Effect of ozone addition on curved detonations

Abstract

The influence of ozone on quasi-steady curved detonations was numerically studied in stoichiometric H 2-air and DME-O 2 (-CO 2) mixtures with 0%, 0.1% and 1% O 3 addition. Detonation speed-curvature (D-κ) relations were determined for both fuels. The H 2-air mixture has one critical point related to high-temperature chemistry whereas the DME-O 2 (-CO 2) mixture has two critical points, one sustained by high-temperature chemistry, and the other supported by low-temperature chemistry. O 3 addition significantly increases the curvature at all the critical points by speeding up both high-and low-temperature chemistry. Two mechanisms were found to be responsible for the results. First, O 3 addition increases the rate of reaction initiation by fast decomposition to provide O radical via O 3 (+M) = O 2 + O (+M). The dominant reaction with fuel therefore changes from a chain propagation reaction to a fuel + O radical chain branching reaction during the initial stage, which establishes the radical pool more rapidly. Second, O 3 influences the reaction pathways. For H 2-air with 1% O 3 , H + O 3 = O 2 + OH becomes the most important reaction for OH radical and heat generation during the initial stage. For DME-O 2-CO 2 , O 3 changes the respective contributions of competing low-temperature chemistry reactions, i.e. CH 3 OCH 2 = CH 2 O + CH 3 vs. CH 3 OCH 2 + O 2 = CH 3 OCH 2 O 2 and CH 2 OCH 2 O 2 H = 2CH 2 O + OH vs. CH 2 OCH 2 O 2 H + O 2 = O 2 CH 2 OCH 2 O 2 H. The change of dominant reactions either enhances (0.1% of O 3) or eliminates (1% O 3) the negative temperature coefficient behavior. Our study contributes to the detailed understanding of the thermo-chemical impact of ozone on detonation limits.

Full text

Effect of ozone addition on curved detonations
Zifeng Wenga, Fernando Veiga-L´opezb,c, Josu´e Melguizo-Gavilanesc, R´emy
M´evela,∗
aTsinghua University, 30 Shuang Qing road, 100084 Beijing, China
bFluid Mechanics Research Group, Universidad Carlos III de Madrid, Av. de la Universidad
30, 28911, Legan´es (Madrid), Espa˜na
cInstitute Pprime, UPR 3346 CNRS, ISAE-ENSMA, 86961, Futuroscope-Chasseneuil,
France
Abstract
The influence of ozone on quasi-steady curved detonations was numerically stud-
ied in stoichiometric H2-air and DME-O2(-CO2) mixtures with 0%, 0.1% and
1% O3addition. Detonation speed - curvature (D-κ) relations were determined
for both fuels. The H2-air mixture has one critical point related to high-
temperature chemistry whereas the DME-O2(-CO2) mixture has two critical
points, one sustained by high-temperature chemistry, and the other supported
by low-temperature chemistry. O3addition significantly increases the curvature
at all the critical points by speeding up both high- and low-temperature chem-
istry. Two mechanisms were found to be responsible for the results. First, O3
addition increases the rate of reaction initiation by fast decomposition to pro-
vide O radical via O3(+M) = O2+ O (+M). The dominant reaction with fuel
therefore changes from a chain propagation reaction to a fuel + O radical chain
branching reaction during the initial stage, which establishes the radical pool
more rapidly. Second, O3influences the reaction pathways. For H2-air with 1%
O3, H + O3= O2+ OH becomes the most important reaction for OH radical
and heat generation during the initial stage. For DME-O2-CO2, O3changes
∗Corresponding author
Email address: mevel@mail.tsinghua.edu.cn (R´emy M´evel)
Preprint submitted to Combustion and Flame October 29, 2022

the respective contributions of competing low-temperature chemistry reactions,
i.e. CH3OCH2= CH2O + CH3vs. CH3OCH2+ O2= CH3OCH2O2and
CH2OCH2O2H = 2CH2O + OH vs. CH2OCH2O2H + O2= O2CH2OCH2O2H.
The change of dominant reactions either enhances (0.1% of O3) or eliminates
(1% O3) the negative temperature coefficient behavior. Our study contributes
to the detailed understanding of the thermo-chemical impact of ozone on deto-
nation limits.
Keywords: Ozone, DME, Detonation, Low-temperature chemistry, Curvature.
1. Introduction
Adding ozone (O3) at the level of thousands of ppm has been found to
significantly promote auto-ignition, enhance the laminar flame speed, provide
improved flame stability, extend the extinction strain rate, and reduce pollutant
emissions [1]. The influence of O3on various aspects of combustion processes
is due to: (i) its rapid decomposition (O3(+M) = O2+ O (+M)), which pro-
motes reaction initiation and enables the fast release of highly reactive oxygen
atoms, O. The presence of O provides a by-pass of the initiation steps, that are
strongly dependent on temperature. (ii) O3addition to the mixture leads to the
transformation of alkene reactants into more reactive species, such as HCO, OH,
and H [2]. These features motivated a large number of fundamental and applied
studies, recently reviewed by Sun et al. [1], that focused on internal combustion
engines and control strategies. For detonation-based propulsion applications,
studies were performed on deflagration-to-detonation-transition (DDT) and det-
onation onset [3, 4], detonation structure/propagation [5, 6, 7, 8, 9, 10, 11] and
near-limit behavior [11] in O3-sensitized fuel-oxygen/air mixtures.
Worth mentioning are the experiments of Sepulveda et al. [3] which showed
reductions of around 77.5% of the detonation run-up time as well as extensions
of the lean flammability limit (from equivalence ratio ϕ= 0.3 to ϕ= 0.2) in
2

C2H2-O2mixtures with the addition of 1% of O3. Wang et al. [4] observed
an interesting non-monotonous effect: ozonolysis reactions can either promote
(O3<1.5%) or hinder (O3>3%) DDT. In addition, hot spot initiation of
detonation in O3-sensitized H2-O2mixtures has been studied by Han et al. [5]
using unsteady one-dimensional (1D) simulation. A sufficient amount of O3,
i.e., at least 0.5%, was required to promote detonation onset. This promoting
effect was attributed to both the decrease of the ignition delay time by ozone
decomposition, and to the stabilization of the detonation which limits pulsation
in the cold mixture and inhibits quenching.
Magzumov et al. [6] investigated the effect of adding 50-1000 ppm of O3on
the Zeldovich-von Neumann-D¨oring (ZND) structures of detonation in H2-air
mixtures. They found that O3could significantly reduce the induction zone
length (lind) over the full range of ϕinvestigated, i.e., ϕ= 0.26 −7.14. A
maximum reduction of lind by approximately 80 times was calculated at ϕ= 0.45
for a O3addition of 1000 ppm. Crane et al. [7] measured detonation cell sizes
(λ), and reported a decrease of up to 70% for a O3content of 0.3%. Their
ZND simulations showed that adding small quantities of O3enables to isolate
the effect of lind on the detonation structure since neither the shape of the
heat release pulse nor the thermodynamic conditions are modified. The study
of Kumar et al. [8] was purely numerical and the results obtained for H2-air
essentially confirm previous calculations by Magzumov et al. [6] and Crane et
al. [7]. Unsteady 1D and 2D simulations performed by Han et al. [9] for O3-
sensitized H2-O2-He mixtures, showed that O3addition modifies the pulsating
behavior, stabilizes the detonation wave, and thus extends the 1D detonability
limits, which is in agreement with [3]. Their 2D results showed more regular
and smaller cells (i.e., 40% smaller λfor 0.25% O3). The cell size reduction is
overall consistent with the findings of Crane et al. [7].
3

