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OPPOSED-FLOW FLAME SPREAD - THE QUIESCENT MICROGRAVITY LIMIT
Subrata (Sooby) Bhattacharjee
Professor, Mechanical Engineering Department
San Diego State University, San Diego, USA
JSME Microgravity Symposium, Oct. 28-30, 2001, Sendai, Japan
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Acknowledgement
• Profs. Kazunori Wakai and Shuhei Takahashi, Gifu University, Japan
• Dr. Sandra Olson, NASA Glenn Research Center.
• Team Members (graduate): Chris Paolini, Tuan Nguyen, Won Chul Jung, Cristian Cortes, Richard Ayala, Chuck Parme
• Team Members (undergraduate): Derrick, Cody, Dave, Monty and Mark.
(Support from NASA and Japan Government is gratefully acknowledged)
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Overview
• Opposed-flow flame spread.
• The thermal limit.
• The quiescent limit.
• The extinction criterion.
• Flammability maps.
• Future work.
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AFP: = 0.08 mm
= 1.8 mm/sfV
Downward Spread Experiment, SDSU Combustion Laboratory
PMMA: = 10 mm
= 0.06 mm/sfV
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Fuel: Thin AFP, =0.08 mm = 4.4 mm/sfV
Thick PMMA
Image sequence showing extinction
Vigorous steady propagation.
Experiments Aboard Shuttle: O2: 50% (Vol.), P=1 atm.
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Mechanism of Flame Spread in Lab. Coordinates
gVVf
Fuel vapor
O2/N2 mixture
The flame spreads forward by preheating the virgin fuel ahead.
Virgin Fuel
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Mechanism of Flame Spread in Flame-Fixed Coord
Vr Vg V f
Vf
O2/N2 mixture
The rate of spread depends on how fast the flame can heat up the solid fuel from ambient temperature to vaporization temperature .
Virgin Fuel
Vaporization Temperature, vT
T
vT
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fgr VVV
Vf
Forward Heat Transfer Pathways: Domination of Gas-to-solid Conduction (GSC)
Preheat Layer
Pyrolysis LayerGas-to-Solid
Conduction
Solid-ForwardConduction
The Leading Edge
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Vr Vg V f
VfGas-phase conduction being the driving force,
The Leading Edge Length Scales
gxL
Lsy
sxL
gyL
gxsx LL ~
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Length Scales - Continued
Vr Vg V f
Vf
gxL
Lsy
gyL
gxL
2
2
~x
T
cuT
x p
2~
gxp
r
gx
rr
Lc
T
L
TV
r
ggx VL
~
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Vr Vg V f
VfLsy
gxL
Heated Layer Thickness – Gas Phase
r
g
r
gxggresggy VV
LtL
~~~ ,
r
gggygx VLLL
~~~
gxL
gyL
r
gxgres V
Lt ~,
f
gxsres V
Lt ~,
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Heated Layer Thickness – Solid Phase
Vf Lsy
gL
f
gsres V
Lt ~,
fr
sg
f
gs
sresssy
VVV
L
tL
~~
~ , gL
gL
fr
sgh VV
,min~
Vf
Lsy
gL
gLvT
f
gsres V
Lt ~,
gL
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Vr Vg V f
Vf
gL
Vaporization Temperature,
Ambient Temperature,
TTcWVQ vsshfsh ~
gL
gL
h
Energy Balance: Characteristic Heating Rate
Sensible heating (sh) rate required to heat up the unburned fuel from to T vT
vT
T
Heating rate due to gas-to-solid (gsc) conduction:
g
vfgggsc L
TTWLQ
~
Flame Temperature, fT
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Vr Vg V f
Vf
gL
TT
TTFF
cV
v
vf
ss
g
hf where,
1~
gL
gL
Conduction-limited or thermal spread rate:
Flame Temperature, fT
Thick Fuel Spread Rate from Energy Equation
gscsh QQ ~
Vaporization Temperature, vT
2, ~ F
c
cVV
sss
gggrthickf
fr
sgsyh VVL
~~
For semi-infinite solid,
2,, F
c
cVV
sss
gggrdeRisthickf
h
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Vr Vg V f
Vf
Lsy
gL
TT
TTFF
cLV
v
vf
ss
g
syf where,
1~
gL
gL
Conduction-limited spread rate: Flame Temperature, fT
gscsh QQ ~
Vaporization Temperature, vT
Fc
Vss
gthinf
~,
For thermally thin solid,
~h
Thin Fuel Spread Rate from Energy Equation
Fc
Vss
gosDelichatsithinf
4,,
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Vr Vg V f
Vf gL
gL
gL
Solid Forward Conduction (sfc)
Gas to Solid Conduction (gsc)
Gas to Environment Radiation (ger)
Gas to Solid Radiation (gsr)
Solid to Environment Radiation (ser)
Parallel Heat Transfer Mechanisms
h
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VfgL
gL
gL
Solid Residence Time: f
gsres V
Lt ~,
Gas to Solid Conduction (gsc)
Solid to Environment Radiation (ser)
The radiation number is inversely proportional to the velocity scale. In the absence of buoyancy, radiation can become important.
