Combustion and Flame The role of low temperature chemistry in combustion mode development under elevated pressures

Abstract

Negative Temperature Coefficient (NTC) behavior is an essential feature of low-temperature oxidation for large hydrocarbon fuels, which is of particular relevance to cool flame and auto-ignition. In this study, using n-heptane as a typical fuel exhibiting NTC, combustion phenomena involving both auto-ignition and flame propagation are computationally studied at initial temperatures within and above NTC regime under elevated pressures in a one-dimensional planar constant-volume configuration, with detailed kinetics and transport. Multi-staged flame structures representing cool flame and hot flame are observed, and consequently, different types of auto-ignition are identified during two-staged and single-staged flame propagation scenarios by varying initial temperature. Specially, as the initial temperature increases, the behavior of cool flame is gradually suppressed and auto-ignition position is transferred from the location ahead of flame front to end-wall region, leading to different combustion modes and peak pressure magnitudes. Moreover, attributed to the chemical reactivity processed by cool flame, the flame propagation of the cases within NTC regime is even faster than those beyond NTC regime. A recently developed two-staged Livengood–Wu integral is further utilized to predict these auto-ignition scenarios, yielding good agreement and further demonstrating the significant role of NTC chemistry in modifying the ther-modynamic state and chemical reactivity at upstream of a reaction front. Finally, different combustion modes and knocking intensity for these detailed calculations are summarized in non-dimensional diagrams , which suggest that a higher initial temperature does not guarantee a higher knocking intensity, instead, the developing and developed detonation wave initiated by an auto-ignition occurring within NTC regime could even induce higher knocking intensity in comparison to the thermal explosion under the temperatures beyond NTC regime.

Full text

Combustion and Flame 174 (2016) 179–193
Contents lists available at ScienceDirect
Combustion and Flame
journal homepage: www.elsevier.com/locate/combustame
The role of low temperature chemistry in combustion mode
development under elevated pressures
Jiaying Pan
a
, Haiqiao Wei
a , ∗, Gequn Shu
a
, Zheng Chen
b
, Peng Zhao
c , ∗
a
State Key Laboratory of Engines, Tianjin University, Tianjin 30 0 072, China
b
SKLTCS, Department of Mechanics and Engineering Science, Peking University, Beijing 100871, China
c
Department of Mechanical Engineering, Oakland University, Rochester, MI 48309, USA
a r t i c l e i n f o
Article history:
Received 4 May 2016
Revised 20 June 2016
Accepted 9 September 2016
Keywo rds:
Negative Temperature Coefficient (NTC)
Auto-ignition
Cool flame
Spontaneous propagation
Livengood–Wu integral
Knocking intensity
a b s t r a c t
Negative Temperature Coefficient (NTC) behavior is an essential feature of low-temperature oxidation for
large hydrocarbon fuels, which is of particular relevance to cool flame and auto-ignition. In this study, us-
ing n-heptane as a typical fuel exhibiting NTC, combustion phenomena involving both auto-ignition and
flame propagation are computationally studied at initial temperatures within and above NTC regime un-
der elevated pressures in a one-dimensional planar constant-volume configuration, with detailed kinetics
and transport. Multi-staged flame structures representing cool flame and hot flame are observed, and
consequently, different types of auto-ignition are identified during two-staged and single-staged flame
propagation scenarios by varying initial temperature. Specially, as the initial temperature increases, the
behavior of cool flame is gradually suppressed and auto-ignition position is transferred from the loca-
tion ahead of flame front to end-wall region, leading to different combustion modes and peak pressure
magnitudes. Moreover, attributed to the chemical reactivity processed by cool flame, the flame propaga-
tion of the cases within NTC regime is even faster than those beyond NTC regime. A recently developed
two-staged Livengood–Wu integral is further utilized to predict these auto-ignition scenarios, yielding
good agreement and further demonstrating the significant role of NTC chemistry in modifying the ther-
modynamic state and chemical reactivity at upstream of a reaction front. Finally, different combustion
modes and knocking intensity for these detailed calculations are summarized in non-dimensional dia-
grams, which suggest that a higher initial temperature does not guarantee a higher knocking intensity,
instead, the developing and developed detonation wave initiated by an auto-ignition occurring within
NTC regime could even induce higher knocking intensity in comparison to the thermal explosion under
the temperatures beyond NTC regime.
©2016 The Combustion Institute. Published by Elsevier Inc. All rights reserved.
1. Introduction
Downsized spark-ignited (SI) engines have become increasingly
attractive because of their high thermal efficiency and low CO
2
emissions. However, the risk of knock and super-knock has been
a large obstacle especially for downsized engines operating under
low-speed and high-load conditions [1] . It is generally considered
that engine knock is caused by end-gas auto-ignition before the
arrival of SI flame [2] , while super-knock is attributed to a de-
veloping detonation resulting from a resonance between acoustic
waves by auto-igniting hot-spots and a reaction wave propagating
along negative temperature gradient in multi-scale turbulent flow
∗Corresponding authors.
E-mail addresses: whq@tju.edu.cn (H. Wei) , pengzhao@oakland.edu ,
zhaodbustc@gmail.com (P. Zhao).
field [3] . When super-knock occurs, the stochastic auto-igniting
hot-spots may consume the entire mixture within less than a mil-
lisecond and thus cause a knocking intensity beyond 200 bar [4] .
Despite the numerous studies devoted to engine knock and super-
knock, due to the complex nature of the problem itself, there are
still many ambiguities associated with the key physical-chemical
mechanisms, such as reaction-pressure wave interactions [5,46,47] ,
deflagration to detonation transition (DDT) [6,46] and the role of
chemistry [7] .
Addressing a thermal hot spot characterized by certain radius
and temperature gradient in one-dimensional (1D) configuration,
a pioneering work by Zel’dovich [8] proposed that there are three
kinds of reaction wave front affected by auto-ignition, correspond-
ing to supersonic auto-ignition, detonation and subsonic auto-
ignition with different propagation speeds compared with speed
of sound, respectively. In this classification, thermal explosion
represents a limiting case of supersonic auto-ignition with an
http://dx.doi.org/10.1016/j.combustflame.2016.09.012
0010-2180/© 2016 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

