Effect of radiation on laminar ﬂame speed determination in spherically propagating NH 3 -air, NH 3 /CH 4 -air and NH 3 /H 2 -air ﬂames at normal temperature and pressure

The use of spherically propagating ﬂames is common for measuring the laminar ﬂame speed in NH 3 - air, NH 3 /CH 4 -air and NH 3 /H 2 -air mixtures. However, the radiation-induced uncertainty in such mixtures has not been thoroughly investigated. Due to the low laminar ﬂame speed of ammonia mixtures, it is anticipated that the radiation effect is considerable for such mixtures. This study aims to ﬁll this gap by conducting numerical simulations using different chemical mechanisms and the adiabatic and optical thin radiation models to examine the effects of radiation on spherically propagating NH 3 -air, NH 3 /CH 4 -air and NH 3 /H 2 -air ﬂames. The simulations are performed for mixtures at normal temperature and pressure ( T u = 298 K and P = 1 atm) and wide range of equivalence ratios. The radiation-induced uncertainty in spherical ﬂames is quantiﬁed and compared to planar ﬂames. The importance of the radiation-induced ﬂow and thermal effects in spherical ﬂames is compared between different mixtures and a correlation is developed to determine the radiation-corrected ﬂame speed for spherical NH 3 -air ﬂames. Considering the radiation effect in NH 3 -air, it was found that using different mechanisms results in considerable discrepancies in laminar ﬂame speed determination. Some mechanisms showed that the radiation-induced ﬂame speed in spherical ﬂames was underpredicted by more than two times compared to planar ﬂames, and the radiation-induced uncertainty for lean and rich spherically propagating NH 3 -air ﬂames exceeds 20%. However, the radiation-induced uncertainty at normal temperature and pressure in spherically propagating NH 3 /CH 4 -air and NH 3 /H 2 -air ﬂames was less signiﬁcant, not exceeding 11%. Finally, an updated correlation is proposed to determine the radiation-corrected ﬂame speed for NH 3 -air ﬂames that can be directly used in spherical ﬂame experiments measuring the laminar ﬂame speed. © 2023 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
Increase in global warming and climate change is predicted to have serious impacts on human health and the environment.Future propulsion and power generation technologies should use non-carbon energy sources combined with advanced high efficiency energy conversion devices to meet net-zero carbon emissions targeted by 2050.Ammonia (NH 3 ) has attracted much attention for combustion applications in recent years due to its established production, transportation, and storage infrastructure [ 1 , 2 ].However, there are important challenges with NH 3 combus-tion including low laminar flame speed, low heating value, narrow flammability limit, and large NOx emissions, which should be overcome before widespread practical use [1] .To overcome these challenges, mixing NH 3 with more reactive fuels, such as hydrogen (H 2 ) and methane (CH 4 ), has been suggested [1] .
There are numerous studies on the application of NH 3 -air, NH 3 /CH 4 -air, and NH 3 /H 2 -air in gas turbines, boilers and internal combustion engines [3][4][5][6][7] .Different detailed chemical mechanisms have been developed to characterize ammonia blends combustion [ 4 , 8-11 ].Among the experimental methods used to develop these chemical mechanisms, the use of spherically propagating flames (SPF) is the preferred option to measure the laminar flame speed (LFS) at engine relevant conditions, (i.e., at P = 20-50 atm and T u = 70 0-80 0 K) [12] .Therefore, the SPF method has been popularly used to measure the LFS of ammonia-blends and to vali-date chemical mechanisms [ 10 , 13-17 ].Chen [18] has shown that even for methane/air mixtures at normal temperature and pressure (NTP, T u = 298 K and P = 1), the maximum difference of reported unstretched laminar flame speed ( S u,0 ) exceeds 20% for φ ≤ 0.9 and φ ≥1.2.Consequently, accurate measurement of LFS is essential due to the low sensitivity of LFS to chemical kinetics [19] .
Different factors including mixture preparation [ 19 , 20 ], ignition [21] , buoyancy [ 22 , 23 ], instability [ 24 , 25 ], confinement [ 26 , 27 ], nonlinear stretch behavior [28] , extrapolation [29] , and radiation [30][31][32] induce uncertainty in SPF measurements.One of the main sources of uncertainty in SPF experiments is radiation [ 30 , 31 , 33 , 34 ], which is noticeable for mixtures with LFS below 10 cm/s [35] .Due to the relatively low LFS of NH 3 -air NH 3 /CH 4 -air, and NH 3 /H 2 -air mixtures with low hydrogen contents, the importance of radiation-induced uncertainty seems to be considerable.However, relatively few studies have been performed to investigate radiation effect in ammonia blends.Nakamura and Shindo [36] used the optically thin model (OTM) [37] and CHEMKIN-PREMIX [38] package to study the radiation effect in steady planar freely propagating NH 3 -air flames.They concluded that for NH 3 air mixtures at NTP, the radiation-induced uncertainty exceeds 15% when φ ≤ 0.8 or φ ≥1.4.Recently, Zheng et al. [39] used a Statistical Narrow-Band (SNB) model [ 40 , 41 ] in PREMIX code [38] to assess the effect of radiation reabsorption in steady freely propagating NH 3 /H 2 -air flame at different pressures and equivalence ratios.They found that, although the radiation effect predicted by OTM is very similar to adiabatic results, the maximum reabsorption effect reached 15.6% compared to the OTM model for NH 3 /H 2 -air flames.Zheng et al. [39] used freely propagating planar flames which has considerably larger optical thickness than the expanding spherical flames.Consequently, the predicted radiation reabsorption effect in [39] is much higher than the one in spherically propagating flames.Although these studies provide valuable insight on the importance of radiation in ammonia blends, they are not able to predict the radiation effect in LFS measured in SPF experiments.Further, the study of radiation in these flames is important to understand its impacts on emissions formation.Ilbas [42] denoted how radiation effects can decrease NO from 10 0 0 to 20 0 ppm in H 2 /CH 4 flames.Daguse et al. [43] found that NO mole fractions were underestimated by ∼25% when radiation effects were not considered in H 2 /O 2 /N 2 diffusive flames.Therefore, it is essential to acknowledge the effect of the radiation on ammonia-based flames, not only to understand flame phenomena but also to accurately predict pollutant emissions when using this chemical.
To the best of the authors' knowledge, the radiation-induced uncertainty in spherically propagating NH 3 -air, NH 3 /CH 4 -air, and NH 3 /H 2 -air flames has not been studied yet.Therefore, the aim of this study is to quantify the effects of radiation on spherically propagating NH 3 -air, NH 3 /CH 4 -air, and NH 3 /H 2 -air flames at normal temperatures and pressures and different equivalent ratios and to provide quantitative assessment of the importance of radiation uncertainties and to investigate the possible approach to correct the measured LFS in SPF experiments.
This paper considers both 1D planar and 1D spherically propagating premixed flames.Two models, the adiabatic (ADI) model and the optical thin model (OTM), are used to analyze the effects of radiation.Specifically, planar flames are used to compare the ADI and OTM models for different mechanisms developed based on SPF, a jet-stirred reactor, and a tubular flow reactor, in order to assess the effects of radiation on these different mechanisms.Using the spherical flame, we explain how radiation affects the determination of laminar flame speed and assess for which mixtures radiation-induced uncertainty is significant.Finally, we demonstrate how the radiation effect can be corrected in SPF measurements.It should be noted that the radiation reabsorption effect is not investigated in this paper; however, we conducted simula-tions for spherically propagating NH 3 -air, and NH 3 /H 2 -air flames using the SNB-CK model [ 30 , 40 ] and considering the radiation reabsorption of H 2 O.The discrepancy between results from OTM and SNB-CK was found to be less than 2%.

