Dietrich, Ross, T'ienandShu
CANDLE
Candle Flames
FLAMES
IN
(Shortened
NASA
Page1
NON-BUOYANT Title:
ATMOSPHERES
CANDLE
D. L. Dietrich* Lewis Research
FLAMES)
and H. D. Ross Center, Cleveland,
Ohio
Y. Shu _ and J. S. T'ien Case Westem
# Currently
* Please
with Diesel
address
Cummings,
all correspondence
Daniel L. Dietrich Mail Stop 110-3 NASA Lewis Research Center 21000 Brookpark Road Cleveland, Ohio 44135 Phone: (216) 433-8759 FAX: (216) 433-3793 e-mail:
[email protected]
Reserve
University,
Columbus,
to:
Indiana.
Cleveland,
Ohio
Dietrich,
Ross, T'ien and Shu
This paper microgravity
yellow
addresses
environment
the Shuttle,
Candle Flames
the flames
(presumably
the behavior
became
soot) in the flame.
transport
to the flame and thus limited
higher
difference designed
content
concentration.
axisymmetric
The paper the gas-phase,
slowly
oxygen
pre-extinction
flame
(OS).
less than 60
flame inhibited
and Mir flames
oxygen
on the Mir OS were because
was primarily
to the flame. decreased
On
of a The
the re-
In both environments, as the ambient
Both sets of experiments
oxygen
showed
just prior to extinction.
liquid/wick
oscillations
Station
for as long as 45 minutes.
model of candle
similar
quiescent
into the flame lifetime
burned
transport
decreased.
a numerical
but uses a simplified
longer
2
there was significant
were typically
The flames
ratio gradually
flame oscillations
with a shape and size quantitatively predicts
the Shuttle
where
the candle
lifetime.
The Mir flames
between
also presents
lifetimes
persisted
and the height-to-width
in the sealed chamber
spontaneous,
the flame
that did not inhibit
the flame intensity
and the Mir Orbiting
that contained
luminosity
in the flame lifetime candlebox
The flame
candlebox
that the yellow
initial oxygen
flame in a long-duration,
dim blue after an initial transient
The safety-mandated
except
of a candle
both on the space Shuttle
seconds.
similar,
Page
phase.
The model
to the Shuttle
if the decrease
flame.
The model predicts
and Mir flames. in ambient
oxygen
is detailed
a steady
in
flame
The model
also
is small enough.
INTRODUCTION The behavior in the absence everyone. system. oxidation transfer.
of a candle
of gravity.
The fuel is a mixture
Despite
they are used often
is the most common
This is primarily
From a fundamental
chemistry.
flame
because
perspective
The flame interacts
these complexities,
hydrocarbon
with a porous
candles
to study a wide range
the candle
the candle
of long chain-
public
about combustion
flame is so familiar
flame is a complex molecules
phenomena
to
combustion
with complicated
wick, with intricate
offer such simplicity
of combustion
inquiry
heat and mass
in experimental
setup
such as flame flicker
that
Dietrich,
Ross, T'ien
(Buckmaster T'ien,
and Shu
and Peters,
1986),
1978), low-gravity
(Carleton
and Weinberg,
magnetic
fields
The candle
away
from the flame.
workers
(Ross
et al., 1991a,b;
flames
typically
produce
drop tower studies, characteristics
a nearly
Both Carleton Dietrich
flames
flame
interested
in how long the candle
interested
in the extinction
microgravity.
We used the candle
the Shuttle
on the Mir Orbiting experiments model
of the candle
The Shuttle
1 and 2 show
hardware
safety engineers,
system
fields
and
These
flame
(USML-1)
burning diffusion
of reduced
gravity show,
mission
could
presents
on
tests with
not study
the
We were We were also
in a large sealed
in 1992.
This paper
consistent
of gravity.
flame
gravity
airplane
environment.
experiments.
of the experiments
and combustion
tests, however,
exist in the absence
flow,
and Ross and co-
the effects
microgravity
Stefan
and present
chamber
in
the results
The first experiment The second the results
to the predictions
flight was
of the
of a numerical
HARDWARE
cm thick polycarbonate,
a crew-worn
and
flame.
EXPERIMENTAL Figures
(1989)
but on occasion
microgravity
(Mir OS) in 1995. the results
1992),
excepting
to the flame
The reduced
flame as the model
on the STS-50
and compares
flame.
of the candle
quiescent,
Station
studied
due to g-jitter,
could
where,
and Weinberg
in a long-duration
behavior
of two sets of long-duration, flew aboard
stationary
et al., 1994)
flame
(Chan
of electric
and Durox,
for fuel and oxygen
hemi-spherical
of the candle
(Villermaux
and drop tower facilities.
fluctuating
oscillations
et al., 1996), effects
is uniquely
mechanism
in both aircraft
flame
1969 ).
flame in microgravity
products
(Urban
gravity
and Weinberg,
is the only trasport
near-extinction
production
1989), elevated
diffusion
candle
spontaneous,
smoke
(Lawton
Page 3
Candle Flames
glove
consisted
the hardware
of a perforated
and a Separate,
permitted
for the Shuttle
fresh oxidizer
or other surrounding
was a loop of 250 gm aluminum
candlebox
manually
operated
and Mir experiments,
respectively.
(11.5 cm on a side) made of a 0.95 igniter.
The box, required
to reach the candle but preempted material from accidentally
igniting.
by
the possibility
of
The ignition
alloy wire heated with a current of approximately
3
Dietrich, Ross, T'ien and Shu
amperes.
Candle Flames
The crew manually
Shuttle's
pressure
ignited
and oxygen
the candle
mole fraction
Page 4
and removed
the hot-wire
after ignition.
