An experimental and kinetic modeling study of ammonia/n-heptane blends

Abstract

Ammonia is carbon free and hence is a promising renewable fuel to achieve a reduction in CO2 emissions. However, due to its relatively low reactivity, ammonia is often blended with other high reactivity fuels in practical combustors. This study aims to understand the chemical kinetics of ammonia blended with n-heptane, which is a primary reference fuel and an important component in diesel and gasoline surrogate models. A high-pressure shock tube is used to measure the ignition delay times of ammonia/n-heptane blends with different blending ratios, for stoichiometric mixtures at 10 atm pressure in the temperature range 1000–1400 K. The experimental results show that fuel reactivity decreases with increasing ammonia concentration. The oxygen concentration also shows a large effect on the reactivity of ammonia/n-heptane blends. A new detailed kinetic model is developed to simulate these new ignition delay times in addition to experimental data available in the literature. Overall, the current kinetic model can predict well the auto-ignition behavior and laminar burning velocities of ammonia/n-heptane blends over a wide range of experimental conditions. Flux and sensitivity analyzes show that the interaction reaction pathways between ammonia and n-heptane via H-atom abstraction from n-heptane by ṄH2 radicals are important in predicting the fuel reactivity of ammonia/n-heptane blends.

Full text

1
An experimental and kinetic modeling study of ammonia/n-heptane
1
blends
2
3
Shijun Dong1, Bowen Wang1, Zuozhou Jiang1, Yuhang Li1, Wenxue Gao1, Zhaowen Wang1, 4
Xiaobei Cheng1*, Henry J. Curran2
5
6
1School of Energy and Power Engineering, Huazhong University of Science and Technology, Wuhan, China
7
2Combustion Chemistry Centre, School of Chemistry, Ryan Institute, MaREI, NUI Galway, Ireland. 8
Abstract
9
Ammonia is carbon free and hence is a promising renewable fuel to achieve a reduction in CO2
10
emissions. However, due to its low fuel reactivity, ammonia is often blended with other high
11
reactivity fuels in practical combustors. This study aims to understand the chemical kinetics of
12
ammonia blended with n-heptane, which is a primary reference fuel and an important component
13
in diesel and gasoline surrogate models. A high-pressure shock tube is used to measure the ignition
14
delay times of ammonia/n-heptane blends with different blending ratios, for stoichiometric
15
mixtures and 10 atm pressure in the temperature range of 1000 – 1400 K. The experimental results
16
show that fuel reactivity decreases with increasing concentration of ammonia. The oxygen
17
concentration also shows a large effect on the fuel reactivity of ammonia/n-heptane blends. A new
18
detailed kinetic model is developed to simulate these new ignition delay times in addition to
19
experimental data available in the literature. Overall, the current kinetic model can predict well the
20
auto-ignition behavior and laminar burning velocities of ammonia/n-heptane blends over a wide
21
range of experimental conditions. Flux and sensitivity analyses show that the interaction reaction
22
pathways between ammonia and n-heptane via H-atom abstraction from n-heptane by ṄH2 radicals
23
are important in predicting the fuel reactivity of ammonia/n-heptane blends.
24
Keywords: Ammonia, n-heptane, kinetics modeling, shock tube, ignition delay time
25
26

2
1. Introduction
1
Ammonia is carbon free and hence does not produce carbon dioxide (CO2) during combustion.
2
Meanwhile, ammonia can be produced via renewable energy such as from wind and solar energy
3
[1]. As a hydrogen carrier, the physical and chemical properties of ammonia facilitate easier
4
storage and transportation compared to hydrogen. Therefore, ammonia is a promising renewable
5
fuel used to achieve CO2 emissions reduction and carbon neutral [2]. However, ammonia shows
6
much lower fuel reactivity compared to hydrocarbon fuels, i.e. it has a much higher octane number
7
and much lower flame speeds compared to conventional fuels. Comparisons of fuel properties for
8
ammonia and hydrogen carbon fuels are provided in Table 1. Therefore, to improve its combustion
9
performance, ammonia is often blended with high reactivity fuels such as hydrogen, natural gas
10
and diesel when burned in practical facilities. This study aims to understand the chemical kinetics
11
of ammonia blended with n-heptane, which is a primary reference fuel and an important
12
component in diesel and gasoline surrogate models.
13
Table 1: Comparisons of fuel properties for ammonia and hydrogen carbon fuels.
14
ammonia
methane
hydrogen
n
-
heptane
iso
-
octane
Lower heating value
(
MJ/kg
)
18.8[2] 50.05[2] 120.0[2] 44.6[4] 44.654[4]
Laminar burning velocity
(m/s)
-
close to stoich.
0.07[2] 0.38[2] 3.51[2] 0.37[3] 0.33[3]
Combustion limit
(volume fraction %)
15.0 ‒ 28.0[2]
5.0 ‒ 15.0[2]
4.7 ‒ 75.0[2]
1.05 ‒ 6.7[6]
0.95 ‒ 6.5[6]
Octane number
130
[2]
120
[1]
-
0
100
Adiabatic flame
temperature
(with air)
(K)
1850[1] 2223[1] 2483[1] 2294[5] 2300[4]
*LBVs measured with fuel in ‘air’ mixture, at 1 atm, initial temperature of 298 K close to stoichiometric
15
condition.
16
Over the past decade, a number of experimental and modeling studies have focused on the
17
combustion characteristics of ammonia and its blends with different fuels, and most of these are
18
carbon free or low-carbon fuels, including hydrogen, methane, methanol and dimethyl ether
19
(DME). Tian et al. [7] measured the intermediates and products formed in premixed
20
NH3/CH4/O2/Ar flames at low pressure, using tunable synchrotron vacuum ultraviolet (VUV)
21
photoionization and molecular-beam mass spectrometry. A detailed kinetic model was proposed
22
to simulate these data. Mathieu et al. [8] studied the high-temperature oxidation of ammonia in a
23
shock tube at pressures of 1.4 – 30 atm and at highly diluted conditions. Shu et al. [9] studied the
24
auto-ignition behavior of ammonia in ‘air’ at intermediate temperatures using a shock tube.
25
Subsequently, He and Shu et al. further investigated the auto-ignition behavior of
26
ammonia/hydrogen blends [10] and ammonia/methane blends [11] at lower temperatures using a
27