M´evel and He [10] added up to 1% O3to lean dimethyl ether (DME)-O2-CO2
mixtures and studied the ZND structures of low-temperature chemistry (LTC)
affected detonations. O3addition was found to strengthen LTC, resulting in an
increase of the heat release rate and decrease in lind. Kumar et al. [8] assessed
the effect of O3addition on lind for C2H4-air mixtures. However, since the
authors seem to have neglected the impact of ozonolysis reactions, their results
should be considered with caution in view of the high reaction rate between
C2H4and O3[1], as well as the known impact of ozonolysis on DDT [4].
Shi et al. [11] added up to 0.3% of O3to H2-O2and CH4-O2mixtures for
varying initial pressure. The authors report a decrease in λand a transition to
spinning modes at lower pressures; a negligible impact of O3addition on the
detonation speed was observed away from the detonability limit. Based on the
evolution of the measured velocity deficit, D/DCJ , as a function of the tube
diameter to cell size ratio, d/λ, two regimes were identified: (i) a loss-governed
regime; and (ii) a geometry-limited regime. The authors also reported that
modified ZND models, accounting for heat and momentum losses or including
a constant mean mass divergence term (see their supplemental material), could
reproduce their experimental data whereas the flow divergence (FD) model of
Fay [12] showed significant discrepancies.
The brief review above provides a good account of the work done to date on
the utilization of O3in combustion, and its overall effect on DDT, and detona-
tion onset and propagation. However, the effect of O3on the reaction structure
of curved detonations has not been investigated. Such a physical situation is
relevant to detonation diffraction [13, 14], detonation propagation in narrow
[15, 16] and expanding [17, 18] channels, and can be described, at least qualita-
tively, using the so-called curved quasi-steady detonation model [19]. While it is
4

acknowledged that this model neglects some important aspects of real detona-
tions, such as local unsteadiness and multidimensional effects, it provides reason-
able and inexpensive estimates relevant to industrial safety and pre-detonator
development for pulsed-detonation engine applications [20]. Velocity-curvature
(D-κ) curves, which can be computed using the quasi-steady model, have been
shown to provide meaningful first order predictions for detonation limits; the
turning point of the D−κcurve, which is normally unique, corresponds to
the maximum curvature that a 1D laminar, inviscid, weakly curved detonation
can sustain. Using this estimate of the limiting conditions, the dimensions of
a pipeline system can be adjusted so that detonation propagation in an indus-
trial setting is avoided, or on the contrary, detonation propagation with a low
velocity deficit is promoted by an efficient pre-detonator design.
Since no work has been done to characterize the changes brought by O3addi-
tion on the locus of steady solutions provided by the quasi-steady detonation
model [19], and to determine whether its predictions are in line with the work
cited above, we aim to fill this gap with the present study. The quasi-steady so-
lutions for H2-air and DME-O2(-CO2) mixtures are computed at different levels
of O3-sensitization, and detailed thermo-chemical analyses that unveil the un-
derlying chemical mechanisms and explain the O3-induced changes to the D-κ
curves are provided.
2. Formulation
The compressible reactive Euler equations with curvature (α) describe the
evolution of the flow. The quasi-steady assumption [19] is applied, which consid-
ers that (i) the length of reaction zone (∆) is small compared to the local radius
of curvature (Rc) of the detonation front, i.e. ∆ ≪Rc, and (ii) the reaction time
scale, that is, the required time for a fluid parcel to traverse the reaction zone,
5

is much shorter than the time scale for changes in detonation front speed (D).
The time scale associated to the former length scale, ∆, can be approximated
by ∆/w, while the latter by D/(dD/dt), which yields ∆/w ≪D/(dD/dt); wis
the flow speed in a frame of reference attached to the leading shock. Examples
of time scale calculations under various detonation situations are included in the
Supplemental Material, which provide supporting evidence that this condition
is satisfied under a wide range of conditions, including direct detonation initia-
tion and diffraction. At the scale of a detonation cellular cycle, the quasi-steady
approximation does not hold during part of the cycle. The governing equations
can be written using time (t) or space (x) as independent variables via the map-
ping, dx =w·dt. With the aforementioned assumptions and considering the
reactive mixture behaves as an ideal gas, the governing equations read:
dYi
dt=Wi˙ωi
ρ,(1a)
dρ
dt=−ρ˙σ−wM2α
η,(1b)
dw
dt=w˙σ−wα
η,(1c)
dP
dt=−ρw dw
dt.(1d)
˙σ=
N
X
i=1 W
Wi−hi
cpTdYi
dt,(2)
α=1
A
dA
dx=κD
w−1,(3)
where ρand pare the density, pressure, respectively. The mass fraction, molec-
ular weight and source term of species iare Yi,Wiand ˙ωi. The symbol η
represents the sonic parameter η= 1 −M2with M=w/afbeing the Mach
number relative to the leading shock and based on the frozen speed of sound,
6

af. ˙σis the thermicity, αis the axial area change, Wis the mean molar mass
of the mixture, cpis the constant-pressure specific heat of the mixture, and hi
is the specific enthalpy of species i. The curvature κis κ= 2/Rcand κ= 1/Rc
for spherical and cylindrical waves, respectively. Further details can be found
in [19]. Equations (1), (2) and (3) were implemented in the Shock and Detona-
tion Toolbox (SDT) [21]. The reaction models employed were that of M´evel et
al. [22] for H2-air, and that of Bhagatwala et al. [23] for DME mixtures. The
ozone sub-mechanism was taken from Zhao et al. [24]. The direct reaction be-
tween fuel and ozone was not considered since no double C-C bond exists. To
differentiate from which mechanism a reaction belongs to, Riis used to repre-
sent the ith reaction in the H2mechanism, and Riin the DME mechanism.
The outcome of the system of equations above are D−κcurves, which
provide the locus of steady solutions that the model admits. Detonations with
curvature losses admit two (or more) steady solutions for a particular value of κ.
The solution methodology consists of marching downstream from the postshock
state until M=w/af= 1. For this to occur, the numerator and denominator
on the RHS in Eqns. (1) should vanish simultaneously. This entails selecting an
initial closed interval, [κmin, κmax ], for a given leading shock velocity, D, and
checking whether (and where) the latter condition is satisfied. Specific details
on the algorithm implemented to automate the procedure described above, as
well as the existence of solutions without a sonic point are provided in [25]. Our
solver has been successfully used to study detonations with friction [25] and
curvature [26] losses.
3. Results and Discussion
3.1. Mixture selection
The mixtures chosen are: (i) H2-air (2H2-O2-3.76N2) and (ii) DME-O2
7

(DME-3O2-aCO2). Both arise as alternatives to replace conventional non-
renewable fuels for transport and industrial applications, and allow us to in-
vestigate how O3-addition influences the detonation limits (D-κcurves) in mix-
tures with (DME) and without (H2) LTC. Note that the sole purpose of adding
CO2to DME (a= 0,3 and 6) is to magnify the LTC effect. The amount of O3
addition is calculated via % O3=nO3/(nfuel +nO2+ndiluent)×100 where n
denotes the number of moles of each constituent in the combustion reaction; all
mixtures are sensitized with 0, 0.1 and 1% O3. Furthermore, at the levels of O3
addition and dilution investigated, the effect of the endothermic decomposition
of O3is essentially negligible. Table 1 lists the initial mixture composition for
all the cases considered. Finally, the initial state is fixed at p0= 100 kPa and
T0= 300 K.
Table 1: Mole fraction of fuel, O2, O3and diluent (Xfuel ,XO2,XO3,Xdiluent) for stoichio-
metric H2-air and DME-3O2-aCO2mixtures with different amount of O3addition.
0% O30.1% O31.0% O3
H2-air (0.296, 0.148, 0, 0.556) (0.296, 0.148, 9.99e-04, 0.556) (0.293, 0.146, 9.90e-03, 0.551)
a= 0 (0.250, 0.750, 0, 0.000) (0.250, 0.749, 9.99e-04, 0.000) (0.248, 0.743, 9.90e-03, 0.000)
a= 3 (0.143, 0.429, 0, 0.429) (0.143, 0.428, 9.99e-04, 0.428) (0.141, 0.424, 9.90e-03, 0.424)
a= 6 (0.100, 0.300, 0, 0.600) (0.100, 0.300, 9.99e-04, 0.599) (0.099, 0.297, 9.90e-03, 0.594)
3.2. D-κcurves
Figure 1 shows the D-κcurves and the induction times (tInd) for H2-air and
DME-O2(-CO2) with increasing O3addition. The shock speed, D, is normal-
ized with the corresponding Chapman-Jouguet (CJ) velocity. The induction
time corresponds to the distance to maximum thermicity. When no ozone is
added, a single peak is obtained for H2-air mixtures as shown in Fig. 1(a), while
for DME-O2(-CO2), two peaks were found, as shown in Fig. 1(b-d). These peaks
correspond to the maximum curvature that the detonation wave can sustain in
the high-speed (D/DC J >0.7) and low-speed regimes (D/DC J <0.7) (It is
8