The
were 1 atm and 0.217 at the time of each
experiment. The hardware container
for the second
was a 20 cm cube-shaped
polycarbonate.
The screen
on the Shuttle flame
was different
experiment)
and combustion
wire mesh
provided
significantly
to diffuse except
preset
for almost
repeatable mole
time (4-5 seconds
process.
fraction
The Mir operated
between
recording
volume
recordings
The primary
observations
and color
various
times
The composition
photographs
video
retracted
was
after a
a more oxygen
facility
lacked
C19-C35
2 mm wick diameter,
cameras
were primarily cameras
the low-light
for both experiments
toughness.
This facility
hydrocarbon)
The Shuttle
video
and a few still color
recordings
of crew
in the design were possible on the Shuttle experiment.
because
sensitivity
The color
necessary
to
on the lights in the glovebox
at
wax. was 80 percent
with 20 percent
experiments
5 mm candle
provided
and
of the flame from a 35 mm SLR camera.
of the candle
to impart
facility.
were audio
of the liquefied
(C18H3602)
The changes demonstrated
and white
video observation
wax (typically
1
black
data in the Mir experiments
an n-parrafin
(approximately
to the
system
with an ambient
experiments
In some of the Mir tests, the crew turned
to allow
to diffuse
the ignition
and 44 1 on the Mir OS), video
located
in the Mir glovebox
the flames.
pressure
inside a glovebox
The data from the Shuttle
photographs.
image
the experiments
from orthogonally
video cameras
to less than 15%
for oxygen
was automatically
all tests), rendering
at atmospheric
(25 1 on the Shuttle
capabilities.
to the perforated
from the flame I. The ignition
that the igniter
The
0.22 and 0.25.
The crew operated a working
as opposed
less resistance
away
the same for the Mir experiments ignition
screen
on the Mir OS.
more than 50% free area (as opposed
yielding
products
set of experiments
diameter,
stearic
used 7 identical 12 mm candle
the safety
(by weight)
of
acid candies length,
of the experiment
and 3
was
Dietrich,
Ross, T'ien
and Shu
mm initial exposed
wick length).
in the Mir experiments two different
Candle Flames
There
were 79 total candles
with three different
candle
diameters
wick diameters
All candles
with the hardware
(approximately lengths
1, 2 and 3 mm), of initially
exposed
in the Mir tests were 2 cm in length
the base of the solid wax to the tip of the wick). A 3-axis
accelerometer
for the Mir experiments volume.
Measured
accleration residual
accelerations
flame became
after ignition,
are consistent
tower experiments
oxygen
resembling
concentration
the liquid wax. gradients)
the yellow,
presumably
with a diameter
the effects
Lewis
tests was spherical
of
and
from soot, disappeared,
of approximately
Center
transient,
and the
1.5 cm (Figure
microgravity
Research
After the ignition
studies
5.2 second
3(a)).
in aircraft drop
the flame luminosity
until extinction. the flames
the Shuttle flames.
were luminous
Unlike
in the Mir OS.
of the liquid.
immediately
after
the yellow
This was due to the increased
candles
(but did not drip)
and within five minutes
of
The candle flame then looked as in Figure 3(b).
from air that had been
This motion was the result
along the surface
however,
The entire mass of wax melted
of ignition for the 5 mm diameter
presumably
and spherical
on the Shuttle,
into the flame lifetime.
for the 10 mm diameter candles.
Small bubbles,
a few Hz, rendering
with the earlier, short-duration
often lasted for minutes
within two minutes ignition
10 .5go (go being
flame in the Shuttle
1989) and the NASA
For the Mir experiments
luminosity
below
working
in these tests.
the candle
(Ross et al., 1991a).
continuously
ignition,
at frequencies
blue and hemispherical
and Weinberg,
decreased
were below
and 25 Hz
OBSERVATIONS
After 8-10 seconds,
These behaviors
experiments
the floor of the glovebox
in both spacecraft
and g-jitter unimportant
Immediately yellow.
