On nanosecond plasma-assisted ammonia combustion: Effects of pulse and mixture properties

In this study, the effects of nanosecond plasma discharges on the combustion characteristics of ammonia are investigated over a wide range of mixture properties and plasma settings. The results reveal that the impacts of the plasma on ammonia combustion change non-monotonically by altering the reduced electric ﬁeld value. Within the studied range of the reduced electric ﬁeld, i.e., 10 0–70 0 Td, it is shown that plasma is most effective in the medium range, e.g., 250–400 Td. At lower values, the main fraction of the plasma energy is consumed to excite the diluent to higher vibrational levels. At very high reduced electric ﬁeld values, a substantial portion of the plasma energy is transferred into the ionization reactions of the diluent, which compromises the effective excitations of fuel and oxi-dizer species. In terms of the pulse energy density, results indicate that an increase in the range of 0–20 mJ/cm 3 , at a given reduced electric ﬁeld, decreases the ignition delay time by ﬁve orders of magnitude, and increases the laminar ﬂame speed up to an order of magnitude, depending on the mixture composition. The results show that the plasma discharge produces more radicals, electronically excited and charged species when He is used as the diluent in the oxidizer instead of N 2 , since NH 3 and O 2 ionization reactions are strengthened in NH 3 /O 2 /He. Moreover, plasma discharge is highly effective in assisting the combustion of preheated lean mixtures. The present study also indicates that ammonia ﬂame thickness is minimum at a critical pulse energy density in the range of 12–14 mJ/cm 3 . Further increases in the pulse energy density can manipulate the inner structure of the ﬂame, altering the pre-heat zone of the ﬂame to include some levels of chemical reactions toward the ﬂameless mode of combustion. © 2022 The Author(s). Published by Elsevier Inc. on behalf of The Combustion Institute. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ )


Introduction
Ammonia is known as the low-hanging fruit for decarbonizing combustion in the industrial sectors, thanks to its high hydrogen content and energy density combined with its relatively simple production, storage, and shipping technologies [1] .Nevertheless, ammonia reactivity is considerably lower than typical hydrocarbon fuels, which makes it a daunting task to supplant widely used fuels with ammonia in conventional engines [1] .Currently, preheating and co-burning are considered the main approaches to improving ammonia reactivity [ 1 , 2 ].However, co-burning (either as a dual or in a blend with other reactive fuels), compromises the advantages of ammonia as a carbon-free fuel if the second fuel is not hydrogen, an issue that seems likely for early system reconversions [2] .An alternative intriguing method would be to assist ammonia flames by plasma [3][4][5] .Compared to preheating, it has been shown that plasma discharge, at the same level of energy input, decreases the ignition delay time (IDT) of hydrogen/air mixtures by an order of magnitude [6] .In principle, plasma assists combustion through various routes including manipulating the mixture's thermophysical properties and kinetics of combustion [7] .Such impacts can also drastically change combustion characteristics as shown by Sun et al. that plasma converts the conventional S-shape ignition-extinction curve to a fully stretched monotonic curve in CH 4 /O 2 /He mixtures [8] .
There are several types of plasma generators including a torch, gliding arc, nanosecond, and microwave discharges [3] .Among these, non-thermal/non-equilibrium nanosecond discharge (NSD) is known as the most energy-efficient technology [ 9 , 10 ].All types of plasma-assisted combustion systems exhibit highly multiscale re-actions, ranging from microsecond chain propagation, termination, quenching, and ion-recombination reactions to picosecond electron impact reactions.However, unlike thermal reactions, electron impact reactions are independent of the gas temperature; hence, they can trigger both low and high-temperature pathways [6] .Recently, Faingold et al. performed zero-dimensional simulations to study IDT of stoichiometric NH 3 /O 2 /He and NH 3 /O 2 /N 2 mixtures assisted by plasma [ 4 , 5 ].They showed that a limited number of low-energy NSD can reduce IDT of high-temperature mixtures by 40-60% [4] .They also showed that the number of pulses and pulse repetition frequency required to ignite the mixture increase drastically as the mixture temperature reduces [4] .Tianeja et al. showed that using plasma discharge can extend the flammability limits of NH 3 /O 2 /He mixtures [11] .Choe et al. presented a brief communication on the flame enhancement of NH 3 /Air mixtures in which they observed experimentally that high-energy NSD lowers the lean blowout limit and NO X emissions [12] .Lin et al. [13] , Kim et al. [14] , and Tang et al. [15] also confirmed that NOx emissions can be reduced in NH 3 /Air flames by using high energy gliding arc plasma, dielectric barrier discharges, and AC powered gliding arc discharges, respectively.Moreover, Tianeja et al. and Jahnson et al. performed numerical simulations on plasma-assisted NH 3 /air combustion [ 11 , 16 ].They showed that ammonia oxidation pathways are dependent on the reduced electric field in the range of 150-550 Td [16] .However, the key chemical phenomena inducing such effects were not addressed in detail.
Despite the above-mentioned valuable community effort s, there are limited data and detailed analyses available in the literature on the effects of the reduced electric field, pulse energy density, equivalence ratio, diluent composition, and temperature on plasma-assisted ammonia combustion.Moreover, the majority of the previous studies were devoted to address the effects of plasma on the ignition delay time of ammonia, and no data is publicly available on the effects of plasma discharge on ammonia flame characteristics.To fill these gaps, the objective of the present study is to evaluate the impacts of nanosecond plasma discharge on the IDT and flame characteristics of ammonia over wide ranges of the reduced electric field, pulse energy density, and the mixture temperature and composition.