180 J. Pan et al. / Combustion and Flame 174 (2016) 179–193
infinite propagation speed of the reactive front. Based on
Zel’dovich auto-ignition concept, Bradley and coworkers
[9–13] showed that depending on initial temperature gradi-
ents within a hot spot, a quantitative diagram consisting of a
normalized temperature gradient ( ξ) and the ratio of acoustic
time to excitation time of chemical energy release ( ε) could
be developed, which is capable of further classifying different
auto-ignition modes with regime boundaries, including subsonic
deflagrative auto-ignition, developing detonation, supersonic
deflagrative auto-ignition and thermal explosion. Recently this
diagram has been extensively utilized to analyze engine knock
and super-knock [13,14] . Later, Rudloff et al . [15] introduced a
third non-dimensional parameter ( π), representing the conversion
of chemical energy in end-gases into overpressure, to evaluate
the efficiency of auto-ignition on knocking severity for pre-
ignition in realistic engines. These methodologies basically provide
quantitative criteria on abnormal combustion based on whether
reaction front can couple with pressure wave or not. More re-
cently, Grogan et al. [16] developed an ignition regime diagram
with consideration of turbulence, chemistry and heat transfer
in rapid compression machines. Im et al . [17] proposed non-
dimensional criteria to predict weak and strong ignition regime of
homogeneous reactant mixture with turbulence and temperature
fluctuations. Therefore, turbulence has been further included to
classify different auto-ignition regimes. However, these studies
only consider simplified chemistry and/or simple fuels, without
accounting for the essential features of the oxidation of large
hydrocarbon fuels, such as low-temperature chemistry (LTC) and
negative-temperature coefficient (NTC) phenomenon [18] , which
will fundamentally affect the auto-ignition kinetics and induce
substantial non-monotonicity into combustion system. Meanwhile,
according to the theoretical analysis on ignition delay gradient in
[9] , severe knock could be induced in NTC regime, while this point
has not been adequately addressed using above non-dimensional
analysis. Therefore, it merits more research on the potential effect
of LTC on above combustion modes and their classifications.
NTC behavior is of significant relevance to engine knock in SI
engines [19] , cool flame [20] , flame stabilization [21] and the com-
bustion of homogeneous charge compression ignition (HCCI) en-
gines [22] . Sun et al . [23] numerically investigated the transitions
from ignition to flames as well as the combustion dynamics in
stratified n-heptane/air mixture, which showed that the rich LTC
reactivity with fuel stratification can lead to knocking and acous-
tic formation. Ju et al . [24] numerically investigated ignition and
flame propagation in n-heptane/air mixture, and they found that
there were at least six different combustion regimes at the tem-
peratures near NTC. Martz et al . [25] analyzed the physical pro-
cesses of auto-igniting end-gas influencing reaction front propa-
gation under spark-assisted compression ignition (SACI) combus-
tion conditions. However, the evolutions of flame propagation and
pressure/shock waves induced by local auto-ignition were not con-
sidered. Chen and coworkers [26,27] identified different super-
sonic auto-ignition modes and reaction-pressure wave interactions
caused by a cool spot in NTC regime for n-heptane/air mixture,
with emphasis on the transient evolutions following an artificial
thermal stratification as an initial condition, while the evolutions
of flame propagation, auto-ignition and subsequent reaction front
remain unclear. In addition, most previous studies have been fo-
cused on high-temperature conditions [28,29] , but systematic stud-
ies are still needed for the conditions involving both hot and cool
flames in NTC regime.
The primary objectives of current numerical investigation are to
further explore the role of LTC on the interactions of flame propa-
gation and auto-ignition, especially in NTC regime, to provide fun-
damental understandings for such physical–chemical processes and
to gain practical insights for LTC effect on knocking combustion.
As a major component of Primary Reference Fuel (PRF), n-heptane
has been extensively studied with its chemistry relatively well un-
derstood and validated. Moreover, it qualitatively shares the same
NTC chemistry pathways with other gasoline surrogates (e.g. iso-
octane), despite its much lower octane index [5,26,30] . Actually,
with the tendency of intake boost and engine downsizing, it is
expecte d that NTC regime shall shift to high temperature region,
leading to greater relevance of low temperature even for regu-
lar gasoline. Therefore, n-heptane is considered in current study
as a representative fuel with NTC behavior. Meanwhile, the cur-
rent work is based on a simplified constant-volume configuration
with well-defined initial and boundary conditions, which allows
detailed chemistry and transport and includes most of the essen-
tial physical and chemical components during knocking combus-
tion, such as flow unsteadiness, hot-spot(s) auto-ignition, deflagra-
tion/detonation wave and pressure/shock wave propagation with
little ambiguity in analysis.
2. Model validation and specifications
The skeletal mechanism for n-heptane oxidation adopted in cur-
rent work is from Yo o et al . [31] , which includes 88 species and
387 reactions, and it has been validated and tested against a wide
range of combustion targets such as ignition delay time and lami-
nar flame speed. Figure 1 (a) shows the comparisons of ignition de-
lay time of stoichiometric n-heptane/air calculated by three reac-
tion mechanisms [31–33] under low and high pressure conditions,
together with shock tube experimental data [34] . These results in-
dicate that current mechanism is able to accurately predict low-to-
high temperature ignition, including NTC regime. Meanwhile, the
current mechanism has been validated against the laminar flame
speed measurement at different pressures and equivalence ratios
[35] , yielding satisfactory agreement, as shown in Fig. 1 (b). An-
other widely used kinetic model Jetsurf 1.0 [36] , without low tem-
perature chemistry, is also utilized to calculate the flame speed
under the same conditions for comparison. The good agreement
demonstrates the capability of both mechanisms in predicting reg-
ular laminar flame propagation and implies the insignificant role
of low temperature chemistry on flame propagation with normal
temperatures.
For laminar flame calculation with normal and elevated un-
burned temperatures, PREMIX [37] is utilized to calculate the 1D
steady planar flame, which is further applied as initial condition
of the unsteady simulation, where the flame front starts to propa-
gate in the auto-ignitive mixture. An in-house code A-SURF (Adap-
tive Simulation of Unsteady Reactive Flow) is used to perform
the simulations of unsteady reactive flow by solving full govern-
ing equations with detailed chemistry and mixture-averaged for-
mulation of the detailed transport properties. During the simula-
tions, the second-order, Strang splitting fractional-step procedure is
adopted to separate the time evolution of stiff reaction term from
that of the convection and diffusion terms. In the first step, the
non-reactive flow is resolved and the second-order Runge–Kutta,
MUSCL-Hancock and central difference schemes are employed to
calculate temporal integration, convective and diffusion flux, re-
spectively. The second step is to solve the chemistry term using the
VODE solver [38] . A multi-level algorithm with dynamic adaptive
mesh refinement has been used here, which can accurately resolve
ignition initiation, reaction front and pressure/shock wave as well
as detonation wave, as shown in previous work [39–41] . In cur-
rent work, the finest mesh x is 0.8 μm, and minimum Courant–
Friedrichs–Lewy (CFL) number is maintained to be less than 0.1
with corresponding time step t = 5 ×10
−13
s, which can keep
good stability and convergence during the whole computation. The
detailed code specifications and validation can be further found in
[39–41] .

