1 opposed-flow flame spread - the quiescent microgravity limit subrata (sooby) bhattacharjee...

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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

8

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 ~

10

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

~

11

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 ~


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 ~


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

17

VfgL

gL

gL

Solid Residence Time: f

gsres V

Lt ~,



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



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

,

21

Vf

syL

gL

gL



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



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

1 opposed-flow flame spread - the quiescent microgravity limit subrata (sooby) bhattacharjee...

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