Advanced Autoignition Theory
A Short (but hopefully sweet) Introduction
by Christos Nicolaos Markides 1, Saturday, 25 of March, 2006.
————————————————————————————————
th
“Humanity has advanced, when it has advanced, not because it has been sober, responsible, and cautious,
but because it has been playful, rebellious, and immature.”
Tom Robbins (1936 - ) 2
“Sometimes he must go alone.
And wait for the World to follow.”
Me
The aim of the current document, is to briefly lay down and attempt to explain our current state of understanding of the phenomenon
of autoignition, as a prelude to the presentation of our most recent advances in this field and how they relate to the existing knowledge
base. I have made it so brief in fact, that at the end you will be undoubtedly begging for more. No self-respecting scientist in this field
likes to admit that there is a — to a lesser or greater degree — pyromaniac in us all. At least to customs. And definitely no serious
autoignition scientist likes to refer to his trade as ‘the study of explosions’. At all. But, that’s what it is. So, join me in this journey
into the exciting field of explosions.
In the three sections below, progressively more complex autoignition cases are presented and analyzed. The insight gained in each
of the more elementary situations are valuable tools for the understanding of the more sophisticated ones, although as we shall see, in
this field, just as it is with so many areas of scientific interest, it is always dangerous to extrapolate results and conclusions outside the
bounds within which they were reached. The fourth and final section contains our latest observations and the — if I may be allowed —
state of the art in this field, at least as we see it here.
1
Hopkinson Laboratory, Department of Engineering, University of Cambridge.
And so I was convinced to write this in an, shall we say ... insubordinate way. But bare with me, it might yet prove to be useful! You decide if the two are
mutually exclusive.
2
1. Homogenous, Stagnant Mixtures
The basic, relevant physical problem here is what we all already know as: a ‘bomb’. The analysis of Mastorakos at http://wwwg.eng.cam.ac.uk/energy/NondasTeaching/3A5/Lecture4.pdf is relevant here. Explore if you wish more. It is fine by me. Consider a
premixed (fuel and oxidizer have been mixed at the molecular level), stagnant (stationary) mixture in a container. Explosion is a term
that corresponds to rapid heat release from a chemical reaction in the mixture. Explosion limits are pressure-temperature boundaries
for a specific fuel-oxidizer mixture equivalence ratio (a non-dimensional fraction of fuel concentration in the mixture) that specify the
boundary between slow and fast reactions.
This explosion can be initiated locally by external means (e.g. by increasing the temperature or pressure at a specific location). In
this case, most – although not all – mixtures will sustain and propagate the localized reaction zone after explosion through the remaining
volume in the container. These mixtures are said to be flammable. Flammability limits are lean (low equivalence ratios) and rich (high
equivalence ratios) mixture equivalence ratios beyond which no flame will propagate. This is the case of forcedignition, or spark ignition,
or even S.I. It will not be considered further.
There is a second, more mystical/strange/exciting way to ignite our mixture known as autoignition, or auto-ignition, or self-ignition,
or spontaneous ignition. In this situation, the explosion is a direct consequence of the — in this case uniform — temperature and pressure
conditions inside the container, in which case it will — theoretically — happen throughout the whole volume simultaneously. Of course, in
practice — I know, surprise — it is not possible to have a mixture that is precisely uniform in fuel concentration, pressure or temperature
everywhere in the space in which it occupies. Somewhere, there will be a slightly higher pressure or temperature which will shift the
local conditions into the explosion limits, before those in the bulk of the mixture. Following this, the fate of the rest of the mixture lies
in the local flammability limits, exactly in the same way as it did for forced ignition.
In other words, and in either case, everything starts with a local phenomenon of rapid heat release called an explosion, followed by
the formation of a small localized flame, and proceeds to become a global effect by flame propagation which depends on the conditions
of the mixture through which it is travelling, as this occurs. It is important to realize that more often than not, these conditions are
affected by the presence of the explosion and the propagation of the flame elsewhere in the container. To sum up, a flame will propagate
through a reactive mixture only if it is,
• Capable of reacting quickly enough to give rise to an explosion, and,
• Inside the flammability limits or if not initially so, shifted within them by the reaction that has already been initiated by a local
explosion as described immediately above.