better to use a larger value, like 0.75 or 0.80. Because for DME+3O2+6CO2
without O3, the LCP locates at D/DCJ = 0.71). In this work, they are re-
ferred to as the upper critical point (UCP) and the lower critical point (LCP),
respectively. The CJ speed, shock speed, and curvature at all the critical points
are summarized in table 2. The LCP seems to originate from the LTC as the
induction time profiles have typical negative temperature coefficient (NTC) be-
havior around the postshock conditions corresponding to the shock speed of
LCP. Without CO2dilution, the curvature at UCP is much larger than that
at LCP. However, as the amount of CO2increases, the post-shock temperature
decreases and thus weakens the high temperature chemistry (HTC) at UCP.
Although the magnitude of curvature at both UCP and LCP decreases, the cur-
vature at LCP becomes comparable with that at UCP in Fig. 1(c) and is even
larger in Fig. 1(d).
0.70.80.91
0
50
100
10-7
10-5
10-3
0.40.60.81
0
50
100
150
200
10-7
10-5
10-3
10-1
0.40.60.81
0
5
10
15
10-7
10-5
10-3
10-1
0.40.60.81
0
1
2
3
4
5
10-5
10-3
10-1
Figure 1: D-κcurves (solid) and induction time (dashed) for H2-air and DME-O2(-CO2)
mixtures with O3addition. UCP was denoted with empty circle while LCP was marked with
empty square.
The addition of O3significantly increases the curvatures at both UCP and
9

Table 2: CJ speed, velocity deficit and curvature values (DCJ [m/s], D/DC J ,κ[m−1]) at
UCP and LCP for stoichiometric H2-air and DME-O2(-CO2) mixtures with 0%, 0.1% and 1%
O3.
O3H2-air DME+3O2DME+3O2+3CO2DME+3O2+6CO2
0.0% UCP (1978.0, 0.93, 16.97) (2318.7, 0.93, 101.32) (1781.5, 0.94, 2.83) (1556.3, 0.94, 0.30)
LCP −(2318.7, 0.58, 3.81) (1781.5, 0.66, 1.21) (1556.3, 0.71, 0.50)
0.1% UCP (1978.7, 0.88, 47.68) (2318.3, 0.92, 113.60) (1781.8, 0.93, 3.90) (1557.0, 0.92, 0.48)
LCP −(2318.3, 0.54, 9.49) (1781.8, 0.62, 3.19) (1557.0, 0.67, 1.22)
1.0% UCP (1981.9, 0.82, 110.12) (2314.7, 0.90, 189.63) (1784.4, 0.91, 11.52) −
LCP −(2314.7, 0.55, 24.58) (1784.4, 0.64, 9.22) (1562.8, 0.69, 3.92)
LCP, but the impact is stronger for LCP. For example, the maximum curvature
for stoichiometric H2-air mixtures increases by 181% and 550% when 0.1% and
1% O3is added, respectively. For stoichiometric DME-O2given in Fig. 1(b), the
curvature at UCP increases by 12% and 149%, and at LCP by 87% and 546%
when 0.1% and 1% O3were added, respectively. Notably, the UCP disappears
for DME-O2with 6 mole CO2dilution and 1% O3sensitization (Fig. 1(d))
showing a single critical point, i.e. the LCP, at low shock speeds. O3addition
also affects the induction time, tInd, and the NTC behavior. For a given shock
speed, tInd decreases with increasing O3. Ozone also seems to have a stronger
impact on LTC than on HTC, as the decrease in tInd at low shock speed is
more pronounced when 0.1% ozone is added, which results in the enhancement
of NTC behavior. However, when 1% O3is added, the NTC region disappears
and tInd increases monotonically with decreasing shock speed; a similar trend
was observed by Liao et al. [27] in their jet-stirred reactor study on the effect of
O3addition to DME-O2-Ar mixtures. Detailed thermo-chemical analyses are
provided in the next section.
10

3.3. Thermo-chemical analysis
3.3.1. Thermicity and temperature profiles
Figure 2 shows the thermicity and temperature profiles obtained with H2-
air and DME-O2(-CO2) at UCP or LCP with different amounts of O3. The
horizontal axis is made dimensionless using the induction time (tInd). Up to
three peaks were found in the thermicity profiles. For simplicity, they are labeled
˙σP1, ˙σP2and ˙σP3depending on the time interval in which they take place.
Specifically, ˙σP1occurs for t/tInd <0.6, ˙σP2for 0.8< t/tInd <1.0 and ˙σP3at
t=tInd.
Without O3addition, ˙σP1is present only for DME + 3O2+ 6CO2and it
is a result of LTC [10]. With O3addition, the thermicity increases significantly
during the early stages of the reaction, indicating that the mixture becomes more
reactive. The enhanced reactivity not only enables ˙σP1in diluted DME-O2to
occur at an earlier time at LCP, but also results in the appearance of ˙σP1at
UCP for H2-air and DME-O2mixtures. The temperature increases accordingly
around the position of the ˙σP1. This increment is more significant at LCP than
at UCP, and is higher when a larger amount of O3is added. ˙σP2only occurs for
DME-O2(-CO2) and originates from the intermediate temperature chemistry
(ITC), consistent with the results of M´evel and He [10]. O3also enables ˙σP2to
take place at an earlier time as shown in Fig. 2(b) and (c). Finally, ˙σP3is induced
by HTC. Note that tInd, i.e., the time to ˙σP3, also becomes shorter when O3is
added but is not visible in the figure because of the choice of time-scale used
for normalization. The effect of O3addition on the magnitude of thermicity
at ˙σP2and ˙σP3is modest compared to its impact at ˙σP1. The increase of
thermicity and appearance of additional thermicity peaks when adding ozone
indicate the reactivity is enhanced, which is correlated with the increase of
curvature at LCP and UCP as shown in Fig. 1. Although the thermicity profile
11

104
105
106
107
1
1.5
2
2.5
3
105
106
107
1
2
3
4
0 0.2 0.4 0.6 0.8 1 1.2
103
104
105
1
1.5
2
2.5
3
Figure 2: Thermicity and temperature profiles of H2-air and DME-O2(-CO2) mixtures with
different O3addition at UCP or LCP. The time is normalized with the induction time. The
solid circles denote the local thermicity peak.
has multiple peaks, there is no causality between multiple critical points and
multiple thermicity peaks. As will be shown below, the multiple critical points
appear for DME-based mixtures because there is a shift of dominant chemical
pathways between the high- and the low-speed regimes, in which the HTC and
LTC respectively dominate.
The thermicity results clearly show that the reactivity of the mixture is en-
hanced especially during the early stage of the reaction and results in a curvature
increase at the critical state and the existence of the LCP. To further investigate
the impact of O3on the reaction pathways at early stages, the rate of progress
12

(RoP) for the fuels considered, heat release rate (HRR) and sensitiviy analysis
are investigated in the following sub-sections.
3.3.2. Impact of ozone on reaction initiation
In Fig. 3, focus is placed on the RoP for reactions between the fuels and
radical species, and on the decomposition of CH3OCH2(R138): CH3OCH2
= CH2O + CH3. The key radicals, OH, CH3and OH in Fig. 3 (a) to (c),
respectively, refer to the major radicals reacting with fuel when no O3is added.
The reactions shown are R13: H2+OH=H+H2O in Fig. 3(a) for H2;
R134: DME + CH3= CH3OCH2+ CH4in Fig. 3(b) and R132: DME +
OH = CH3OCH2+ H2O in Fig. 3(c) for DME. As previously mentioned, O3
decomposes quickly, which generates O radical to initiate the reaction of the
mixture [1].
It was found that the O radical replaces the key radicals to react with the
fuels during the early stage of the reaction when O3is added. In the conditions
of Fig. 3(a), the dominant reaction that consumes H2at the beginning of the in-
duction period changes from R13 to R6: H2+ O = H + OH. Since R6 is a chain
branching reaction and R13 is an exothermic chain propagation reaction, R6 not
only contributes to a faster production of radicals in the O3-sensitized mixture,
but also sustains the production OH radicals and release heat through R13. The
rate of R13 surpasses that of R6 when t/tInd >0.03, at which time OH becomes
the major chain carrier. With 1% O3addition, the enhanced R13 exhibits a
peak which coincides with ˙σP1. This peak therefore results from the increase of
OH radical concentration via the sequence O3decomposition followed by R6.
Similarly, in the conditions of Fig. 3(b), R135 (DME + O = CH3OCH2+ OH),
a chain branching reaction, replaces R134, a chain propagation reaction, as the
major reaction consuming DME at the beginning of the induction period. R135
also supplies CH3OCH2radical for R138 which decomposes and provides CH3
13