J. Pan et al. / Combustion and Flame 174 (2016) 179–193 181
0.6 0.8 1.0 1.2 1.4 1.6 1.8
0.01
0.1
1
10
100
1000
a
b
41.5 atm
)sm(emityalednoitingI
1000/T (1/K)
Yoo et al.
Shock tube exp.
Mehl et al.
KUCRS
13.5 atm
0.6 0.8 1.0 1.2 1.4
0
10
20
30
40
50
60
)s/mc(deepsemalfranimaL
E
q
uivalence ratio
P
0
=1 atm
P
0
=5 atm
P
0
=10 atm
Fig. 1. (a) Ignition delay time for stoichiometric n-heptane/air mixture at adiabatic constant-volume conditions. (b) Comparisons of laminar flame speed between experiments
(symbols) [35] and calculations at different equivalence ratios (Solid lines for JetSurF 1.0 [36] , Dashed lines for current mechanism).
3. Results and discussion
3.1. NTC-affected flame propagation
It is expected with gradually elevated inlet temperature, the
role of auto-ignition and NTC chemistry should be more significant
on flame propagation. To demonstrate such effects, 1D steady pre-
mixed flame under P
0
= 40 atm is calculated for stoichiometric n-
heptane/air mixture at different inlet temperatures from T
in
= 700
to 110 0 K, with temperature and heat release rate profile presented
in Fig. 2 , which is shown in a reference frame that is moving with
the flame. It is observed that as T
in
increases from 700 to 760 K,
a single-staged flame transforms into a two-staged one, and it re-
turns to the single-staged structure with further increment in inlet
temperature (e.g. T
in
= 110 0 K), manifesting the counterpart of NTC
behavior in flame propagation. For the two-staged flame structure,
the first stage represents cool flame and second one corresponds
to hot flame; and the higher the inlet temperature, the closer the
cool flame to the inlet.
Further, the flame speed corresponding to different inlet tem-
peratures at three computation domain lengths is presented in
Fig. 3 (a), which shows the non-monotonic change in laminar flame
speed with the upstream affected by LTC reactivity. Taking the
computation domain of L = 2 cm for example, the flame speed
at T
in
= 700 K is approximate S
u
= 1.1 m/s while it increases up
to S
u
= 20 m/s at T
in
= 860 K where two-staged flame structure
emerges. As the inlet temperature further increases to T
in
= 960 K,
the flame speed shows a decreasing trend due to the weakend LTC
reactivity in NTC regime, and it then increases again with further
increment in inlet temperature at high-temperature region.
It should be noted that both temperature increment and par-
tial reaction should affect the flame speed in NTC and higher