Thus, the evolution of our system inside the container/bomb depends on the chemistry, which will determine the heat released from
the reaction, and the overall thermodynamic process, which will determine what happens to this heat and how the conditions of the
mixture in the container will be affected. This interplay between heat losses from the system to its environment and temperature rise is
a key concept in autoignition. Great interest has developed not only focusing on the conditions under which explosive reactions occur,
but also, in the rates and mechanisms of steady reactions during which most of the known pollutants form in zones of steady, usually
lower temperature reactions.
We return now to our ‘bomb’ and delve into the — theoretical — situation of a simultaneous explosion due to the global characteristics
of the premixed mixture. The propagation of the reaction zone will not be an issue for two reasons. Firstly, because we set the mixture
pressure and temperature to be inside the flammability limits and secondly, because we only really care about the events leading up to
the event of explosion/ignition. On the other hand, the effects of the walls of the container are very important, since they affect the heat
transfer out of the system. Let myself, explain ... myself? It is not sufficient to consider the initial conditions of the mixture. Even if
the mixture is not initially explosive and the fast chemistry of explosions does not exist, the mixture can be brought within the explosive
limits. As long as fuel and oxidizer are simultaneously present, there will be a finite — although very slow — reaction occurring in the
container. The chemical energy contained in the reactant molecule bonds is greater than that contained in the product molecule bonds
and the progress of the exothermic reactions inevitably leads to both heat release, and consequently, temperature rise. With the help
of the heat released and the particular characteristics of the system, the explosive conditions may be reached. Yet, due to the coupling
between the heat release and the temperature in the container, nothing can be said of either of these two quantities, unless the nature
of the overall thermodynamic process is known.
(i) Without Heat Losses, or Adiabatic
This is the most straightforward case of autoignition. We consider an insulated vessel containing a reactive mixture, initially at
uniform temperature T (x, t = 0) = T0 and pressure p(x, t = 0) = p0 . The initial mixture composition is completely described by the
of f uel
of oxidizer
mass fractions: YF (x, t = 0) = mass ofmass
= Y0F and YO (x, t = 0) = massmass
= Y0O . The vessel is flexible so
f uel and oxidizer
of f uel and oxidizer
that the pressure remains constant and equal to the pressure of the surrounding atmosphere p0 = p∞ . After a period of time, called the
autoignition delay time, τign. , the temperature will rise abruptly and the fuel will be completely consumed. Due to symmetry, autoignition
occurs everywhere simultaneously. The effect of the walls are ignored. The change in mass fractions of the reactants occurs in a uniform
fashion so that: Yf uel (x, t) = YF (t) and Yoxid. (x, t) = YO (t). Consequently, for the temperature T (x, t) = T (t). For a generalized fuel
we may write the chemical equation between fuel F and oxidizer O as:
F + ro O −→ Products
(1)
Throughout this analysis a one-step, second order global reaction is considered. Thus, from chemical kinetics the reaction rate is given
by:
Eact.
A%2 YF YO − Eact.
d[F]
= −Ae− RT [F][O] =⇒ ẇF = −
e RT
dt
M WO
(2)
where [F] is the fuel concentration, A the Arrhenius Pre-exponential Factor, Eact. the Molar Activation Energy, R the Universal Gas
Constant, ẇF the fuel reaction rate, M WO the molecular weight of the fuel and % the density of the mixture.
We now consider the process in more detail. We assume unity Lewis number, Le = %cλp D = 1 and so %D = cλp , where λ is
the molecular conductivity of the mixture, cp the heat capacity at constant pressure and D the Fickian coefficient of mass diffusivity.
Initially, T0 is low and the chemistry is slow but finite. This slow exothermic reaction will release heat. Since the system is insulated,
the thermodynamic process is adiabatic and the heat will be retained causing the temperature to rise slightly. This causes the reaction
rate to increase. Thus, an unstable feedback mechanism is set-up, in which the temperature and reaction rate increase by mutually
promoting each other. Eventually fully-fledged combustion breaks out. This self-acceleration of autoignition is termed thermal runaway.
Even though the consumption of reactants leads to a reduction in reaction rate as described by Equation (2), the explosive increase
due to the increasing temperature in the exponential term more than compensates for this. Finally, as the reactants approach complete
consumption, the reaction can no longer be sustained, the mass fractions take over and the rate decreases to zero. Since there are no
spatial variables, there is no diffusion or convection and the governing equation for energy is reduced to:
Q A%2 YF YO − Eact.
∂T
=
e RT
∂t
c p M WO
(3)
with Q the Heat of Combustion.