3
rapid compression machine (RCM). Dai et al. studied the auto-ignition behavior of ammonia,
1
ammonia/hydrogen [12], ammonia/methane [13] and ammonia/DME [14] at low to intermediate
2
temperatures using an RCM, and proposed a kinetic model based on that from Glarborg et al. [15]
3
which showed good agreement with the data. Chen et al. [16] experimentally studied the auto-
4
ignition behavior of ammonia/hydrogen blends in a shock tube at 1.2 and 10 atm at highly diluted
5
conditions. The kinetic model proposed by Glarborg et al. [15] could simulate these data well.
6
The flame speed of ammonia with different fuel blends have been a focus of previous studies
7
over the years, as the significantly lower flame speed of ammonia is the major issue which
8
restricting its application in practical facilities. Okafor et al. [17] measured the laminar burning
9
velocities (LBVs) of ammonia/CH4/air mixtures. Han and Wang et al. [18], [19] studied the LBVs
10
of ammonia and ammonia blended with different fuels, including hydrogen, carbon monoxide,
11
methane and alcohol fuels. Mei et al. [20], [21] measured the LBVs of ammonia and
12
ammonia/syngas mixtures at different oxygen conditions and at elevated pressures. In these studies,
13
a number of kinetic models have been proposed and can simulate well these LBVs.
14
Currently, the ammonia/diesel dual fuel combustion strategy has been proved to be a promising
15
strategy to reduce engine CO2 emissions [22], [23]. Feng et al. [24] measured ignition delay times
16
(IDTs) of ammonia/diesel blends using an RCM at low-temperatures in the range of 670 – 910 K
17
at both 10 and 20 atm, with energy fraction of ammonia up to 50%. As n-heptane is one of the
18
primary reference fuels and is an important component of diesel and gasoline surrogate models, it
19
is essential to understand the chemical kinetics of ammonia/n-heptane blends. Yu et al. [25] studied
20
the auto-ignition behavior of ammonia/n-heptane blends in an RCM at 10 and 15 bar in the
21
temperature range of 600 – 1000 K. However, the kinetic model proposed in their study does not
22
capture well the low-temperature chemistry of ammonia/n-heptane blends, which is mainly
23
because some important interaction reaction pathways between ammonia and n-heptane are
24
missing as they state in their paper. Moreover, Lavadera et al. [26] experimentally studied the
25
effects of ammonia addition on LBVs of n-heptane and iso-octane in ‘air’ mixtures, and a semi-
26
detailed model which only includes the high-temperature oxidation of n-heptane and NOx was
27
used to simulate these LBV data [27], [28]. To the author’s knowledge, the model predictions of
28
ammonia/n-heptane IDTs available in the literature need to be improved at lower temperatures
29
(600–1000 K). Moreover, currently there is no shock tube IDT data measured for ammonia/n-
30
heptane blends at temperatures above 1000 K. These IDT data measured from the low- to high-
31
temperature range will be needed to explore the interaction reaction pathways between ammonia
32
and n-heptane.
33

