Effects of Ambient Condition on Flame Spread over a Thin PMMA Sheet Shuhei Takahashi, Takeshi Nagumo and Kazunori Wakai Department of Mechanical and Systems.

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.