Furthermore, the governing equation for the non-reactive or conserved scalar, or Schvab–Zel’dovich coupling functions βF = YF + cpQT
and βO = YO +
%
Scp T
Q
are both of the form:
Dβ
∂ h
∂β i
=
%D(
)
Dt
∂xj
∂xj
(4)
WO
where, S = M
. Note the absence of a source term, hence the ‘non-reactive’ or ‘conserved’. From the aforementioned considerations
M WF
of the conserved scalars and for a premixed system there are no spatial variations in (Equation 4) so that:
%
∂β
= 0 =⇒ β = constant
∂t
(5)
which implies that β must have the same value for both the reactants and the products, in which case:
YF = Y0F −
cp
(T − T0 )
Q
YO = Y0O − ro S
cp
(T − T0 )
Q
(6)
(7)
We may say, that the solution of all equations of the form of (Equation 4) is a unique function of the initial and boundary conditions,
and not of the degree of reaction. Substituting these results into (Equation 3) results in:
ih
i Eact.
Q A%2 h F cp
∂T
cp
=
Y0 − (T − T0 ) Y0O − ro S (T − T0 ) e− RT
∂t
c p M WO
Q
Q
(8)
It is relatively straightforward to solve (Equation 8) numerically, yet in order to gain some insight we shall make a slight approximation.
Prior to autoignition, the chemical time scales are large, the temperature is still low so that the rate of change of species is negligible.
Mathematically, YF ∼
= Y0F , YO ∼
= Y0O and % ∼
= %0 . The essence of this problem lies in the exponential term with the temperature
dependence and this is kept. For our system, up to the point of autoignition, we have:
Q A%20 Y0F Y0O − Eact.
∂T
=
e RT
∂t
c p M WO
(9)
A common linearizing manipulation of the exponential term, for which the essential assumption is that the temperature rise before
ignition is small, e−
Eact.
RT
−
≈ e
Eact.
RT0
−
e
Eact. (T − T0 )
RT02
, allows us to obtain an analytical solution to the problem:
h
i−1 act.
Q A%20 Y0F Y0O Eact. − ERT
RT02
0 t
e
ln 1 −
T = T0 +
Eact.
c p M WO
RT02
(10)
or in terms of time — just stay with me —:
t=
h
i
E
act.
− act.
Q A%20 Y0F Y0O −1 RT02 ERT
2 (T −T0 )
e 0 1 − e RT0
c p M WO
Eact.
(11)
This solution looks graphically something like:
T
.
w
T0
.
w0
Tadiab.
τign.
t
Figure 1: Temperature prior to Autoignition of Premixed, Stagnant Mixture without Heat Losses
Tf
T
Figure 2: Heat Generation prior to Autoignition of
Premixed, Stagnant Mixture without Heat Losses
A subtle point is that in (Figure 1) the temperature will actually level out at the adiabatic flame temperature. And, now we can
define τign. as the Autoignition Delay Time. This can be defined in many ways. For this — theoretical — problem we can define it as
the time at which the temperature becomes infinite, i.e. the asymptote in (Figure 1):
τign. =
act.
Q A%20 Y0F Y0O −1 RT02 ERT
e 0
c p M WO
Eact.
(12)
In this form the rough analysis reveals that τign. :
• Decreases very quickly with increasing initial temperature T0 ,
• Is proportional to the initial density %0 , and thus, inversely proportional to the initial pressure p0 , and,
• Decreases as the initial mass fractions move away from their median, 0.5 so that it obtains a maximum value when Y0F = Y0O = 0.5.
We recall, that these two variables are not mutually independent.
The use of one-step chemistry seems to give trends close to those observed in experimental work. Better results can be obtained by more
complex chemistry. One of the basic conclusions, is that this physical problem will always result in autoignition since there are no heat
losses, which leads nicely to the next section.
(ii) With Heat Losses
A very good place to start is http://www.leeds.ac.uk/fuel/tutorial/frames.html. We consider an identical problem but allow heat
to escape through the walls of the container, which are kept constant at a temperature T0 . There are two classical approaches to this
problem. Semenov considered a one-dimensional situation, with a top-hat (uniform) temperature field in the container and no heat
conduction. This is a rather oversimplified approach, yet it yields qualitative results that are representative of the process. On the other
hand, Frank–Kamenetskii included the heat conduction due to a temperature distribution through the volume of the premixed mixture.