Numerical solver
An open-source Boltzmann equation solver called ZDPlaskin [17] was coupled with in-house Cantera [18] codes.Each computational iteration involved a two-way coupling between ZDPlaskin and Cantera in which the electron impact equations were solved, and the results were passed on to Cantera for integrating the ODEs of thermal reactions.Here, the ignition delay time was calculated using an adiabatic constant-volume reactor, in which both plasma and thermal kinetics were solved over each time step.Furthermore, a one-dimensional freely propagating flame model was used to study the effects of plasma on unstrained premixed flame characteristics.To such an aim, first, fresh mixtures were stimulated by 20 nanosecond plasma pulses in an adiabatic constant-pressure reactor.Then, the output of this reactor was used as an input for the one-dimensional freely-propagating flame model.The pulse was modeled as a square wave as shown in Fig. 1 .Here, an adaptive temporal resolution method was used to refine the time step during each pulse while minimizing the overall computational time.In this way, the chemical reactions during the plasma discharge were resolved using a time step of approximately 1 × 10 −12 s, whereas the ODEs of thermal reactions were integrated using a timescale of 1 × 10 −9 s.An example of the scheme used in this study can be found in Fig. 1 .

Kinetic model
Preliminary studies, presented in the Supplementary Material, show that the mechanism developed by Han et al. [19] is an accurate and computationally efficient mechanism to predict ammonia combustion characteristics.Hence, this mechanism was used in the present study, which comprises 298 elementary reactions, including reactions of excited species, such as O 2 (a 1 g ), O( 1 D), etc. introduced by Konnov [20] .The plasma kinetic mechanism was then assembled by incorporating the mechanism presented by Faingold et al. for NH 3 /O 2 /He [4] alongside the plasma reactions for N 2 from the study of Zhong et al. [21] with the collision cross sections for electron-species interactions obtained from LX-Cat database [22] .These allow to include excitations, ionizations, quenching, recombination, charge exchanges, and neutral state elementary reactions for NH 3 /O 2 /N 2 /He mixtures into a unified mechanism.

Modeling parameters
The initial ammonia mixture temperature, T in , and equivalence ratio, φ, were varied in the range of 298-10 0 0 K, and 0.8-1.2,respectively.The mixture pressure was fixed at 1 atm.The amount of oxygen in O 2 /N 2 and O 2 /He was always 21%.The NSD settings were based on available plasma generators [ 23 , 24 ].The plasma repetition frequency ( PRF ) was set at 50 kHz, while the reduced electric field, E/N , was varied in the range of 10 0-70 0 Td to find the most effective E/N to assist ammonia/air combustion.In each simulation, 20 pulses were discharged, which were shown to be sufficient for self-accelerating low-temperature chain branching reactions.Two ranges of NSD pulse energy density, E p , were considered, one in the range of 0-1 mJ/cm 3 and the other 1-20 mJ/cm 3 , with increments of 0.2 mJ/cm 3 and 1 mJ/cm 3 , respectively.These are similar to the range that is typically used in literature.In previous studies, although low E p values, i.e., E p < 1.3 mJ/cm 3 , were used to assist combustion of hydrocarbon fuels and ammonia [ 4 , 5 , 10 , 11 , 23 , 25 , 26 ], however, a relatively high E p was required to reduce NOx emissions [ 13 , 15 , 27 ].It is worth noting that increasing the number of pulses with low E p values would result in similar reductions in NOx emissions as those with high E p values, since both of these parameters control the amount of the plasma energy discharged into the mixture.Further investigations are needed to compare the effects of number of pulses and E p on plasma-assisted ammonia combustion.The highest E p value in the present study is limited to ensure that the mixture does not ignite prior to the discharging of 20 pulses.Here, an adaptive NSD pulse width, w , was employed, ensuring the specified E p was released during each pulse.It should be mentioned that the pulse width is always less than 10 ns for the selected cases in this study, which is in the range of the ones used in the literature [ 4 , 11 , 16 , 27-30 ].Here, simulations over the pulse width and between the pulses are denoted by "plasma phase" and "thermal phase" terms, respectively.

