidation of DME and DMM, is involved in many important reactions that affect the LBV. For example, the reaction CH₃ + HO₂ = CH₃O + OH is crucial for driving the oxidation of CH₃ radicals. The reaction CH₃ + H (+M) = CH₄ (+M) is the main reaction causing the reduction in CH₃ radicals to CH₄ at lower flame temperatures and inhibiting the combustion process.

Overall, the main reactions controlling the LBVs of NH₃/DME/air and NH₃/DMM/air mixtures are almost identical, the LBVs are primarily dominated by the reactions of small radicals, and no C–N interaction reactions or fuel dissociations were found among these reactions. This suggests that the variations in LBVs for both mixtures are primarily influenced by changes in the shared OH, H, and O radical pool during the oxidation of NH₃ and DME, rather than by mutual reactions between C and N elements. This finding is consistent with the research results of Xiao et al. [24] and Elbaz et al. [33].

3.2.2. NO_x Emission Analysis

The effect of DMM and DME addition on NO_x emissions and temperature as a function of $\phi$ is shown in Figure 10. For NH₃/DME/air mixtures with different DME fraction, a similar trend can be observed that the NO_x emission initially increases from leanest condition to $\phi$ = 0.9 and then decrease after the peak. The contribution of thermal NO_x from pure DME combustion is negligible compared to the fuel NO_x coming from NH₃ as shown in Figure 10a. This suggests that the NO_x emissions generated during laminar burning of NH₃/DME/air mixtures are influenced to some extent by temperature, but the relationship with temperature is not directly correlated. Notably, under different DME fractions, the temperature increases with higher DME fractions, while NO_x emissions exhibit an initial increase followed by a decrease, peaking within the range of 40% to 50%. As shown in Figure 10b, the trend of NO_x emissions for NH₃/DMM/air mixtures is similar to that of NH₃/DME/air mixtures, but the peak NO_x emissions occur at $\phi$ of 0.9 within the range of the 30% to 40% DMM fraction.

Kinetic analysis reveals that the main component of NO_x emissions in NH₃/DME/air and NH₃/DMM/air mixtures is NO, while the emissions of other nitrogen oxides are approximately two orders of magnitude lower than NO. This study conducted a rate of production analysis on NO at T_u = 298 K and P_u = 1 bar, with $\phi$ of 0.9 and DME (Figure 11a) and DMM (Figure 11b) fractions of 40%. As shown in Figure 11, the generation and consumption of NO in NH₃/DME and NH₃/DMM mixtures are primarily influenced by six reactions. The reactions involving H + NO₂ = NO + OH, H + HNO = H₂ + NO, HNO + OH = H₂O + NO, and H + NO = NH + O contribute to the production of NO, while the reactions HO₂ + NO = NO₂ + OH and NH + NO = H + N₂O participate in NO consumption. It is noteworthy that four reactions involve H radicals, and three reactions involve OH radicals, indicating the significant impact of highly reactive radicals such as H and OH on NO_x emissions.

To investigate the impact of highly reactive free radicals such as H and OH on NO_x emissions, this study focuses on the analysis of the ROP and concentration changes of the H radical in NH₃/DMM/air mixtures as an example. As shown in Figure 12a, under different DMM fractions, all NO reactions involving the H radical exhibit a promoting effect on the NO formation. The ROP of these reactions demonstrates a similar trend to Figure 11, where the NO emissions are higher at X_DMM = 40% compared to X_DMM = 20% and X_DMM = 80%. Further analysis of the concentration changes of the H radical and related NO precursors (e.g., NO₂, HNO, and N₂O) at the same flame length is presented in Figure 12b. It is evident that both the H radical and NO precursors show a monotonic correlation with the DMM fraction, meaning that the concentration of the H radical increases overall while the concentration of NO precursors decreases with an increase in the DMM fraction. This is because the combustion process of DMM generates a significantly higher concentration of the H radical compared to NH₃, while the formation of NO precursors relies mainly on the oxidation of NH₃. In the NH₃/DMM/air combustion process, a lower DMM fraction leads to a decrease in NO emissions due to the lack of highly reactive free radicals such as the H radical, while a higher DMM fraction results in a decrease in NO emissions due to the deficiency of NO precursors. Only within an appropriate range of the DMM fraction can the generation of an appropriate concentration of highly reactive free radicals such as the H radical and the presence of NO precursors lead to the peak generation of NO during the combustion process. Figure 13 compares the concentration changes of the H radical and NO precursors in NH₃/DME/air and NH₃/DMM/air mixtures at T_u = 298 K, P_u = 1 bar and $\phi$ = 0.9. This demonstrates that under the same conditions, the addition of DMM produces a higher concentration of the H radical compared to DME, while the concentration of NO precursors is lower than that of DME. This explains why the peak NO_x emissions in NH₃/DMM/air combustion with a blending ratio of hydrocarbon fuel are 10% lower than those of NH₃/DME/air. In conclusion, the fraction of DME or DMM in NH₃ combustion does not show the monotonical effect of NO_x emissions. One of the crucial factors influencing the phenomenon is the ‘trade-off’ relationship between highly reactive radicals (e.g., H, OH, and O) and NO precursors caused by DME or DMM addition.

4. Summary and Conclusions

In this study, we proposed a NH₃/DMM mechanism that can accurately predict the LBVs and IDTs of NH₃/DMM and NH₃/DME mixtures, which can be used as the core mechanism for developing a combustion mechanism of NH₃ with heavier PODE_n. Furthermore, we conducted kinetic analysis of NH₃/DMM and NH₃/DME flames based on the present mechanism. Some of the key findings are as follows.

• Updates of some key reactions using the latest dataset, e.g., NH, NNH, and H-relevant reactions and the interactions between DMM and NH₂/NO_x are crucial to increase the accuracy of the present mechanism.
• Reaction path analysis revealed that early C–N interaction reactions play an important role in the oxidation pathway of NH₃. The dehydrogenation of NH₃ leads to the formation of NH₂, which then combines with a significant amount of CH₃ produced by the oxidation of DMM through collisions with other radicals, forming CH₃NH₂.
• The analysis of NO_x emission shows that fuel NO_x coming from NH₃ dominates the NO_x emissions and NO turns out to be the main component of NO_x emissions.
• The calculated NO_x emissions initially increase and then decrease with higher DME or DMM fraction, reaching a peak around a fraction of 40%. This phenomenon can be attributed to the ‘trade-off’ relationship between the high-activity radicals (e.g., H, OH, and O) and NO precursors promoted by the addition of DME or DMM.
• The difference in NO_x mole fraction between NH₃/DMM and NH₃/DME flames does not exceed 830 ppm according to the calculations.