WLTT
Qt
sxv
charser 44
~
vfrgg
v
ser
sres
TTVc
TT
t
t
44
, ~
rV
h
Radiative Term Becomes Important in Microgravity
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VfgL
gL
gL
Gas to Solid Conduction (gsc)
Solid to Environment Radiation (ser)
Include the radiative losses in the energy balance equation: rV
WTT
WLTTTTWcV
vfg
gvvhssf
~
44
1~,, ThermalThinf
fthin V
V 21~
,, ThermalThickf
fthick V
V
Algebraic manipulation leads to:
Spread Rate in the Microgravity Regime
h
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ESTf
f
V
V
,
Mild Opposing Flow: Computational Results for Thin AFP
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0.1 2.1 4.1 6.1 8.1
21%
50%
70%
100%
As the opposing flow velocity decreases, the radiative effects reduces the spread rate
vfrgg
v
ser
sres
TTVc
TT
t
t
44
, ~
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Mild Opposing Flow: MGLAB Data for Thin PMMA
vfrgg
v
ser
sres
TTVc
TT
t
t
44
, ~
0
0.2
0.4
0.6
0.8
1
1.2
0 0.05 0.1 0.15 0.2
Eq. (5)
7.5 micro-m, 50%
25 micro-m, 50%
7.5 micro-m, 30%
25 micro-m, 30%
7.5 micro-m, 21%
25 micro-m, 21%
ESTf
f
V
V
,
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Vf
syL
gL
gL
Gas to Solid Conduction (gsc)
Solid to Environment Radiation (ser)
The minimum thickness of the heated layer can be estimated as:
All fuels, regardless of physical thickness, must be thermally thin in the quiescent limit.
fr VV
The Quiescent Microgravity Limit: Fuel Thickness
ggg
sss
Thinf
gs
sy
f
gs
rf
gssy
c
cF
VL
VVVL
,
),min( syh L
syL Therefore,
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0fV
gL
gL
Gas to Solid Conduction (gsc)
Solid to Environment Radiation (ser)
The spread rate can be obtained from the energy balance that includes radiation.
where,
0fr VV
The Quiescent Microgravity Limit: Spread Rate
WTT
WLTTTTWcV
vfg
gvvssf
~
440
0,
00 41
2
1
2
1~
Thinf
f
V
V
TT
TT
c
c
F v
v
gss
gg44
20
1
0~0020
reduces to:
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In a quiescent environment steady spread rate cannot occur for
The Quiescent Limit: Extinction Criterion
0,
00 41
2
1
2
1~
Thinf
f
V
V
2
1~ ,
4
1~For 00
imaginary. is , 4
1For 00
3
2
4 v
g
gg
ss
Tc
cF
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Extinction criterion proposed is supported by the limited amount of data we have acquired thus far.
The Quiescent Limit: MGLAB Experiments
0For 0.24 ,
steady spread does not occur.
0
0.2
0.4
0.6
0.8
1
1.2
0.01 0.1 1 10
21% O2
30% O2
50% O2
Eq. (8)
0
0
2
4 4
This translates to:
. 4
g g g v
s s v
c T TF
c T T
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Empty symbols stand for extinction and filled symbols for steady spread.
The Quiescent Limit: Flammability Map for PMMA
0
0.2
0.4
0.6
0.8
1
1 100 10000
Extinction Boundary (Eq. 15)MGLAB DataWest et. al [8]MGLAB Data
micron ,
,2Oy
No steady flame over PMMA beyond this half-thickness even in a pure oxygen environment
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0
0.2
0.4
0.6
0.8
1
0 100 200 300 400 500
Extinction Boundary (Eq. 15)
Olson et al. [7 ]
Bhattacharjee et. al [8]
Empty symbols stand for extinction and filled symbols for steady spread.
The Quiescent Limit: Flammability Map for AFP
micron ,
,2Oy
No steady flame over Ashless Filter Paper beyond this half-thickness even in a pure oxygen environment
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• In a completely quiescent environment all fuels behave like thermally thin fuels.
• The spread rate in a quiescent environment:
• The critical thickness above which there cannot be any steady flame spread is:
Conclusions
0 0
1 1~ 1 4
2 2
2
4 4 .
4g g g v
s s v
c T TF
c T T