10-4
100
104
10-2
102
106
10-5 10-4 10-3 10-2 10-1 100
10-3
100
103
<latexit sha1_base64="MhMbhL+wk9QXBDPoIl0dwawpiWg=">AAACDnicbVDLSsNAFJ34rPUVdelmsBQKQkmKVBGEgpvsrGIf0IQwmU7aoZMHMxOhhHyBG3/FjQtF3Lp25984abPQ1gPDHM65l3vv8WJGhTSMb21ldW19Y7O0Vd7e2d3b1w8OuyJKOCYdHLGI9z0kCKMh6UgqGenHnKDAY6TnTa5zv/dAuKBReC+nMXECNAqpTzGSSnL1qs2D1A6QHGPE0ruseQktN21k8BTewCto5b+VuXrFqBszwGViFqQCCrRd/cseRjgJSCgxQ0IMTCOWToq4pJiRrGwngsQIT9CIDBQNUUCEk87OyWBVKUPoR1y9UMKZ+rsjRYEQ08BTlfniYtHLxf+8QSL9CyelYZxIEuL5ID9hUEYwzwYOKSdYsqkiCHOqdoV4jDjCUiVYViGYiycvk26jbjbr5u1ZpVUr4iiBY3ACasAE56AFLNAGHYDBI3gGr+BNe9JetHftY166ohU9R+APtM8fVW6Zng==</latexit>
R6:H
2+O=H+OH
<latexit sha1_base64="Ke6th+E+70Sp8DFhi2emXJzFfhY=">AAACFHicbZDLSsNAFIYn9VbrLerSzWARCoWSVFERhIKb7FrFXqAtZTKdtkNnkjAzEUrIQ7jxVdy4UMStC3e+jZM0C239YeDjP+cw5/xuwKhUlvVt5FZW19Y38puFre2d3T1z/6Al/VBg0sQ+80XHRZIw6pGmooqRTiAI4i4jbXd6k9TbD0RI6nv3ahaQPkdjj44oRkpbA7PcEzzqcaQmGLHoLrZPr6AziKoxLMO6A6+hoyE16vHALFoVKxVcBjuDIsjUGJhfvaGPQ048hRmSsmtbgepHSCiKGYkLvVCSAOEpGpOuRg9xIvtRelQMT7QzhCNf6OcpmLq/JyLEpZxxV3cm68vFWmL+V+uGanTZj6gXhIp4eP7RKGRQ+TBJCA6pIFixmQaEBdW7QjxBAmGlcyzoEOzFk5ehVa3Y5xX79qxYK2Vx5MEROAYlYIMLUAMOaIAmwOARPINX8GY8GS/Gu/Exb80Z2cwh+CPj8weEzpvZ</latexit>
R13 : H2+OH=H+H
2O
<latexit sha1_base64="cJnCq0sv/XrsdhDwIzErcqJHmBU=">AAACGXicbZDLSgMxFIYz9VbrbdSlm2AVBKHMtEVFEApV6EasYi/QDiWTZtrQzIUkI5RhXsONr+LGhSIudeXbmGlnoa0HQj7+/xyS89sBo0IaxreWWVhcWl7JrubW1jc2t/TtnabwQ45JA/vM520bCcKoRxqSSkbaASfItRlp2aNq4rceCBfU9+7lOCCWiwYedShGUkk93ehyN7ozS+VzeHl9BY9htdaLSjG8SOEmuYpxapTjuKfnjYIxKTgPZgp5kFa9p392+z4OXeJJzJAQHdMIpBUhLilmJM51Q0EChEdoQDoKPeQSYUWTzWJ4qJQ+dHyujifhRP09ESFXiLFrq04XyaGY9RLxP68TSufMiqgXhJJ4ePqQEzIofZjEBPuUEyzZWAHCnKq/QjxEHGGpwsypEMzZleehWSyYJwXztpyvHKRxZMEe2AdHwASnoAJqoA4aAINH8AxewZv2pL1o79rHtDWjpTO74E9pXz9XFJy2</latexit>
R134 : DME + CH3=CH
3OCH2+CH
4
<latexit sha1_base64="k0a7t6Ti3CZzFl1AP1z57fjMWsc=">AAACFXicbVDLSgMxFM3UV62vqks3wSoISplpRUUQClXoRlrFPqAdhkyaaUOTmSHJCGWYn3Djr7hxoYhbwZ1/Y/pYaPVAuIdz7uXmHjdkVCrT/DJSc/MLi0vp5czK6tr6RnZzqyGDSGBSxwELRMtFkjDqk7qiipFWKAjiLiNNd1Ae+c17IiQN/Ds1DInNUc+nHsVIacnJHnUEj2+tYuEcXl5fwUNYrcALWK44cTGpjkoh0eK4VhMnmzPz5hjwL7GmJAemqDnZz043wBEnvsIMSdm2zFDZMRKKYkaSTCeSJER4gHqkramPOJF2PL4qgfta6UIvEPr5Co7VnxMx4lIOuas7OVJ9OeuNxP+8dqS8Mzumfhgp4uPJIi9iUAVwFBHsUkGwYkNNEBZU/xXiPhIIKx1kRodgzZ78lzQKeeskb90c50p70zjSYAfsggNggVNQAhVQA3WAwQN4Ai/g1Xg0no03433SmjKmM9vgF4yPb07Dmxg=</latexit>
R132 : DME + OH = CH3OCH2+H
2O
<latexit sha1_base64="qltokoP5+qbCE/ejMRs05c72/50=">AAACFHicbZDLSgMxFIYz9VbrbdSlm2AVhEKZaUWLIBS66a5VbC20w5BJM21o5kKSEcowD+HGV3HjQhG3Ltz5NmbaWWjrgZCP/z+H5PxOyKiQhvGt5VZW19Y38puFre2d3T19/6Argohj0sEBC3jPQYIw6pOOpJKRXsgJ8hxG7p1JI/XvHwgXNPDv5DQklodGPnUpRlJJtl4acC++Nau1K9ho2nE1aaVXJYHXcA4tWMqcxNaLRtmYFVwGM4MiyKpt61+DYYAjj/gSMyRE3zRCacWIS4oZSQqDSJAQ4Qkakb5CH3lEWPFsqQSeKmUI3YCr40s4U39PxMgTYuo5qtNDciwWvVT8z+tH0q1ZMfXDSBIfzx9yIwZlANOE4JBygiWbKkCYU/VXiMeIIyxVjgUVgrm48jJ0K2XzomzenBfrJ1kceXAEjsEZMMElqIMmaIMOwOARPINX8KY9aS/au/Yxb81p2cwh+FPa5w8DxpuU</latexit>
R138 : CH3OCH2=CH
2O+CH
3
<latexit sha1_base64="y767FJoFb1X163JGvZyrFEmklnY=">AAACEHicbVDLSgMxFM3UV62vUZduglUUhDLT+kIQClXoRlrFPqAtJZNm2tDMgyQjlGE+wY2/4saFIm5duvNvzLSz0NYDl3s4516SeyyfUSEN41tLzc0vLC6llzMrq2vrG/rmVl14Acekhj3m8aaFBGHUJTVJJSNNnxPkWIw0rGEp9hsPhAvqufdy5JOOg/outSlGUkld/aDNnfDOLJxcwKuba3gEK/ASlsrdsBBV4paPYq0cdfWskTPGgLPETEgWJKh29a92z8OBQ1yJGRKiZRq+7ISIS4oZiTLtQBAf4SHqk5aiLnKI6ITjgyK4r5QetD2uypVwrP7eCJEjxMix1KSD5EBMe7H4n9cKpH3eCanrB5K4ePKQHTAoPRinA3uUEyzZSBGEOVV/hXiAOMJSZZhRIZjTJ8+Sej5nnubM2+NscS+JIw12wC44BCY4A0VQBlVQAxg8gmfwCt60J+1Fe9c+JqMpLdnZBn+gff4AniWZGA==</latexit>
R135 : DME + O = CH3OCH2+OH
<latexit sha1_base64="I7XTyQq1qaGu5XUbh9m387OqZFY=">AAAB8HicbVDLTsMwENyUVymvAkcuFgWJU5XwPlbiwrEg+kBtVDmu01q1nch2kKooX8GFAwhx5XO48Te4bQ7QMtJKo5ld7e4EMWfauO63U1haXlldK66XNja3tnfKu3tNHSWK0AaJeKTaAdaUM0kbhhlO27GiWASctoLRzcRvPVGlWSQfzDimvsADyUJGsLHSY1eJ9N47u8h65YpbdadAi8TLSQVy1Hvlr24/Iomg0hCOte54bmz8FCvDCKdZqZtoGmMywgPasVRiQbWfTg/O0LFV+iiMlC1p0FT9PZFiofVYBLZTYDPU895E/M/rJCa89lMm48RQSWaLwoQjE6HJ96jPFCWGjy3BRDF7KyJDrDAxNqOSDcGbf3mRNE+r3mXVuzuv1I7yOIpwAIdwAh5cQQ1uoQ4NICDgGV7hzVHOi/PufMxaC04+sw9/4Hz+ABfej9o=</latexit>
R135
<latexit sha1_base64="vARmK1/K9wKw2Hi/MeJWJSGh6yw=">AAAB8HicbVBNSwMxEJ2tX7V+VT16CVbBU9lV0R4LXjxWsR/SLiWbZtvQJLskWaEs/RVePCji1Z/jzX9jtt2Dtj4YeLw3w8y8IOZMG9f9dgorq2vrG8XN0tb2zu5eef+gpaNEEdokEY9UJ8CaciZp0zDDaSdWFIuA03Ywvsn89hNVmkXywUxi6gs8lCxkBBsrPfaUSO+9i9q0X664VXcGtEy8nFQgR6Nf/uoNIpIIKg3hWOuu58bGT7EyjHA6LfUSTWNMxnhIu5ZKLKj209nBU3RqlQEKI2VLGjRTf0+kWGg9EYHtFNiM9KKXif953cSENT9lMk4MlWS+KEw4MhHKvkcDpigxfGIJJorZWxEZYYWJsRmVbAje4svLpHVe9a6q3t1lpX6Sx1GEIziGM/DgGupwCw1oAgEBz/AKb45yXpx352PeWnDymUP4A+fzBxxtj90=</latexit>
R138
Figure 3: RoP profiles (absolute value) of the fuels and CH3OCH2. For the fuels RoP, the
reactions between the key radicals were considered. These radicals are OH, CH3and OH
in sub-figure (a) to (c), respectively. For CH3OCH2RoP, only the main reaction R138:
CH3OCH2= CH2O + CH3, is shown. The solid circle marks the location of ˙σP1.
radical for R134. The rate of R134 then surpasses that of R135 and becomes the
dominant reaction for DME consumption. In the conditions of Fig. 3(c), R135
replaces R132, a chain propagation reaction, as the main pathway for DME
consumption. The OH radical generated by R135 speeds up R132. Note that
the rates of R132 and R135 are comparable in the interval 10−4< t/tInd <10−2.
14

