(c)2001 American Institute
of
Aeronautics
&
Astronautics
or
Published with Permission
of
Author(s) and/or Author(s)' Sponsoring Organization.
AIAA
2000-1078
Shapes
of
Soot-free Laminar
Coflowing
Jet
Diffusion
Flames
Z.
Dai,
F. Xu and G. M.
Faeth
The
University
of
Michigan
Ann
Arbor,
Ml
48109-2140
39th
AIAA
Aerospace Sciences
Meeting
&
Exhibit
8-11
January 2001
/
Reno,
NV
For
permission
to
copy
or
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the
American Institute
of
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and
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1801 Alexander Bell
Drive,
Suite 500, Reston,
VA
20191
(c)2001 American Institute
of
Aeronautics
&
Astronautics
or
Published with Permission
of
Author(s) and/or Author(s)' Sponsoring Organization.
2001-1078
SHAPES
OF
SOOT-FREE
LAMINAR
COFLOWING
JET
DIFFUSION
FLAMES
by
Z.
Dai*,
F. Xir and
G.M.
Faeth*
The
University
of
Michigan,
Ann
Arbor,
Michigan
48109-2140
Abstract
The
shapes
(flame-sheet
and
luminous-flame
boundaries)
of
steady
nonbuoyant
round
hydrocarbon-fueled
laminar-jet
diffusion
flames
in
still
and
coflowing
air
were
studied
both
experimentally
and
theoretically.
Flame-
sheet
shapes
were
measured
from
photographs
using
a CH
optical
filter
to
distinguish
flame-sheet
boundaries
in the
presence
of
blue
CO
2
and OH
emissions
and
yellow
continuum
radiation
from
soot.
Present
experimental
conditions
included
acetylene-,
methane-,
propane-,
and
ethylene-fueled
flames
having
initial
reactant
temperatures
of
300 K,
ambient
pressures
of
4-50 kPa,
jet
exit
Reynolds
number
of
3-54,
initial
air/fuel
velocity
ratios
of 0-9 and
luminous
flame
lengths
of
5-55
mm;
earlier
measurements
for
propylene-
and
1,3-butadiene-fueled
flames
for
similar
conditions
were
considered
as
well.
Nonbuoyant
flames
in
still
air
were
observed
at
micro-gravity
conditions;
essentially
nonbuoyant
flames
in
coflowing
air
were
observed
at
small
pressures
to
control
effects
of
buoyancy.
Predictions
of
luminous
flame
boundaries
from
soot
luminosity
were
limited
to
laminar
smoke-point
conditions,
whereas
predictions
of
flame-sheet
boundaries
ranged
from
soot-free
to
smoke-point
conditions.
Flame-
shape
predictions
were
based
on
simplified
analyses
using
the
boundary
layer
approximations
along
with
empirical
parameters
to
distinguish
flame-sheet
and
luminous-flame
(at the
laminar
smoke
point)
boundaries.
The
comparison
between
measurements
and
predictions
was
remarkably
good
and
showed
that
both
flame-sheet
and
luminous-flame
lengths
are
primarily
controlled
by
fuel
flow
rates
with
lengths
in
coflowing
air
approaching
2/3
lengths
in
still
air as
coflowing
air
velocities
are
increased.
Finally,
luminous
flame
lengths
at
laminar
smoke-point
conditions
were
roughly
twice
as
long
as
flame-sheet
lengths
at
comparable
conditions
due to the
presence
of
luminous
soot
particles
in the
fuel-lean
region
of the
flames.
c
n
D
d
Fr
a
,Fr
f
L
o
m
Nomenclature
=
empirical
soot
factor
=
empirical
coflow
factor
=
mass
diffusivity
=
jet-exit
diameter
: air and
fuel
stream
Froude
numbers,
U
ao
/(2gL
f
)andU
f9
/(2gL
f
)
:
acceleration
of
gravity
=
distance
from
jet
exit
to
either
flame-
sheet
or
luminous-flame
tip
:
distance
from
jet
exit
to
virtual
origin
:
burner
mass
flow
rate
m
f
p
Re
r
Sc
u
w
w
lrt
M-
V
=
burner
fuel
mass
flow
rate
=
pressure
=
jet
Reynolds
number,
4 m
/(nd\i)
=
radial
distance
=
Schmidt
number,
v/D
=
streamwise
velocity
=
luminous
flame
diameter
=
luminous
flame
diameter
at
£
= 1/2
=
streamwise
distance
-
stoichiometric
mixture
fraction
=
normalized
streamwise
distance;
Eq. (4)
=
dynamic
viscosity
=
kinematic
viscosity
'Research
Associate,
Department
of
Aerospace
Engineering.;
currently
Lead
Engineer,
G.E.
