1

A Time-Scale Analysis of Opposed-Flow Flame Spread – The Foundations

Subrata (Sooby) Bhattacharjee

Professor, Mechanical Engineering Department

San Diego State University, San Diego, USA

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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, Isaac, Tahir and Mark.

(Support from NASA and Japan Government is gratefully acknowledged)

3

Overview

• What is opposed-flow flame spread?• Flame spread in different

environment. • Mechanism of flame spread.• Length scales and time scales.• Spread rate in normal gravity.• Spread rate in microgravity• The quiescent limit

4

Upward or any other flow-assisted flame spread becomes large and turbulent very quickly.

Opposed-flow flame spread is also known as laminar flame spread.

5

AFP: = 0.08 mm

= 1.8 mm/sfV

Downward Spread Experiment, SDSU Combustion Laboratory

PMMA: = 10 mm

= 0.06 mm/sfV

6

•Gravity Level: 1.e-6g

•Environment: 50-50 O2/N2 mixture at 1.0 atm.

•Flow Velocity: 50 mm/s

•Fuel: Thick PMMA (Black)

•Spread Rate: 0.45 mm/smm

Sounding Rocket Experiment Spread Over PMMA: Infrared Image at 2.7

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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

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

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

10

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 ~

12

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

~

13

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 ~,

14

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

15

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

17

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

19

Vr Vg V f

Vf gL

gL

gL

Gas to Environment Radiation (ger)

Time Scales Relevant to Gas Phase

h

r

ggres V

Lt ,

tcomb

gert

Available Time

20

Vr Vg V f

Vf gL

gL

gL

Time Scales Relevant to Gas Phase: Thermal Regime

h

r

ggres V

Lt ,

Available Time in Gas Phase

combgresger ttt ,

Gas to Solid Radiation (gsr)

Solid to Env. Radiation (ser)

tcomb

gert

21

VfgL

gL

gL

rV

h

Time Scales Relevant to Solid Phase

f

gsres V

Lt ,

tshvapt

tgsc

sfct

gsrtsert

Available Time

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VfgL

gL

gL

rV

h

Time Scales Relevant to Solid Phase: Thermal Regime

f

gsres V

Lt ,

tshvapt

tgsc

sfct

gsrtsert

Available Time

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VfgL

gL

gL

rV

h

The Thermal Regime Governing Equation

f

gsres V

Lt ,

gscsh tt ~

r

ggres V

Lt ,

gscsres tt ~,

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VfgL

gL

gL

Gas to Solid Conduction (gsc)

mechanismgiven by the rate Heating

tRequiremenHeat sticCharacterimechanismt

TTWLcQ vghsschar ~

Fc

c

VWL

L

TT

TTWLc

WLq

Qt

gg

ss

r

h

gg

vfg

vghss

ggsc

chargsc

1~~~

The characteristic heat is the heat required to raise the solid-phase control volume

from to . vT T

Gas-to-surface conduction time:

rV

h

Time Scales – Gas to Surface Conduction

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VfgL

gL

gL

Gas to Solid Conduction (gsc)

Fc

c

VV

L

gg

ss

r

h

f

g 1~

Substitute the two limits of

rV

h

Thermal Regime: Spread Rates Using Time Scales

gscsres tt ~,

h

2, ~ F

c

cVV

sss

gggrthickf

F

cV

ss

gthinf

~,

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VfgL

gL

gL

Solid Forward Conduction (sfc)

Gas to Solid Conduction (gsc)

s

gss

hg

v

vghss

hsfc

charsfc

Lc

WLTT

TTWLc

Wq

Qt

2

~

~

~

FLt

tN

gg

hs

sfc

gscsfc

1~

2

2

,max,

1~

1~~

FFL

LNN

g

s

gg

sysThicksfcsfc

rV

h

Relative dominance of GSC over SFC

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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

occur.not does spreadsteady

, 4.0For 0

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

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• A phenomenological model for opposed flow flame spread is built around two residence times, one in the gas phase and one in the solid.

• Theoretical solutions in the thermal regime are reproduced using the time scale analysis.

• Deviation from the thermal regime can be quantified by comparing the time scale of the added physics with the appropriate residence time.

• In the quiescent microgravity environment all fuels behave like thin fuels.

• A critical thickness is proposed beyond which a spreading flame cannot be sustained in such environment.

Conclusions