182 J. Pan et al. / Combustion and Flame 174 (2016) 179–193
Fig. 2. Profile of temperature and heat release rate of premixed steady flame propagation for stoichiometric n-heptane/air mixture at pressure P
0
= 40 atm.
temperature regimes, and their effects are largely coupled. To
further evaluate their individual contribution and isolate the role
of the LTC in flame propagation with elevated inlet temperatures,
simulations based on Jetsurf 1.0 are performed and compared
with those obtained using the current mechanism in variable
domain length, as shown in Fig. 3 (b). It presents that for low
inlet temperature ( T
in
< 700 K), the flame speed obtained from
both mechanisms increases slowly with the inlet temperature and
seems insensitive to domain length, implying negligible role of
auto-ignition in flame propagation, although quantitative differ-
ence does exist in flame speed between these two mechanisms.
For high enough inlet temperature (e.g. T
in
= 110 0 and 120 0 K),
both mechanisms show similar increasing trend in flame speed
with very close values, which further implies the negligible in-
fluence from the LTC under high enough temperature. For the
intermediate temperature regime within NTC, two mechanisms
show different trends in flame speed with inlet temperature as
well as different dependence on domain length. With LTC, flame
speed firstly increases and then decreases with temperature,
showing the similar NTC behavior as ignition delay. This implies
the inherent non-monotonicity induced by LTC in flame propaga-
tion within NTC regime. Therefore, comparing the results of the
two mechanisms, it is highly suggested that the source of the
variations in the flame speed within NTC regime is mainly due to
the reactive intermediates from auto-ignition chemistry.
Meanwhile, it is observed that different from the behavior un-
der normal conditions, the flame speed with partially reactive up-
stream boundary quantitatively depends on the length of compu-
tational domain. It is normally considered that the flame burn-
ing flux is an eigen-value of the energy or species conservation
equation, which could be uniquely identified by imposing proper
boundary conditions. Note that in such cases, the so-called “cold
boundary difficulty” is avoided by setting zero reaction rate at up-
stream boundary for the temperature below a certain value, so
that no reaction occurs in the preheat zone. In current cases, the
“cold boundary difficulty” is inevitable due to the much higher el-
evated temperature and more pronounced partial reactions from
auto-ignition, so that the basic assumption for the above relations
fails and the flame burning flux cannot be uniquely determined
any more, as demonstrated by computations in Fig. 3 (b) with vari-
able domain lengths. This dependence basically implies the un-
steady nature of the auto-ignitive upstream boundary and the criti-
cal role of residence time for the auto-ignition-affected flame prop-
agation, similar to the recently identified laminar premixed cool
flame [20] . The non-monotonic NTC behavior of the laminar flame
propagation nevertheless holds qualitatively for different domain
lengths in NTC regime.
To further identify the controlling chemistry in flame prop-
agation, sensitivity analysis of laminar flame speed is investi-
gated at three different initial temperatures, T
in
= 600 K below NTC,
T
in
= 900 K within NTC and T
in
= 110 0 K beyond NTC regime, as
shown in Fig. 4 . It is observed that for the case of T
in
= 600 K,
the most important reactions are the chain branching reaction
H + O
2
= OH + O and chain propagation reaction CO + OH = CO
2
+ H,
consistent to existing understandings of flame chemistry un-
der normal thermodynamic conditions [42] . For the case of
T
in
= 110 0 K, the dominant chain branching reaction transforms
into H
2
O
2
+ M = OH + OH + M, implying the controlling role of auto-
ignition chemistry. Unlike the cases of T
in
= 600 K and 110 0 K, the
dominant chemical reactions of T
in
= 900 K within NTC regime in-
volve typical low-temperature chemistry pathways such as the iso-
merization reaction C
7
H
15
O
2
= C
7
H
14
OOH, and the low-temperature
chain branching C
7
H
14
OOHO
2
= NC
7
KET + OH. From the above analy-
sis, it is suggested that the involvement of auto-ignition chemistry
and the corresponding variation of flame structure should be ac-
counted for in order to understand and describe the flame propa-
gation under elevated thermodynamic conditions, such as those in
internal combustion engines [43] .
In order to mimic the complex combustion under engine-
relevant conditions, the solutions of premixed steady flame are ex-
actly extracted, including local thermodynamic state and species
concentration by a point-to-point manner, and then are utilized as
the initial condition of the unsteady reactive flow [44–46] in a 1D,
planar, constant-volume combustion chamber with reflective and

J. Pan et al. / Combustion and Flame 174 (2016) 179–193 183
a
b
Fig. 3. (a) NTC-affected flame speed as a function of inlet temperature with domain size of 2, 4 and 6 cm. (b) Flame speed variation with domain length at different inlet
temperatures using Jetsurf 1.0 and current mechanism for stoichiometric n-heptane/air mixture at P
0
= 40 atm.
adiabatic right boundaries. Symmetric condition has been set up
at the left boundary and the computation domain length is 4.0 cm.
Initially, all hot flame fronts are located at x = 1.0 cm in the un-
steady reactive flow with a stationary initial state, and then these
flame fronts start to propagate, as shown in Fig. 5 . The initial flow
is static and the initial pressure of P
0
=40 atm is uniformly dis-
tributed in the computational domain. Due to the thermal and ki-
netic inhomogeneities caused by pressure wave disturbances, local
auto-ignition may occur at its most favorable locations across the
combustion chamber, such as in the end-gas region [46] or even in
the preheat zone of a propagating flame [47] . The subsequent evo-
lutions of main flame propagation, auto-ignition (AI) initiation and
AI reaction front propagation are then investigated in details.
3.2. Auto-ignition scenarios during flame propagation
Figure 6 shows the evolutions of temperature, pressure, heat re-
lease rate and species mass fraction for the case with T
i
= 760 K,
below the lower boundary of NTC regime. It is observed that a
two-staged flame initially propagates into stationary reactive mix-
ture, with hot flame front located at x = 1.0 cm and cool flame front
at x = 1.8 cm. During the following process, the temperature and
pressure of the bulk mixture gradually increase. It is observed that
at the reaction front defined by local maximum temperature gra-
dient, the peaks of heat release rate for hot and cool flame are
approximately Q
max
= 10
13 and 10
11
J/m
3
s, respectively, indicating
two-orders of magnitude higher heat release rate from the hot