at 125 Hz for the Shuttle
underneath
due to gravity at sea level)
gravity
(Carleton
sampling
was mounted
EXPERIMENTAL
bright
supplied
(5 and 10 mm) and two different
wick (3 and 6 mm) in the Mir experiments. (from
Page 5
trapped inside the wick, circulated
of surface
tension gradients
At some point, this molten
inside
(temperature ball of wax suddenly
Dietrich, Ross, T'ienandShu
Candle Flames
Page6
becameunstable,collapsedandmovedbackalongthecandleholderasin Figure3(c). The flamechangedonly slowly thenuntil extinction. FortheShuttletests,extinctiontypically occurredbetween40and60 seconds, exceptoneflamethathada lifetimeof 105seconds.All of thecandlesin the Mir tests burnedlongerthanthe Shuttlecandles.The flamelifetimesvariedfrom over 100seconds toover 45minutes.Forthe Mir tests,thecandleswith the largestwick diameterstypically hadtheshortestflamelifetimesandthecandleswith the smallestwick diameterstypically hadthelargest. In theMir experiments,thecrewswitchedthelightsin thegloveboxonafterflame extinction,anda white,sphericalcloudwith a diameter2-3 timesthatof thecandleflame waspresent(Figure3(d)). This cloud is probablya mist of condensedwaxdroplets(and possiblywaterdroplets)thatformedwhile waxcontinuedtovaporizeaftertheflame extinguished. Eachcandleflameon theShuttleoscillatedspontaneously in thefinal 5 seconds. Theflametracedsymmetricallybackandforthalongthecandleaxisin eachcycle(Figure 4). The topof theflamedid not moveduringtheoscillation. Thebaseof theflame retreatedandflashedbackwith a frequencyof about1 Hz with anamplitudethatstarted smallandgrewuntil extinction. No oscillationsoccurredin anyMir testswith thesmallest wick diameter,which wassmallerthanthewicks usedin theShuttleexperiments.The flamesin theMir testswith thetwo largerwick diameters,however,did oscillatebefore extinction.Theoscillationfrequencywassimilarto thatin theShuttleexperiments,only for a muchlongerperiodof time,up to 90 seconds. Analysisof thevideo recordingsfor the Shuttleexperimentsandthe35mm photographsfor the Mir experimentsyieldedboththeflamediameter,D (maximumvisible flamedimensionperpendicularto thecandleaxis),andheight,H (maximumvisibleflame dimensionparallelto the wick), asfunctionsof time (seedefinitionof H andD in Fig. 7). For theShuttleexperiments,therewasnoconsistentbehaviorof the flameswith respectto
Dietrich, Ross, T'ienandShu
Candle Flames
Page7
H andD. The flamediameterandheightsometimesincreasedwith time andsometimes decreased with time. This wasduetovariationsin theignitionprocedureandin theinitial ambientenvironmentin thecandlebox.Figure5 showsD andH asa functionof time for thethreedifferentwick sizesin theMir experiments.The flamediameterandheightin the Mir experimentsalwaysstartedsmallandincreasedwith time. This consistencywasthe resultof a morerepeatableignition method.The flamegrowthfor thefirst 50-75seconds for all of thecandlesin Figure5 corresponds to thetime for thesolid waxto melt. Around this time, the liquid wax collapsed changed
only slowly,
wick size, the larger
(Figures
if at all, with time. the quasi-steady
For both the Shuttle
H/D as a function
for each test in Figure
Additionally,
flame
Figure
of time for a Shuttle
test and two Mir tests.
One of the Mir tests in Figure
2 mm diameter)
(approximately
1 mm diameter).
While
were consistent
with the Shuttle,
the value of H/D is somewhat
the Mir tests. increased
at 75 seconds
NUMERICAL
rate chemistry the porous
corresponds
the
Figure
The candle
6
diameter
6 had the same wick wick size
of the flame size of the Mir experiments
with the larger
higher
ambient
for the Mir tests.
oxygen
wick diameter
then decreased
to the collapse
slightly
concentration
in Figure
until extinction.
in
6, H/D
The change
in
of the liquid wax.
MO1)I_L
The numerical the gas-phase.
the values
for the first 75 seconds,
decreased
test, and the other had the smaller
be due to the increased
For the Mir experiment
slightly
behavior
as the Shuttle
is probably
that the larger
from test to test.
(approximately
This latter observation
5 shows
the ratio IadD always
and was quite repeatable
6 was 5 mm.
the flame size
size, as expected.
and Mir experiments,
with time (over the flame lifetime) shows
3c and 3d), and afterward
While
model
of the candle
the model
and radiative
flame is two-dimensional
is relatively
loss, the detailed
wick and solid wax are neglected.
detailed
and axisymmetric
in
by considering
finite-
in the gas-phase
heat and mass transfer Specifically,
processes
we assume
occuring
that the fuel
in
Dietrich,
Ross, T'ien and Shu
evaporates
from a small
Candle
porous
sphere
liquid fuel at its boiling
temperature.
prescribed
distribution.
temperature
sink to simulate a schematic
the flame
The gas-phase
constant
specific
and no buoyant
species
assumes:
1994).
wick and wax 2. Figure
7 shows
one-step,
different,
This includes
Flame
radiative
second-order constant
constant
allows
overall
Lewis
number
Lewis
numbers),
a simplified
treatment
the assumption losses
spherical
of potential
coordinate
Arrhenius
for each species ideal gas behavior of the momentum
flow and the product
from CO 2 and H20 are accounted
non-dimensional
variables
are defined
reaction,
as (bars
for by a gray indicate
quantities):
_ ;
The non-dimensional
qr =
cp-._---_.
equations
are:
1 ,9 , 2 3_. 1 r 2 _rr tr -'a-r-r)-_ rsin0
o_ sin0 o_ ¢aF-qr 00 ('--7-- ("_ -)) = Too
paY__p ¢_ t
O0
2
with a pure
to an inert cone with a
a two-dimensional
conductivity,
can have
The following
= "p2 _pR-2 -x
aT P'ff-i'+PUr
R, that is coated
has a half angle of 23", acts as a heat
of the candle
utilizes
The last assumption
(,_T) to be constant.
Da
model
force.
(Baum,
gas treatment.
formulation
heats and thermal
different
dimensional
radius,
is connected
The cone, which aspect
Page
of the problem.
system.
equation
with constant This sphere
quenching
The mathematical
(although
Flames
u aYi_puooYi r dr ' r
OT P u0 aT a"_r 4 r O0
1 a (r2,aYi,, 1 t"_'r ))-LeirsinO00 Leir2c_ r
1 o3 (r2O_T) r 2 Or Or
1 rsin0
O _'(
a (si__(oY. r o._t)) = Vi_F
sinO(OT -'7-- -'_-))=
°JF -qr
A cone rather than a rod is easier to prescribe in the spherical coordinate system used. Also, examination of the photos shows that the liquid ball of wax may more closely resemble a cone than a rod.
8
Dietrich,
Ross, T'ien
and Shu
Page 9
Candle Flames
=o p2rorr • is a coupling
variable.
