The qualitative notion that ignition processes have similar behavior, even over an extensive range of starting conditions, is quantitatively demonstrated through the production of a single ’generic’ ignition curve. The key to the production of the generic curve is the recognition that the basic shapes of the species and temperature profiles occurring in the ignition process differ only in their ’timing’. By ’morphing’ the time scale, the profile shapes can be made to align. From the aligned profile shapes a generic or ’average’ profile can be derived. Synchronizing chemical events modifies the ignition progress times. In addition to fixing the ignition time to have the progress value of one, intermediate ignition events (such as selected profile maxima or inflection points) that occur before ignition are also aligned to have specific ’normalized’ times.

1. RESEARCH POSTER PRESENTATION DESIGN © 2012
www.PosterPresentations.com
The qualitative notion that ignition processes have similar behavior, even
over an extensive range of starting conditions, is quantitatively
demonstrated through the production of a single ’generic’ ignition curve.
The key to the production of the generic curve is the recognition that the
basic shapes of the species and temperature profiles occurring in the
ignition process differ only in their ’timing’. By ’morphing’ the time scale,
the profile shapes can be made to align. From the aligned profile shapes a
generic or ’average’ profile can be derived. Synchronizing chemical events
modifies the ignition progress times. In addition to fixing the ignition time
to have the progress value of one, intermediate ignition events (such as
selected profile maxima or inflection points) that occur before ignition are
also aligned to have specific ’normalized’ times.
Abstract
Synchroniza@on
Time
Devia@ons
from
Linear
Mul@ple
Synchroniza@ons
Generic
Curves
The inherent assumption is that a given progress value, regardless of its
origin, should represent a given stage of the ignition process. In terms of
species profiles, for example, this means that a given species reaches a
maxima at the same progress value regardless of starting conditions. The
one assumption is that relatively the same mechanistic steps are involved.
Different mechanistic steps would imply another generic curve.
Edward
S.
Blurock,
REACTION,
Sweden
Characterizing
Igni@on
behavior
through
morphing
to
generic
curves
This work exploits
the similarities of an ignition process
to produce generic ignition curves,
uniting ignition curves,
each with different starting conditions,
into one common behavior
using one single progress variable.
0 0.0005 0.001 0.0015
Ignition Process Time (s)
1000
1500
2000
2500
3000
Temperature(Kelvin)
0 0.0005 0.001
Ignition Process Time (s)
0
0.001
0.002
0.003
0.004
0.005
0.006
0.007
MassFractionofSpecies
CH2O
H2O2
HO2
CHO
0 1 2
Normalized Time (Ignition at 1.0)
1000
1500
2000
2500
3000
Temperature(Kelvin)
0.50
0.75
1.00
0 0.5 1
Normalized Time (Ignition at 1.0)
0
0.001
0.002
0.003
0.004
0.005
0.006
0.007
SpeciesMassFractions
CH2O
H2O2
HO2
CHO
0 0.2 0.4 0.6 0.8 1
Normalized Time (both with T and H2O2 max)
0
0.0005
0.001
0.0015
0.002
MassFractions
O.50
0.75
1.00
Equivalence Ratio
H2O2 Max Time Norm
0 0.2 0.4 0.6 0.8 1
Normalized Time (with both T and H2O2 Max)
0
0.2
0.4
0.6
0.8
1
NormalizedMassFraction
0.50
0.75
1.00
Equivalence Ratio
All
figures
show
a
range
of
condi/ons,
with
3
star/ng
temperatures
(1200,
1250,
1300
Kelvin),
two
star/ng
pressures
(1,11
atm)
and
three
different
equivalence
ra/os
(0.50,
0.75,
1.00.
The
first
is
a
plot
of
the
H2O2
with
a
/me
normaliza/on
at
both
the
maximum
of
the
H2O2
mole
frac/on
(derived
from
the
average
of
the
set,
0.745)
and
at
the
igni/on
/me
(1.0).The
second
is
with
the
H2O2
maximum
normalized
to
1.0.
A
set
of
igni/on
curves
where
the
/me
is
normalized
to
be
at
the
point
of
igni/on.
The
first
curve
is
/me
versus
temperature
with
5
different
star/ng
temperatures
from
1200
to
1300
and
three
different
equivalence
ra/os
(see
legend).
The
second
curve
shows
the
evolu/on
of
intermediate
species
at
ten
star/ng
temperatures
between
1200
and
1300
Kelvin.
Only
values
several
(20
/mes
10{-­‐5)
past
igni/on
were
calculated.
For
some
star/ng
condi/ons,
the
equilibrium
was
not
reached.
0 0.2 0.4 0.6 0.8 1
Normalized Time
-0.02
-0.01
0
0.01
0.02
0.03
Deviation
0.5
0.6
0.7
0.8
0.9
1.0
0 0.2 0.4 0.6 0.8 1
Normalized Time
-0.05
0
0.05
Deviation
1200K
1210K
1220K
1230K
1240K
1250K
1260K
1270K
1280K
1290K
1300K
The
devia/on
from
linear
progression
based
only
on
igni/on
/me.