Validations
In the absence of publicly available detailed experimental data about the time history of species concentrations and temperature for ammonia combustion enhanced by using NSD, the solver was first validated by reproducing Faingold et al. numerical results on plasma-assisted NH 3 /O 2 /He ignition at φ = 1 and p = 1 atm [4] .Fig. 1 shows the time history of the OH mole fraction and that of Faingold et al. [4] .Here, the initial number density of electrons was 1 cm −3 , without any electronically excited and charged species, "reactive plasma species", or radicals as initial conditions.The predicted results are in good agreement with those of reference [4] .The lower OH mole fraction predicted in this study in the post-plasma phase, i.e., time > 0.1 ms, is consistent with the smaller peak values of OH during the pulses.This is not attributed to the numerical resolutions in the present simulations as here, the effort s were made to ensure sufficiently fine time steps, t , to obtain temporal resolution-independent results as can be seen in Fig. 1 .It should be mentioned that details of the temporal resolution and the initial conditions are not fully provided in [4] .
To further validate the numerical method, simulations were performed to reproduce the experimental data provided by Lefkowitz et al. on plasma-assisted CH 4 /O 2 /He combustion [31] .The kinetic mechanism developed by Mao et al. [32] was used to simulate plasma-assisted CH 4 /O 2 /He combustion in a constantvolume reactor.Fig. 2 shows the temporal evolution of temperature under 300 nanosecond plasma pulses.The instant of the last plasma discharge is shown by a vertical dash-dot line in Fig. 2 .Here, the pulse repetition frequency is 30 kHz, and the reduced electric field is 180 Td.Similar modeling as the one used in reference [31] is utilized to include heat loss to the dielectrics.The uncertainty of the experimental data obtained by Lefkowitz et al. [31] is also shown in Fig. 2 .Simulations were performed using different tem poral resolutions to achieve resolution-independent data.The results show that the present numerical setup can well predict the temporal evolution of temperature under nanosecond plasma discharges.

Reduced electric field in plasma-assisted ammonia combustion
Fig. 3 shows IDT and laminar flame speed of stoichiometric NH 3 /O 2 /N 2 at T in = 850 K, p = 1 atm assisted by 20 nanosecond plasma pulses with E p = 5 mJ/cm 3 as functions of E/N .The results show that both IDT and laminar flame speed change non-monotonically with E/N .This non-monotonic trend is in-line with the previously reported trends of the ignition delay time of plasma-assisted H 2 /air [9] , the fuel conversion in plasma-assisted CH 4 oxidation in the air [33] , and ammonia oxidation in the air [16] as functions of E/N.Fig. 3 shows that plasma-assisted combustion has relatively low effectiveness at low E/N values, i.e., E/N < 250 Td.Increasing the reduced electric field toward the medium range of E/N , i.e., 250 < E/N < 400 Td, significantly improves the effects of plasma on combustion.However, further increases in E/N slightly reduce the beneficial effects of the plasma discharge on the combustion characteristics.
More detailed studies on the effects of E/N on the plasmaassisted combustion are carried out by comparing the numerical results obtained for E/N = 100, 350, and 700 Td chosen as the representatives of the low, medium, and high reduced electric field values, respectively.Fig. 4 shows the percentage of the plasma energy taken by the electrons into different dominant excitation and ionization reactions as well as the main consumption path fluxes of a selected number of species in plasma-assisted ammonia/air combustion at φ = 1, T in = 850 K, p = 1 atm.Path fluxes were calculated during 20 plasma pulses.Further details of the branching of the plasma energy through the major reactions consuming the plasma energy are presented in the Supplementary Material.Considering the energy taken into the excitation and ionization reactions of N 2 , the results show that the main part of the plasma energy, i.e., 46%, is used to excite the N 2 to the higher vibrational levels, i.e., v1-v8, for E/N = 100 Td.Such electronically excited species have negligible effects on the production of other reactive plasma species or radicals.Therefore, plasma energy is not used discreetly at low E/N values to produce effective reactive plasma species and radicals, e.g., O, H, OH, to assist ammonia combustion.This is demonstrated in Fig. 5 by plotting the maximum value of the mole fraction of the selected radicals and electronically excited  species during the plasma deposition averaged over 20 sequential pulses of the plasma deposition with E p = 5 mJ/cm 3 in the stoichiometric NH 3 /O 2 /N 2 mixture.Contrary to this, at medium and high E/N values, the plasma energy is utilized to excite and ionize N 2 molecule to effectively assist combustion, while a negligible amount of the plasma energy is used to excite N 2 to the higher vibrational levels.Fig. 4 shows that 39.9% and 34.2% of the plasma energy, respectively for E/N = 350 and 700 Td, is taken by the electrons into the reactions to generate N 2 (B), N 2 (ab), N 2 (C), and N( 2 D) excited species.The path fluxes of these species show that all the above-mentioned electronically excited species react with  Besides, as it is shown in Fig. 5 , compared with E/N = 700 Td, more OH radical is produced at E/N = 350 Td, e.g., via using more plasma energy to produce O( 1 D) which reacts with the fuel to produce OH radical.The more OH radicals, the quicker activation of the high-temperature reactions and subsequently faster ignition and flame propagation, as is observed in Fig. 3 .