The gas-phase
coefficient,
A, is ._ -- 0.4[Pco
of species
i and _(i)
mean
absorption
factor
of 0.4 reflects
loss from liquid
selected (mole
energy,
atr=
for the candle
conditions
oxygen
is 30 kcal/mole. index
for a candle
=p u,Y_
/)O/_
= (1/oL
form are:
- 1/T.o)*/)T//)r
/)Y//)0 /)O//)0
at
= 0 ( i - F, 02, CO2, H20) = - (I/T.o)*/)T//)0
at r = co: T=T Y_=0
( T b - To) at (1< r< rc)
(r¢
wax are in the nomenclature.
with a 0.6 mm radius
in non-dimensional
at 0 -- 157°:
T(r)=T_
overestimate
The radiative
The pre-exponential
cm3/(g
(i - 02, CO2, H20)
T(r) = T c + (r¢-r)/(r¢-l)*
+ 0.31
value for ,_ is 1.0 (10")
=p Ur (1 "YF)
/)Y/0r
The multiplication
et al. 1997).
of the candle
b
-/)YF/Or
Bedir,
pressure
i. The Planck-
of the flame and the possible
1: T=T
P_ is the partial
of species
and Tien (1967).
wax is C_H52
properties
E, of the reaction
The resulting
The boundary
thin nature
coefficient
data (Liu, et al., 1981;
The physical
such that the limiting fraction).
absorption
where
is neglected.
reaction
2 + 31.58H20.
+ PH2o .,_,(H20)],
are from Abu-Romia
absorption surface
qr, is qr -- -_ o (T 4 - 'I".4). The mean aborption
2 .,_,(CO2)
the non-optically
The one-step
The activation
loss term,
is the Planck-mean
coefficients
of the Planck-mean
30.58CO
radiative
s) which
is quite
factor,
A, is
is 0.19 reasonable.
Dietrich, Ross, T'ien and Shu
Candle Flames
Page 1 0
o-_/o-h"= - (1/T.,)*c3T/_ at 0 = 0: /)T/_0
= 3_/00
The computations
= OY,/O0
below
the temperature
Solution
( i - F, 02, CO2, H20)
are for a porous
T b = 620 K. The temperature simulates
=0
distribution
distribution
sphere
radius,
boundary
equations
momentum
for temperature
time marching difference
techniques.
typically
equation
is solved
are solved
The explicit terms
scheme
profile
evolves
The computation system.
The number
variable
grid distribution is placed
r-direction, surface
near the spherical
the minimum
and expands
far from the flame boundary
Numerical
satisfies
spherical
is 36 in the r-direction
different wick,
radius,
conditions
and solution
predicts
that the candle
The
solution
A steady
flame
grid
concentration
sphere radius
boundary
r = 206.
procedures
flame
and the reaction
cell size is 0.1 times the porous
at a non-dimensional
terms.
non-uniform
The highest
the cone surface,
r. The far-field
and
the central
and 26 in the 0 direction.
requirements.
with increasing
The
procedure.
out on a two-dimensional
of grid points
converged
as the initial condition.
from the time marching
is carried
terms,
for the convective
or a previously
solution
solver.
based on finite difference
difference
as the case to be computed)
(or extinction)
Poisson
is used for the unsteady
and the upwind
starts with a 'hot'
using an efficient
numerically
(not the same condition
conditions
A complete
is available
zone.
The
of grid Along
the
close to the sphere are sufficiently
description
of the
in Shu (1998).
Results
The model ambient.
at 0 = 157 ° and r > 1
of the wick and the molten wax.
and species
for the diffusion
computation
model,
condition
Procedure The reduced
points
R -- 0.6 mm, r¢ = 3.2 cm, and
The inner portion
outer portion
takes
of the flame
tens of seconds
flame will reach reaches
to reach steady
steady-state
a steady-state within
state (similar
in an infinite
10 seconds,
to King,
1996).
but_the The time
Dietrich, Ross, T'ienandShu
Candle Flames
tOreachsteadystateatan arbitraryradius,£., estimates
[ (£_2/_) or (f_.2/Dp ], where'_
diffusion
coefficient,
experimental
respectively.
observations,
that it is possible
and dimension
in short-duration
limit.
It is, however,
not possible
tests because
takes much longer Figure R=0.6
8(a) shows
mass fraction,
The maximum
of the wick.
surface
is located
Equation
reaction
profiles
outside
limit in short the flame zone
which
large
and diffuse,
distribution.
rate, _F, which
flame
region Figure
8(b) shows
the
to the rate of combustion concentration
at the side of the wick, instead
because
et al. (1994),
of the higher
Choosing
flame in the experiment,
bottom
not present
_'F -- 0.2 (10 s) g/cm3s, although
in the experiment.
10.0 mm, respectively,
the model
The model
in the constant
one in the experiment).
we can compare
oxygen
This compares
visible
oxygen
of at
concentration
flame shapes
the contour
predicts predicts ambient
resembles
a slight inward a steady
using a the visible
hook at the
D and H of 14.6 mm
(as opposed
quite favorably
in
close to the cone
of the fuel and oxygen
_'F occurs
of flames
8(c)). to Grayson
with
and an ambient
as is typical
is proportional
that ffF is a function
is a mazimum,
for a steady candle
axis (0 --- 0°), 5 mm from the center
a low temperature
The maximum
the temperature
rate contour.
decreasing
from the extinction
wick in the experiment)
zone is quite
reaction
candle
and
flame
of that in Mir at the time of the experiments).
on the temperaure
5 shows
as well as the temperature.
