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Effects of Ambient Condition on FlaEffects of Ambient Condition on Flame Spread over a Thin PMMA Sheetme Spread over a Thin PMMA Sheet
Shuhei Takahashi, Takeshi Nagumoand Kazunori Wakai
Department of Mechanical and Systems Engineering,Gifu University, JAPAN
e-mail: [email protected]
Subrata BhattacharjeeDepartment of Mechanical Engineering,
San Diego State University, USAe-mail: [email protected]
BackgroundBackground
• To measure the spread rate of thin PMMA sheets in normal- and micro-gravity with varying O2 level, pressure and opposed-flow velocity.
ObjectiveObjective
• Spread rate over a thermally-thin PMMA sheet, where the thickness is less than 1mm, has not been investigated extensively.
• It is predicted that steady flame spread over PMMA in quiescent micro-gravity is achieved if the thickness is sufficiently thin.
x
y
sfc
gscgsr
esr ser
Lsx
Lsy
Lgx
Lgy
Vr=Vg+Vf
Pyrolysis zone
Preheat zone
Environment (e)
Gas (g)
Solid (s)
Control Volumes in the gas and solid phases at the leading edgeControl Volumes in the gas and solid phases at the leading edge
Vf
tcomb
r
gxgres V
Lt ,
gert
tvap
f
sxsres V
Lt ,
tsh
gsctgsrtsfct
sertesrt
...(i) ...(ii)
t t tchem res g ger ,
Thermal-regimeThermal-regimeif
andt t t t t tres s gsc sfc gsr esr gsc, ~ min( , , , ) ~ The dominant driving force of
flame spread is the conduction from the gas phase to the solid phase.
Vg is not too high to cause kinetic effect and not too low to cause radiative effect.Oxygen level is high enough to allow fast reaction.
LV
L t Lgxg
rgy g res g gx~ , ~ ,
L LVsx gxg
r
~
gg
g gc
LL
V V Vsy ssx
f
s s
f r
~ min , min ,
Q c L L W T Tchar s s sy sx v F~ ( ),
tQ
q L W
c L L W T TT T
LL W
L
V
c
c Fgscchar
gsc gx
s s sy sx v F
gf v
gygx
sy
r
s s
g g
~ ~( )
( ),
1F
T T
T Tf v
v F
,
Vc L
Ffg
s s sy
~
V
cFf thin
g
s s, ~
V Vc
cFf thick r
g g g
s s s, ~
2
where
where
Scales of the control volume in the gas phase
Scales of the control volume in the solid phase
Heat required to preheat the fuel
...(vi)
...(iv)
...(v)
Substituting Eqs. (i), (iv), (v) and (vi) into Eq. (iii)
for thermally-thin fuel
and
for thermally-thick fuel
...(iii)
These expressions are identical to the analytical solutions of de Ris [1] and Delichatsios [4].
t t tchem res g ger ,
In the thermal-regimeIn the thermal-regime
The extended simplified theory (EST)The extended simplified theory (EST)(S. Bhattacharjee et al.: Proc. Combust. Inst. 26: 1477-1485)
Vc
c
T T
T Tf thin ESThd g
s s
f ad deRis v
v, ,
, ,
4
Vc
c
T T
T TVf thick EST
g g g
s s s
f eqv v
veqv, ,
,
2
for thermally-thin fuel
for thermally-thick fuel
t t t t t tres s gsc sfc gsr esr gsc, ~ min( , , , ) ~
Nt
t
a L V T T
c V T Tger
res g
ger
P gy f f
g g r f
, ~( )
( )
4 4
2 0 Nt
t
T T
c V T Tserres s
ser
v
g g r f
, ~( )
( )
4 4
0
Dat
t V y B T Tres g
chem
g
eqv o g g act
,
,
~ /exp( / )
2
1
0.000
0.200
0.400
0.600
0.800
1.000
1.200
10 100 1000 10000
21%
50%
70%
100%
0.001
0.01
0.1
1
0 10 20 30 40 50 60 70 80 90 100
Oxygen Volume Fraction ,Oy (%)
Vf (cm/s)
Eq. (1)
Infinite rate kinetics (Computations)
Finite rate kinetics (Computations)
Experimental Data12
The kinetic effect reduces the spread rate in low oxygen level. (low Da effect)
( )
( )
T T
c V T Tv
g g r f
4 4
The radiative loss reduces the spread rate with low opposed-flow. (high R effect)
Blow off Radiative extinction
Thermal-region limit
Effect of Effect of DamköhlerDamköhler number and radiative loss on spread rate (numerical simulation) number and radiative loss on spread rate (numerical simulation)
This line corresponds to the Vr of 10cm/sec.