3.3.3. Impact of ozone on reaction pathways at UCP
The impact of O3not only manifests itself in the initiation of the overall
reaction by providing O radical, it also influences the overall reaction pathway
of the chemical system, especially when the amount of O3is large. We analyzed
the RoP of OH radical and the HRR at all the thermicity peaks for the H2-air
mixture, as shown in Fig. 4. At ˙σP1, the OH radical is mainly consumed by
R13 and is mostly generated by R33 (H + O3= O2+ OH). R33 is also the
dominant reaction in releasing heat at ˙σP1. Our results indicate that O3addition
provides additional reaction pathways for the mixture and these reactions are
of primary importance for the existence of ˙σP1.R33 was also demonstrated to
be an important reaction by Gao et al. [28] when studying the sensitizing effect
of O3on the laminar flame speed of three fuels, i.e. CH4, C2H4, and C3H8.
At ˙σP3, although the amplitudes of the RoP and HRR change, the dominant
reactions are similar, regardless of the amount of O3added. This indicates that
the impact of O3on the reaction pathways is limited to the early stages of
reaction because O3quickly decomposes or reacts with H.
Similar analyses were also performed for all the thermicity peaks at the
UCP of DME-O2mixture (see Fig. 5). However, R179, i.e., R33 in hydrogen
mechanism, is not as important as in the H2-O2mixture. At ˙σP1, R135 is the
major reaction for the generation of OH radical, in which DME reacts with
O radical from ozone decomposition and forms CH3OCH2. The OH radical is
mostly consumed by R132 which also generates CH3OCH2radical. According to
the HRR analysis, the further decomposition of CH3OCH2absorbs most amount
of heat at ˙σP1. The energy is mainly provided by R48 (2CH3(+M) = C2H6
(+M)) and R134. In these two reactions, CH3is an important chain-carrier.
The dominant reactions at ˙σP2and ˙σP3were again not affected by O3addition.
15

R6: H2+O=H+OH R9: H + O2=O+OH
R10: H + O2(+M) = HO2(+M) R13: H2+OH=H+H2O
R17:H+OH+M=H2O+M R21: H + HO2= 2OH
R33: H + O3= O2+ OH
Figure 4: RoP of OH radical and HRR at ˙σP1and ˙σP3for a stoichiometric H2-air mixture.
Only the four most important reactions are shown.
Put differently, the chemical pathway at the UCP of DME-O2mixture is not
significantly affected by ozone, except that O3speeds up the initiation via R135
as discussed in the previous section. Nevertheless, the change of NTC behavior
shown in Fig. 1 indicates the reaction pathway is modified by the addition of
O3. Liao et al. [27] argued that O3makes the establishment of the radical
pool easier, and thus enhances the reactivity in the NTC region. To obtain an
in-depth understanding of this feature and of the associated reaction pathways,
a reaction pathway analysis at the LCP for DME + 3O2+ 6CO2is performed
next.
16

-4 -2 0 2 4
R132
R135
R47
R40
-40 -20 0 20 40
R16
R40
R52
R1
-50 0 50 100
R1
R3
R2
R52
R11
-5 0 5 10
R48
R134
R138
R132
-100 0 100
R26
R27
R40
R16
-50 0 50 100
R44
R1
R26
R116
R1: H + O2=O+OH R2: H2+O=H+OH
R3: H2+OH=H+H2OR11: H + HO2= 2OH
R16: H2O2(+M) = 2OH (+M) R26:HCO+M=CO+H+M
R27: HCO + O2= CO + HO2R40: CH2O+OH=H2O + HCO
R44: CH3+O=CH2O+H R47: CH3+ HO2= CH3O + OH
R48: 2CH3(+M) = C2H6(+M) R52: CH4 + OH = CH3+ H2O
R116: CH2+ O2= HCO + OH R132: DME + OH = CH3OCH2+ H2O
R134: CH3+ CH3OCH3= CH3OCH2+ CH4 R135: DME + O = CH3OCH2+ OH
R138: CH3OCH2= CH2O + CH3
Figure 5: RoP of OH radical and HRR at ˙σP1, ˙σP2and ˙σP3for the UCP of stoichiometric
DME-O2mixture. Only the four most important reactions are shown.
3.3.4. Impact of ozone on reaction pathways at LCP
Figure 6 presents a reaction pathway diagram established based on the con-
tribution of each reaction in consuming a given species. The calculation was
restricted to 0 ≤t/tInd ≤0.6 because: (i) O3mainly affects the LTC at ˙σP1
and (ii) the RoP at ˙σP2and ˙σP3are much larger due to the higher temperature,
which masks the contribution of reactions at ˙σP1. At t/tInd = 0.6, the thermic-
ity is at least one order of magnitude lower than that at ˙σP1, which means the
17