Similar
with
steady-state
the extinction
to the region
on the symmetry
The cold, inert cone creates
the side (Figure
determine
to the small diameter
The high temperature
the top where
the approximate away
time
and fuel vapor
in agreement
for flames
temperature
Yo, -- 0.254 (typical
of the fuel vapor
heat release.
to accurately
diffusivity
indicate,
to observe
drop towers
the computed
and has a large effect
contours
results
the flame is sensitive
temperature
microgravity.
with the diffusion
to develop.
mm (corresponding
oxygen
scales
and D F are the thermal
The model
shape
microgravity
roughly
Page1 1
to the slowly
with the experimental
at
Dietrich. Ross, T'ienandShu
Candle Flames
Page12
valuesof 14.5mmand11.2mm. The disagreement betweenthemodelandexperimentis probablydueto thesphericalwick geometryin themodelasopposedto the more cylindricalshapein theexperiment. Figure9 showsthetemperature,oxygenmassfraction,fuel massfraction,andfuel vaporreactionrateasa functionof radialdistancefromthecenterof thesphereat 0 _ 0°. This figureclearlyshowsa singletemperaturepeak,buttwo peaksin thereactionrate. The low peakis dueto thequenchzoneatthebaseof theflamewhichenablesoxygentodiffuse to thewick surface.This createsapocketof low reactivitythatpeaksnearthewick inside themainreactionzone(notabovethethreshholdfor avisibleflamethough). Notethatthe locationof theminimumoxygenconcentrationis notatthewick surface(asis thecasewith thesphericallysymmetricdropletin microgravity),butis located3 mm awayfrom the wick surface. Figure10showsthereactionratecontourscorresponding to threedifferentambient oxygenmassfractions. As theoxygenmassfractiondecreases from 0.254to 0.22,the contoursatthecenterline(0 --0°) moveonly slightly,but thereis a substantialupward retreatof bottomportionof theflame. This is similarto theexperiments,whereasthe ambientoxygenconcentrationslowly decreases, theflameheightdecreases (relativeto the diameter).The otherinterestingfeatureof Figure10is thattheflamesize(D andH) decreases slightly with decreasingambientoxygenmassfraction. This is in contrastwith theexperiments thatshowthattheflamediameterremainsrelativelyconstantin the decreasingoxygenambientof the glovebox.Thereasonfor thisdisagreement is currently not known. Thefact thatthe flamediameterdecreases with decreasingambientoxygen is in contrastwith thesphericallysymmetricdroplettheorywheretheflamesizeincreases with decreasingambientoxygenconcentration.Numericalmodelsof flamespreadovera solid surface,however,showthatflamesizedecreases with decreasingambientoxygen concentration.It appearsthenthatthecandleflamesharessomefeaturesof bothsystems.
Dietrich, Ross, T'ienandShu
Candle Flames
Page13
The numericalmodelalsopredictsspontaneous flameoscillationsnearthe extinctionlimit. The extinctionconditionis approached by imposinga stepdecrease of the ambientoxygenconcentrationon a previouslysteadyflame. Thestepdecrease in oxygen simulatesthegraduallydecreasingoxygenconcentration in thesealedgloveboxin the experiment. If this stepis too large (e.g.from Yo_ = 0.22 extinguishes small
by a monotonic
(e.g.
from
extinction.
from a stable,
does not predict
a steady
of the oscillation
oscillation.
The oscillation
increases
resulting
amplification
11 shows
mass fraction,
is approximately
1994) where results
Lewis
number
sphere).
(Shu,
1998) show
half of an oscillation the entire
near the bottom experiment,
portion
although
This is probably
coefficient
that the frequency
that starts3.375
There
is a variation
of the flame.
the magnitude
due to the difference
oxygen
and (D/2)
seconds
step
mass fraction,
fuel
results.
] (Dietrich
This is et al.,
is the flame radius.
decreases
increases
The
as the fuel
(smaller
porous
above. flame
before
of the flame
for 1.875 seconds flame extinction.
during
consistent
is much greater
in the wick geometry.
one
The oscillation
width and an up-and-down
The latter is qualitatively of the movement
The
at one point in the flame.
of the oscillation
of the visible
the model
extinction.
to the experimental
or the flame radius
the movement
words,
with a smaller
time given by [(D/2)2/DF
with the time scale estimate
cycle
flame.
diffusion
(D F increases),
This is consistent 12 shows
diffusion
as the flame
The amplification
oxygen,
the oscillation
is similar
In other
occurs.
of temperature,
rate during
fuel vapor
decreases
Figure
affects
variation
but occurs
before
is
prior to
leads to extinction.
rate and more oscillations
0.7 Hz which
D F is the fuel vapor
model
always
to the step size of the ambient
the temporal
also close to the estimated
state.
with time until extinction
and fuel vapor reaction
The frequency
oscillates
phenomena,
to a non-flammable
the flame
If the step decrease
the flame
steady-state
is related
in a smaller
however,
is not a steady-state
rate of the oscillation
Figure
of the flame temperature.
Yo_ = 0.22 to 0.21875),
The flame oscillation
transitions
amplitude
decrease
to 0.215)
motion
with the
in the experiment.
Specifically,
the cylindrical
Dietrich, Ross, T'ien and Shu
wick in the experiment as compared
Candle Flames
allows a more extended
to the spherical
Page 1 4
evaporating
surface
in the vertical
direction
wick in the model.