Fuel: thick PMMA
Fuel: thin ashless filter paper
Front view camera
Side view camera
Fuel holder
O2 portN2 port
Vacuum pump portManometer port
Apparatus for normal-gravity experimentsApparatus for normal-gravity experiments
CCD camera
Air
Honeycomb
Fan
PMMA :30mm x 10mm x 15,50,125m
Fuel holder
Igniter (Ni-Cr wire)
Apparatus for micro-gravity experiments conducted with the 4.5sec trop-tower Apparatus for micro-gravity experiments conducted with the 4.5sec trop-tower (100meter-drop) of MGLAB in Japan.(100meter-drop) of MGLAB in Japan.
Igniter (Ni-Cr wire)
Fuel holder
VacuumO2
CCD camera
Air
Igniter (Ni-Cr wire)
Vf
Vf
Fuel holder
Vg Vg~300mm/sec
PMMA : 30mm x 10mm x 15,50,125m
O2 : 50%O2 : 30%O2 : 21%O2 : 18%Prediction
Fuel half-thickness [mm]
Fla
me
spre
ad r
ate
[mm
/s]
21%
18%
30%
50%
11%
0.01 0.1 1 100.01
0.1
1
10
100
Fuel half-thickness [mm]
Fla
me
spre
ad r
ate
[mm
/s]
1.0atm 0.75atm 0.5atm 0.25atm Prediction
1.0atm
0.75atm
0.5atm
0.25atm
0.01 0.1 1 100.01
0.1
1
10
100
Vc L
Ffg
s s sy
~
V
cFf thin
g
s s, ~
V Vc
cFf thick r
g g g
s s s, ~
2
for thermally-thin fuel
and
for thermally-thick fuel
Downward spread rate vs. fuel half-thickness in normal-gravityDownward spread rate vs. fuel half-thickness in normal-gravity
V cg T T
TBC eqv BCg g c
,,
/( )
1 3
T T K cg c v BC, , . 620 0575 where
V
VTf
f thick EST crit EST, , ,
,
min ,11
Twhere
Non
-dim
ensi
onal
sp
read
rat
e
Non-dimensional fuel half-thickness
0.25atm 50% 0.5atm 50% 0.75atm 50% 1.0atm 50% 1.0atm 30% 1.0atm 21% 1.0atm 18% Prediction
0.01 0.1 1 100.1
1
10
100
Non-dimensional downward spread rate vs. non-dimensional fuel half-Non-dimensional downward spread rate vs. non-dimensional fuel half-thicknessthickness
15m 50m 125m
Opposed-flow velocity [mm/s]
Fla
me
spre
ad r
ate
[mm
/s]
ExtinctExtinct
Extinct
0 50 100 150 200
5
10
15
Vr = Vf + Vg
Spread rate in micro-gravity with varying opposed-flow Spread rate in micro-gravity with varying opposed-flow velocity, oxygen level and fuel thicknessvelocity, oxygen level and fuel thickness
Spread rate in quiescent normal- and micro-gravity
O2 level: 21%Pressure: 1atm
Spread rate in a quiescent environment with varying the oxygenlevel and the fuel thickness.
Thickness
O2 level15m 50m 125m
extinct extinct extinct21%
13.4mm/s 4.2 mm/s 1.4 mm/s18.6 mm/s 4.1 mm/s extinct
30%28.3 mm/s 10.0 mm/s 3.2 mm/s39.1 mm/s 18.9 mm/s unsteady
50%55.1 mm/s 22.8 mm/s 8.1 mm/s
The upper is the spread rate in micro-gravity and the lower is thatin normal-gravity.
The ratio of spread rate in mcro-gravity to that in normal-gravity.
Thickness
O2 level15m 50m 125m
21% 0 0 030% 0.657 0.410 050% 0.710 0.829 -
Spread rate in G
Spread rate in NG
Ratiative effect due to small Vf.
Thermal-regime spread due to large Vf
0.00sec (Ignition) 0.918sec 1.836sec 2.584sec
2.720sec 2.754sec 2.822sec 3.400sec
The unsteady spread observed when the oxygen level is 50% and the fuel thickness is 125m
Radiative loss
flame
Mass diffusion layer Temperature diffusion layer
Unsteady flame spread in micro-gravity (quiescent condition)Unsteady flame spread in micro-gravity (quiescent condition)
Scale of the temperature diffusion layer shrinks.
ConclusionsConclusions
• The prediction, EST, can accurately predict the downward spread rate in the thermal-regime throughout thin and thick regimes.
• Low oxygen level and low opposed-flow velocity can cause the kinetics effect and the ratiative effect, respectively, to break thermal-regime.
• If the fuel is very thin (less than 50m), the thermal-regime holds in a relatively wide range, even under a quiescent micro-gravity condition.