LTC has essentially reached its completion. During the LTC-dominated period,
DME firstly undergoes hydrogen-abstraction which leads to the formation of
CH3OCH2(R132). Starting from CH3OCH2, the successive reactions include:
an oxygen addition reaction (R151), an isomerization (R156), a second oxygen
addition (R158), and decomposition reactions (R159, R160). It was shown in
Fig. 3 that O3speeds up the initiation of the overall reaction via R135. With-
out O3addition, R135 contributes to only 0.2% of DME consumption. This
percentage increases dramatically to 16.4% when adding 1% O3. O3also in-
fluences the respective contributions of several competing pathways: R151 vs.
R138, R156 vs. R152, R153 and R158 vs. R157. R156 is the dominant reac-
tion compared to R152 and R153. Although its contribution decreases with the
increasing amount of O3added, it still consumes one order of magnitude more
CH3OCH2O2than R152 and R153. In the competition between R157 and R158,
the fate of CH2OCH2O2H radical determines the reactivity of the mixture at
low temperature [29]. R158 increases the reactivity while the decomposition
reaction R157 decreases the reactivity.
The impact of R157 and R158 on the induction time is compared in Fig. 7
by perturbing their reaction rate constants and by calculating the sensitivity of
induction time to their reaction rate constants. The sensitivity coefficient (Si),
defined as Si= (ki/tInd)∂tInd/∂ki, was calculated by doubling and halving the
reaction rate constants of R157 and R158 at LCP. As shown in Fig. 7(a), by
increasing the rate of R158, the NTC behavior is enhanced and the induction
time in the NTC region decreases. On the contrary, increasing the rate of R157
attenuates the NTC behavior and increases the induction time. Adding 0.1%
O3increases the contribution of R158 from 23.8% to 28.3%, whereas the con-
tribution of R157 decreases from 76.2% to 71.7%. Furthermore, the addition of
18

R132: 82.7%, 78.2%, 67.7%
R133: 6.0%, 7.4%, 6.3%
R151
R157: 76.2%,
71.7%, 81.2%
R159 R40
R138: 21.9%,
26.3%, 43.6%
R135: 0.2%, 3.2%, 16.4%
75.3%
70.2%
51.0%
R152: 1.7%,
6.5%, 8.7%
R153: 0.7%,
2.8%, 3.7%
R158: 23.8%,
28.3%, 18.8%
65.4%
60.6%
60.6%
R27: 97.1%,
96.1%, 92.3%
100%
100%
100%
R156
97.6%
90.7%
87.5%
R160: 100%,
100%, 100%
H atomO atom C atom
R27: HCO + O2= CO + HO2R40: CH2O+OH=H2O + HCO
R132: DME + OH = CH3OCH2+ H2OR133: DME + H = CH3OCH2+ H2
R135: DME + O = CH3OCH2+ OH R138: CH3OCH2= CH2O + CH3
R151: CH3OCH2+ O2= CH3OCH2O2R152: 2CH3OCH2O2= 2 CH3OCH2O+O2
R153: 2CH3OCH2O2= CH3OCH2OH + CH3OCHO + O2
R156: CH3OCH2O2= CH2OCH2O2HR157: CH2OCH2O2H = 2CH2O + OH
R158: CH2OCH2O2H+O2= O2CH2OCH2O2HR160: HO2CH2OCHO = OCH2OCHO + OH
R159: O2CH2OCH2O2H = HO2CH2OCHO + OH
Figure 6: Low temperature reaction pathways analysis based on integrated ROP in 0 ≤
t/tInd ≤0.6 at LCP. The mixtures are DME + 3O2+ 6CO2with 0.0%, 0.1% and 1.0% O3
addition. The percentage denotes the contribution of a given reaction in consuming the given
species.
O3increases the sensitivity of the induction time to these two reactions, com-
pared to the case without O3addition. This explains why the NTC behavior is
enhanced in Fig. 1. Adding 1% O3decreases the contribution of R158 whereas
that of R157 increases, which partly explains the disappearance of the NTC be-
havior in Fig. 1. Note that the sensitivity decreases significantly when 1.0% O3
is added, which implies that other pairs of competiting reactions, such as R138
vs. R151, become more important. Figure 6 also shows that, as the amount of
O3increases, R138 becomes a stronger and stronger consumption pathway for
19

CH3OCH2compared to R151. With 1% O3, the contribution of R138 (43.6%)
becomes comparable to that of R151 (51.0%). The sensitivity coefficient of in-
duction time to the reaction rate constant of R138 was also calculated for this
condition. The result is 0.31, which is larger than that of R157 (0.19) and R158
(−0.16). This reaction pathway reduces the influence of LTC, which results in
the disappearance of NTC behavior.
0.60.81
10-4
10-3
10-2
10-1
R157
R158
<latexit sha1_base64="GgQXDXigMN4PPpI8aBb5VLtMOH8=">AAACU3icbZFLSwMxFIUz47u+qi7dBKviapgpProsuHGpYh/QKSWT3mpsJjMkd4Qy9D+K4MI/4saFZmoX2vZC4PDdc7nJSZRKYdD3Pxx3aXlldW19o7S5tb2zW97bb5ok0xwaPJGJbkfMgBQKGihQQjvVwOJIQisaXhf91gtoIxL1gKMUujF7VGIgOEOLeuXn01DHtKFS0JjpCPphWDr1vYsQRQyGDnv5fXBxNS5o1fMX0FlvbaG3oL1yxff8SdF5EUxFhUzrtld+C/sJz2JQyCUzphP4KXZzplFwCeNSmBlIGR+yR+hYqZjd180nmYzpiSV9Oki0PQrphP6dyFlszCiOrDNm+GRmewVc1OtkOKh1c6HSDEHx30WDTFJMaBEw7QsNHOXICsa1sHel/IlpxtF+Q8mGEMw+eV40q15w6QV355X68TSOdXJIjsgZCcgVqZMbcksahJNX8km+HeK8O1+u6y7/Wl1nOnNA/pW7/QMH766o</latexit>
Unperturbed
0.5⇥kR157
2.0⇥kR157
0.5⇥kR158
2.0⇥kR158
\
\
\
(a) (b)
Figure 7: Comparison between R157 and R158 in affecting the induction time via (a) per-
turbing their reaction rate constants without O3addition and (b) calculating the sensitivity
coefficient of the induction time with respect to their reaction rate constants at LCP. The
mixture is DME + 3O2+ 6CO2. In (b), 0.0%, 0.1% and 1.0% O3were added.
Figure 8 compares the net reaction rate of R138 and R151 in 0 ≤t/tInd ≤0.6
for different O3addition. The net reaction rate of R151 is larger than that of
R138 at the beginning of the combustion process. Then the ˙rR151- ˙rR138 curve
crosses the ˙rR151 = ˙rR138 line, indicating R138 becomes dominant. Without
O3addition, the curve crosses the dashed line at a relatively late time, i.e.,
t/tInd = 0.55. However, with the increase of O3, the time at which the curve
crosses the dashed line decreases to t/tInd = 0.27 and 0.15 for 0.1% and 1% O3,
respectively. Furthermore, the maximum net reaction rate of R138 increases
20

with the amount of O3added but the net reaction rate of R151 becomes negative
after a short period, indicating that the direction of the reaction is reversed.
Although the increase of CH3OCH2concentration tends to increase the forward
reaction rate of both R138 and R151, the reverse reaction rate of R151 is also
significantly increased; CH3OCH2O2decomposes more easily as the amount of
O3addition increases. The addition of O3enhances the LTC and thus increases
the heat release and temperature of the mixture. For instance, the temperature
increment between 0 ≤t/tInd ≤0.6 is 157.8 K, 251.7 K and 327.0 K for 0%,
0.1% and 1% O3addition, respectively. The forward reaction rate constant
of R151 is temperature independent and therefore the forward reaction rate of
R151 is not sensitive to the temperature increment in the first stage of heat
release. However, the reverse reaction rate of R151 is largely affected by the
temperature increment and results in an overall decrease of the net reaction rate
of R151.
0 50 100 150 200 250 300
-100
-50
0
50
100
150
200
250
0
0.1
0.2
0.3
0.4
0.5
0.6
Figure 8: Comparison of the net reaction rates of R138 and R151 in the range 0 ≤t/tInd ≤0.6.
The black dashed line denotes ˙rR151 = ˙rR138. The mixtures are DME + 3O2+ 6CO2with
0.0%, 0.1% and 1.0% O3addition. R138: CH3OCH2= CH2O + CH3, R151: CH3OCH2+
O2= CH3OCH2O2.
21