DISCUSSIO_N The results
show that the candle
than those on the Shuttle. oxygen
in the vicinity
The Shuttle
of the flame.
flames
candle
extinguished
because
This was not due to oxygen
depletion
glovebox,
but because
perforated
polycarbonate
the Shuttle
tests (0.217)
by a factor
of 10 or more, as the experiments
the observed
increase
of the restriction
in flame lifetime
because
of a lack of fuel.
holder
transport
When
to 0.249)
would
Thus,
The Mir candle
the wax 'collapsed' to the wick.
all of the candles,
oxygen
inside
mole
fraction
not extend
there
the lifetimes reason resistance primarily
back along
the candle
this fuel was
unavailable
was a film of wax surrounding
the
between
extinguished
and moved As a result,
the sealed
through
the predominant
flames
lifetimes
of a lack of
from the ambient
in the ambient
showed.
longer
for the Mir tests was the diminished
the container.
it was not in close proximity
for to
for
the candle
after the flame extinguished. Given
quasi-steady, reasonable
a flame
lifetime
implying
candle
quasi-steady seconds.
space-based
transport
for the gas-phase
outside
but the changes
small during
gas-phase
was steady
flame will exist in air.
behavior Further
of up to 45 minutes,
that the flame
characteristic
steady-state
seconds,
through
For nearly
to oxygen
and the Mir tests (0.225
transport
burning.
flames
box. The difference
oxygen
holder,
in the Mir tests had much
time.
The numerical
The model
region
in the flame as gauged This is in good
experiments.
Visually,
10 seconds.
agreement
the candle
The changes
that the gas-phase
over a time period
results
much model
longer predicts
the flame
may be on the order
with previous reaches
that occur during
than any that a
is less than 10
by the fuel vapor reaction
flame
was
show that the time to reach
in the vicinity
the flame the time to steady-state
this time.
and color within
we believe
rate contours
drop tower a quasi-steady
longer
of 100
time-scales
are
and these size, shape are not the
Dietrich, Ross, T'ienandShu
Candle Flames
Page15
resultof an inherentgas-phase unsteadiness in a purediffusionflame,but arefrom unsteadybehaviorin thesolid/liquidphaseand/orasa resultof thegraduallydecreasing oxygenconcentrationin the sealed-glovebox volume. Spontaneous oscillationsareinherentto thenear-extinctionbumingof these flames.Theapparentdependence of theexistenceof oscillationsonwick diameterin the experiments,implyinga dependence on flamesize,suggests thatflameradiativelossesmay contributeto theonsetof oscillations.CheathamandMatalon(1996,1997)recently investigated themechanismof near-limitflameoscillationsin thesphericaldroplet. They determineda stabilityboundarywith heatlossandLewis numberascoordinates.Whenthe heatlossis zero(adiabaticcase),theLewisnumbermustbemuchlargerthanunity to have anoscillation.With increasingheatloss,thecritical Lewisnumberdecreases andcanbe lessthanunity with a sufficientlylargeheatlossrate. While wehavenot tried to verify the entirestabilityboundary(thiswould bevery expensiveusingthepresentnumericalmodel), we havemadesomecomparrisons. Theoxygenandfuel Lewis numbersin thepresentmodelare 1.11and2.5, respectively.With theLewis numbersin themodelequalto eachotherandthevalueused by CheathamandMatalon,theexistenceof oscillationsalsodependson themagnitudeof theheatloss. Specifically,for R = monotonic
temperature
decrease
(qr -- 0). This is regardless decrease
as low as 0.025
oscillates results Schmitz,
before
of Cheatham
These
different
and one-dimensional,
leading
to extinction
of the step decrease was tested).
With
and T'ien, theories
premixed,
A number 1974) point
above).
out the possibility
solid-propellant
planar flame
(a step
the flame
is consistent
with the
(e.g. Kirkby
and
of near-limit
of Lewis
number,
flame in Kirkby
in Baliga
loss
concentration
however,
theories
the effect
of radiative
oxygen
This result
of previous
(one-dimensional
a non-oscillatory,
in the absence
heat loss included,
did not investigate
types of flames
predicts
in ambient
(the case presented
and Matalon.
1966; Baliga
with heat loss. represent
extinction
0.6 mm, the model
and T'ien).
oscillations but they do and Schmitz, All of these
Dietrich, Ross, T'ienandShu results
suggest
Candle Flames
that heat loss plays an essential
Page16
role in the occurrence
of near-limit
flame
oscillations.
ACKNOWLEDGMENTS The authors would Bonnie
Dunbar
like to extend
for performing
the space
performing
the Mir experiments.
preparation
of the hardware
the analysis
of the Shuttle
special
thanks
Shuttle
experiments
We also thank David
for the Mir experiments.
to mission
specialists
Carl Meade
and to Shannon
Lucid
Frate for his assistance Peter
Struk is thanked
and
for
in the for his help in
data.
REFERENCES Abu-Romia, M.M. and Tien, C.L. (1967). Appropriate Mean Absorption Coefficient Infared Radiation of Gases. ASME Journal of Heat Transfer 89C, 321. Baliga, B.R. and T'ien, J.S. (1975). of Solid Propellants. A/AA Journal.
Unsteady Effects 13, 1653.
on Low-Pressure
Extinction
for
Limit
Baum, H.R. (1994). Modeling Low Reynolds Number Microgravity Combustion Problems. Modeling in Combustion Science, edited by Buckmaster, J. and Takeno, T., Springer, 118. Bedir, H., T'ien, J.S. and Lee, H.S. (1997). Comparison of Different Radiation Treatments for One Dimensional Diffusion Flame. Fall Technical Meeting of the Eastern States Section of the Combustion Institute, Princeton, New Jersey. Buckmaster, J. and Peters, N. (1986). The Infinite Candle and its Stability - A Paradigm for Flickering Diffusion Flames. Twenty-First Symposium (International) on Combustion / The Combustion Institute, Pittsburgh, Pennsylvania, 1829. Carleton, Absence
F. and Weinberg, F. (1989). Electric of Gravity. Nature 330, 635.
Chan, W.Y. and T'ien, J.S. (1978). to Extinction. Combust. Sci. Tech.