Aircraft
Engines,
Cincinnati,
Ohio.
'Research
Associate,
Department
of
Aerospace
Engineering.
*A.B.M.
Modine
Professor,
Department
of
Aerospace
Engineering;
Fellow
AIAA.
Copyright
©
2000
The
American
Institute
of
Aeronautics
and
Astronautics
Inc.
All
rights
reserved.
Subscripts
a
f
MAX
o
=
air-stream
property
=
fuel-stream
property
=
maximum
value
=
burner
exit
plane
condition
(c)2001
American
Institute
of
Aeronautics
&
Astronautics
or
Published
with
Permission
of
Author(s)
and/or
Author(s)'
Sponsoring
Organization.
Introduction
Laminar
nonpremixed
(diffusion)
flames
are
of
interest
because
they
provide
model
flame
systems
that
are far
more
tractable
for
analysis
and
experiments
than
practical
turbulent
diffusion
flames.
Clearly,
understanding
of
laminar
diffusion
flames
must
precede
understanding
of
more
complex
turbulent
diffusion
flames.
In
addition,
many
properties
of
laminar
diffusion
flames
are
directly
relevant
to
turbulent
diffusion
flames
using
laminar
flamelet
concepts.
Finally,
laminar
diffusion
flame
shapes
have
been
of
interest
since
the
classical
study
of
Burke
and
Schumann
1
because
they
involve
a
simple
nonintrusive
measurement
that
is
convenient
for
evaluating
flame
structure
predictions.
Motivated
by
these
observations,
the
shapes
of
round
laminar
jet
diffusion
flames
were
considered
both
experimentally
and
theoretically
during
the
present
investigation.
The
study
was
limited
to
nonbuoyant
flames,
however,
in
order
to
minimize
parameters
and
because
most
practical
flames
are not
buoyant.
Most
earlier
studies
of the
shapes
of
hydrocarbon-fueled
nonbuoyant
laminar-jet
diffusion
flames
have
considered
combustion
in
still
air,
see
Refs.
2-6 and
references
cited
therein.
These
studies
have
shown
that
soot-containing
flames
at the
laminar
smoke
point
(flames
at the
condition
of
onset
of
soot
emissions)
have
luminous
flame
lengths
roughly
twice
as
long
as the
length
of
flame
sheet
(the
position
where
fuel
and
oxidant
combine
in
roughly
stoichiometric
proportions
generally
within
a
thin
reaction
zone)
and
have
developed
simple
but
effective
ways
to
estimate
their
shapes.
4
'
5
Corresponding
studies
of
hydrocarbon-
fueled
nearly-nonbuoyant
(weakly-buoyant)
laminar
jet
diffusion
flames
burning
in
coflowing
air
have
also
been
reported,
see
Refs.
1,7-9
and
references
cited
therein.
These
studies
were
limited
to
soot-containing
flames
at
laminar-smoke
point
conditions
and
also
developed
simple
but
effective
ways
to
estimate
their
shapes,
however,
the
corresponding
behavior
of the
flame
sheet
for
these
conditions
(in
either
soot-free
(blue)
flames
or in
soot-containing
flames)
has not
been
addressed.
This
is
unfortunate
because
hydrodynamic
effects
to
reduce
soot
concentrations
in
diffusion
flames
are of
great
interest.
10
"
19
In
addition,
soot-free
hydrocarbon-fueled
flames
are
fundamentally
important
because
they
have
enhanced
computational
tractability
compared
to
soot-containing
flames
due to
the
absence
of the
complexities
of
soot
chemistry,
and
they
provide
results
useful
for
evaluating
detailed
models
of
hydrocarbon-fueled
flame
chemistry
and
transport.
The
ability
to
achieve
soot-free
laminar
diffusion
flames
by
subjecting
the
fuel
stream
to
higher
momentum
(velocity)
oxidant
streams
(e.g.,
by
strong
coflows),
similar
to the
behavior
of air
atomization
processes,
11
'
18
'
19
is
discussed
by Lin and
Faeth
18
and Dai
and
Faeth.
19
The
effect
of
enhanced
coflow
comes
about
because
the
position
of the
flame
sheet
tends
to
be
fixed
by the
fuel
flow
rate
independent
of the
coflow
velocity
at
large
coflow
velocities,
9
which
implies
that
characteristic
residence
times
for
soot
formation
are
inversely
proportional
to the
coflow
velocity.