Effects of NSD on ignition delay time
Fig. 6 shows ammonia IDT in O 2 /N 2 and O 2 /He at T in = 850 K, p = 1 atm and φ = 0.9-1.1.Increasing E p strengthens the electron impact reactions during the plasma discharge, which subsequently raises the concentration of radicals and reactive plasma species, as well as the mixture temperature, which results in a considerable reduction of IDT.Fig. 7 shows the maximum value of the mole fraction of radicals, electronically excited, and charged  The results show that the mole fractions of the radicals and reactive plasma species generated by the NSD increase almost linearly by raising the E p value.Linear curves are fitted into the data and the slopes of the fitted curves are presented in the legend, Fig. 7 .The results also show that NSD with low E p values ( E p < 3 mJ/cm 3 ), produces a considerable amount of O 2 (a 1 g ).However, other electronically excited and charged species, i.e., NH 3 + , O( 1 D), N( 2 D), N 2 (B), and O 2 (b 1 g + ), are significantly produced at higher E p values.Increasing the pulse energy density noticeably enlarges the mole fractions of NH 2 , H, and O radicals.It is worth noting that radicals are produced in both plasma and thermal phases.The plasma phase is the main source of radicals at low pulse energy densities, while at higher E p values, the thermal phase plays the key role in generating radicals.For instance, path flux analyses show that 79% of H radical is generated by electron impact reactions in plasma-assisted stoichiometric NH 3 /O 2 /N 2 mixture at T in = 850 K with E p = 5 mJ/cm 3 , while the corresponding value with E p = 15 mJ/cm 3 is 31%.This is mainly because, unlike the cases with low E p values, plasma discharges with a high pulse energy density produce large pools of reactive plasma species and radicals during the initial pulses, which in turn results in a rapid temperature augmentation.Subsequently, the thermal phase considerably contributes to generating the radicals between the underlying pulses.To further delineate the effects of the diluent composition on plasma-assisted ammonia combustion, the path fluxes of electron and NH 3 are plotted in Fig. 9 .The fluxes were calculated over 20 plasma pulses discharged in the mixtures initiated at 850 K and 1 atm.The path flux of the electrons shows that the electrons are mainly produced during the electron impact reactions with NH 3 and O 2 rather than the diluent in NH 3 /O 2 /He, while a considerable amount of the electrons is generated during the diluent ionization in NH 3 /O 2 /N 2 mixture.Subsequently, ionization reactions produce more charged NH 3 + and O 2 + species in NH 3 /O 2 /He as that in NH 3 /O 2 /N 2 .This is consistent with the results presented in Fig. 8 .The analyses also show that the ratios of the production and consumption rates of the electrons in NH 3 /O 2 /He to the corresponding rates in the NH 3 /O 2 /N 2 mixture are 2.6 and 2, respectively.This indicates that the electrons are produced and consumed faster when N 2 is replaced in the oxidizer by He, which results in faster ionization reactions in the presence of He than that when N 2 is used as the diluent.Consequently, the fuel dissociates more in the plasma phase in NH 3 /O 2 /He mixture than that in NH 3 /O 2 /N 2 .The path flux of NH 3 shows that 64% of the fuel is dissociated during the plasma discharge in NH 3 /O 2 /He, while the corresponding value in NH 3 /O 2 /N 2 is 52%.The higher fuel dissociation in the plasmaassisted NH 3 /O 2 /He mixture as those in NH 3 /O 2 /N 2 results in relatively faster OH radical production and consumption rates before the ignition, as it is shown in Fig. 10 .In Fig. 10 , the rates are calculated up to the instance of the ignition.The results show that the production rate of OH radical via H + O 2 ↔ OH + O reaction, as  the main source of OH production, increases by a factor of 3 when N 2 is replaced by He.This is in the order of the ratio of the IDT of plasma-assisted NH 3 /O 2 /He to that of NH 3 /O 2 /N 2 mixtures with E p = 5 mJ/cm 3 , i.e., 2, which can be found in Fig. 6 .It should be noted that the quenching reaction of the electronically excited N 2 with NH 3 directly dissociate the fuel via N 2 (A) + NH 3 → N 2 + H + NH 2 reaction, while the quenching reactions of electronically excited He, i.e., He * , with NH 3 result in ionized species, i.e., NH 3 + , NH 2 + , NH + , and H radical.To further evaluate the effects of such reactions on plasma-assisted combustion, simulations were performed for plasma-assisted stoichiometric NH 3 /O 2 /He at T in = 850 K assisted by 20 nanosecond plasma pulses with E p = 5 mJ/cm 3 with and without considering the quenching reactions of He * with NH 3 .It is found that the IDT and flame speed change by 5% and 0.6%, when such reactions are neglected in the simulations.
Two zoom-ins shown in Fig. 6 , depict the different responses of IDT, depending on the range of E p , as follows.For low and medium E p values, e.g., E p < 7 mJ/cm 3 , the IDT weakly depends on φ, similar to the non-plasma cases.Interestingly, contrary to this trend, the plasma is more effective in assisting lean mixtures in terms of IDT at high E p values, e.g., E p > 7 mJ/cm 3 .Fig. 11 shows the production and consumption rates of OH radical under different equivalence ratios and pulse energy densities calculated over 20 pulses of the plasma discharge.At low pulse energy densities, NH 2 + NO ↔ NNH + OH is the main source of the OH radical, while H + O 2 ↔ OH + O plays the key role in producing OH at high E p values.Such differences in the main route of OH radical production can be explained by examining the pathways of H radical plotted in Fig. 12 11 also shows that, in all the cases, OH radical is mainly consumed during the thermal phase to dissociate the fuel into NH 2 .The equivalence ratio has negligible effects on the production and consumption rates of OH radical at low pulse energy density values, which results in an insignificant impact of the equivalence ratio on IDT at low pulse energy density values, as observed in Fig. 6 .However, increasing the pulse energy density amplifies the rates of production and consumption of OH radical, as it can be found in Fig. 11 , being more pronounced for φ = 0.9 than φ = 1.1.This is because O 2 is abundant under the lean conditions, which facilitates OH production via H + O 2 ↔ OH + O.This trend is analogous to the effects of preheating reported in previous non-plasma studies showing that lean ammonia flames are more sensitive to the increase of the initial mixture temperature as compared to the stoichiometric and moderately rich ones [19] .
The question posed here concerns the precise contribution of plasma in assisting lean and rich mixtures.To address this, plasma energy branching is computed during a single plasma pulse discharged in lean and rich mixtures.The results and the path fluxes of a selected number of species are presented in Fig. 13 .The main differences between the selected cases, i.e., φ = 0.9 and 1.1, are that the percentage of the energy used to excite and ionize O 2 and N 2 is higher in the lean mixture than that in the rich mixture, since more O 2 and N 2 molecules exist in the lean mixture as those in the rich one.In a similar way, the energy taken by the reactions to excite NH 3 is higher in the rich mixture than that in + active plasma species, which subsequently take part in reactions to form O, OH, NH 2 , H, NH radicals, as shown in Fig. 13 .On the other hand, the higher energy taken to the excitation reaction of NH 3 , the more NH 2 , NH, and H radicals.The above analyses show that more OH radicals should be directly generated by the plasma discharge in lean mixtures than that in rich mixtures.In order to justify this, the maximum value of OH radical generated in a single plasma pulse with E p = 15 mJ/cm 3 discharged in NH 3 /O 2 /N 2 at T in = 850 K was measured for both lean and rich cases.It is found that plasma generates 183 and 170 ppm of OH radical in lean and rich mixtures, respectively.Therefore, besides the superior thermal effects under the lean condition addressed before by Han et al. [19] , the plasma discharges also contribute to the observed higher enhancements in IDT achieved under the lean condition as those under the rich and stoichiometric cases, shown in Fig. 6 .