Numerical methods
Both 1D steady planar and positively-stretched unsteady spherically propagating flame configurations are considered in this study.The PREMIX code [38] was used to simulate the planar steady flame and to get the flame structure and unstretched LFS.Thermal diffusion and multicomponent molecular transport models were included in all the simulations.To control gradient and curvature, the adaptive mesh parameters GRAD and CURVE were set to 0.01 in all simulations to obtain well resolved flame structures.
The in-house code ASURF [ 27 , 44 , 45 ] was used to simulate SPF [ 46 , 47 ].The finite volume method was used in ASURF to solve the conservation equations for compressible, multicomponent, reactive flows, and the spherical coordination system was used in the formulations.The CHEMKIN package [48] which calculates the transport properties, thermodynamic properties and reaction rates was incorporated into ASURF.ASURF has been successfully used in previous studies to investigate the radiation effect [ 30-32 , 49 ] on SPF and alternative fuels [ 46 , 50 , 51 ].The readers are referred to Refs.[ 44 , 52 ] for details on numerical schemes used in ASURF.To accurately resolve the spherical flame front, the dynamic adaptive mesh was used in the code.The finest mesh size of 16 μm and the smallest time step of 12 ns have been used in all the simulations.Numerical convergence of the simulations has been ensured by further decreasing the time step and mesh size and is provided as a supplementary material.To diminish the confinement effect [ 27 , 47 ], a large chamber radius of R w = 50 cm was used in all simulations.
In SPF, the unstretched laminar flame speed, S b,0 , and the Markstein length, L b , both relative to the burned gas, are obtained from extrapolations using linear model, i.
recorded, as it is difficult to measure the flow speed of burned gas in experiments [ 53 , 54 ].Consequently, the flame propagation speed is usually considered as the laminar flame speed relative to burned gas (i.e., S b ≈S ), and the accuracy of laminar flame speed measurement depends on the magnitude of the burned gas speed, i.e., | u b |.
On the other hand, different factors affect the accuracy of LFS measurements in SPF as discussed in [18] .In this study, the authors focused on the influence of radiation, thereby other factors such as buoyancy and flame instability were not considered.To avoid the ignition effect in unsteady simulations, the flame is initiated using the extracted output temperature and mole fraction profiles for 1D planar premixed flames predicted by CHEMKIN-PREMIX.
The radiation effect was considered in simulations for both steady planar flames and SPF.The original PREMIX code was modified, and the optical thin model (OTM) was incorporated to take into account of the radiation effect.To validate this modified PREMIX code, the results obtained via PREMIX in Chemkin-Pro were compared with those calculated by Shindo and Nakamura [36] with the similar reaction mechanism for NH 3 -air flames at T u = 298 K and P = 1 atm for 0.7 ≤φ≤1.4.
To include the radiation effect, the Planck-mean (PMAC) absorption coefficients were obtained from Hitran database [55] for NH 3 , H 2 O, NO, N 2 O, CH 4 , CO, and CO 2 .PMACs were used as a polynomial function of temperature to be compatible with the CHEMKIN thermodynamic format that is also incorporated in ASURF [ 27 , 40 , 56 ].
The detailed kinetics mechanisms were selected and used in all simulations of the steady planar flame and SPF.The mechanisms of Gotama et al. [8] , Nakamura et al. [11] , and Stagni et al. [57] were used to simulate the flame propagation in NH 3 -air mixture.For simplicity, these mechanisms are named Gotama, Nakamura and Stagni in the following section.Gotama mechanism, which includes 32 species and 165 reactions, has been developed based on SPF measurements.Stagni mechanism, which includes 31 species and 203 reactions, was developed based on measurements performed using jet-stirred reactor and a tubular flow reactor.Finally, the Nakamura mechanism, which includes 38 species and 232 reactions, was developed based on data obtained from a micro flow reactor.The rationale of using these different mechanisms was to study the radiation effect in NH 3 -air mixtures by comparing mechanisms that exhibit significant discrepancies in the measured LFS.
The concentration of ammonia in binary fuels NH 3 /CH 4 and NH 3 /H 2 is expressed in terms of ammonia heat fraction in the binary fuel [9] ; where X and LHV denote the mole fraction and lower heating value, and α is the second fuel used with ammonia, i.e., CH 4 or The mechanism developed by Okafor et al. [9] was used for NH 3 /CH 4 -air mixtures.In this section the radiation effect for NH 3 /CH 4 -air mixtures at T u = 298 K and p = 1 atm and different equivalence ratios was studied.Similar to [9] , three different E NH3 of 0.1, 0.2, and 0.3 are considered in this study.
Finally, for NH 3 /H 2 -air mixtures, the mechanism of Gotama et al. [8] was used.Here, we study the radiation effect for NH 3 /H 2air mixtures at T u = 298 K and p = 1 atm for 0.8 ≤ φ ≤1.8, when E NH3 = 0.89 or equivalently the H 2 mole fraction in binary fuel, X H2 , equals 0.4.
It should be noted that we also used the Okafor mechanism [9] to study the radiation effect for the NH 3 -air mixture.However, for rich NH 3 -air mixture, the simulation results after including the radiation effect were not consistent with the ones from other mechanisms.Since the Gotama Mechanism [8] was developed based on the optimization of the Okafor Mechanism, and since it is more accurate than the Okafor Mechanism, the results obtained from the latter are not presented here.