4
In this study, a high-pressure shock tube (HPST) is used to measure the IDTs of different
1
ammonia/n-heptane blends in the high temperature range (1000–1400 K) and at 10 atm. A new
2
kinetic model is developed and validated against these new IDT data in addition to experimental
3
data available in the literature.
4
2. Experimental specifications
5
2.1. Ignition delay time measurements
6
A HPST made of stainless steel was used to conduct the experiments. The facility has been
7
described in detail in previous work [29], [30] and only a brief introduction is given here. The
8
shock tube has an internal diameter of 100 mm and a total length of 12.2 m, divided into three
9
parts: an 8.0 m long driven section, a 4.0 m long driver section and a 0.2 m long middle section.
10
These sections are separated by two polyester terephthalate (PET) diaphragms in the experiments.
11
During the experiments, the driver gas pressure in the middle section is first filled to half that used
12
in the driver section. The diaphragm is burst by venting the middle section. The gas temperature
13
and pressure behind the reflected shock wave were calculated using GasEq [31] based on the
14
measured incident shock velocity and initial conditions of temperature, pressure and mixture
15
composition.
16
Table 2: Experimental conditions studied for ammonia/n-heptane in the HPST.
17
Mixture
Mole fraction
Ratios of energy
φ p (bar)
T (K)
NH3 n-heptane
N2 O2
NH3 n-heptane
1 0 0.0095 0.8865
0.1040
0 1.0
1.0 10 1000 – 1400
2 0.0264
0.0074 0.8647
0.1015
0.2 0.8
3 0.0518
0.0055 0.8437
0.0990
0.4 0.6
4 0.0980
0.0103 0.7044
0.1873
0.4 0.6
The IDTs of ammonia/n-heptane were measured for fuel/O2/N2 mixtures at 10 bar in the
18
temperature range 1000 – 1400 K. The experimental conditions studied are summarized in Table
19
2, and these conditions are consistent with the RCM experiments performed by Yu et al. [25],
20
except that nitrogen is used as the diluent gas in the current experiments whereas Yu et al. [25]
21
used argon as the diluent. As suggested in previous studies [12], [32], ammonia has a strong
22
tendency to be absorbed by the steel surface. Therefore, the inner surfaces of the mixing tank and
23
the shock tube were passivated before the mixture preparation and each shot in the experiments.
24
For the passivation process, 100 mbar pure ammonia was introduced into the mixing tank and the
25
shock tube, maintained for about 10 min and then evacuated.
26

5
The definitions of IDTs measured in the HPST are shown in Fig. 1, which are based on the
1
measured pressure trace and OH* emission at 308 nm. The pressure trace used to determine the
2
IDTs is measured by the piezoelectric pressure transducer (PCB 113B24) installed in the sidewall,
3
which is embedded 20 mm away from the endwall. OH* emission is detected using a
4
photomultiplier, with a band-pass filter of 307 ± 10 nm, mounted at the endwall. The IDT is defined
5
as the time interval between the arrival of the reflected shock wave and the onset of the ignition,
6
and the onset of ignition corresponds to the intersection of the maximum slope of the OH*
7
emission profile back to the zero baseline. As the same methods were used for mixture preparation
8
and gas temperature and temperature calculation, a 20% uncertainty is assigned to all of the IDT
9
measurements in the HPST according to previous studies [33]–[35].
10
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
2.64% NH
3
/ 0.74% n-heptane / 10.15% O
2
(Mixture 2),

=
1.0
T
c
= 1150.1 K, p
c
= 10 bar,

= 1.194 ms
Signal
time / ms
Pressure
Normalized Emission

11
Figure 1. Definition of ignition delay time measured in the shock tube.
12
The purity of ammonia is > 99% and the purity of n-heptane is > 99%. High purity oxygen (>
13
99%), nitrogen (> 99%) were used in the experiments. The new IDT data obtained in this study
14
are provided in Table S1 of the Supplementary material.
15
3. Model development
16
The current kinetic model is developed based on NUIGMech1.2, in which the NOx chemistry is
17
mostly from Glarborg et al. [15] and the interaction reaction pathways between NOx and C1 – C3
18
alkanes have been updated and well validated [36], [37]. The n-heptane sub-mechanism in
19
NUIGMech1.2 is originally taken from [38] and was constructed based on alkane rate rules [39].
20
The n-heptane sub-chemistry has been well validated previously [40], [41], and hence no further
21
updates were made to the n-heptane sub-chemistry in this study. The pyrolysis chemistry of
22
ammonia was updated based on the study of Alturaif et al. [42]. As suggested in their paper, the
23
updates of the ammonia pyrolysis chemistry significantly improve ammonia LBV predictions from
24
the Glarborg et al. [15] mechanism. Another major update of ammonia chemistry is the ṄH2 + HȮ2
25
reaction system. Stagni et al. [43] theoretically calculated the rate constant for the reaction of NH3
26