The former approach will suffice in this case, but for the more intense reader I recommend the aforementioned internet pages. The
equation for energy is:
dT
Q
A
=
wf uel −
hsurf. (T − T0 ) = G − L
dt
%cp
V %cp
(13)
Figure 3: Heat Generation and Loss Terms for Autoignition of Premixed, Stagnant Mixture with Heat Losses
The r.h.s has two terms. The first one, G, is the same as before and describes the non-linear generation of heat due to the chemical
reaction, whereas the additional term, L, is for the linear convective heat losses at the container walls, with A the inside area of the
container, V its volume and hsurf. the convective surface heat transfer coefficient. Figure (3) demonstrates the various solutions of
(Equation 3).
• High heat losses L (Curve L1) and G3:
– Point A is a stable solution; heat generation and loss balance and thermal runaway does not occur. The vessel keeps
reacting, at very low rate, yet the heat of the reaction is lost as soon as it is generated. Autoignition does not occur,
dT
= 0 =⇒ T = TA ∼
= T0 .
dt
– Point B is an unstable solution. For a small deviation away from this point and to the left, the system will move back to A,
due to the fact L is greater than the G. A perturbation to the right, will cause autoignition, due to the fact G is now greater
than the L. The heat that is generated cannot be removed in its entirety and the feedback mechanism of the autoignition
process is set-up in the same way as with the no-heat losses case.
• Curves L1 and G2 are mutually tangential at point C and show the critical condition. Autoignition will always occur, only for this
case — with respect to B — it occurs at a lower temperature and is thus considered as the actual autoignition condition.
• For very low heat losses (Curve L2), G is always larger than L. Autoignition will always occur.
The behaviour of the system changes. With high heat losses, autoignition can be completely avoided. With low heat losses autoignition
is possible. This is a key autoignition feature. Successful combustion is possible only if the heat loss is not excessive. This concept is
extremely important in the qualitative understanding of combustion. All combustion technologies, one way or another, are built around
an exploitation of the balance between heat generation and heat loss.
Now try ‘Batch Reactor’ with the GRI-Mech calculator at http://diesel.me.berkeley.edu/ gri mech/cal22/. It is a good place to
start because you can try blowing up — ok, igniting — various mixtures and see what will happen. The applet actually solves the more
generalized species and temperature equations for a closed vessel filled with natural gas and air, i.e.:
∂ ∂Yσ DYσ
= ẇσ +
%D
Dt
∂xj
∂xj
h
Dho
∂p
∂
∂uj
∂uk i
∂ ∂T %
=
+
µ
+
uk +
λ
Dt
∂t ∂xj
∂xk ∂xj
∂xj ∂xj
%
only simplified for uniform mixtures.
(14)
(15)
2. In-homogeneous, Laminar Mixing Layers
The phenomenon of non-premixed autoignition is dominated by scalar mixing due to non-uniformities including those inherent in
turbulent flows. It should be stressed that premixed, turbulent autoignition is not of much interest, since the fluctuations of the velocity
field cannot give rise to fluctuations in the species mass fractions and temperature. The only source terms in the governing equations
for the turbulent fluctuations of Yσ and T come from the chemistry. In other words, fluctuations can be ‘transported’, but not created
by turbulence.
A very important graph for non-premixed autoignition is the S-shaped temperature, T(t), or heat release versus Damköhler number,
Da, non-dimensionalized time,
Da =
residence time
τres.
−→
τchem.
chemical time scale
(16)
Figure (4), with the sharp rise indicating thermal runaway at the autoignition time t = τign. is characteristic of autoignition. The
lower left hand side of the curve corresponds to the slowly reacting state prior to autoignition, when the short residence times, τres. , are
much smaller than the large times of slow chemistry. This prevents autoignition. As the chemistry becomes faster or the residence time
increases, so does Da until the autoignition point is reached. For Da values greater than this have fully fledged combustion. Chemical
reactions that take place at the high temperatures are nearly always fast compared to all turbulent time scales, whereas at the low
temperatures of very low Da, the chemistry is very slow relative to the turbulence. In both these cases, the length and time scales of
the chemistry and turbulence may be separated. This is the region of operation for most engineering combustion processes that classical
combustion models are based on. However, in the regime just prior to ignition the chemical time scales are of the same order as those
of the chemistry and the scale separation assumption is no longer valid.