NH 3 -air flames
The laminar flame speed measurements of NH 3 -air mixtures in the literature at normal temperature and pressure [ 13-17 , 58 , 59 ] (see Table 1 ) are plotted in Fig. 1 .Lower discrepancy is observed for stoichiometric mixtures, whilst greater scattering is observed for off-stoichiometric conditions.Even for stoichiometric mixtures, the scattering reaches 15%.It is interesting to note that the discrepancy at non-stoichiometric condition, i.e., φ= 0.9 and 1.2, reaches 30%.This huge discrepancy in measured LFS directly influences the accuracy of the kinetic mechanisms of interest.
As mentioned earlier, the buoyancy and radiation effects are significantly important for NH 3 -air as, S u,0, is less than 10 cm/s.The importance of buoyancy effect in SPF for mixtures with low LFS has already been discussed in [61] .The importance of the buoyancy effect can also be explained by observing Fig. 1 , and comparing the results obtained by Ronney [13] , in which the SPF experi- ments were done in micro-gravity condition.The reported LFS results by Ronney were considerably higher than the ones from other researchers with the exception of work by Mei et al. [17] which was not performed under micro-gravity conditions.
To isolate the radiation effect in this study we needed to choose the proper extrapolation method and flame radius ranges, which is discussed here.There are mainly three different extrapolation methods used in SPF to extract unstretched laminar flame speed [28] : As shown by Chen [62] and Wu et al. [28] , depending on the Markstein length ( L b ), it is expected that either LM, NM1, or NM2 would be more accurate to extract unstretched laminar flame speed, S u,0 .It was suggested in [62] , to use NM2 for mixtures with negative L b and NM1 for mixtures with large positive L b .In this study, we compared the Markstein length for lean, stoichiometric, and rich mixtures to choose the proper extrapolation method.It was found that the unstretched laminar flame speed is highly sensitive to the extrapolation method and range for NH 3 -air mixture.Figure 2 shows the normalized laminar flame speed for lean, stoichiometric and rich NH 3 -air mixture as a function of the extrapolation range when 1 cm < R f < 2 cm (i.e., R f,L = 1 cm) and 2 cm < R f < 3 cm (i.e., R f,L = 2 cm).The laminar flame speeds determined either by NM1 or NM2 were normalized by LM.It was found that for lean mixture ( Fig. 2 a) when radiation is included the Markstein length is negative, and for rich mixture ( Fig. 2 c), the Markstein length is more than 3. Consequently, if we choose R f,L = 1 cm for the extrapolation range, it had been logical to use NM2 for  [13] Normal temperature * * 1 0.85-1.25 Cylindrical chamber-constant pressure method 6.78 d i = 25 cm, h = 25 cm micro-gravity condition Takizawa, 2008, [16] Normal temperature * * 1.05 0.9-1.2Spherical chamber-constant pressure method 6.6 d i = 18 cm Takizawa, 2008, [16] Normal temperature * * 1.05 0.9-1.lean mixtures and NM1 for rich mixtures.However, we intended to isolate the radiation effect in this study and avoid using different extrapolation methods for different equivalence ratios.It was found that by increasing the lower range of extrapolation, i.e., R f,L , the discrepancy between LM, NM1, and NM2 would diminish.As shown in Fig. 2 , the discrepancy between LM and NM2 is less than 1% and for rich mixture and that between LM and NM1 is within 2% for lean mixture.As a result, by choosing 2 cm < R f < 3 cm we were able to acquire similar accuracy from LM, NM1 and NM2 and we were able to only use linear model to extract unstretched laminar flame speed.It is noted that due to the confinement effect and the amplification of radiation effect for R f,L > 2 cm, it is not a vi-able option to increase the extrapolation range beyond 2 cm < R f < 3 cm.
To further justify the flame radius ranges to do the extrapolation, Fig. 3 shows the flame propagation speed with respect to the burned gas, S b , as a function of stretch rate, K , for lean, stoichiometric, and rich NH 3 -air mixtures at T u = 298 K and P = 1 atm.The dashed and solid lines in the figure show the linear extrapolation to zero stretch rate (based on LM), when 1 cm < R f < 2 cm and 2 cm < R f < 3 cm, respectively.The squares and circles represent the ADI simulation, and the diamonds and triangles represent the radiation included simulation using the OTM model.When φ= 0.8 ( Fig. 3  3) flames at T u = 298 K and P = 1 atm.The symbols are data for spherical flames; the dashed and solid lines stand for linear extrapolation according to LM with 1 cm < R f < 2 cm and 2 < R f < 3 cm, respectively.The discrepancy between unstretched laminar flame speed with respect to burned gas, S b, 0 , between the extrapolated data for 1 cm < R f < 2 cm and 2 cm < R f < 3 cm is shown.Gotama mechanism is used in the simulations.
1 cm < R f < 2 cm and 2 cm < R f < 3 cm, and the range influence of the extrapolation on S b, 0 is less than 3%.Referring to Fig. 3 b, the initiation effect of flame radius on extrapolation method becomes considerable for stoichiometric mixtures when 1 cm < R f < 2 cm; however, by increasing the extrapolation range to 2 cm < R f < 3 cm, S b would change linearly with K , similar to what is shown in Fig. 2 b.
It is also noted that when φ= 1.0, the deviation between S b, 0 defined by 1 cm < R f < 2 cm and 2 cm < R f < 3 cm reaches to 5%.Finally, for rich NH 3 -air mixtures, e.g., φ= 1.3 for 1 cm < R f < 2 cm, the extrapolation effect is significant, and it is necessary to use 2 cm < R f < 3 cm for linear extrapolation.The discrepancy between the S b, 0 based on 1 cm < R f < 2 cm and 2 cm < R f < 3 cm reaches 23% and 46% for ADI and OTM, respectively.The results presented in Figs. 2 and 3 , indicate that when using 1 cm < R f < 2 cm for stoichiometric and rich mixtures, the computation of S b, 0 led to under-prediction and inaccurate determination of the radiation effect.Based on the results obtained and to avoid initiation effect of flame radius on extrapolation method for radiation induced uncertainty investigations, LM for the flame radius ranging from 2 to 3 cm was used in all the simulations.Since the negative burned gas velocity increases with the flame radius [31] , it is anticipated that the radiation-induced uncertainty would increase with the flame radius.However, the underprediction of S b, 0 in the current study when 1 cm < R f < 2 cm is due to the exceptionally low laminar flame speed of NH 3 -air mixtures.Since the PREMIX results have been used in the current study to initiate the SPF, it takes time for the propagating spherical flame to reach the quasi-steady condition and the initiation effect to become negligible.Similar effects are also expected from SPF experiments for NH 3 -air mixture with low LFS.However, unlike the current simulations, the inaccuracy of the extrapolation from low flame radii in experiment is expected to originate from the high ignition energy that is required for NH 3 -air flame to initiate.Further investigation is needed to choose the proper extrapolation method and flame radii ranges for ammonia blends in SPF.
The performance of different mechanisms to predict, S u, 0 , using steady planar flames (PREMIX code), with ADI and OTM models were studied in Fig. 4 a.The solid lines represent the ADI calculations, and the dashed lines show the OTM results.While the Gotama mechanism predicts larger S u, 0 when φ ≤1.1, Stagni mechanism predicts larger S u, 0 for φ ≥1.2.The maximum discrepancy of the predicted S u, 0 based on Nakamura, Stagni and Gotama mechanisms for φ = 0.7, 1 and 1.5 are 15%, 10% and 16%, respectively.
The large deviation between the predicted S u, 0 by different mechanisms is related to the huge uncertainty in LFS measurement and different experimental methods that have been used as is shown in Fig. 1 .The relative LFS, S u,0 °TM /, S u, 0 ADI , as a function of equivalence ratio for each mechanism is shown in Fig. 4 b.It is noteworthy to see that the change of relative LFS based on Nakamura mechanism is the same as the one calculated earlier by Nakamura and Shindo [36] .Although the same PMAC has been used in all the simulations, the predicted relative LFS based on different mecha- nisms scatter significantly for lean and rich mixtures.For φ = 0.7, the relative LFS is less than 75% based on all mechanisms and it reaches 67% based on Stagni mechanism.Meanwhile, the relative LFS based on Stagni and Nakamura mechanism do not exceed 10% for rich mixtures but reaches up to 21% for φ = 1.5, based on Gotama mechanism.
Apart from the differences in reaction coefficients that have been used in these different mechanisms, the importance of the radiation effects in the experimental methods to develop the former has also direct effects in the scattering between the relative laminar flame speeds.Since the focus of this study is to quantify the radiation-induced uncertainty in LFS determination using SPF measurements, and Gotama mechanism is the one obtained based on SPF experiments, we have used the Gotama mechanism to study the radiation effect in SPF for NH 3 -air mixtures.
Figure 5 a compares the S u, 0 calculated using ADI and OTM as a function of equivalence ratio.As anticipated, the radiation inclusion reduces the S u, 0 significantly.The mechanism of LFS reduction in SPF by radiation effects will be discussed further in Fig. 6 .To compare the importance of the radiation in steady planar flame and SPF, Fig. 5 b shows the relative LFS for planar steady flames, S u, 0 °TM / S u, 0 ADI (PREMIX) , SPF, S u, 0 °TM / S u, 0 ADI (SPF), and the relative laminar flame speed including the radiation effect based on SPF and planar steady flames, S u, 0 SPF / S u, 0 PREMIX (OTM) .Comparing S u, 0 °TM / S u, 0 ADI (PREMIX) and S u, 0 °TM / S u, 0 ADI (SPF) , the results show how the radiation-induced uncertainty increases in the studied spherically propagating flames.The black circles, which represent S u, 0 SPF / S u, 0 PREMIX (OTM) , show that the radiation effect in SPF is around 15% greater than the one for planar steady flames, both including the radiation effect.
To further investigate the sources of radiation-induced uncertainties in SPF, the evolution of flow speed and temperature in a stoichiometric NH 3 -air spherical flame were assessed, Fig. 6 .A comparison between ADI and OTM shows the negative burned gas velocity after considering radiation heat loss.As was discussed earlier, conventionally the burned gas velocity is assumed to be zero, i.e., u b = 0; while this assumption is true for adiabatic condition (solid lines in Fig. 6 a), when the radiation is considered, inward flow in burned gas leads to u b < 0. Although this was already reported in previous works [34] , the effect of negative burned gas velocity is much higher for NH 3 -air spherical flames compared to conventional hydrocarbons and hydrogen blends in air.The importance of this negative burned gas velocity in NH 3 -air is due to the low reaction rate of NH 3 -air compared to CH 4 -air and H 2 -air.For H 2 -air with LFS ∼ 200 cm/s at normal temperature and pressure, the same value of negative burned gas velocity induces much less uncertainty compared to NH 3 -air with LFS as small as 5 cm/s.One way to avoid the uncertainty related to negative burned gas velocity is to use direct flow and flame front speed measurements with Particle Image Velocimetry (PIV) dur- ing experiments [53] .Although this method has been used for hydrocarbon-air blends [63] and H 2 -air [64] , direct measurements have not been used for spherical NH 3 -air flames.Figure 6 b shows that the peak flame temperature is reduced after considering radiative loss.Due to radiation, the peak flame temperature constantly reduces in time and decreases by 250 K at t = 90 ms.Due to radiation-induced reductions in the flame temperature, the overall reaction rate decreases and so does the flame propagation speed.
The flow velocity and temperature evolution in Fig. 6 also confirm that the radiation effect magnifies by flame propagation as negative burned gas velocity increases and the overall reaction rate decreases.
To differentiate between the radiation-induced flow and thermal effects that were observed in Fig. 6 , Fig. 7 (a & c) compares the stretched flame speeds relative to the burned gas by ADI and OTM under lean and rich conditions, i.e., φ = 0.8 and 1.3.While line 1 and 2 show dR f /dt with and without radiation, line 3 shows the accurate S b ( radiati v e ) = dR f dt − u b .As a result, the difference between line 1 and line 3 is caused by radiation-induced thermal effect and the difference between line 2 and line 3 is caused by radiation-induced thermal effect.It was already shown in Fig. 6 a, as flame propagates, that the magnitude of inward burned gas velocity increases and so does the difference between line 2 and line 3.This indicates that flow effects increase with the flame radius.As was discussed in [34] , the inward flow is induced by radiation cooling due to mass conservation inside the spherical flame.Radiation cooling induces negative flow speed by decreasing the burned gas temperature and increasing its density.Comparing Line 1 and 3 shows that the radiation-induced thermal effect is less sensitive to flame size.To further investigate the effect of radiation-induced flow and thermal effect on unstretched laminar flame speed determination, Fig. 7 (b & d) plot S b, 0 with flame radius ranges for φ = 0.8 and 1.3.flame radius ranges, R f,L , in Fig. 7 (b & d for which U b is assumed to be zero, diverges from line 3, for which the radiation-induced flow effect is considered.However for φ = 1.3 (see Fig. 7 d), line 3 does not start to decrease at the various extrapolation ranges before R f,L = 3 cm.This can be justified with the results obtained in Fig. 3 c and is originated from two different factors; firstly, as was shown in Fig. 3 c, LM, that was used to determine S b, 0 is not accurate for rich NH 3 -air mixture when 1 cm < R f < 2 cm and alternative extrapolation method may be more accurate [28] ; and secondly, this can be attributed to the fact that when φ = 1.3, the spherical flame does not reach quasi-steady propagation before R f = 2 cm and is still affected by initiation effect of flame radius on extrapolation method when 1 cm < R f < 2 cm.It is noted that in this study the ignition effect [18] is avoided by using the temperature profile obtained from PREMIX code to initiate the unsteady simulation.Further studies are needed to investigate the ignition effect on spherical flame propagation and to determine the appropriate extrapolation range that accounts for this effect.Finally, com paring Fig. 7 c and Fig. 7 d shows that the radiation-induced flow and thermal effect have similar influence for both lean and rich mixtures when R f,L = 2 cm.Meanwhile, the radiation-induced thermal effect responsible for around 15% heat-loss, i.e., S b, 0 reduction, and the radiation-induced flow causes further 9% reduction of S b,0 .