Field-Induced
An Experiment 18, 139.
Cheatham, S. and Matalon, M. (1996). Flames. AIAA Journal 34(7), 1403.
Flame
on Spontaneous
Near Limit Oscillations
Convection
in the
flame Oscillation
of Spherical
Prior
Diffusion
Cheatham, S. and Matalon, M. (1997). Heat Loss and Lewis Number Effects on the Onset of Oscillations. Twenty-SixthSymposium (International) on Combustion / The Combustion Institute, Pittsburgh, Pennsylvania, 1063.
Dietrich, Ross, T'ienandShu
Candle Flames
Page17
Dietrich, D.L., Ross,H.D. andT'ien, J.S.(1994). CandleFlamesin Weakly Buoyantand Non-BuoyantAtmospheres.AIAA-94-0429, 32ndAerospaceSciencesMeetingandExhibit, Reno,Nevada. Grayson,G.D., Sacksteder,K.R., Ferkul, P.V. andT'ien, J.S. (1994). FlameSpreading Overa Thin Solid in Low-SpeedConcurrentFlow - DropTowerExperimentalResultsand Comparisonwith Theory. Microgravity Sci.Tech. VII/2, 182 King, M. (1996).An UnsteadyAnalysisof PorousSphereandDropletFuel Combustion UnderMicrogravityConditions. Twenty-Sixth Symposium (International) on Combustion / The Combustion
Institute,
1227.
Kirkby, L.L. and Schmitz, R.A. (1966). An Analytical Diffusion Flame. Combust. Flame. 10, 205. Lawton, Oxford,
J., and Weinberg, pp. 336-340.
F.J.
(1969).
Electrical
Liu, K.V., Lloyd, J.R. and Yang, K.T. (1981) Flame Adjacent to a Vertical Flat Plate Burner. Transfer 24(12), 1959.
Study of the Stability
Aspects
of Combustion
of a Laminar
Clarenton,
An Investigation of Laminar Diffusion International Journal of Heat andMass
Ross, H.D., Dietrich, D.L. and T'ien, J.S. (1991b) Pressure and Low Gravity. Fall Technical Meeting Combustion Institute, Orlando, Florida.
Observations of the Eastern
of Candle Flames in Low States Section of the
Ross, H., Sotos, R. and T'ien, J.S. (1991a). Observations of Candle Flames Various Atmospheres in Microgravity. Combust. Sci. Tech. 75, 155. Shu (1998) Modelling Thesis, Case Western Urban, D.L., Griffin, Preliminary Results. Workshop, 205. Villermaux, Sci. Tech.
of Candle Flame and Near-Limit Reserve University.
Oscillation
Under
in Microgravity.
MS
D.W. and Gard, M.Y. (1996). Comparative Soot Diagnostics: NASA CP 10194, Fourth International Microgravity Combustion
E. and Durox, 84, 279.
D. (1992).
On the Physics
of Jet Diffusion
Flames.
Combust.
Dietrich, Ross, T'ien and Shu
Candle Flames
LIST
OF
Figure
I.
Picture
of the Shuttle
Figure
2.
Picture
of the Mir experimental
Figure
3.
Page 1 8
FIGURES
a-c. Pictures The candle Space
a typical
Shuttle;
4.
Schematic
Figure
5.
Flame
hardware.
microgravity
3b) Mir, before superimposed,
3d) Vapor
Figure
hardware.
candle
was 5 mm in diameter
(two images off.
experimental
cloud
with an approximately
wax collapse;
formed
Figure
6.
Figure
7. 8.
shape,
H, as a function
H/D, as a function
9.
of the simplified
Numerical
results
Radial
0.254 10.
I 1.
contours
12.
was 5 mm in all
mass
ambient,
reaction
in the numerical
ambient,
8b) Fuel vapor reaction
fraction
with'R" ,, 0.6
rate (if'F)
(Yo) contours.
('T), oxygen fraction
mass
fraction
mass
fraction
(Yo), fuel vapor
(YF) at 0 _ 0" for a candle
reaction
of temperature
in a Yo_ =
cycle
that starts3.375
mass
0.276). (Yo), fuel vapor
in a candle
flame
oscillation.
for 1.875 seconds
seconds
0.254,
fraction
(Y_) at a point flame
contours
with R -- 0.6 mm in three
(Yo_ = 0.232,
(_), oxygen
a pre-extinction rate (_)
for a candle
ambients
rate (_F), and fuel mass fraction
an oscillation
and
model.
in a Yo_ "0.254
rate (_v) contours
variation
Fuel vapor
experiment
with R -- 0.6 mm.
oxygen
Temporal
Shuttle
wick sizes).
flame
of temperature
(R -- 0.6 mm) during Figure
candle
rate (w'F), and fuel mass
Fuel vapor
reaction
diameter
of time for a typical
(T) contours;
8c) Oxygen
different Figure
of time for the 3 different
The candle
different
for a candle
8a) Temperature
reaction
Figure
(with
Schematic
contours; Figure
on the Mir experiments.
cases.
Flame
mm.
with the lights
flame oscillation.
D, and height,
two Mir experiments Figure
3a)
3c) Mir, after wax collapse.
after flame extinction
wick sizes from the Mir experiments. three
transient).
2 mm wick.
one with the lights on, the other
of pre-extinction
diameter,
flame (after ignition
before
during
extinction.
one half of
Dietrich,
Ross, T'ien
and Shu
Candle
Page 19
Flames
NOMENCLATURE gas-phase A
A
mean
thermal
absorbtion
pre-exponential
diffusivity. coefficient.
factor
Api
Planck
Cp
gas-phase
D
Flame
D
Gas phase
diffusion
Ira
Damkohler
number.