1819
Thus,
increasing
the
coflow
velocity
inhibits
soot
emissions
and
eventually
leads
to
completely
soot
free
(blue)
flames
as
long
as
flame
lift-off
conditions
are not
exceeded.
This
tactic
was
exploited
during
the
present
study
in
order
to
provide
conditions
where
the
shapes
of the
flame
sheet
of
hydrocarbon-fueled
laminar
jet
diffusion
flames
in
coflowing
air
could
be
observed.
Thus,
the
objectives
of the
present
investigation
were
to
observe
the
flame-sheet
shapes
of
weakly-buoyant
laminar
jet
diffusion
flames
in
coflowing
air
considering
both
soot-free
and
soot-
containing
flames,
and to use
these
results
to
develop
a
simplified
model
of
flame-sheet
shape
for
these
conditions.
Corresponding
results
for
laminar
jet
diffusion
flames
in
nearly
still
air are
also
considered,
in
order
to
highlight
effects
of
coflow
on
flame
structure,
soot
formation
and
soot
emission
properties.
Finally,
luminous
flame
shapes
at the
laminar
smoke
point,
in
both
still
and
coflowing
air,
are
also
considered
for
completeness,
exploiting
earlier
measurements
in the
literature.
59
Experimental
Methods
Test
Apparatus
Experimental
methods
were
similar
to Lin et
al.,
5
Lin and
Faeth
9
and
Lin
17
and
will
be
described
only
briefly.
Effects
of
buoyancy
were
minimized
by
observing
flames
at
relatively
small
pressures
(< 50
kPa)
with
either
relatively
large
coflow
velocities
(air/fuel
velocity
ratios
up to 9) or
with
relatively
large
source
fuel
Froude
numbers
when
coflow
velocities
were
small.
The
burner
was
placed
within
a
windowed
cylindrical
chamber
and
directed
vertically
upward
along
the
chamber
axis.
The
windowed
chamber
had a
diameter
of 300 mm and a
length
of
1200
mm.
Optical
access
was
provided
by two
pairs
of
opposing
windows
having
diameters
of 100 mm and
centered
on a
(c)2001
American
Institute
of
Aeronautics
&
Astronautics
or
Published
with
Permission
of
Author(s)
and/or
Author(s)'
Sponsoring
Organization.
horizontal
plane
located
500 mm
above
the
base
of the
windowed
chamber.
The
flames
were
positioned
so
that
their
full
lengths
could
be
observed
and
photographed
through
the
windows.
The
burner
was a
coaxial-tube
arrangement
with
the
fuel
flowing
from
the
inner
port
(1.6-,3-2-
and
4.8-mm
inside
diameters
with
the
outer
wall
of the
tube
tapered
to
provide
a
negligible
thickness
at the
tube
exit)
and air
flowing
from
a
concentric
outer
port
(60-
mm
inside
diameter).
The
inner
port
had
sufficient
length
to
provide
fully-developed
laminar
pipe
flow
at
the
burner
exit.
The
outer
port
had
several
layers
of
beads
and
screens
to
provide
a
uniform
nonturbulent
flow
at the
burner
exit.
Flame
lengths
were
limited
so
that
test
conditions
approximated
flames
in a
uniform
air
coflow
based
on
earlier
laser
velocimetry
measurements
of
flow
velocity
distributions.
17
'
18
The
Test
Conditions
burner
tube
exit
was
placed
10 mm
above
the
last
screen
of the air
coflow
so
that
the
flames
were
free
to
attach
somewhat
below
the
burner
exit
(which
often
was the
case
unless
lift-off
conditions
were
approached).
significant
afterglow
of OH
luminosity
for the
low-
pressure
flames
observed
during
the
present
experiments).
In
order
to
locate
the
flame
sheet,
however,
dark-field
photographs
were
obtained
using
a
narrow-band
filter
designed
to
pass
radiation
from
the
excited
CH
band
associated
with
radical
reactions
at the
flame
sheet
(430
nm
center
frequency
with
a 10 nm
half
width
pass
band).
This
luminosity
was
relatively
weak
but the
present
flames
were
very
steady
so
that
exposure
times
could
be
increased
to
obtain
satisfactory
photographs.
The
outer
extremity
of the CH
image
was
taken
as the
flame
sheet
location,
because
CH
luminosity
is not
associated
with
fuel-lean
regions
of
the
present
flames.
Experimental
uncertainties
of the
flame
sheet
measurements
are the
same
as the
luminous
flame
boundary
measurements.
Fuel
was
supplied
to the
inside
port
from
commercial
gas
cylinders.
Fuel
flow
rates
were
controlled
and
metered
using
critical
flow
orifices
in
conjunction
with
pressure
regulators;
the
flow
properties
of the
orifices
were
calibrated
using
wet-test
meters.
