Transcript ｽﾗｲﾄﾞ ﾀｲﾄﾙなし

Effects of Ambient Condition
on Flame Spread over a Thin
PMMA Sheet
Shuhei Takahashi, Takeshi Nagumo
and Kazunori Wakai
Department of Mechanical and Systems Engineering,
Gifu University, JAPAN
e-mail: [email protected]
Subrata Bhattacharjee
Department of Mechanical Engineering,
San Diego State University, USA
e-mail: [email protected]
Background
• 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.
Objective
• To measure the spread rate of thin PMMA sheets
in normal- and micro-gravity with varying O2 level,
pressure and opposed-flow velocity.
y
Vr=Vg+Vf
Lgx
Pyrolysis zone
t
t ser
tesr
t sfc
t gsr
t gsc
Lgy
x
Lsy
Preheat zone
Vf
Lsx
Environment
esr ser
(e)
Gas (g)
t ger
tvap
tsh
tcomb
gsr
gsc
sfc
t res, s 
Lsx
Vf
...(i)
t res, g 
Lgx
Vr
...(ii)
Solid (s)
Control Volumes in the gas and solid phases at the leading edge
Thermal-regime
if
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.
tchem  tres, g  t ger
and
tres,s ~ min(t gsc , t sfc , t gsr , tesr ) ~ t gsc
...(iii)
Lgx ~
g
Vr
, Lgy ~  g tres, g  Lgx
Lsx ~ Lgx 
g
Vr
g
 g cg
Scales of the control volume
in the gas phase
...(iv)


Lsx 
 s s 
Lsy ~ min t ,  s
  min t ,

V
V
V


f 
f r 


Qchar ~ scs Lsy LsxW (Tv  TF , )
t gsc ~
g 
where
The dominant driving force
of flame spread is the
conduction from the gas
phase to the solid phase.
Scales of the control volume
in the solid phase
...(v)
Heat required to preheat the fuel
s cs Lsy LsxW (Tv  TF , ) Lsy s cs 1
Qchar
~

(Tf  Tv )
q gsc LgxW
Vr g cg F
g
LgxW
Lgy
where F

Tf  Tv
Tv  TF ,
...(vi)
Substituting Eqs. (i), (iv), (v) and (vi) into Eq. (iii)
Vf ~
g
s cs Lsy
F
V f ,thin ~
g
F
scst
and
for thermally-thin fuel
V f ,thick ~ Vr
 g  g cg 2
F
s scs
These expressions are
identical to the
analytical solutions of
de Ris [1] and
Delichatsios [4].
for thermally-thick fuel
The extended simplified theory (EST)
(S. Bhattacharjee et al.: Proc. Combust. Inst. 26: 1477-1485)
V f ,thick , EST
 g g cg   Tf ,eqv  Tv 


 Veqv
 s s cs   Tv  T 
V f ,thin , EST
chd   g   Tf ,ad ,deRis  Tv 




4  scst   Tv  T 
2
for thermally-thick fuel
for thermally-thin fuel
In the thermal-regime
tchem  tres, g  t ger
tres,s ~ min(t gsc , t sfc , t gsr , tesr ) ~ t gsc
Da 
tres, g
tchem
N ger 
 g  

1
 /
  
~ 
2 
 Veqv   yo , g Bg exp(T / Tact ) 
t res , g
t ger
a P LgyV f  (Tf  T )
4
~
g cgVr (Tf  T )
2
4
0
N ser 
t res ,s
t ser
 (Tv 4  T 4 )
~
0
g cgVr (Tf  T )
Fuel: thick PMMA
1
Vf (cm/s)
0.1
Infinite rate kinetics (Computations)
Finite rate kinetics (Computations)
12
Experimental Data
Eq. (1)
0.01
0.001
0
10
20
30
40
50
60
70
80
90
100
The kinetic effect reduces
the spread rate in low
oxygen level.
(low Da effect)
Oxygen Volume Fraction yO , (%)
Fuel: thin ashless filter paper
1.200
Thermal-region limit
This line corresponds to the
Vr of 10cm/sec.
1.000
0.800