6
+ O2 ↔ ṄH2 + HȮ2. Cañas et al. [44] and Klippenstein et al. [45] theoretically studied the ṄH2 +
1
HȮ2 reaction system, and provided rate constants as well as branching ratios for all three reaction
2
pathways. The calculation results of Klippenstein et al. [45] suggest that ṄH2 + HȮ2 mainly
3
proceeds via chain termination forming NH3 + O2. This is significantly different with most of the
4
rate constants in previous studies, which suggest that this channel mainly forms H2NȮ and ȮH
5
radicals. The rate constants of ṄH2 + HȮ2 ↔ NH3 + O2 calculated in both the studies of Stagni et
6
al. [43] and Klippenstein et al. [45] are within a factor of two of one another at low temperatures
7
and are very similar, within 20% difference at high temperatures. In this study, the rate constant
8
calculated by Stagni et al. [43] are used. This update affects the prediction of low-temperature
9
chemistry of ammonia/n-heptane blends. Meanwhile, the rate constants of NH3+ȮH are increased
10
by a factor of two compared to the original very high temperature measurements by Salimian et al.
11
[46]. The most important updates in the current model are the H-atom abstraction reactions from
12
n-heptane by ṄH2. The importance of fuel + ṄH2 reactions have been discussed in a few previous
13
studies, for instance, CH4 + ṄH2 by Song et al. [47], DME + ṄH2 by Dai et al. [14] and Issayev et
14
al. [48]. The rate constants are estimated by analogy with CH4 + ṄH2 reactions measured by Song
15
et al. [47], with the activation energy decreased for 2 kcal mol–1 and 5 kcal mol–1 respectively for
16
primary and second carbon sites. These reactions are the major interaction reaction pathways
17
between the ammonia and n-heptane systems. As shown in Fig. 2, these interaction reactions
18
significantly increase the predicted fuel reactivity in the low- to intermediate-temperature regime.
19
The chemistry of how these interaction reactions affect fuel reactivity is discussed in detail in
20
Section 4.3. Other updates include the reactions between linear alkenes and ṄH2 radicals, with rate
21
constants estimated by analogy with ethylene + ṄH2 calculated by Mai et al. [49]. Some reactions
22
in the C-N interaction subsets are also updated based on new calculations. A list of all the important
23
updated reactions are provided in Table S2 of the Supplementary material.
24
0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6
0.1
1
10
100
RCM 10 bar
1st-stage IDT 10 bar
HPST 10 bar
Ignition delay time / ms
1000 K / T
1400 1200 1000 800
40%NH
3
/60%NC
7
H
16
/9.9%O
2
,


=
1.0
Temperature
(
K
)
25
Figure 2. Effects of the nC7H16 + ṄH2 reaction class on model predictions of ammonia/n-heptane
26
IDTs. Solid symbols: new HPST IDT data obtained in this study. Half-filled symbols and open
27

7
symbols represent the first-stage and second-stage RCM IDT data from Yu et al. [25]. Solid lines:
1
constant-volume simulations. Dashed lines: RCM simulations including facility effect. Short
2
dotted lines: constant-volume simulations without the nC7H16 + ṄH2 reaction class.
3
All of the simulations in this study were performed using Chemkin software [50]. The HPST
4
data are simulated assuming constant volume conditions. For the simulations of the RCM data
5
from Yu et al. [25] effective volume history profiles derived from the non-reactive pressure traces
6
were used to account for the volume change and the facility effects in the RCM (i.e. heat losses,
7
etc.). Moreover, flux and sensitivity analyses were performed using the Chemkin software to
8
understand the fuel chemistry.
9
4. Results and discussions
10
4.1. Model performance against experimental IDT data
11
Figure 3 shows the current model performance against the shock tube IDTs measured in this
12
study as well as the RCM IDTs taken by Yu et al. [25]. The blending effects of ammonia/n-heptane
13
over the low-temperature range were discussed in detail by Yu et al. In general, the ammonia
14
addition significantly slows down the fuel reactivity of ammonia/n-heptane blends in the low-
15
temperature regime, Fig. 3(a). However, at high temperatures, the experimental results show that
16
the IDTs of the ammonia/n-heptane blends slightly increase with increasing ammonia
17
concentration, and the current model can capture this trend well. This will be discussed in detail
18
in Section 4.3. With increasing oxygen concentration, the fuel reactivity of the ammonia/n-heptane
19
blends increase over the studied temperature range, Fig. 3(b). The fuel reactivity of the ammonia/n-
20
heptane blends also increases with increasing pressure and equivalence ratio in the low-
21
temperature regime.
22
0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6
0.1
1
10
100
Share by heating value
100% NC
7
H
16
80% NC
7
H
16
20% NH
3
60% NC
7
H
16
40% NH
3
Ignition delay time / ms
1000 K / T
(a)
16001400 1200 1000 800