Effects of NSD on laminar flame structure 4.3.1. Flame speed and thickness
Fig. 14 shows the laminar flame speed of ammonia at T in = 850 K as a function of E p in lean, stoichiometric and rich mixtures.
Both multi-component diffusion and radiation heat losses effects were considered in the calculations.The results show that using NSD with E p > 10 mJ/cm 3 increases the laminar flame speed of ammonia by an order of magnitude.These effects are more pronounced in the lean mixture, which is consistent with the details presented in the previous section.
Fig. 15 shows the laminar flame thickness of NH 3 /O 2 /N 2 and NH 3 /O 2 /He as a function of E p and φ.The flame thickness is defined as , where T b is the temperature of burned gases, T u is the temperature of fresh reactants, and (d T /d X ) Max. is the maximum temperature gradient through the flame [34] .Unlike the flame speed (see Fig. 14 ), results show that the flame thickness is a non-monotonic function of E p .For each φ, there exists a unique E p , the critical value (shown by E pm in Fig. 15 ), at which the flame thickness takes its minimum.The trend at low E p values is analogous to the effects of the mixture temperature on the flame thickness.The higher the mixture temperature, the thinner the flame.Depending on the equivalence ratio, E pm is in the range of 12-15 mJ/cm 3 .Such effects are further examined by analyzing the inner structure of the flame in Fig. 16 , showing the profiles of heat release rate across the flame.Fig. 16 also includes the profile of the heat release rate across a highly preheated flame of T in = 1500 K, to clarify the differences between the heat release rates of a plasma-assisted flame and a highly preheated non-  plasma flame.In Fig. 16 , the spatial location involves an offset to ensure the location of maximum heat release at the origin in all cases.The results show that for low E p values, e.g., E p 5 mJ/cm 3 , the flame structure is virtually identical to the non-plasma and highly preheated cases, namely, the preheating zone does not involve any significant heat release.However, at high E p values, e.g., E p = 20 mJ/cm 3 , the heat release across the flame is shifted to-ward the preheat zone, explaining the increase in the flame thickness observed for E p E pm in Fig. 15 .Such a broadening of the heat release profile is comparable to the well-distributed reaction zone in flameless combustion mode, with significant implications for the turbulent flame regime [35] .It is worth noting that the well-distributed reaction zone is the key characteristic of flameless combustion mode, which results in low temperature gradients and low NOx emissions [35] .Further investigations are mandatory to quantify the effects of E p on the regime of combustion and its implication in the modeling of plasma-assisted turbulent premixed flame.