3.4. Discussion
Ozone has been considered as an ideal ignition promoter to isolate the impact
of the induction zone length on detonation [7]. Because of the rapid decomposi-
tion of O3which generates O radical and speeds up the initiation of the overall
chemical reaction, the addition of few thousand of ppm of O3can effectively
reduce the induction distance without modifying the shape of the heat-release
profile and thermodynamic properties. However, results from the literature and
the present data tend to indicate that such an ideal behavior is restricted to a
limited range of conditions and to specific fuel-oxidizer mixtures. As the amount
of O3increases, the reaction rates of competing reactions are modified, which
results in a change in reaction pathways and heat release profile. Kumar et
al. [8] added 1.4% O3to a stoichiometric H2-air mixture and found an addi-
tional thermicity peak in the ZND detonation structure; see their supplemental
material. In the present work, a similar result was obtained at the UCP of a
stoichiometric H2-air mixture with 1% O3addition (see Fig. 2). The early peak
of thermicity originates from the O3related reaction pathway, i.e., R33: H + O3
= O2+ OH. For the DME-O2-CO2mixtures considered, O3addition was also
found to impact a number of competing reaction pathways in the LTC regime.
These modifications change the NTC behavior even at low O3concentrations
(0.1% O3) which results in the modification of the heat release profile. In the
thermicity profile given in Fig. 2(c), the distance between ˙σP1and ˙σP3increases
even with small amounts of O3addition. Aside from the reaction pathways and
heat release profile, the addition of O3changes the stability of the mixture as
well. Kumar et al. [8] also found that the addition of O3decreases the stability
parameters, i.e., the reduced activation energy and the χparameter, making
the detonation more stable. These results are consistent with the observation
of Han et al. [9] who performed 1D and 2D unsteady simulations in H2-O2-He
22

mixtures. The addition of O3reduces unburnt pockets behind the detonation
front and thus increases detonation stability. Because the stability level controls
the inner structure and near-limit behavior of detonations, caution should be
exercised when interpreting the effect of O3on detonation.
When evaluating the impact of an additive on the dynamics of detonation, it
is important to differentiate between thermal and chemical kinetic effects. Ther-
mal effects are related to the modification of the detonation speed, which results
in post-shock temperature changes. Chemical kinetics effects are related to a
speed-up or a modification of the chemical pathways which are separate from
changes of post-shock temperature. Since for slightly curved detonations, the
critical point is affected by both thermal and kinetics aspects simultaneously,
it is not trivial to isolate their individual influence while keeping the location
of the critical point fixed. Nevertheless, based on the analyses some inferences
can be made. According to table 2, the CJ speed is essentially not affected
by the amount of O3but the shock speed at critical points may change signif-
icantly. For H2-air mixtures, the shock speed at UCP decreases by 5.3% and
11.7% with 0.1% and 1.0% O3addition, respectively. As a result, the post-shock
temperature shows a decrease of 7.7% (0.1% O3) and 16.1% (1.0% O3). Since
H2-air mixtures do not have LTC, the thermal effect has a negative impact on
the reactivity. It is the kinetic effect that is responsible for the higher mixture
reactivity. At UCP, the post-shock temperature for DME + 3O2also decreases
as increasing amounts of O3are added. Since the HTC dominates at UCP, the
thermal effect has a negative impact on the reactivity of the mixture and the ki-
netic effect dominates. At LCP, the post-shock temperature for DME + 3O2+
6CO2decreases by 6.2% and 4.4% for 0.1% and 1.0% O3addition, respectively.
With LTC being active for this case, the thermal effect plausibly has a positive
23

impact on the mixture reactivity, but the temperature change alone is unlikely
to result in an increase of the thermicity peak by several orders of magnitude.
While the addition of ozone has both a thermal effect and a kinetic effect, it
seems that the enhanced reactivity observed under the conditions studied is
mainly induced by the kinetic effect.
Concerning the D−κrelationship, although the quasi-steady model used
neglects the intrinsically unsteady nature of detonation waves, configurations
that seem to satisfy its underlying assumptions have been previously discussed
in literature: (i) Chao et al. [16] showed that it characterizes well detonation
failure for weakly unstable waves; (ii) Arienti and Shepherd [13] reported D−κ
curves obtained from 2-D simulations of sub-critical diffracting detonations that
exhibit the same qualitative behavior as that described for H2-air in the current
manuscript; super-/near-critical behaviors on the other hand require reinstating
unsteady terms; and (iii) Radulescu and Borzou [17] and Xiao et al. [30], exper-
imentally realized quasi-steady detonations in constant divergence channels and
showed D−κcurves to be useful for describing the curvature-induced loss in
weakly unstable detonations. In principle, the quasi-steady model can provide
detonation propagation limits and is a useful tool to perform thermo-chemical
analyses, as done in section 3.2, since the main loss mechanism in multidi-
mensional fronts propagating in channels is retained, i.e., weak curvature. For
H2-air mixtures, the shift of the position of the UCP towards larger curvatures
and lower detonation speeds as increasing amounts of O3are added appears
to be consistent with the experimental results of Shi et al. [11] who noted an
extension of the detonation propagation limits to lower pressures. This feature
seems mostly related to the speed-up of the overall reaction by O3decompo-
sition since it is effectively observed at conditions for which no modification
24

of the heat release profile is induced, i.e., for 0.1% addition of O3. The effect
of ozone on DME-O2-CO2mixtures is more complex since important changes
of the reaction pathways were observed and that the shape of the D-κcurves
is strongly modified, even for O3addition of 0.1%. The maximum curvature
is increased at both UCP and LCP, which would theoretically make detona-
tion propagation and re-initiation easier in both the high-speed and low-speed
regimes. Nevertheless, the interpretation of D-κcurves exhibiting multiple turn-
ing points remains unclear in terms of near-limit behavior. The present results
motivate additional numerical and experimental studies on the propagation of
detonation in O3-sensitized mixtures under near-limit conditions, especially for
mixtures with LTC.
Before providing concluding remarks, it is important to discuss the applica-
bility of the quasi-steady model to the mixtures and conditions studied and to
give estimates of the accuracy of the results in terms of critical conditions. It
is well known that the quasi-steady model provides quite accurate results for
regular detonations, but that significant discrepancies exist for highly irregular
detonations [15]. Yet, quantitative estimates of the expected error as a function
of the regularity or stability of the detonation are rarely given. The reduced ac-
tivation energy for all the mixtures studied in the present work was calculated to
assess their stability. The results are provided in the Supplemental Material. In
addition, a number of papers were selected [15, 14, 31, 30, 18] which employed
the quasi-steady model and compared its predictions to various experimental
results, and have quantitatively analyzed the discrepancies between the model
and the measurements. These analyses are also included in the Supplemental
Material. These previous studies show that: (i) For most of the hydrogen-based
mixtures, the reduced activation energies are relatively low and no issue with
the applicability of the quasi-steady approach is expected, consistent with the
25

study of Shi et al. [11]. The uncertainty on the curvature at critical conditions is
expected to be less than 50%. (ii) For the DME-based mixtures, the calculated
reduced activation energies are usually higher than those of the hydrogen-based
mixtures. For such values, qualitative agreement between the experimental be-
havior and the model’s predictions is expected. Nevertheless, the maximum
uncertainty on the curvature at critical conditions is observed to be a factor
of 2 to 4. (iii) For all the mixtures, the maximum uncertainty on the detona-
tion velocity at critical conditions is in the range 10 −20%. It is emphasized
that for some of the hydrogen-based mixtures and the DME-based mixtures,
the situation is complex and previous results are not sufficient to draw defini-
tive unambiguous conclusions concerning the applicability of the quasi-steady
model, and the level of accuracy that can be reasonably expected. This is be-
cause several peaks of heat release of comparable amplitude exist even for ideal
ZND detonations. Such a feature can significantly influence the detonation sta-
bility, and criteria such as the reduced activation energy or the χparameter
may fail to predict the experimentally observed trends; see work on detonation
in DME-O2mixtures by Ng et al. [32] and Mevel and Gallier [33] for further
insight regarding this point.
4. Conclusion
The impact of ozone on the D-κcurves for H2-air and DME-O2(-CO2) mix-
tures was investigated. Our results show a significant increase in the maximum
curvature that a detonation can sustain, both, in the high-speed and low-speed
regimes, by accelerating the high- and low-temperature chemistry. Two mech-
anisms were revealed via detailed thermo-chemical analyses: (i) O3speeds up
the initiation of the overall reaction by fast thermal decomposition to provide
O radical: O3(+M) = O2+ O (+M). The dominant reaction with fuels shifts
26