Four
events
(see
text)
were
chosen
as
/me
normaliza/on
points.
The
graphs
show
the
devia/ons
along
the
normalized
/me
for
a
(le]
graph)
a
range
of
temperatures,
1200K
to
1300K
(1
atmosphere
pressure
and
equivalence
ra/o
of
1.0),
and
(right
graph)
a
range
of
equivalence
ra/os,
0.5
to
1.0
(Temperature
130
and
pressure
1
atmosphere).}
0 0.2 0.4 0.6 0.8 1
Temperature Normalized Progress
0
0.2
0.4
0.6
0.8
1
CH2
ONormalizedtoMaximum
0.50
0.75
1.00
0 0.2 0.4 0.6 0.8 1
Time Normalized (T, H2O2 Max)
0
0.2
0.4
0.6
0.8
1
NormalizedtoMaximum
0.50
0.75
1.00
0 0.2 0.4 0.6 0.8 1
Time Normalized (T, H2O2 Max, CH2O Max)
0
0.2
0.4
0.6
0.8
1
NormalizedtoMaximum
0.50
0.75
1.00
1 atm
11 atm
The
effect
of
progression
of
/me
normaliza/on
on
the
maximum
normalized
mass
frac/on
curves
of
CH2O
are
shown.
With
each
addi/onal
normaliza/on,
the
spread
of
curves
diminishes.
From
just
igni/on
/me
(le]),
adding
H2O2
maximum
(center),
to
adding
both
H2O2
and
HO2
maximum
(right).
All
figures
show
a
range
of
condi/ons,
with
3
star/ng
temperatures
(1200,
1250,
1300
Kelvin),
two
star/ng
pressures
(1,11
atm)
and
three
different
equivalence
ra/os
(0.50,
0.75,
1.00).
0 0.2 0.4 0.6 0.8 1
Normalized Time
0
0.2
0.4
0.6
0.8
1
NormalizedH2
O2
0 0.2 0.4 0.6 0.8 1
Normalized Time
0
0.2
0.4
0.6
0.8
1
NormalizedHO2
Range
of
Validity
and
the
Choice
of
Events
A
single
generic
curve
is
produced
by
morphing
the
individual
curves
to
coincide
at
specified
sequen/al
chemical
events.
This
is
a
mathema/cal
descrip/on
of
the
statement
that
the
set
of
igni/on
curves
have
the
same
mechanis/c
chemistry.
A
combus/on
process
undergoing
a
different
set
of
mechanis/c
events
should
be
described
by
a
different
generic
curve.
In
this
formula/on
a
different
set
of
mechanis/c
events
is
defined
as
being
a
set
of
curves
in
which
the
set
of
chemical
events
occur
and
occur
in
the
same
order.
This
can
be
used
as
a
criteria
for
differen/a/ng
combus/on
events
with
different
mechanis/c
steps.
A
complete
descrip/on
of
a
combus/on
process
over
the
complete
set
of
ranges
would
be
described
by
a
set
of
generic
curves.
0 0.2 0.4 0.6 0.8 1
Normalized Time
-0.2
-0.1
0
0.1
0.2
DifferenceFromAverage
0 0.2 0.4 0.6 0.8 1
Normalized Time
-0.02
-0.01
0
0.01
0.02
0.03
DifferenceFromPiecewisePolynomial
The
le]
plot
shows
the
difference
between
the
average
generic
curve
and
the
actual
curves
of
the
individual
star/ng
condi/ons.
The
le]
plot
shows
differences
between
the
piecewise
second
degree
polynomial
approxima/on
of
the
curve
differences.
The
solid
lines
denote
minimum
and
maximum
values
and
the
doaed
lines
between
are
the
difference
values.
Towards
Parameteriza@on
Average,
maximum
and
minimum
value
plots
of
HO2
(le])
and
H2O2
(right)
under
a
wider
range
of
pressures
(1,11,21,31
atms),
temperatures
(1200-­‐1300K
at
10K
intervals)
and
equivalence
ra/os
(0.5,0.75
and
1.00)
are
shown.
The
solid
lines
are
/me
normalized
with
four
fixed
points,
including
igni/on
/me
and
the
doaed
lines
is
normalized
/me
with
respect
to
just
igni/on
/me.
0.5 0.6 0.7 0.8 0.9 1
Equivalence Ratio
-0.02
-0.01
0
0.01
0.02
0.03
Deviation
0.77
0.21
0.86
0.94
1200 1220 1240 1260 1280 1300
Starting Temperature
-0.05
0
0.05
Deviation
0.23
0.78
0.88
0.93
The
devia/on
from
linear
progression
based
only
on
igni/on
/me.
Four
events
(see
text)
were
chosen
as
/me
normaliza/on
points.
The
graphs
show
the
devia/ons
along
the
normalized
/me
for
a
(le]
graph)
a
range
of
temperatures,
1200K
to
1300K
(1
atmosphere
pressure
and
equivalence
ra/o
of
1.0),
and
(right
graph)
a
range
of
equivalence
ra/os,
0.5
to
1.0
(Temperature
1300
and
pressure
1
atmosphere).