NOx emissions
The NOx emissions of the studied cases are plotted in Fig. 17 , which are determined at 6 cm downstream of the flame.In Fig. 17 , the NOx levels are adjusted to the reference 15% O 2 level.In all cases, NO X emissions initially rise as E p increases.However, there is a certain value, E pc , at which NO X emissions tend to reach their peak values, beyond which further increases in E p decrease the NOx emissions.Fig. 17 shows that E pc is larger as the mixture gets richer.The non-monotonic trend of NOx emissions as a function of E p is a result of competing processes controlling the production and consumption of NO, as is elaborated in Fig. 18 showing rates of consumption and production of NO for NH 3 /O 2 /N 2 mixture at T in = 850 K with PRF = 50 kHz and E/N = 350 Td.Increasing E p accelerates the overall consumption rate of fuel-originated species, e.g., NH 2 , and thus NO X formation.

Preheating
It is of both practical and fundamental interest to evaluate the plasma potential in assisting combustion under engine-like condi-tions, specifically during a cold start-up.To address this, Fig. 19  show that the nanosecond plasma discharge with E p = 5 mJ/cm 3 can increase the flame speed of ammonia by over 40% at T in = 298 K.Such flame speed enhancements are more noticeable under the lean condition as compared with stoichiometric and rich mixtures as discussed above.Anyhow, the results show that preheating has considerable effects on plasma-assisted ammonia combustion.For instance, the percentage increase in the flame speed rises from 35% to 76% in the stoichiometric mixture as the mixture temperature is elevated from 298 to 10 0 0 K.To compare the effects of pure preheating with those of plasma discharge on ammonia combustion, the required preheat temperature ( T ) was calculated for NH 3 /O 2 /N 2 at φ = 0.8-1.2 to achieve the same level of enhancements in the flame speed without using plasma discharges as the ones presented in Fig. 19 (a).The results plotted in Fig. 19 (b) show that relatively low preheat temperatures are needed to gain a similar percentage increase in the flame speed of NH 3 /O 2 /N 2 at low T in values assisted by 20 nanosecond plasma pulses with E p = 5 mJ/cm 3 .However, the required T for a similar flame speed enhancement as that achieved by using plasma discharges increases considerably when T in is elevated.For instance, preheating the stoichiometric NH 3 /O 2 /N 2 mixture at T in = 850 K with T = 149 K results in a similar flame speed enhancement as that attained by discharging 20 nanosecond plasma pulses.It should be noted that in Fig. 19 (a) the pulse energy density was kept constant at 5 mJ/cm 3 .Obviously, the more pulse energy density, the higher required preheat temperature to achieve an identical enhancement in the flame speed by relying on just preheating.For instance, stoichiometric NH 3 /O 2 /N 2 mixture at T in = 850 K should be preheated by 310 K and 549 K to rise the flame speed of stoichiometric NH 3 /O 2 /N 2 mixture to those achieved by discharg-      22 shows the spatial distribution of the normalized sensitivity coefficien of OH mole fraction along the one-dimensional freely propagating flame caused by changing the pre-exponential factor of the abovementioned reactions.In Fig. 22 , the spatial location involves an off-