E
activation
H
Flame
L
mean absorbtion specific
energy
heat (0.334
for species
cal/g
i.
K).
coefficient.
(3
x 10 4
cal/mole).
height.
velocity
potential.
Arbitrary
radius.
latent
coefficient
s).
diameter.
gas-phase L
(1 x 10 f_ cm3/g
thermal
conductivity
heat of vaporization
Pi
partial
0
angular
q
heat release
P
gas density.
r
radial coordinate.
R
radius
Ro
universal
T
temperature.
t
time.
u
velocity.
w F
fuel vapor reaction
Y
mass fraction.
pressure
of species
(1.87
(296.12
x 10 .4
cal/K s cm).
cal/g).
i.
coordinate. per unit mass
of the porous
of fuel (10170
sphere.
gas constant.
rate per unit volume.
cal/g).
Dietrich,
Ross, T'ien
and Shu
Subscripts b
boiling
point of the fuel.
c
cold point of the rod.
CO2
carbon
F
fuel.
H20
water
O
oxygen.
0
0 direction.
r
radial direction.
oo, e
ambient.
dioxide.
vapor.
Candle Flames
Page 20
Orr _11t
G
.e-*
-1 I; Q
t
,4 i-
.o "i; Z
)
_.
_
z,_
_
• •
,
r _
O_ _4_ G
Wt_ _n
_B r-
o II
Natl(_f_al Aeronaulics
and Space Administration LewiB Resemch C_lter
Increasing ]3me
TotalTime 1second
Figure 4. Schematic
of pre-extinction
flame oscillation.
D, H O
(mm)
0
0
O
'
I
_. "rl mo •
I m'l mmm,IF
I
I
|
I
¢I_
c:
mo
.-,,_
au_ 3" ,-,.-m'l
0
• [] •
(.'1 O
0
[]
I_[> (D
[]
•
P_
CD moo 13
i°
• 0
x
-o3
• m_
(I)
O,
[] [] 0
0 []
00 l_l
[> n
0
(_
_1o_ ,mL _°
o(.O
--I
(.rm o
[]
m>
[]
0
m0
O.
0 • ON 0
:I (I)
O__
7
3-i.
_"
0
A
3_ •
D
V
0
O
0 0)
•
mpo _°
0
-I•
O
0
• O • O
CO O_ _° '-_
o
(1) •
_°
c) GO (,11 O
0 •
0
I
,
HID .o
§'-n _"
_3
_"r
_b a; _'m
__.g N
('_
m
0
"O
.g
0
.o
.o
.o
o
.._
..,.
X X \, X------Sphere liquid Inert
Conical
Prescribed Distribution
Rod
with
Coated fuel
a
Temperature
Figure 7. Schematic
of the simplified
candle
in the numerical
model.
with
(a)
10
(b) WF (rag/| cm3)
8 Temp (K) 6
4
2
2
4
6
8
10
12
14
6
x (ram)
8
10
12
14
X (ram)
10
8
8
4
2
2
4
6
8
10
12
14
X (men)
Figure
8.
Numerical
results
for a candle
flame
8a) Temperature (T) contours; 8b) Fuel vapor and fuel (YF) mass fraction contours.
in a YOe = 0.254 reaction
ambient,
rate (_'F) contours;
with R" = 0.6 mm. 8c) Oxygen
(YO)
2000 0.01
1750
1500
12so
E lOOO
R (mm)
Q I--
Temp
750
YO
500
250
0
0
5
10
0
R (cm)
Figure 9. Radial contours of temperature reaction rate (_w.F),and fuel mass fraction ambient, with R = 0.6 mm.
(_), oxygen mass fraction (YO), fuel vapor (YF) at 0 ° for a candle in a YOe = 0.254
-10 0
5
10
15
X (mm)
Figure three
10.
Fuel
different
vapor
oxygen
reaction mass
rate
fraction
(_F)
contours
ambients
for a candle
( YOe
= 0.232,
with R = 0.6 mm in 0.254,
0.276).
1300
_"
_oor-'
-_ -- 0.3
/
:,-:iii_il/
_._--\ -, ."'."-'--:I
-1°.'_` 1
o
°°°b .... ---yoV-Vt:_.kgl 1
,ooF 0
i
jl/_i _ oo, \"--4 i
i, ,i, to 5
10
15
Time (S)
Figure 11. Temporal variation of temperature (_, oxygen mass fraction (YO), fuel vapor reaction rate (wF), and fuel mass fraction (YF) at a point in a candle flame (R = 0.6 mm) during a pre-extinction flame oscillation.
(as Relemnce)
a
I
at time
1.1Zl
0
.................................
0_-,-_
................................
*2
\
1
-4
x (mini
x (ram)
!
;
WF(m_ ¢m,1)
i
tim-"
ll.,l?|
•
I
J*l
i
e
i
WF (mg/s cm3
ii i
lit tim@ s 1.6 8
° 2
.................................
0 I
i
\'
*4
• . i . . , , ! _ . . . _ . . S
10
ltS
I
I $
10
x (mill
15
X |ram|
iv
WF(n_s an3 trnu - 0.76 •
,.......................... i i
0
| S
,
Ime - 1.1171 •
'[ -"_\
il
2
; i
0
i
-4
WF(n_s arts) 8
* 10
x (mini
....
I IS
•
_,"
i-.-- ....
: 0
...................
[ S
x (.n)
I 10
,
,
-
-
I IS
,
Figure 12. Fuel vapor reaction rate (_F) contours for 1.875 seconds during one half of an oscillation cycle 3.375 seconds before extinction.