NH 3 /CH 4 -air flames
Starting from a planar steady solution, the solid lines in Fig. 8 show the relative LFS, S u,0 °TM / S u, 0 ADI , as a function of equivalence ratio for different E NH3 , calculated by PREMIX code.Based on Fig. 8 , the calculated S u,0 °TM / S u, 0 ADI is always above 0.98 and decreases slightly by increasing the ammonia content.The dashed lines denote the S u,0 °TM / S u, 0 ADI based on SPF simulations.To keep the consistency with the procedures used for NH 3 -air spherical flames, LM has been used to determine S u, 0 with the extrapolation range of 2 cm < R f < 3 cm.It is observed that the radiation-induced uncertainty has considerably increased for spherical flames compared to steady planar flames with the same E NH3 .Unlike steady planar flames, by increasing the ammonia content the radiation-induced uncertainty increases significantly for the same equivalence ratio; meanwhile for rich NH 3 /CH 4 -air spherical flames, S u,0 °TM / S u, 0 ADI is 0.96 for E NH3 = 0.1, until it reaches 0.92 for E NH3 = 0.3.
For the spherical flames, the reduction in S u,0 °TM / S u, 0 ADI produced by increasing E NH3 , Fig. 8 , is related to the reduction of reaction rate of the mixture.cussed for NH 3 -air mixtures in the previous section.Figure 9 b shows S u, 0 SPF / S u, 0 PREMIX (OTM) for E NH3 = 0.1, 0.2 and 0.3.It is interesting to note that S u, 0 SPF / S u, 0 PREMIX (OTM) is relatively constant regardless of the equivalence ratio and decreases slightly by increasing E NH3 .This is in consistent with what was observed for S u, 0 SPF / S u, 0 PREMIX (OTM) behavior for NH 3 -air mixtures in Fig. 5 b at different equivalence ratios.This also shows that the relative relation between LFS defined by SPF and PREMIX when including radiation effect is relatively independent of equivalence ratio.