Conclusions
The effects of nanosecond plasma discharge on ammonia combustion under various pulse energy densities, reduced electric fields, and thermophysical conditions were investigated by coupling ZDPlasKin and Cantera open-source codes.The assembled kinetic model includes the excitations, ionizations, quenching, recombination, charge exchanges, and neutral state reactions for NH 3 /O 2 /N 2 /He mixtures.Moreover, a non-uniform time step method was used to accurately resolve multi-time-scale chemical reactions in plasma-assisted ammonia combustion.
Analyses revealed that ignition delay time and laminar flame speed of ammonia/air respond non-monotonically to the reduced electric field, being maximum at the medium ranges of the reduced electric field.At low reduced electric field values, the major part of the plasma energy is used to excite the diluent to higher vibrational levels, which have trivial impacts on ammonia combustion.On the other hand, plasma discharges with a high reduced electric field activate ionization reactions of the diluent, which lowers O and OH radical productions.It was shown that unlike the non-plasma or low-energy plasma-assisted cases, the ignition delay time with high-energy plasma discharges, e.g., E p > 10 mJ/cm 3 , drops when the equivalence ratio of the mixtures is decreased.This is attributed to the higher rates of production and consumption of OH in lean mixtures as compared with stoichiometric and fuelrich mixtures.The results showed that NSD produces more reactive plasma species during the pulses when N 2 is replaced by He in the oxidizer, thanks to the strengthened NH 3 and O 2 ionization reactions in NH 3 /O 2 / He as that in NH 3 /O 2 /N 2 .It was also shown that increasing the mixture temperature enhances the plasma performance.
In terms of the effects of plasma on the flame structure, it was observed that the flame thickness non-monotonically depends on the pulse energy density.For all the equivalence ratios examined here, there is a certain pulse energy density at which the flame attains its minimum thickness.Further increases in the pulse energy density tend to disrupt the flame structure by broadening the heat releases rate profile, and substantial increases in the flame thickness toward a reactive preheat zone structure.

Declaration of Competing Interest
None.
KAW2019.0084 COCALD.Cardiff University gratefully acknowledges the support from the Welsh European Funding Office through "Flexible Integrated Energy Systems", project 80835 .

Fig. 4
shows that percentages of the plasma energy taken into the excitation reaction of O 2 and NH 3 are higher for E/N = 350 Td than the corresponding percentages in the cases with E/N = 100 or 700 Td.These excitation reactions produce NH 2 , NH, H, and O( 1 D) radicals.The consumption path flux of O( 1 D) shown in Fig.4indicates that this species reacts with NH 3 and N 2 to generate OH, NH 2 , and O radicals.

O 2 Fig. 4 .Fig. 5 .
Fig. 4. Distribution of the plasma energy (dashed-arrows) as well as the consumption path flux (arrows) of a selected number of species (enclosed by rectangles) in plasmaassisted NH 3 /O 2 /N 2 combustion for T in = 850 K, φ = 1.0 with PRF = 50 kHz and E/N = 100 Td (blue), 350 Td (black), and 700 Td (red).(For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 7 .
Fig. 7. Ensemble-averaged local maxima of mole fraction of radicals, electronically excited and charged species in 20 sequential pulses of plasma discharge in NH 3 /O 2 /N 2 mixture at T in = 850 K, φ = 1.0 with PRF = 50 kHz and E/N = 350 Td.

Fig. 6
also shows that NSD is more effective in reducing the IDT of NH 3 /O 2 /He as compared with NH 3 /O 2 /N 2 for the selected plasma settings.Temporal evolutions of the electronically excited

Fig. 9 .
Fig. 9. Path fluxes of electron (top) and NH 3 (bottom) in plasma (dashed-arrows) and thermal (arrows) phases in plasma-assisted NH 3 /O 2 /N 2 (black) and NH 3 /O 2 /He (red) combustion for T in = 850 K, φ = 1.0 with E p = 5 mJ/cm 3 , PRF = 50 kHz, and E/N = 350 Td. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
. Here, the pathways are obtained over 20 pulses of plasma.The results show that H + O 2 + M ↔ HO 2 + M and HNO + H ↔ NO + H 2 compete with H + O 2 ↔ OH + O chain branching reaction for H radical at low pulse energy density values, which lowers the direct OH radical production via H + O 2 ↔ OH + O.This in turn impels the OH radical production to the other alternative route, i.e., NH 2 + NO ↔ NNH + OH.Such competitions are considerably incidental at high E p values.Fig.