=
1.0, p
c
=10 bar, ~ 10% O
2
Temperature
(
K
)
0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6
0.1
1
10
100
9.9% O
2
RCM
1st-stage IDT
HPST
18.37% O
2
RCM
1st-stage IDT
HPST
Ignition delay time / ms
1000 K / T
1400 1200 1000 800
40%NH
3
/60%NC
7
H
16
,

=
1.0, 10 bar
Temperature
(
K
)
(b)
23

8
1.0 1.1 1.2 1.3 1.4 1.5 1.6
10
100
40%NH
3
/60%NC
7
H
16
, ~85% dilution

= 1.0, 10 bar

= 2.0, 10 bar

= 1.0, 15 bar

= 2.0, 15 bar
Ignition delay time / ms
1000 K / T
(c)
1000 900 800 700
Temperature
(
K
)
1
Figure 3. Effects of (a) blending ratios, (b) dilution degree and (c)equivalence ratio and pressure
2
on ammonia/n-heptane IDTs. Solid symbols: new HPST IDT data obtained in this study. The half-
3
filled symbols and open symbols represent the first-stage and second-stage RCM IDT data from
4
Yu et al. [25]. Solid lines: constant-volume simulations. Dashed lines: RCM simulations including
5
facility effect. Dotted lines: RCM simulations of first-stage IDTs.
6
In the low- to intermediate temperature range, the current model slightly over-predicts the IDTs
7
at the relative high temperatures of the RCM data. This is due to the n-heptane sub-chemistry as
8
the under-predicted fuel reactivity is consistent for both pure n-heptane and ammonia/n-heptane
9
blends. Overall, the current model can capture well both the first-stage and second-stage IDTs at
10
different experimental conditions for different mixtures. The comparisons between the simulation
11
results using the current model and the previous model [25] are shown in Fig. S1 of the
12
Supplementary material. The current model predictions are improved significantly compared to
13
those of the original model in the low- to intermediate-temperature range.
14
Figure 4 shows the comparisons between the simulation results of the current model and the
15
experimental RCM IDTs of ammonia. As can be seen, the current model slightly over-predicts the
16
RCM IDTs at φ = 1.0 and 2.0, while the trend is well captured by the current model. Therefore, the
17
current model can capture well the IDTs of both pure n-heptane and ammonia, as well as their
18
blends over a wide temperature range.
19
0.82 0.84 0.86 0.88 0.90 0.92 0.94
10
100
Dai et al. 2020

= 0.5

= 1.0

= 2.0
Ignition delay time / ms
1000 K / T
1200 1175 1150 1125 1100 1075
100%NH
3
, 60 bar, 75% dilution
Temperature
(
K
)
20

9
Figure 4. Effects of equivalence ratio on ammonia IDTs. Open symbols: RCM data from Dai et
1
al. [12]. Dashed lines: RCM simulations including facility effect.
2
4.2. Model performance against experimental LBV data
3
The current model is also validated against experimental LBVs of ammonia and ammonia/n-
4
heptane blends available in the literature [26], Fig. 5. The LBVs of ammonia in ‘air’ at 298 K and
5
at 1 atm have been measured by different groups using different facilities over the years [18], [20],
6
[51], [52]. There was large discrepancy (~2 cm·s-1) between these experimental data of the fuel
7
rich conditions, Fig. 5(a). The peak value of LBVs measured at this condition is around 8 cm·s-1,
8
and the lower flame speed of ammonia compared to hydrocarbon fuels lead to large uncertainties
9
in the measurements. The simulation results of the current model match well with the experimental
10
results from Ronney et al. [51] and Mei et al. [20]. The n-heptane sub-chemistry of the current
11
model was validated previously against the LBVs measured by Sileghem et al. [53], open symbols
12
in Fig. 5(b). In a recent study, Lavadera et al. [26] corrected the measured data of Sileghem et al.
13
[53], half-filled symbols in Fig. 5(b). Lavadera et al. [26] also measured the LBVs of n-heptane
14
and ammonia/n-heptane blends, solid symbols in Fig. 5(b). As can be seen, the current model can
15
predict well the LBVs of n-heptane originally measured by Sileghem et al. [53], while the
16
simulation results are slightly slower compared to the LBVs measured by Lavadera et al. [26] and
17
the corrected results for the fuel lean conditions. For the ammonia/n-heptane blends, the LBVs of
18
blends decrease with increasing ammonia percentage. The equivalence ratios (φ) of the peak flame
19
speed for different fuel blends are around φ = 1.1. The current model slightly under-predicts the
20
LBVs at the fuel lean conditions, which is consistent with that of the pure n-heptane. The
21
simulation results without the nC7H16 + ṄH2 reaction class are also given in Fig. 5(b). It is observed
22
that this reaction class only affects the fuel-lean predicted LBVs when the mole fraction of
23
ammonia is 50%. However, the energy fraction from ammonia for this condition is only 5.9%,
24
which indicates that more LBV data with higher mole fractions of ammonia are needed for model
25
validation. Overall, the current model predicts the LBVs of ammonia and different ammonia/n-
26
heptane blends reasonably well at the test conditions.
27