184 J. Pan et al. / Combustion and Flame 174 (2016) 179–193
Fig. 4. Sensitivity analysis of laminar flame speed for stoichiometric n-heptane/air
mixture at T
in
= 60 0–10 0 0 K and P
0
= 40 atm.
flame. While at other locations, both temperature and pressure
fields are largely uniform, without obvious disturbance by acoustic
waves. Until t = 248 μs, end-gas mixture experiences the first-stage
auto-ignition and its temperature rises simultaneously, such that
the cool flame front disappears at x = 2.35 cm. Therefore, a portion
of n-C
7
H
16
(approximate 63.4%) is oxidized by low-temperature
combustion and CH
2
O concentration increases to the maximum
level in the bulk mixture, implying chemical reactivity of the cool
flame. Subsequently, an auto-ignition event occurs around the lo-
cation where cool flame disappears around x = 2.4 cm, and two
AI flame fronts develop and spread out accompanied with strong
pressure waves. The AI flame spreading to the left interacts with
the hot flame, burns up the mixture trapped in the middle and
eventually leads to a local pressure mutation of P
max
= 30 atm,
while the one spreading to the right develops into a detonation
wave, with a very high pressure peak of P
max
= 600 atm and heat
release rate peak of Q
max
= 10
15
J/m
3
s, two-orders of magnitude
higher than the regular hot flame.
The transient propagation speeds of all reaction fronts involved
are shown in Fig. 7 , with the local sound speed plotted as a ref-
erence. It is observed that the hot flame and cool flame initially
propagate with a mean deflagration speed of ν=40 and 28 m/s,
respectively, with a weak oscillating behavior due to acoustic
wave disturbances in current constant-volume combustion cham-
ber. Subsequently, an auto-ignition event is initiated at x ≈2.3 cm
and produces two fast-propagating reaction fronts 1 and 2. The AI
front 1 develops from subsonic mode into supersonic mode while
the AI flame front 2 quickly develops into supersonic mode with
the maximum speed of νmax
=2460 m/s which then gradually de-
creases to ν=2150 m/s. This speed is much higher than the CJ det-
onation speed of νCJ
= 1854 m/s for stoichiometric n-heptane/air
mixture at T
i
= 120 0 K and P
0
= 70 atm.
Figure 8 shows the evolutions of temperature, pressure, heat re-
lease rate and typical species mass fraction for T
i
= 820 K, close to
the NTC lower boundary. It is observed that in contrast to the case
of T
i
= 760 K, auto-ignition not only occurs at the location where
cool flame front disappears, but also at end-wall region, result-
ing in more complex combustion mode with multiple flame fronts.
When t = 174 μs, auto-ignition is initiated at x = 2.5 cm and gen-
erates two fast-propagating AI flame fronts. Similar to the pre-
vious case, the one spreading to the right develops into a deto-
nation wave with P
max
= 800 atm and Q
max
= 10
16
J/m
3
s. However,
another AI front originated from end-wall region quickly propa-
gates to the left of combustion chamber, with P
max
= 600 atm and
Q
max
= 10
15
J/m
3
s. Eventually, the two AI flame fronts collide at
x = 3.4 cm, resulting in a substantial local pressure mutation with
P
max
> 180 0 atm. Meanwhile, it is observed that there are new AI
spots induced by pressure wave occurring just ahead of AI flame
front, which may contribute to the detonation formation. The spa-
tial distributions of OH, CH
2
O and n-C
7
H
16
mass fraction are con-
sistent with the evolutions of flame propagation, auto-ignition oc-
currence and its development in the reactive flow.
Figure 9 shows the evolutions of temperature, pressure, heat
release rate and species mass fraction for T
i
= 900 K, right in the
NTC regime under the pressure of 40 atm. Compared with previ-
ous two cases, new observations can be obtained as the follow-
ing. Firstly, there is no apparent auto-ignition event taking place
Fig. 5. Initial profiles of single-staged and two-staged flame in the unsteady reaction flow with left symmetric boundary and right wall boundary.

J. Pan et al. / Combustion and Flame 174 (2016) 179–193 185
a
b
Fig. 6. Evolutions of (a) temperature T (K), pressure P (atm), heat release rate Q (J/m
3
s) and (b) mass fraction of OH, CH
2
O and n-C
7
H
16
species for T
i
= 760 K and P
0
= 40
atm.
at the location ahead of hot flame front. This is due to the fact
that the corresponding cool flame temperature rise is much lower,
which leads to reduced upstream cool flame reactivity. Secondly,
for the end-wall auto-ignition, it does not immediately develop
into a detonation wave but firstly experiences a supersonic com-
bustion process without strong discontinuity in local pressure field.
The reason for this is that some mixture in the upstream of AI
flame front reaches the auto-ignition threshold and tends to ex-
perience auto-ignition simultaneously, as shall be analyzed later.
Thirdly, during the evolution of the AI front in the end-gas region,
the variations in pressure peak from P
max
= 200 atm at t = 155 s
to P
max
= 570 atm at t = 158 s as well as substantial changes in
heat release rate suggest that there is a transition in combustion
mode, and this can also be identified by the characteristic sponta-
neous ignition front propagation speed presented in the following
section.
With initial temperature further increased to T
i
= 110 0 K be-
yond NTC regime, there is only hot flame propagation, as shown
in Fig. 10 . It is observed that an auto-ignition is initiated at
t= 288.58 s and subsequently generates an AI flame front with a
much flatter temperature gradient. Unlike cases of T
i
= 760 and
820 K, the pressure amplitude for current AI flame is P
max
=170
atm before interacting with the hot flame, without observable
shock wave due to the much faster flame propagation. Meanwhile,
the heat release rate peak with Q
max
=10
14
J/m
3
s for the AI flame
is close to that of the initial hot flame, and one-order of mag-
nitude lower than that of the normal detonation wave as shown
in Fig. 6 . These observations indicate that end-wall auto-ignition
does not develop into a detonation wave and appears to fall
into a conventional engine knock. Actually, it is shown in the
following that the AI reaction front at T
i
=110 0 K propagates at the
level of spontaneous ignition front propagation speed, in which
subsequent auto-ignition occurs due to the substantial chemical
reactivity gradient ahead of AI flame front. This can be also sup-
ported by the gradual increases of OH mass fraction and decreases
of CH
2
O and n-C
7
H
16
mass fraction in the unburned zone.