Fig. 14 .
Fig. 14.Laminar flame speed of NH 3 /O 2 /N 2 (solid lines) and NH 3 /O 2 /He (dash lines) as functions of E p and φ for T in = 850 K with PRF = 50 kHz and E/N = 350 Td.

Fig. 15 .
Fig. 15.Laminar flame thickness of NH 3 /O 2 /N 2 (solid lines) and NH 3 /O 2 /He (dash lines) as functions of E p and φ for T in = 850 K with PRF = 50 kHz and E/N = 350 Td.
Fig. 18 supports this by showing that increasing the pulse energy density, considerably raises the production rate of NO, specifically through HNO + H ↔ NO + H 2 , NH 2 + O ↔ H 2 + NO, and NH + O 2 ↔ NO + OH reactions.The other dichotomy process is the reburning of the nitrogen oxides mostly in reactions with NH 2 and NH radicals, i.e., NH 2 + NO ↔ NNH + OH, NH 2 + NO ↔ N 2 + H 2 O, NH + NO ↔ N 2 O + H.In rich flames, NH 2 and NH radicals are naturally predominant, leading to lower NO X emissions.In such cases, higher values of E p are required to produce more NH 2 and NH radicals as compared to the intrinsic levels in a flame not affected by the plasma discharge to increase the consumption rate of NO.
(a) shows the percentage increase from the laminar flame speed of the non-plasma NH 3 /O 2 /N 2 (S L-NP ) to the laminar flame speed by using NSD (S L-P ) at φ = 0.8-1.2 and T in = 298-10 0 0 K.The results

Fig. 17 .
Fig. 17.NOx emissions of plasma-assisted NH 3 /O 2 /N 2 (solid lines) and NH 3 /O 2 /He (dash lines) flames as functions of E p and φ for T in = 850 K with PRF = 50 kHz and E/N = 350 Td.

Fig. 18 .
Fig. 18.Rates of consumption and production of NO in plasma-assisted NH 3 /O 2 /N 2 combustion for T in = 850 K and φ = 0.9 with PRF = 50 kHz and E/N = 350 Td.

Fig. 19 .Fig. 20 .
Fig. 19.(a) Percentage increase in NH 3 /O 2 /N 2 flame speed as a function of initial temperature for φ = 0.8, 1, 1.2 with PRF = 50 kHz, E/N = 350 Td, E p = 5 mJ/cm 3 and (b) required preheat temperature without using plasma discharges to achieve similar enhancement in the flame speed as those presented in subfigure a. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 21 .
Fig. 21.Path fluxes of O (top) and H (bottom) in plasma (dashed-arrows) and thermal (arrows) phases in plasma-assisted stoichiometric NH 3 /O 2 /N 2 for T in = 298 K (blue) and T in = 10 0 0 K (red) with E p = 5 mJ/cm 3 , PRF = 50 kHz, and E/N = 350 Td. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 21
also shows that plasma is the main source of H radical in the cold mixture, i.e., 96.1%, while in the high-temperature case, 53.1% of H radical is produced in the thermal phase.The H radical is solely consumed in the thermal phase in all cases, during which H + O 2 ↔ OH + O and H + O 2 + M ↔ HO 2 + M play the key role in consuming H radical in low and high-temperature cases, respectively.The pathway analyses of HO 2 radical for T in = 298 K, presented in the Supplementary Material, show that over 55% of HO 2 radical takes part in NO + HO 2 ↔ NO 2 + OH and NH 2 + HO 2 ↔ H 2 NO + OH reactions to directly produce OH radical.Here, sensitivity analyses are carried out to further assess the contribution of H + O 2 ↔ OH + O and H + O 2 + M ↔ HO 2 + M reactions to changing OH radical pools under low and temperature conditions.Fig.

Fig. 22 .
Fig. 22. Normalized sensitivity coefficient of OH mole fraction along the laminar flame caused by changing the pre-exponential factors of the selected reactions for plasmaassisted stoichiometric NH 3 /O 2 /N 2 for T in = 298 K and T in = 10 0 0 K with E p = 5 mJ/cm 3 , PRF = 50 kHz, and E/N = 350 Td.