The autoignition of laminar non-premixed counterflow Liñán, Seiser et al and co-flow Liñán and Crespo mixing layers, is described
theoretically by activation energy asymptotics.
(i) Elliptic Flows (e.g. Counterflows)
This configuration forms the basis of the flamelet model, Wan et al. In steady counterflow mixing layers, diffusion is balanced by
Figure 4: Maximum Flame Temperature versus Damköhler Number
species advection that brings the reactants together in the mixing zone. Mathematically, this is a boundary value problem,
u
∂Yσ
∂ 2 Yσ wσ
=D 2 +
∂x
∂x
%
(17)
and involves only two time scales; one from the chemistry and one from the fluid-mechanics.
Autoignition will only occur if the mixing rate is below a critical value, τign. increasing as the mixing rate increases. This molecular
mixing of the fuel and oxidizer is quantified by the scalar dissipation rate, χ, or the strain rate of the counterflow velocity field. Theory
and numerical simulations have indicated, that indeed, autoignition is not possible for χ < χcrit. . An expression for χ has been proposed
by Peters in the form,
χ=
a + s −2[erf c−1 (2β)]2
e
π
(18)
For the counter-flow diffusion configuration Da can be related to the inverse of the scalar dissipation rate at stoichiometric conditions via
χ−1
τdif f.
stoic.
= τchem.
. Hence, the S-shaped dependence of maximum diffusion flame temperature as a function of the
the diffusive time, Da = τchem.
inverse dissipation rate at stoichiometric conditions χ−1
stoic. , shows the quenching and possible autoignition dependence on this important
parameter on the overall process. Experiments with CO, H2 and C7 H16 have validated this finding for laminar flows. This result has
important implications for the effects of turbulence. Taken at face value, this result would mean that in a CI engine, autoignition would
occur later if the mixing rate is increased and possibly not at all. Of course, we know from experiments that high turbulence intensities
and smaller spatial scales, as associated with faster mixing, in fact results in earlier autoignition. It is a textbook case of not being able
to extrapolate knowledge from laminar to turbulent flows. In this configuration the mixing layer thickness will increase with time due to
thermal diffusion. Mathematically, this is an initial value problem, and will always result in autoignition [Liñán and Crespo, 1973]. The
autoignition time, τign. , depends on the chemistry, the initial temperatures in the fuel and air streams, T0F and T0O and mass fractions,
Y0F and Y0O .
Figure 5: Maximum Flame Temperature versus Scalar Dissipation Rate
3. In-homogeneous, Turbulent Flows
Since, as pointed out previously, the examination of laminar autoignition cannot help us grasp the fundamental issues of turbulent
autoignition, an understanding must come from truly dealing with the turbulent case. Theoretical approaches are extremely difficult
because of the very complex chemical kinetics of the slower chemistry of autoignition, the turbulent closure problem and the strong
coupling of these two. Experimentally there has been a lack of interest in treating this highly complex problem, given not only the
complexity of the underlying process and the additional difficulties introduced by their mutual cross-interference, but also the difficulty
of performing measurements in the ‘hostile’ combustion environment. A true understanding of turbulent autoignition has mostly come
from quite recent DNS studies. Unfortunately, the validity of the DNS results is unknown since the complexity and sheer number of
calculations involved, force these studies to make simplifications. A prime example is the use of quite basic chemistry models.
(i) Stagnant Mixtures
In turbulent autoignition DNS studies, the autoignition spot is more rigorously defined by examining the local heat release, or the
so-called reactedness field and not the temperature, at locations of a certain mixture fraction ξ = ξM R . They are collectively called
iso-surfaces. The reactedness is defined as the temperature increment from initial conditions, conditioned on some value of the mixture
fraction η and can be non-dimensionalized,
b = h(T |ξ = η) − (T0 |ξ = η)i
B=
h(T |ξ = ξM R ) − (T0 |ξ = ξM R )i
h(T |ξ = η) − (T0 |ξ = η)i
=⇒ Bauto. =
∆Tadiab.
∆Tadiab.
(19)
(20)
where ∆Tadiab. = ξQ
is the temperature increase due to reaction in a stoichiometric adiabatic flame. The most important DNS finding,
cp
for isotropic, homogeneous decaying two-dimensional turbulence in a shear-less mixing layer and a simple chemistry model, came from
Mastorakos et al. According to this work,
1. Autoignition always occurs at a well defined mixture fraction ξM R , defined as the most reactive mixture fraction. At any instant,
there are many such possible locations in the mixture. In fact, iso − ξM R lines (this is a two-dimensional domain) can be drawn in
the field and can be predetermined by the laminar flow analysis of Liñán and Crespo, i.e. effectively by the chemistry.