10
0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7
0
2
4
6
8
10
Ronney et al. 1988
Mei et al. 2019
Jabbour et al. 2004
Han et al. 2019
Laminar Burning Velocity (cm/s)
Equivalence ratio
Ammonia in 'air', T
u
=298 K, 1 atm
(a)
0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4
0
10
20
30
40
50
60
(b)
Laminar Burning Velocity (cm/s)
Equivalence ratio
Mole fractions of fuels
100% NC
7
H
16
, Sileghem et al. 2013
100% NC
7
H
16
, Lavadera et al. 2021
75% NC
7
H
16
/ 25% NH
3
, Lavadera et al. 2021
50% NC
7
H
16
/ 50% NH
3
, Lavadera et al. 2021
Ammonia/n-heptane in 'air', T
u
=338 K, 1 atm
1
Figure 5. Experimental and simulated results of LBVs for (a) ammonia, experimental data from
2
Ref. [18],[20],[51],[52] and (b) n-heptane and ammonia/n-heptane blends. Solid and half-filled
3
symbols from Ref. [26] and open symbols from Ref. [53]. Symbols represent experimental data
4
and solid lines represent simulations based on current model. The dashed lines represent
5
simulations without the reaction class of nC7H16 + ṄH2.
6
4.3. Flux and Sensitivity analyses using the current model
7
Figure 6 shows the species traces during the auto-ignition process of the 40% ammonia/60% n-
8
heptane (by energy) blends (Mixture 4) at an initial pressure p = 10 atm and at an initial
9
temperature T = 650 K. Over 70% of n-heptane is consumed during the first-stage heat release,
10
while only around 4% of ammonia is consumed at this stage. Therefore, the first stage heat release
11
is dominated by the oxidation of n-heptane. The mole fractions of HȮ2 and ȮH radicals increase
12
during the first-stage heat release, and H2O2 accumulates at this stage. The temperature increases
13
slowly after the first-stage heat release, and consequently the decomposition of H2O2 is accelerated
14
at a temperature of approximately 900 K. At this stage almost all of the n-heptane is consumed,
15
and ammonia starts to be consumed quickly due to the formation of ȮH radicals.
16
0.00
0.01
0.02
0.03
0.04
0.05
0.06
Mole fraction
Mole fraction
NC7H16*10
NH3
Temperature
Mole fraction
700
800
900
1000
1100
1200
Temperature / K
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
0.0
2.0x10
-7
4.0x10
-7
Time
(
s
)
( )
HO
2

0.01
OH
( )
( )
0.0
5.0x10
-4
1.0x10
-3
H
2
O
2
17
Figure 6. Temperature and species mole fraction traces for 40% ammonia/60% n-heptane (by
18
energy) at φ = 1.0 and ~85% dilution (Mixture 4), with initial pressure p = 10 atm and initial
19
temperature T = 650 K. Solid symbols: 20% fuel consumption timing.
20

11
To further investigate the reaction pathways, flux and sensitivity analyses were performed for
1
Mixture 4 at 10 atm and at different temperatures using the Chemkin [50] software, and the results
2
are depicted in Figs. 7 and 8. The three temperatures are selected to represent different temperature
3
regimes controlled by different reaction pathways, with 650 K and 1200 K representing low and
4
high temperature regime and 750 K representing the negative temperature coefficient (NTC)
5
region. As the low-temperature reaction pathways of n-heptane are well known, only simplified
6
flux analyses results are given here. At 650 K, more than 90% of n-heptane is consumed via H-
7
atom abstraction by ȮH radicals, and around 10% of n-heptane is consumed via H-atom
8
abstraction by ṄH2 leading to the formation of ammonia and heptyl radicals. The heptyl radicals
9
so formed mainly add to O2 leading to the formation of RȮ2 radicals. These radicals subsequently
10
undergo isomerization and HȮ2 elimination reactions, similar to the low-temperature chemistry of
11
pure n-heptane. For RȮ2 species formed in the low-temperature chemistry of n-heptane, the
12
reactions with ṄO forming NȮ2 and alkyl oxide radicals are also included. However, these reaction
13
pathways are not important at this condition as the competing channels of RȮ2 isomerization to
14
Q
OOH have lower energy barriers.
15
The ṄH2 radicals are mainly formed via H-atom abstraction from ammonia by ȮH radicals. As
16
only ~4% of ammonia is consumed at this stage, ȮH and HȮ2 radicals are mainly formed during
17
the oxidation of n-heptane. As discussed above, H-atom abstraction reactions from n-heptane by
18
ṄH2 significantly increase the predicted fuel reactivity of the ammonia/n-heptane blends in the
19
low- to intermediate-temperature regime. These reactions are the major interaction reaction
20
pathways between ammonia and n-heptane in the low- to intermediate-temperature range. The
21
ṄH2 radicals can also react with HȮ2 radicals forming ammonia and O2, which is chain terminating
22
and hence slows down the consumption rate of ammonia. Meanwhile, about 10% of ṄH2 radicals
23
undergo recombination forming N2H4. Over 30% of ṄH2 radicals react with HȮ2 and NȮ2 radicals
24
forming H2NȮ radicals, which further react with NȮ2 and forms HONO. The HONO then react
25
with ṄH2 forming ammonia and NȮ2.
26