Air was
supplied
from
the
room
using
critical-
flow
orifices
to
control
and
meter
air
flow
rates.
The
exhaust
products
were
diluted
with
air to
reduce
flow
temperatures
and
then
removed
using
the
laboratory
vacuum
pump
system.
The
flames
were
ignited
using
a
small
torch
that
was
removed
from
the
flow-field
after
the
flames
had
stabilized.
Instrumentation
Dark-field
photographs
of the
flames
were
obtained
using
a
35-mm
reflex
camera.
The
photographs
were
subsequently
printed
using
a 100 x
125
mm
film
format,
and
then
scanned.
Flame
shapes
were
measured
directly
from
the
scanned
images,
using
objects
of
known
size
to
calibrate
vertical
and
horizontal
distances.
Experimental
uncertainties
(95%
confidence)
of
luminous
flame
diameters
and
lengths
were
less
than
2%.
The
dark-field
color
photographs
sufficed
to
locate
luminous-flame
boundaries
as
either
the
outer
extremity
of
yellow
luminosity
due to
continuum
radiation
from
soot,
or the
inner
boundary
of
blue
luminosity
from
the
flame
sheet
(which
exhibited
a
Test
conditions
are
summarized
in
Table
1.
Present
measurements
considered
methane-,
acetylene-,
ethylene-
and
propane-fueled
flames;
earlier
measurments
considered
propylene-
and
1,3-butadiene-
fueled
flames.
Gas
purities
were
greater
than
99%,
by
volume,
for all the
fuel
gases
except
acetylene
which
only
had a 98%
purity,
by
volume,
due to
contamination
by
acetone
which
is
present
in
commercial
acetylene
gas
cylinders
for
safety
purposes.
The
effect
of
acetone
on the
properties
of
flames
similar
to the
present
flames
was
evaluated
during
earlier
experiments.
17
'
18
This
was
done
by
comparing
observations
with
and
without
acetone
vapor
present,
using
the
acetone
removal
system
described
by
Hamins
et
al.
20
to
create
an
acetone-free
acetylene
fuel
stream.
The
effect
of
acetone
on
luminous
flame
shapes
and
laminar
smoke-point
flame
lengths
was
found
to be
11
17,18
small.
Table
1
Summary
of
test
conditions"
Parameter"
C,H.
Fuel
flowrate,().49-3.12
mg/s
Re(-)
">,„(-)
p,kPa
d, mm
[!,„,
mg/s-m
L
p
mm
w,
p
,
mm
z/(-)
2.7-45.6
0.41-4.88
9.9-54.1
0.008-7.140.0058-5.01
21.3-49.4
1.6,4.8
48.0
5.7-41.5
6.5-17.7
0.0552
4.1-21.3
1.6,4.8
51.7
5.0-54.9
7.9-24.4
0.0704
0.50-4.66
3.6-47.6
0.009-8.80
3.5-21.5
1.6,4.8
49.7
7.1-47.0
7.9-24.7
0.0638
1.53-4.08
8.3-219
0.3-7.0
19-50
4.8
49.3
41-108
5.9-13.1
0.0636
0.59-3.81
4.9-48.5
0.012-5.71
11.3-35.2
1.6,4.8
47.0
9.4-51.3
8.1-22.4
0.0603
0.74-2.71
39-14.4
0.8-32.5
19-50
4.8
49.8
21-75
4.3-10.0
0.0668
"Air
port
inside
diameter
of 60 mm
with
burner
directed
vertically
upward.
Reactant
temperatures
of
roughly
300 K.
"Commercial
gases
in
cylinders
with
purities
as
follows:
greater
than
98.0%
by
volume
for
C
2
H
?
and
greater
than
99.0%
by
volume
for the
rest.
(c)2001
American
Institute
of
Aeronautics
&
Astronautics
or
Published
with
Permission
of
Author(s)
and/or
Author(s)'
Sponsoring
Organization.
Theoretical
Methods
Flame
shape
predictions
were
obtained
using
the
simplified
analysis
of Lin et
al.
5
for
laminar
diffusion
flames
in
still
air and Lin and
Faeth
9
for
laminar
diffusion
flames
in
coflowing
air.
In
both
instances,
a set of
easily
used
equations
was
sought,
along
with
recommendations
for
selecting
the
thermochemical
and
transport
properties
appearing
in
the
equations,
rather
than
more
complete
methods
that
would
require
numerical
solution
using
a
computer.