2. The fluid particle that will eventually autoignite, is the one with small gradients of the mixture fraction ξ, i.e. experienced a low
value of conditional scalar dissipation rate, hχ|ξ = ηi. Plots of Bauto. and hχ|ξ = ξM R i have been demonstrated to be very well
correlated as far as the first autoignition location is concerned.
Since then, evidence to support these findings has come from simulations with different codes Sreedhara and Lakshmisha and with
detailed chemical mechanisms for H2 and a quite reliable four-step reduced mechanism for C7 H16 . Recently, an extension has been
made to three-dimensional simulations Sreedhara and Lakshmisha for proper hydrocarbon chemistry, fully validating the earlier results.
Additional features revealed by these simulations include:
1. Vortical structures are more prone to autoignition than strained layers. It is believed that the well-mixed vortex cores, with uniform
vorticity, temperature and concentration — thus associated with much lower χ —, trap heat released by the pre-ignition reactions
and have much less heat losses Thevenin and Candel. Also, at least in the two-dimensional flow fields, autoignition spots are likely
to be small-scale vortex cores and not small-scale diffusion layers Mastorakos et al.
2. The fluctuations of the mixing rate hχ00 |ξ = ηi are important for autoignition, possibly because regions of steep gradients lead to
increased local heat losses, reduced temperatures and much slower reaction rates (recall the exponential Arrhenius dependence on
temperature).
These points have significant modelling inferences. It might be, that the consideration of the means of the mixing rate is insufficient. A
point is being reached, where we are just beginning to be able to reasonably predict the location of autoignition, but these predictions
can only be confirmed by experiment.
The effect of the turbulence character, length and time scales on the magnitude and randomness of τign. is far from understood
and these are exactly the questions this project aims to answer. For the purposes of the current study, the exploration of autoignition
sensitivity to the aforementioned parameters, is best attempted in conditions in which the chemical time scales are of the same order, or
close to the order, of the fluid-mechanical time scales. The direct effect of turbulent mixing is most significant for the non-uniformities
of non-premixed autoignition, but the effect of partial premixing is something that is also very interesting to examine.
(ii) Elliptic Flows (e.g. Counterflows)
Experimental work in the field of turbulent autoignition has always been driven by practical necessities. Until recently, there has
not been an immediate need to understand the phenomenon and this is the main reason for its almost complete inability to address
fundamental questions concerning the nature of autoignition. Most early experimental studies have been, either:
1. Concerned with the effect of global variables, such as pressure and temperature, on τign. in laminar flows Blouch et al and turbulent
flows Fotache et al, which can reveal very little about the effect of the turbulence character on the autoignition sites, or,
2. Based on a well premixed mixture in a uniform turbulent flow that is not characterized at all, with no localized measurements,
Cowell and Lefebre and Spadaccini and TeVelde, or,
3. Performed with the use of shock tubes, Goy et al and Horning et al, in which the turbulence scales are irrelevant.
In addition, for most of the above experiments, it is unknown to what degree the results can be treated with generality and dissociated
from the individual geometry of each case. A questionable inference, is the insensitivity of the global temperature, Tign. , observed in
Blouch et al to the flow intensity, both bulk and turbulent, which seems to contradict findings mentioned in the following paragraph.
It might be that this insensitivity is entirely due to the particular geometric configuration, but also possibly because Tign. as a single,
global experimental variable, fails to say anything about the local autoignition sites.
Overall, there is currently very little data available concerning the effect of the local turbulence character on autoignition. It is
only recently, with the increase in residence times τres. and consequently Da associated with the low emission LPP industrial turbines,
that this issue has become relevant. Appropriate work has been done by Mizutani et al. and Mizutani and Takada in this direction,
although the second paper is concerned with liquid fuel sprays. They conclude that autoignition delay times are notably increased by
strong turbulence. Yet there are still many questions that need to be addressed. The primary focus of these studies are the conditions
for which autoignition is possible. The topology (location and spread) and time evolution of the autoignition sites, or autoignition spots,
with specific reference to turbulence has not been addressed. The experimental database of turbulent autoignition needs to be vastly
improved.