12
1
Figure 7. Flux analyses for 40% ammonia / 60% n-heptane (by energy) at φ = 1.0 and ~85%
2
dilution (Mixture 4), p = 10 atm and 20% n-heptane consumed. Numbers represent the percentage
3
of fuel flux that goes into a particular species. Black numbers represent flux at 650 K, blue numbers
4
represent flux at 750 K, and red numbers represent flux at 1200 K. Ṙ is the sum of ȮH, HȮ2 and
5
ĊH3 radicals and Ḣ and Ö atoms.
6
At 750 K, the flux of H-atom abstraction from n-heptane by ṄH2 increases. To simulate the
7
ammonia/n-heptane blends, adding the reaction pathways of H-atom abstraction by ṄH2 radicals
8
promotes the consumption of n-heptane and reduces the flux to chain termination, and
9
consequently increases the predicted fuel reactivity of the ammonia/n-heptane blends in the low-
10
to intermediate-temperature range. The reactivity of n-heptane in the NTC region depends on the
11
competition between chain branching (first Ṙ and second Q
OOH addition to O2) and chain
12
propagation (HȮ2 elimination from RȮ2 species) reaction pathways. The HȮ2 radicals so formed
13
promote the chain terminating pathway of ṄH2 with HȮ2 forming ammonia and oxygen, and hence
14
decrease the reactivity. This explains why ammonia addition has large effects on the fuel reactivity
15
of ammonia/n-heptane blends in the NTC region.
16
At 1200 K, over 58% of ṄH2 radicals react with n-heptane producing heptyl radicals and
17
ammonia, and hence fewer ṄH2 radicals undergo chain termination reaction pathways. This
18
explains why ammonia fraction has relatively smaller effects on fuel reactivity at high
19
temperatures than that at lower temperatures.
20
Figure 8 shows brute force sensitivity analyses for IDTs of ammonia/n-heptane blends at
21
different temperatures. The sensitivity coefficient, Sτ, is defined as: = ln(
⁄ ) /ln (
⁄),
22
which is computed for every reaction by perturbing the A-factor by factors of 2.0 and 0.5. Here 
23
is the original pre-exponential factor of the target reaction;  and  are the  factor is multiplied
24
by 2.0 and 0.5, respectively;  and  are the corresponding IDTs obtained with  and ,
25

13
respectively. Positive  values indicate reactions that inhibit reactivity and negative values
1
indicate reactions that promote reactivity. The reaction pathways highlighted in the sensitivity
2
analysis results are consistent with those in the flux analysis results. At 650 K, the reaction
3
pathways of H-atom abstraction from n-heptane forming Ċ7H15-2 and Ċ7H15-4 radicals promote
4
fuel reactivity, as these radicals mainly undergo chain branching via Ṙ and Q
OOH radical
5
additions to O2. Both the reaction channels of ṄH2 radicals with NȮ2 and HȮ2 forming H2NȮ
6
radicals promotes reactivity as they compete with the two main chain terminating reaction
7
pathways. The most sensitive reaction inhibiting fuel reactivity is H-atom abstraction from
8
ammonia by ȮH radicals, and the ṄH2 radicals so formed react with HȮ2 producing NH3 and O2,
9
which also inhibits reactivity. At 750 K, both the channels of ṄH2 radicals reacting with NȮ2 and
10
HȮ2 producing H2NȮ radicals promote reactivity, which is similar to that at 650 K. Q
OOH radical
11
addition to O2 also promotes reactivity as these lead to chain branching. The most sensitive
12
reactions which inhibit reactivity are the same as those at 650 K. At 1200 K, the sensitivity analysis
13
results show that H-atom abstraction from ethylene by ṄH2 significantly promotes fuel reactivity.
14
This is because a high concentration of ethylene is produced during the oxidation of n-heptane at
15
high temperatures, and the vinyl radicals formed after H-atom abstraction from ethylene can
16
undergo chain branching reaction pathways by reacting with O2. It is interesting to see that the
17
reaction of vinyl radicals reacting with oxygen producing formaldehyde, Ḣ and CO, R315, slightly
18
decreases fuel reactivity. This is because this channel competes with another channel forming Ö
19
atoms, R310.
20
Ċ2H3 + O2 ↔ CH2O + Ḣ + CO R315
21
Ċ2H3 + O2 ↔ ĊH2CHO + Ö R310
22
The reaction of ṄH2 and HȮ2 radicals producing NH3 and O2 inhibit fuel reactivity in the low-
23
to high-temperature range.
24