from a chain-propagation reaction to a chain-branching reaction at the initial
stage, which establishes the radical pool more quickly; (ii) the reaction pathways
change as the amount of O3increases. For H2-air with 1% O3, OH RoP and
HRR analyses reveal that R33: H + O3= O2+ OH produces an additional
thermicity peak at early time. For DME-O2-CO2, the reaction pathways anal-
ysis showed that the contributions of several competing reactions, i.e., R138:
CH3OCH2= CH2O + CH3vs. R151: CH3OCH2+ O2= CH3OCH2O2and
R157: CH2OCH2O2H = 2CH2O + OH vs. R158: CH2OCH2O2H+O2=
O2CH2OCH2O2H, are sensitive to the amount of O3. Their competition en-
hances (0.1% O3) or eliminates (1% O3) the NTC behavior. In addition, mul-
tiple thermicity peaks were found for DME-based mixtures in the low-speed
regime, and for both fuels in the high-speed regime with 1% O3sensitization.
However, there is no causality between the appearance of multiple peak of ther-
micity and the appearance of multiple critical points. The change of dominant
chemical pathways between the high- and low-speed regimes is the main feature
responsible for the appearance of multiple critical points on the D-κcurves.
Acknowledgments
FVL and JMG acknowledge the financial support from the Agence Nationale
de la Recherche Program JCJC (FASTD ANR-20-CE05-0011-01).
Supplemental material
Detailed reaction models in Cantera (.cti) format and time scale calcula-
tions under various detonation situations providing supporting evidence that
the quasi-steady assumption is satisfied under a wide range of conditions, in-
cluding direct detonation initiation, diffraction and in part of the cellular cycle.
27

References
[1] W. Sun, X. Gao, B. Wu, T. Ombrello, The effect of ozone addition on
combustion: Kinetics and dynamics, Prog. Energy Combust. Sci 73 (2019)
1–25.
[2] A. Rousso, N. Hansen, A. Jasper, Y. Ju, Low-temperature oxidation of
ethylene by ozone in a jet-stirred reactor, Journal of Physical Chemistry A
122 (2018) 8674–8685.
[3] J. Sepulveda, A. Rousso, H. Ha, T. Chen, V. Cheng, W. Kong, Y. Ju, Ki-
netic enhancement of microchannel detonation transition by ozone addition
to acetylene mixtures, AIAA Journal 57 (2) (2019) 476–481.
[4] C. Wang, G. Gu, W. Han, Y. Cai, Role of o3addition in the deflagration-to-
detonation transition of an ethylene-oxygen mixture in a macroscale tube,
Shock Waves 30 (2020) 781–787.
[5] W. Han, W. Liang, C. Wang, X. JWen, C. Law, Spontaneous initiation
and development of hydrogen-oxygen detonation with ozone sensitization,
Proc. Comb. Inst. 38 (3) (2021) 3575–3583.
[6] A. Magzumov, I. Kirillov, R. V.D., Effect of small additives of ozone and
hydrogen peroxide on the induction-zone length of hydrogen-air mixtures
in a one-dimensional model of a detonation wave, Combust. Explos. Shock
Waves 34 (3) (1998) 338–341.
[7] J. Crane, X. Shi, A. Singh, Y. Tao, H. Wang, Isolating the effect of in-
duction length on detonation structure: Hydrogen-oxygen detonation pro-
moted by ozone, Combust. Flame 200 (2019) 44–52.
[8] D. S. Kumar, K. Ivin, A. V. Singh, Sensitizing gaseous detonations for
hydrogen/ethylene-air mixtures using ozone and H2O2as dopants for ap-
28

plication in rotating detonation engines, Proc. Comb. Inst. 38 (3) (2021)
3825–3834.
[9] W. Han, J. Huang, C. Wang, Pulsating and cellular instabilities of
hydrogen-oxygen detonations with ozone sensitization, Phys. Fluids 33
(2021) # 076113.
[10] R. Mevel, Y. He, Effect of oxygen atom precursors addition on LTC-affected
detonation in DME-O2-CO2mixtures, Shock Waves 30 (2020) 799–807.
[11] X. Shi, J. Crane, H. Wang, Detonation and its limit in small tubes with
ozone sensitization, Proc. Comb. Inst. 38 (2021) 3547–3554.
[12] J. Fay, Two-dimensional gaseous detonations: velocity deficit, Phys. Fluids
2 (3) (1959) 283–289.
[13] M. Arienti, J. Shepherd, A numerical study of detonation diffraction, J.
Fluid Mech. 529 (2005) 117–146.
[14] Q. Xiao, R. Mevel, S. Gallier, M. Radulescu, Ray-tracking methods for
characterizing the dynamics of curved detonation, Physics of Fluids 34
(2022) # 066104.
[15] A. Camargo, H. Ng, J. Chao, J. Lee, Propagation of near-limit gaseous
detonations in small diameter tubes, Shock Waves 20 (6) (2010) 499–508.
[16] J. Chao, H. Ng, J. Lee, Detonability limits in thin annular channels, Pro-
ceedings of the Combustion Institute 32 (2) (2009) 2349–2354.
[17] M. Radulescu, B. Borzou, Dynamics of detonations with a constant mean
flow divergence, J. Fluid Mech. 845 (2018) 346–377.
[18] Q. Xiao, M. Radulescu, Role of instability on the limits of laterally strained
detonation waves, Combust. Flame 220 (2020) 410–428.
29

[19] R. Klein, J. Krok, J. Shepherd, Curved quasi-steady detonations. asymp-
totic analysis and detailed chemical kinetics., Tech. Rep. FM95-04, GAL-
CIT (1995).
[20] S. Jackson, Gaseous detonation initiation via wave implosion, Ph.D. thesis,
California Institute of Technology (2005).
[21] S. Browne, J. Ziegler, J. Shepherd, Numerical solution methods for shock
and detonation jump conditions, GALCIT report FM2006 6 (2008) 90.
[22] R. M´evel, S. Javoy, F. Lafosse, N. Chaumeix, G. Dupr´e, C. E. Paillard,
Hydrogen-nitrous oxide delay time: shock tube experimental study and
kinetic modelling, Proc. Comb. Inst. 32 (2009) 359–366.
[23] A. Bhagatwala, Z. Luo, H. Shen, J. A. Sutton, T. Lu, J. H. Chen, Numerical
and experimental investigation of turbulent DME jet flames, Proc. Comb.
Inst. 35 (2) (2015) 1157–1166.
[24] H. Zhao, X. Yang, Y. Ju, Kinetic studies of ozone assisted low temperature
oxidation of dimethyl ether in a flow reactor using molecular-beam mass
spectrometry, Combust. Flame 173 (2016) 187–194.
[25] F. Veiga-L´opez, L. M. Faria, J. Melguizo-Gavilanes, Influence of chemistry
on the steady solutions of hydrogen gaseous detonations with friction losses,
Combustion and Flame 240 (2022) 112050.
[26] F. Veiga-L´opez, A. Chinnayya, J. Melguizo-Gavilanes, A methodology
to develop simplified kinetic schemes for detonation simulations, 28th
ICDERS, Naples, Italy, 2022.
[27] H. Liao, S. Kang, N. Hansen, F. Zhang, B. Yang, Influence of ozone addition
on the low-temperature oxidation of dimethyl ether in a jet-stirred reactor,
Combust. Flame 214 (2020) 277–286.
30

[28] X. Gao, Y. Zhang, S. Adusumilli, J. Seitzman, W. Sun, T. Ombrello,
C. Carter, The effect of ozone addition on laminar flame speed, Combust.
Flame 162 (10) (2015) 3914–3924.
[29] H. J. Curran, S. L. Fischer, F. L. Dryer, The reaction kinetics of dimethyl
ether. ii: Low-temperature oxidation in flow reactors, Int. J. Chem. Kinet.
32 (12) (2000) 741–759.
[30] Q. Xiao, M. Radulescu, Dynamics of hydrogen-oxygen-argon cellular det-
onations with a constant mean lateral strain rate, Combustion and Flame
215 (2020) 437–457.
[31] M. Radulescu, J. Lee, The failure mechanism of gaseous detonations: ex-
periments in porous wall tubes, Combust. Flame 131 (2002) 29–46.
[32] H. Ng, J. Chao, T. Yatsufusa, J. Lee, Measurement and chemical kinetic
prediction of detonation sensitivity and cellular structure characteristics in
dimethyl ether-oxygen mixtures, Fuel 88 (2009) 124–131.
[33] R. Mevel, S. Gallier, Structure of detonation propagating in lean and rich
dimethyl ether-oxygen mixtures, Shock Waves 28 (2018) 955–966.
31