Dietrich,Ross,T'ienandShu CandleFlames Page1 CANDLE

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


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


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.


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


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.


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


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


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.


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.


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.