0.600
21%
50%
0.400
70%
0.200
Blow off
100%
Radiative extinction
0.000
10
100

1000
 (Tv  T )
4
4
10000
The radiative loss reduces
the spread rate with low
opposed-flow.
(high R effect)
g cgVr (Tf  T )
Effect of Damköhler number and radiative loss on spread rate (numerical simulation)
Manometer
port
N2 port
O2 port
Igniter (Ni-Cr wire)
Vacuum pump port
Vf
Vf
Vg
Vg~300mm/sec
Fuel holder
Fuel holder
Side view camera
Front view camera
Apparatus for normal-gravity experiments
CCD camera
Fan
PMMA ： 30mm x 10mm x 15,50,125mm
Honeycomb
Fuel holder
CCD camera
Igniter (Ni-Cr wire)
Air
O2
Vacuum
Air
Fuel holder
PMMA：
30mm x 10mm x 15,50,125mm
Igniter (Ni-Cr wire)
Apparatus for micro-gravity experiments conducted with the 4.5sec trop-tower
(100meter-drop) of MGLAB in Japan.
100
O2 : 50%
O2 : 30%
O2 : 21%
O2 : 18%
Prediction
10
50%
1
30%
21%
18%
0.1
Flame spread rate [mm/s]
Flame spread rate [mm/s]
100
1.0atm
0.75atm
0.5atm
0.25atm
Prediction
10
1.0atm
0.75atm
1
0.5atm
0.25atm
0.1
11%
0.01
0.01
0.1
1
0.01
10
0.01
Fuel half-thickness [mm]
VBC ,eqv
Vf ~
  g g (Tg ,c  T ) 
 cBC 

T


g
s cs Lsy
F
0.1
1
Fuel half-thickness [mm]
1/ 3
where Tg ,c  Tv  620 K , cBC  0.575
V f ,thin ~
g
F
scst
and
for thermally-thin fuel
V f ,thick ~ Vr
 g  g cg 2
F
s scs
for thermally-thick fuel
Downward spread rate vs. fuel half-thickness in normal-gravity
10
0.25atm 50%
0.5atm 50%
0.75atm 50%
1.0atm 50%
1.0atm 30%
1.0atm 21%
1.0atm 18%
Prediction
Non-dimensional spread rate 
100
10
1
0.1
0.01
0.1
1
10
Non-dimensional fuel half-thickness t
 1
  min 1, 
 T
where

Vf
V f ,thick , EST
,T
t
t crit , EST
Non-dimensional downward spread rate vs. non-dimensional fuel half-thickness
Spread rate in quiescent normal- and micro-gravity
Spread rate in mG
Spread rate in a quiescent environment with varying the oxygen
level and the fuel thickness.
Spread rate in NG
Thickness
15mm
50mm
125mm
O2 level
15mm
50mm
125mm
Flame spread rate [mm/s]
15
extinct
extinct
13.4mm/s
4.2 mm/s
18.6 mm/s
4.1 mm/s
30%
28.3 mm/s
10.0 mm/s
39.1 mm/s
18.9 mm/s
50%
55.1 mm/s
22.8 mm/s
The upper is the spread rate in micro-gravity and the
in normal-gravity.
O2 level: 21%
Pressure: 1atm
21%
10
extinct
1.4 mm/s
extinct
3.2 mm/s
unsteady
8.1 mm/s
lower is that
The ratio of spread rate in mcro-gravity to that in normal-gravity.
Thickness
5
O2 level
21%
30%
50%
Extinct
Extinct
Extinct
0
50
100
150
15mm
50mm
125mm
0
0.657
0.710
0
0.410
0.829
0
0
-
200
Opposed-flow velocity [mm/s]
Vr = Vf + Vg
Ratiative effect due
to small Vf.
Thermal-regime spread
due to large Vf
Spread rate in micro-gravity with varying opposed-flow velocity,
oxygen level and fuel thickness
Mass diffusion layer
Temperature
diffusion layer
The unsteady spread
observed when the
oxygen level is 50%
and the fuel thickness
is 125mm
Radiative loss
Scale of the temperature
diffusion layer shrinks.
flame
0.00sec (Ignition)
0.918sec
1.836sec
2.584sec
2.720sec
2.754sec
2.822sec
3.400sec
Unsteady flame spread in micro-gravity (quiescent condition)
Conclusions
• 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 50mm), the
thermal-regime holds in a relatively wide range,
even under a quiescent micro-gravity condition.