NH 3 /H 2 -air flames
Figure 10 a shows the LFS employing spherical flames using ADI and OTM for different equivalence ratios initially at T u = 298 K and P = 1 atm.Unlike NH 3 -air, radiation heat loss only has minor effects on LFS.This is related to the higher LFS of NH 3 /H 2 -air compared to NH 3 -air.To quantify the radiation induced uncertainty in SPF and compare it with steady planar calculations, Fig. 10 b shows S u,0 °TM / S u, 0 ADI for planar steady flames (red line with squares) and SPF (blue line with triangle).S u,0 °TM / S u, 0 ADI for steady planar flame is identical to what was found in [39] .Similar to the radiation effect for NH 3 -air and of NH 3 /CH 4 -air discussed in previous sections, the radiation induced uncertainty increases in spherically propagating flames and it reaches a maximum 6% for NH 3 /H 2 -air when φ = 1.8.Remembering that radiation reabsorption can enhance the LFS for this mixture in planar steady flames [39] , it can be expected that using the SNB model to include radiation reabsorption can compensate the radiation heat loss in spherical NH 3 /H 2air flames.However, Zheng et al. [39] used freely propagating planar flames which has considerably larger optical thickness than the expanding spherical flames.Consequently, the predicted radiation reabsorption effect in [39] is much higher than the one in spherically propagating flames.Further studies on the effect of radiation reabsorption in SPF to accurately quantify the uncertainty requires a separate study.