186 J. Pan et al. / Combustion and Flame 174 (2016) 179–193
Fig. 7. Transient flame speed and sound speed ahead of different flame fronts for
T
i
= 760 K.
Figure 11 shows the transient propagation speed of different re-
action fronts with the local speed of sound as a reference. It is ob-
served that the transient AI front propagation speed of T
i
= 110 0 K
case is much higher than that of T
i
= 900 K. Meanwhile, both auto-
ignition events issue supersonic propagating flame front; however,
it fails to develop into a detonation wave for the AI flame of
T
i
= 110 0 K case in terms of flame thickness, peak heat release rate
and peak pressure. Further, the comparison of hot flame speed be-
tween T
i
= 900 and 11 0 0 K case shows that due to the absence
of cool flame, the mean propagation speed for T
i
= 110 0 K case is
lower even though its initial temperature is much higher, as shown
in Fig. 12 (a), consistent with the results of the NTC-affected lam-
inar flame speed shown in Fig 3 . Figure 12 (b) further gives the
distributions of temperature and mass fraction of typical species
for OH, H and CH
2
O during the flame propagation at T
i
= 900 and
110 0 K. It is observed that although the temperature is much lower,
the mass fraction of typical species (OH, H and CH
2
O) ahead of
flame front for T
i
= 900 K case are always higher, especially for the
CH
2
O mass fraction. Above observations basically suggest the sig-
a
b
Fig. 8. Evolutions of (a) temperature T (K), pressure P (atm), heat release rate Q (J/m
3
s) and (b) mass fraction of OH, CH
2
O and n-C
7
H
16
species for T
i
= 820 K.

J. Pan et al. / Combustion and Flame 174 (2016) 179–193 187
a
b
Fig. 9. Evolutions of (a) temperature T (K), pressure P (atm), heat release rate Q (J/m
3
s) and (b) mass fraction of OH, CH
2
O and n-C
7
H
16
species for T
i
= 900 K.
nificant role of NTC chemistry on the propagation of a flame front
in the unsteady reactive flow, potentially by elevated thermody-
namic conditions and the feed of active intermediates from low-
temperature chemistry.
From the comparison and analysis from Figs. 11 to 12 , it is then
evident that NTC could significantly promote flame propagation,
and the sensitivity of ignition delay to temperature within the NTC
regime largely affects the combustion mode of the AI front. An-
other interesting point could be raised among these cases is about
the location that auto-ignition could occur. This could be analyzed
by investigating the detailed local temperature and pressure his-
tory on a case-by-case basis, since in general, a location achieving
auto-ignition or not primarily depends on its pressure and temper-
ature trajectory. In any of these complicated scenarios, both pres-
sure fluctuation and local heat release from slow oxidation con-
tribute to the pressure and temperature history and leads to the
eventual observations.
In order to clarify the combustion mode during local auto-
ignition development, the spontaneous propagation speed intro-
duced by Zel’dovich [8] is further discussed here:
S
ig
=




dτ
dT




·|
∇T
|
−1
(1)
where S
ig
is the spontaneous ignition front propagation speed and
τthe ignition delay time for the homogeneous mixture at the aver-
age or bulk temperature and pressure. S
ig
addresses that combus-
tion wave propagates forward as a result of spontaneous ignition of
local mixture. If S
ig
is close to or comparable to the speed of sound,
the combustion wave can be coupled to the acoustic wave, even-
tually leading to a detonation wave. When S
ig
approaches infin-
ity, thermal explosion is the corresponding physical phenomenon
where all the homogeneous mixture auto-ignites simultaneously
[8,9,48] .
The profiles of temperature and spontaneous ignition front
propagation speed for T
i
= 900 and 110 0 K are further plotted in
Fig. 13 , corresponding to the instant of 10% maximum heat release
rate of end-wall auto-ignition. It is observed that the temperature
field is relatively uniform for T
i
= 110 0 K case, and consequently
the spontaneous ignition front propagation speed is significantly
higher, with a mean S
ig
> 10, 0 0 0 m/s. This propagation speed is