The
approach
used
for
flames
in
still
gases
was to
extend
the
analysis
of
Spalding,
2
which
is
described
in
more
detail
by
Kuo;
3
the
approach
used
for
flames
in
coflowing
gases
was to
extend
the
analysis
of
Mahalingam
et
al.
8
Except
for
ambient
flow
properties,
the
major
assumptions
of
flame
shape
analyses
in
still
and
coflowing
gases
were
the
same,
9
as
follows:
steady,
axisymmetric
laminar
jet
diffusion
flames
at
constant
pressure
in an
unbounded
environment
having
uniform
properties
(velocities
and
scalar
properties);
effects
of
buoyancy
are
negligible;
flow
Mach
numbers
are
small
so
that
effects
of
kinetic
energy
and
viscous
dissipation
are
negligible;
the
flames
have
a
large
aspect
ratio
so
that
diffusion
of
mass
(species),
momentum
and
energy
in
the
streamwise
direction
is
small;
for the
same
reasons,
the
solution
of the
governing
equations
can be
approximated
by
far-field
conditions
where
the
details
of
the
initial
conditions
can be
replaced
by
integral
invariants
of the
flow
for the
conservation
of
mass,
momentum
and
energy;
similarly,
the
convection
velocities
of the
flow
can be
approximated
by
ambient
streamwise
velocities;
all
chemical
reactions
occur
in a
thin-flame
sheet
with
fast
chemistry
so
that
fuel
and
oxidant
are
never
simultaneously
present
at
finite
concentrations;
the
diffusivities
of
mass
(of all
species),
momentum
and
energy
are all
equal;
all
thermophysical
and
transport
properties
are
constant
throughout
the
flame;
and
effects
of
radiation
are
small.
These
assumptions
are
discussed
in
Refs.
5 and 9;
they
are
justified
mainly
by
their
past
success
in
providing
good
estimates
of
flame-sheet
and
flame-luminosity
boundaries
based
on
simplified
analyses.
5
'
9
Under
these
assumptions
a
simple
formula
can
be
obtained
for
flame-sheet
and
luminous-
flame
lengths
both
in
still
and
strongly
coflowing
gases,
as
follows:
9
where
C
n
=
3/32
and
2/32
for
weak
and
strong
coflow
and C
f
is
roughly
0.5 and 1.0 for the
flame-sheet
location
and the
location
of the
luminous-flame
boundary
for
laminar
smoke-point
conditions,
respectively
(more
accurate
selections
of C
f
will
be
considered
later).
The
algorithm
for
computing
flame
properties
from
Eq. (1) was
completed
by
using
the
values
for the
Schmidt
number
and the
viscosity
of air
at
the
average
of the
adiabatic
flame
temperature
and
the
ambient
temperature
from
Braun
et
al.
21
Typical
of
past
work
with
hydrocarbon-fueled
laminar-jet
diffusion
flames
burning
in
air,
the
value
of the
Schmidt
number
did not
change
significantly
over
the
test
range;
thus,
Sc =
0.76
was
used
for all the
results
considered
during
the
present
investigation.
Similarly,
the
correlations
of
flame
lengths
were
improved
during
past
work
by
introducing
the
empirical
virtual
origin
parameter
L
0
/d.
see
Refs.
5 and 9. The
effect
of a
virtual
origin
was not
very
significant
for
present
conditions,
however,
so
that
L/d = 0 was
used
instead.
The
expressions
for
luminous
flame
diameters
differ
for
laminar-jet
diffusion
flames
in
still
and
coflowing
air.
5
'
9
For
flames
in
still
air the
expression
becomes:
5
wZd =
(2)
whereas
the
corresponding
equation
for
flames
in
coflowing
air
becomes:
9
wZ
s
/d
=
KK/uJ
where
in
both
cases,
£
=
(x-L
o
)/(L
f
-L
o
)
(3)
(4)
(L
f
L
0
)/d
=
C.C.Re
Sc/Z
sl
(1)
Other
expressions
for
maximum
value
of w,
W
MAX
,
and
the
value
of w at the mid
position
of
flame,
w
1/2
,
can be
found
in
Refs.
5 and 9.
Results
and
Discussion
Flame
Appearance
Photographs
of a
soot-free
acetylene-fueled
laminar
jet
diffusion
flame
in
coflowing
air at
near
lift-
off
conditions
are
illustrated
in
Fig.
1. The
figure
on
the
left
is a
black
and
white
image
of
conventional
dark-field
color
photograph.
The
figure
at the
right
is a
black
and
white
image
of a
dark-field
color
photograph
obtained
using
the CH
filter.
Both
images
are
essentially
the
same
indicating
that
the
flame
sheet
in