Radiation-corrected flame speed
It was observed that the radiation induced uncertainty in spherical ammonia-blend flames is considerable and needed to be cor- rected.Yu et al. [34] studied the radiation-induced uncertainty in different mixtures including hydrocarbons and H 2 /CO blends in air using SPF simulations and the SNB model, and introduced a single correlation to correct the radiation induced uncertainty in experiments for different fuel-air mixtures with a variety of equivalence ratios, initial temperatures and pressures.Defining the relative reduction in unstretched laminar flame speed caused by radiation, R, as where S b, 0 is the unstretched laminar flame speed with respect to burned gas, with the unstretched laminar flame speed with respect to the unburned gas being S u, 0 , which is commonly approximated as S u, 0 ≈ ( ρ b / ρ u ) eq S b,0 .In this equation, ( ρ b / ρ u ) eq denotes the density ratio in equilibrium conditions.This simple approximation, also used in this study, avoids the complexity of defining the accurate density ratio for different conditions that were considered in [ 46 , 51 ].Using ( ρ b / ρ u ) eq Yu et al. [34] defined the correlation at normal temperatures and pressures;   2) , the accuracy of the correlation for NH 3 /CH 4 -air and NH 3 /H 2 -air is confirmed; it is observed that "%Error" does not exceed 4% for these mixtures.It should be noted that Yu et al. [34] determined S u, 0 radiative considering the radiation reabsorption for CO 2 , CH 4 and H 2 O.However, here we only considered the radiation heat loss using OTM, and radiation reabsorption is not considered.It is expected that considering the radiation reabsorption in simulations may improve the accuracy of the correlation even further for NH 3 /CH 4 -air and NH 3 /H 2 -air.However, looking at Fig. 11 shows that the correlation is unable to predict R accurately for NH 3 -air and "%Error" increases by reducing S u, 0 ADI as it reaches 15% for S u,0 ADI = 5 cm/s.Since the correlation works well for both NH 3 /CH 4 -air and NH 3 /H 2 -air, it can be stated that the main conclusion made by Yu et al. [34] around the relation between R and LFS, which shows nearly independency between the fuel type and equivalence ratio, is valid.It is important to notice that the mixtures used in [34] to adopt the correlation have laminar flame speeds above 9 cm/s and the error in R predicted by Eq. (3) for Takizawa et al. [16] , and (b) Hayakawa et al. [58] and Mei et al. [17] .. The solid lines denote radiation included LFS, S u, 0 EXP , and dashed lines denote the radiation corrected ones, S u, 0 RC , using Eq. ( 5) .
NH 3 -air mixtures can be associated to the fact that LFS for this mixture is always less than 8 cm/s.To further extend the application of Eq. ( 3) , the LFS calculated with and without radiation heat-loss for NH 3 -air using Okafor, Gotama, Nakamura and Stagni mechanism have been used to develop a correlation specifically for NH 3 -air with S u,0 < 9 cm/s; For S u, 0 < 9 cm / s : S ADI u, 0 − S radiati v e u, 0 The LFS determined by Okafor mechanism for NH 3 -air spherical flames for φ = 1.2 and 1.3 are not used to develop Eq. ( 4) .This is because the Okafor mechanism underpredicts S u, 0 radiative by more than 35% and 65% for φ = 1.2 and 1.3 when compared to other mechanisms.Figure 12 a compares the relative laminar flame speed reduction predicted by Eq. ( 4) and the accurate definition of Eq. ( 2) .It is observed that Eq. ( 4) is able to predict R accurately for spherical NH 3 -air flames initially at T u = 298 K and P = 1 atm and different equivalence ratios.To further calculate the uncertainty of using Eq. ( 4) to predict S u, 0 , Fig. 12 b shows the correlation error as a function of normalized flame speed.It can be observed that the scattering between the accurate S u, 0 and the one predicted by Eq. ( 4) is less than 5% for all the mechanisms disregarding equivalence ratio.Remembering radiation induced uncertainty for lean and rich spherical NH 3 -air flames reaches up to 25% ( Fig. 5 b), the updated correlation can significantly improve the accuracy of LFS measurements in SPF for NH 3 -air flames.
The laminar flame speed measured in SPF experiments, S u, 0 EXP , is close to the radiative one, i.e., S u, 0 EXP ≈ S u,0 radiative and the radiation corrected LFS is equal to S u,0 ADI , S u, 0 RC = S u,0 ADI .Combining Eqs. ( 3) and ( 4) and using the Newton iteration method, once the laminar flame speed is measured by SPF experiments, the radiation corrected LFS can be estimated as; S u, 0 RC can be further used in experiments instead of S u, 0 EXP , to develop and optimize the reaction mechanisms using spherically propagating flame experiments.Figure 13 plots the LFS measured using SPF experiments reported in [ 13 , 16 , 17 , 58 ].The solid lines denote the measured LFS reported in the articles and the dashed lines are the radiation-corrected LFS determined in this study using Eq.(5) .It is observed that the corrected laminar flame speeds increased significantly compared to the original LFS and these radiation-corrected LFS can furtherly be used to develop and optimize the detailed mechanisms for ammonia mixtures.