188 J. Pan et al. / Combustion and Flame 174 (2016) 179–193
a
b
Fig. 10. Evolutions of (a) temperature T (K), pressure P (atm), heat release rate Q (J/m
3
s) and (b) mass fraction of OH, CH
2
O and n-C
7
H
16
species for T
i
= 110 0 K.
Fig. 11. Transient flame speed and sound speed ahead of different flame fronts for
T
i
= 900 and 11 0 0 K.
much higher than that of local sound with a ≈680 m/s, leading
to negligible interactions between the reaction front and pressure
wave, such that the combustion mode is dominant by the spon-
taneous ignition. For the case of T
i
= 900 K, the spontaneous igni-
tion front speed S
ig
is much lower across the domain and ranges
from supersonic to subsonic modes. This then leads to more sig-
nificant effects of pressure wave on the development of reaction
fronts, and facilitates the formation of detonation wave. Therefore,
the AI reaction front induced by end-wall auto-ignition propagates
with spontaneous propagation mode for T
i
= 110 0 K, while there is
a mode transition to detonation for the case of T
i
= 900 K, consis-
tent with the simulation results shown in Figs. 8 –10.
3.3. Prediction of auto-ignition timing
Now we have demonstrated the evolutions of flame propaga-
tion, auto-ignition and pressure/shock waves with different ini-
tial temperatures. To further analyze the auto-ignition process,
instantaneous thermodynamic state of auto-ignition location is
extracted and then utilized to calculate the instantaneous ignition

J. Pan et al. / Combustion and Flame 174 (2016) 179–193 189
a
b
Fig. 12. (a) Comparison of hot flame speed between T
i
= 90 0 and 110 0 K case. (b) Temperature and species mass fraction of three different scenarios during flame propaga-
tion.
Fig. 13. Comparison of temperature and AI front speed between T
i
= 900 and 11 0 0 K case.

190 J. Pan et al. / Combustion and Flame 174 (2016) 179–193
a
b
Fig. 14. Temperature evolution of (a) end-wall auto-ignition at T
i
= 760 and 90 0 K and (b) auto-ignition ahead of flame front at T
i
= 820 K and corresponding staged
Livengood–Wu integration.
delay based on current n-heptane mechanism. Subsequently, a
recently developed two-staged Livengood–Wu (L–W) integration
method [49] is introduced with the capacity of accommodating the
LTC and change of thermodynamic conditions at cool flame state.
The formula of two-staged L–W integral used for low- and high-
temperature auto-ignition prediction can be expressed as:
1 =
 t
1
t
0
dt
τ1
(
T , P
)
(2)
1 =
 t
2
t
1
dt
τ
(
T

, P

)
(3)
where t
0
is the initial time when chemistry becomes important,
t
1
the time for the appearance of cool flame, t
2
the instant for the
major ignition, and τ1
and τ’ corresponds to the first-stage ignition
delay and second-stage ignition delay ( τ2
in NTC regime or τh
in
higher temperature regime), respectively. Previous work [49] has
validated its enhanced performance in the prediction of two-stage
auto-ignition timing under extensive HCCI engine conditions.
As stated in L–W equation, the integration is proposed to pre-
dict the auto-ignition timing under variable thermodynamic con-
ditions by using the inverse of ignition delay at constant volume
conditions as an indicator for chemical reactivity. If the integral at-
tains a value of unity before end-gas has been entirely consumed
by flame front, auto-ignition will occur. Otherwise, the end-gas will
be burned up by the propagating main flame. Figure 14 shows
the results of temperature evolution and corresponding staged
L–W integration for different auto-ignition events. For the end-wall
auto-ignition events at T
i
= 760 and 900 K, the first-stage auto-
ignition of both cases are well predicted by the first-stage L–W
integral. For the second-stage auto-ignition, the integral value for
T
i
= 760 K just attains a level of approximately 0.5 when the hot
flame arrives, demonstrating that the local mixture is consumed
by the propagating hot flame rather than auto-ignition; while for
T
i
= 900 K case, the second-stage integral gradually increase to
unity before the hot flame arrival, demonstrating the continuously
accumulated reaction progress due to auto-ignition. To explain the
auto-ignition event ahead of hot flame front, the data from the lo-
cation of x = 2.6 cm has been processed for the cases of T
i
= 820 K,
as shown in Fig. 14 (b). It is seen that both integrals well predict
the first- and second-stage auto-ignition timing, with the integral
value continuously increasing to unity. This analysis further indi-
cates the significant role of the LTC in auto-ignition phenomena,
which not only modifies the thermodynamic state, but also en-
hances the local chemical reactivity.
3.4. Combustion mode and knocking intensity
It is suggested that the pressure peak and knocking intensity
greatly depend on combustion mode during local auto-ignition