14
-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6
NH
3
+OH<=>NH
2
+H
2
O
NH
3
+O
2
<=>NH
2
+HO
2
HO
2
+HO
2
<=>H
2
O
2
+O
2
HCO+O
2
<=>CO+HO
2
NH
2
+NO
2
<=>N
2
O+H
2
O
OH+NO<=>HONO
NC
7
H
16
+OH<=>C
7
H
15
-2+H
2
O
NH
2
+HO
2
<=>OH+H
2
NO
NH
2
+NO
2
<=>H
2
NO+NO
Sensitivity Coefficient
NC
7
H
16
+OH<=>C
7
H
15
-4+H
2
O

= 1.0, 10 atm, 650 K
(a)
-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6
NH
3
+O
2
<=>NH
2
+HO
2
NH
3
+OH<=>NH
2
+H
2
O
CH
3
NO
2
(+M)=CH
3
+NO
2
(+M)
NH
2
+NO
2
<=>N
2
O+H
2
O
C
7
H
15
-4O
2
<=>C
7
H
14
-3+HO
2
C
7
H
14
OOH4-2+O
2
<=>C
7
H
14
OOH4-2O
2
C
7
H
14
OOH2-4+O
2
<=>C
7
H
14
OOH2-4O
2
OH+NO<=>HONO
NH
2
+NO
2
<=>H
2
NO+NO
Sensitivity Coefficient
NH
2
+HO
2
<=>OH+H
2
NO

= 1.0, 10 atm, 750 K
(b)
1
-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6
NH
3
+O
2
<=>NH
2
+HO
2
NH
3
+OH<=>NH
2
+H
2
O
C
2
H
3
+O
2
=>CH
2
O+H+CO
CH
3
+HO
2
<=>CH
4
+O
2
NC
7
H
16
+H<=>C
7
H
15
-3+H
2
C
2
H
5
+O
2
<=>C
2
H
4
+HO
2
NC
7
H
16
<=>PC
4
H
9
+NC
3
H
7
NH
2
+HO
2
<=>OH+H
2
NO
O
2
+H<=>O+OH
Sensitivity Coefficient
C
2
H
4
+NH
2
<=>C
2
H
3
+NH
3

= 1.0, 10 atm, 1200 K
(c)
2
Figure 8. Sensitivity analyses for IDTs of 40% ammonia / 60% n-heptane (by energy) at φ = 1.0
3
and ~85% dilution (Mixture 4), with p = 10 atm and T = 650, 750, 1200 K. The positive values
4
indicate reactions that inhibit reactivity and negative values promote reactivity.
5
The LBV sensitivity analyses for the 50% ammonia/50% n-heptane blends at φ = 0.8 and φ =
6
1.1 are given as Fig. S2 of the Supplementary material. The most sensitive reactions are from the
7
core hydrocarbon chemistry. The H-atom abstraction reactions from n-heptane by ṄH2 radicals
8
and the overall ammonia chemistry are less important in simulating LBVs of the fuel-rich mixture
9
for ammonia/n-heptane blends at the condition studied.
10
5. Conclusions
11
(1) In this study, a high-pressure shock tube was used to measure the IDTs of different ammonia/n-
12
heptane blends in the high temperature regime. By comparing the new ST IDTs with the RCM
13
IDTs available in the literature, the experimental results show that ammonia fraction has a relative
14
smaller effect on the IDTs at high temperatures compared to the low- to intermediate-temperature
15
range.
16
(2) A new kinetic model for ammonia/n-heptane blends was developed and validated against the
17
new measured ST IDTs in addition to existing experimental data available in the literature. Overall,
18
the current model can predict well both the auto-ignition behavior and flame speeds of pure
19
ammonia and different ammonia/n-heptane blends. The current model performance shows
20
significant improvement compared to the previous ammonia/n-heptane model in the literature.
21
(3) The flux and sensitivity analysis results highlight the importance of interaction reactions of H-
22
atom abstraction from n-heptane by ṄH2, which significantly increase the predicted fuel reactivity
23

15
in the low- to intermediate-temperature range. Moreover, this interaction reaction class also
1
improves the predicted LBVs of the fuel-lean mixture of the ammonia/n-heptane blends, but only
2
when the mole fraction of ammonia is higher than 50%.
3
Acknowledgements
4
5
6

16
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