Conclusions
Numerical simulations with detailed chemistry and transport were conducted for planar and spherically propagating NH 3 -air, NH 3 /CH 4 -air and NH 3 /H 2 -air flames with different equivalence ratios at normal temperature and pressure.The radiation effect was included in the simulations using the optical thin model, and the Planck-mean (PMAC) absorption coefficients were obtained from the Hitran database.The main findings were as follows: 1.The uncertainty in SPF was attributed to the radiation-induced flow and thermal effects.While the radiation-induced flow effect increases with flame radius, the thermal effect was relatively constant.The deviation between the LFS defined by planar and spherically propagating flames ( S u,0 SPF / S u,0 PREMIX ) was relatively constant disregard to the blend richness for all the mixtures.For NH 3 -air flames it was around 15%.For NH 3 /CH 4air flames the deviation increased with ammonia content and reached up to 10% when E NH3 = 0.3.Finally, for NH 3 /H 2 -air flames with E NH3 = 0.89, the deviation decreased to around 4%. 2. For stoichiometric and rich NH 3 -air flames, the initiation effect of flame radius on extrapolation method was considerable for 1 cm < R f < 2 cm; to avoid employing different extrapolation methods for different mixtures and conditions, the flame radii to do the extrapolation was set to 2 cm < R f < 3 cm.It was also shown that even the nonlinear model is unable to accurately predict the unstretched laminar flame speed for rich NH 3 -air flames when 1 cm < R f < 2 cm.Although a qualitative match was found among the LFS using different mechanisms, they vary quantitatively; this was attributed to the fact that the radiation-induced uncertainty was not accounted for, changing on the basis of the experimental method.3.For NH 3 /CH 4 -air flames, when ammonia content was increased, the radiation-induced uncertainty also increased, phenomenon that can be attributed to the longer residual time of the flame in the combustion chamber.NH 3 /H 2 -air flames were less affected by the radiation-induced uncertainty than other mixtures studied in this work.4. It was shown that the correlation from [34] works well for NH 3 /CH 4 -air and NH 3 /H 2 -air flames, where the LFS is above 9 cm/s.However, this correlation is unable to predict the radiation-induced reduction for NH 3 -air flames where LFS is less than 9 cm/s, and therefore a new correlation is proposed for NH 3 -air flames.The newly developed correlation was further used to determine the radiation-corrected LFS in NH 3 -air flames measured by SPF experiments and reported in [ 13 , 16 , 17 , 58 ].The updated correlation, Eq. ( 5) , can be used for different ranges of flame speeds regardless of the type of mixture.
It should be emphasised that Eq. ( 4) was only validated for NH 3 -air, NH 3 /CH 4 -air, and NH 3 /H 2 -air flames.Further verification needs to be carried out to expand its application to other mixtures with low laminar flame speed, i.e., S u,0 < 9 cm/s.Hydrofluorocarbons with low LFS should be considered in future studies; however, based on [34] , it is anticipated that changing the fuel type will not considerably affect the accuracy of Eq. (4) .To further increase the accuracy of predicting radiation-induced uncertainty in ammonia blends in SPF experiments, future work should include the consideration of radiation reabsorption.