J. Pan et al. / Combustion and Flame 174 (2016) 179–193 191
Fig. 15. Summary of combustion mode and knocking intensity in non-dimensional diagrams of ( ξ, ε) and ( η, ε). The read block symbols respectively present normal
combustion (N), knock(K), super-knock (S) and thermal explosion (E) from Kalghatgi and Bradley’s work [14] .
development [15,46] : auto-ignition can induce high amplitude of
pressure wave similar to conventional knock while (developing)
detonation wave can cause extremely high amplitude of shock
wave as observed in super-knock. To address this relation, further
analysis is performed based on the 1D diagrams. According to the
“detonation peninsula” theory proposed by Bradley et al. [9–10] ,
a non-dimensional parameter, ξ, describing the coupling between
acoustic wave and reaction front propagation, can be defined as:
ξ= a/ u
a
=
(
∂ T /∂ r
) (
∂ τi
/∂T
)
a (4)
where a is local sound speed, u
a AI flame speed and r the spatial
coordinate of reactive zone.
And meanwhile, a second non-dimensional parameter, ε, as-
sessing the rapidity of reaction energy release, is expressed by:
ε =
(
r
0
/a
)
/ τe (5)
where r
0
represents the initial radius of hot spot determined by
temperature gradient, and τe is the excitation time defined as the
time interval between 5% and maximum heat release rate.
In order to fully characterize the knocking intensity, an addi-
tional non-dimensional parameter is introduced here:
η=
(
P
max
−P
AI
)
/
(
P
isoc
−P
AI
) (6)
where P
AI
is the pressure at auto-ignition timing (corresponding to
the instant of 10% maximum heat release rate in current work),
P
max the maximum pressure during AI flame propagation, and P
isoc
the maximum pressure obtained from theoretical isochoric com-
bustion based on the initial auto-ignition conditions.
Based on the above definitions, the non-dimensional parame-
ters ξand ε are evaluated at the main auto-ignition timing cor-
responding to the instant of 10% maximum heat release rate to
accommodate the cool flame heat release, while non-dimensional
parameter ηis evaluated during auto-ignition development. Fi-
nally, two non-dimensional diagrams, ( ξ, ε) and ( η, ε), are plot-
ted, to evaluate and analyze the combustion mode and knock-
ing intensity for T
i
= 760–1100 K cases, as summarized in Fig. 15 ,
where B(1) represents the auto-ignition ahead of flame front (i.e.
front AI) and B(2) the end-wall auto-ignition (i.e. wall AI) for the
820 K case. Previous experimental work by Kalghatgi and Bradley
[14] showed that as engine combustion process shifts from nor-
mal combustion to knocking combustion and thermal explosion, ξ
quickly decreases and ε increases. For current work, it is observed
that as initial temperature increases, there is a transition for the
auto-ignition position from the location ahead of flame front to
end-wall region, accompanied by obvious variations in combustion
mode and knocking intensity. The diagram ( ξ, ε) shows that the
combustion mode for T
i
= 760–900 K cases is located in developing
detonation regime, while the one for T
i
= 110 0 K case is in ther-
mal explosion regime with a higher propagation speed but much
lower pressure magnitude. These observations demonstrate that
with NTC chemistry, (developing) detonation wave with high pres-
sure peak could be triggered even at much lower temperatures and
at different locations of the combustion field. More importantly,
the diagram ( η, ε) shows that most developing detonation cases
(point A, B(2) and C) correspond to a knocking intensity of ap-
proximate η=4, however, it attains an level of η=6.2 for B(1) case,
demonstrating the significant effect of the LTC on knocking inten-
sity. While for the scenario with a much higher initial temperature
T
i
= 110 0 K (point D), the knocking intensity caused by thermal ex-
plosion is much less severe. Therefore, the combination of these
non-dimensional diagrams well characterizes different combustion
modes and knocking intensity, with more complete guidance on
knocking combustion.
4. Conclusions
In the present study, one-dimensional simulations are per-
formed to study the auto-ignition and flame propagation of n-
heptane/air mixture in a broad temperature range including NTC
regime under elevated pressure conditions. Fundamental insights
for low-temperature chemistry effect on knocking combustion are
provided. It shows that affected by NTC chemistry, steady pre-
mixed flame propagation shows a two-stage behavior, including
both hot and cool flame segments. With the increases of inlet tem-
perature, the flame speed shows the corresponding non-monotonic
NTC behavior: it first increases with increasing initial temperature,
then decreases with further increasing initial temperature in NTC
regime, and increases again with the initial temperature beyond

192 J. Pan et al. / Combustion and Flame 174 (2016) 179–193
NTC regime. Further calculations show such behavior qualitatively
retains with variable domain length, while the quantitative depen-
dences of flame speed and structure on domain length with el-
evated temperature basically implies that flame speed is not an
eigenvalue anymore due to the aggravated cold boundary difficulty
with auto-ignition inlet temperatures.
These steady premixed flames are then utilized as the initial
conditions of the unsteady simulations in a one-dimensional, pla-
nar, constant-volume combustion chamber with adiabatic and re-
flective boundary. The results show that different auto-ignition sce-
narios are identified during two-staged and single-staged flame
propagation. As initial temperature increases, there is a transition
for auto-ignition position from the location ahead of flame front
to end-wall region. The transition of auto-ignition position is ac-
companied by obvious variations in flame speed, local pressure
and heat release rate, suggesting that these auto-ignition events
induce different auto-ignitive reaction fronts with various combus-
tion modes and pressure peaks. Chemical structure analysis further
demonstrates the essential role of reactive intermediates feeding
within the NTC regime, which consequently leads to faster flame
propagation.
To predict auto-ignition timing in these scenarios, a recently de-
veloped staged Livengood-Wu correlation has been utilized to ana-
lyze the auto-ignition processes occurring both at end-wall region
and ahead of flame front. The results show that both first- and
second-stage Livengood–Wu integral gradually increase to unity at
the simulated low- and high-temperature auto-ignition events, re-
spectively. Such prediction further identifies the controlling role of
low temperature chemistry in modifying the thermodynamic state
and local chemical reactivity, triggering auto-ignition at different
favored locations.
Finally, two non-dimensional diagrams are introduced to an-
alyze the combustion mode and knocking intensity. It is found
that with low temperature chemistry, the combustion mode with
(developing) detonation could be induced at much lower initial
temperatures, while thermal explosion is triggered at even higher
initial temperature with a lower pressure peak, leading to con-
ventional engine knock. Moreover, depending on the subsequent
evolutions of different reaction fronts, knocking intensity could
vary even with the same combustion mode determined by initial
hot-spots properties. The most severe knock is actually induced in
the case with initial temperature right below the NTC regime and
involves the collision of different reaction fronts from multiple
hot-spots.
Acknowledgment
This work was supported by National Natural Science Foun-
dation of China (Grant No. 51476114 ), China Postdoctoral Science
Foundation ( 2016M590201 ) and 2016 Industry, Education and Re-
search Foundation of Tianjin University. PZ is supported by the
startup funding at Oakland University.
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