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.
e., S b = S b, 0 − L b K.The reason behind choosing the linear model over nonlinear model and the extrapolation range used in this paper is discussed in the next section.For a spherically propagating flame, stretch rate, K , is equal to 2 R f × dR f dt and S b = dR f dt − u b where u b is the flow speed of burned gas close to the reaction front.Usually only the flame front history

Fig. 3 .
Fig. 3. Change of the flame speed relative to burned gas, S b , with stretch rate, K , for spherical NH 3 -air ( φ= 0.8, 1, and 1.3) flames at T u = 298 K and P = 1 atm.The symbols

Fig. 4 .Fig. 5 .
Fig. 4. (a) Computed adiabatic (solid lines) and radiative (dashed lines) flame speeds for freely propagating NH 3 -air flames, and (b) the relative laminar flame speed with and without radiation heat loss.T u = 298 K and P = 1 atm.The Nakamura et al. [11] , Stagni et al.[57] and Gotama et al.[8] mechanisms have been used in the calculations.The PREMIX code[38] has been used to calculate the laminar flame speed.

Figure 9 aFig. 8 .
Fig. 8. Relative laminar flame speed (OTM to ADI) for freely propagating flames (solid lines) and SPF (dashed lines) as a function of equivalence ratio for NH 3 /CH 4air at T u = 298 K and P = 1 atm with different E NH3 .The red square, blue triangle, and black circle denote E NH3 = 0.1, 0.2, and 0.3, respectively.The mechanism developed by Okafor et al. [9] was used.(For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

S 0
S ADIu, 0 − S radiati v e u, 0 = 0 .82 S ADI u, in the above equation is equal to 1 cm/s.

Figure 11 a
Figure 11 a shows R versus the adiabatic laminar flame speed, S u,0 ADI .The solid line shows the R prediction based on Eq. (3) and symbols denote the accurate R for NH 3 -air, NH 3 /CH 4 -air, and NH 3 /H 2 -air initially at T u = 298 K and P = 1 atm.It is observed that Eq. (3) predicts the trend of R reduction with S u, 0 ADI accurately.Furthermore, looking at Fig.11b that plots the "%Error" of Eq. (3) compared to accurate R values directly computed using Eq.(2) , the accuracy of the correlation for NH 3 /CH 4 -air and NH 3 /H 2 -air is confirmed; it is observed that "%Error" does not exceed 4% for these mixtures.It should be noted that Yu et al.[34] determined S u, 0 radiative considering the radiation reabsorption for CO 2 , CH 4 and H 2 O.However, here we only considered the radiation heat loss using OTM, and radiation reabsorption is not considered.It is expected that considering the radiation reabsorption in simulations may improve the accuracy of the correlation even further for NH 3 /CH 4 -air and NH 3 /H 2 -air.However, looking at Fig.11shows that the correlation is unable to predict R accurately for NH 3 -air and "%Error" increases by reducing S u, 0 ADI as it reaches 15% for S u,0 ADI = 5 cm/s.Since the correlation works well for both NH 3 /CH 4 -air and NH 3 /H 2 -air, it can be stated that the main conclusion made by Yu et al.[34] around the relation between R and LFS, which shows nearly independency between the fuel type and equivalence ratio, is valid.It is important to notice that the mixtures used in[34] to adopt the correlation have laminar flame speeds above 9 cm/s and the error in R predicted by Eq. (3) for

Fig. 11 .Fig. 12 .Fig. 13 .
Fig. 11.Relative laminar flame speed reduction, R , (a) and the correlation error (b) as a function of normalized laminar flame speed, S u, 0 ,ADI / S 0 (where S 0 = 1 cm/s), for NH 3air, NH 3 /CH 4 -air, and NH 3 /H 2 -air.Okafor and Gotama mechanisms have been used for NH 3 /CH 4 -air, and NH 3 /H 2 -air mixtures, respectively.The mechanisms used to simulate SPF for NH 3 -air are stated in the figure.T u = 298 K and P = 1 atm.The solid line in (a) is the correlation developed in [34] .

Table 1
Previous experimental studies on LFS measurement of NH 3 -air mixtures at normal temperature and pressure.
Ronney, 1988, = 130 cmRonney, 1988, < S u,0 < 7.22 cm/s * d i and h denote the size of inner diameter and height of the chamber, respectively.* * S u,0 is the reported uncertainty of the measurements.