radiationdrivenextinctioninfires

Radiation-Driven Flame Extinction in Fires

Praveen Narayanan, Vivien Lecoustre& Arnaud Trouvé

Department of Fire Protection EngineeringUniversity of Maryland, College Park, MD 20742

• Sponsors: National Science Foundation Office ofCyberinfrastructure (PetaApps Program); and DOE Office ofScience (INCITE - Innovative and Novel Computational Impacton Theory and Experiment – Program).

• Motivation:

Combustion science

• Flame extinction has a significant impact on the performance of non-premixed combustion systems. It determines in part the turbulent flamestructure and the levels of pollutant emission (NOx, CO, soot).

Diesel engine

Engine applications

• Extinction due to high turbulence intensitiesin IC- or gas-turbine engines (momentum-driven, high-Reynolds number flames)

Diffusion Flame Extinction

• Motivation:

Fire applications

• Extinction due to air vitiation in under-ventilated compartment fires or large-scalepool fires (buoyancy-driven, moderate-Reynolds number flames)

• Extinction due to inert gaseous agents orwater sprays in fire suppression applications

pool fire

sprinklers


• Different flame extinction phenomena:

Aerodynamic quenching: flame weakeningdue to flow-induced perturbations (i.e.decrease in flame residence time)

Thermal quenching: flame weakening due toheat losses (e.g. heat losses byconvection/conduction to walls, by thermalradiation, by water evaporative cooling infire suppression applications)

Quenching by dilution: flame weakeningdue to changes in fuel stream or oxidizerstream composition (e.g. air vitiation inunder-ventilated fires)


Fuel side Oxidizer side

Flame

aOO YY,22

1FY


Flame

adflameflame TT


Flame


Single criterion to predict extinction (laminarflame theory):

Two fundamental limits:

• Fast mixing limit: Da is small because cst islarge (e.g., aerodynamic quenching)

• Slow mixing limit: Da is small because Tst issmall (e.g., thermal or dilution quenching)


critical

chemical

mixingDaDa

)/exp(

)/1(~

sta

st

chemical

mixing

TTDa


Fast mixing limit: also called kineticextinction

Criterion for extinction:

Sources: aerodynamic quenching

• Liñán (1974) Acta Astronautica

• Williams (1985) “Combustion Theory”

• Peters (2000) “Turbulent Combustion”


criticalst


Slow mixing limit: also called radiationextinction

Criterion for extinction:

Sources: thermal quenching in microgravitycombustion

• Sohrab, Liñán & Williams (1982)Combustion Science and Technology

• T’ien (1986) Combustion and Flame

• Chao, Law & T’ien (1990) ProceedingsCombustion Institute 23

• Bedir & T’ien (1998) Combustion andFlame


criticalrad ΓΓ *criticalst

• Relation between radiation extinctionand soot emission/smoke point studies:

Unclear: many recent studies of radiationextinction correspond to one-dimensionalflames that are soot-free at the extinctionlimit

But: past studies of the smoke point (SP) oflaminar jet diffusion flames suggest that SPis controlled by the flame luminosity; hence,SP may be interpreted as a radiationextinction event

Source:

• Markstein, de Ris (1984) ProceedingsCombustion Symposium


FuelAir Air

Flame

Soot region

open flametip (flame

extinction?)

soot emission

• Study mechanisms responsible for diffusion flame extinction inlaminar and turbulent flames (focus on conditions relevant tofire applications)

Establish flame extinction criterion; construct flammability map(s)

• Tools:

Asymptotic analysis of extinction limits of laminar counter-flowdiffusion flames exposed to different levels of radiant losses

Direct Numerical Simulations (DNS) of laminar counter-flow and co-flow diffusion flames, and of turbulent diffusion flames

• Explore relationship between flame extinction and sootemission

Objectives

pool fire

Cold Soot

Hot Soot

under-ventilated fire

• Use direct numerical simulation (DNS)

Leverage DOE-sponsored SciDAC collaboration on DNS solver calledS3D – Sandia Ntl. Laboratories (J.H. Chen), Univ. Michigan (H.G. Im)

• DNS solver S3D

Navier-Stokes solver; fully compressible flow formulation

High-order methods: 8th order finite difference; 4th order explicitRunge-Kutta time integrator

Characteristic-based boundary condition treatment (NSCBC)

Structured Cartesian grids

Parallel (MPI-based, excellent scalability)

Flame modeling: detailed fuel-air chemistry (CHEMKIN-compatible);simplified soot formation model; thermal radiation model (DiscreteOrdinate/Discrete Transfer Methods); Lagrangian particle model todescribe dilute liquid sprays

Numerical approach

Flame Modeling

• Combustion model: single-step chemistry, ethylene-aircombustion (Westbrook & Dryer, 1981)

Counter-flow flame: comparison of laminar flame response to changes instrain rate for single-step and detailed chemistry

)exp()()( 2

T

T

M

Y

M

YB aq

F

Op

F

FRRF

Flame Modeling

• Soot formation model: a phenomenological approach (Moss etal., Lindstedt et al.) Two-variable model; empirical description of fundamental soot formation

processes (nucleation, surface growth, coagulation, oxidation)

Model parameters are fuel-dependent

No PAH chemistry

Monodispersed soot particle size distribution

ncoagulationnucleationn

A

soot

jj

it

A

soot

iA

sooti

iA

soot

oxidationsgrowth

surfacesnucleations

j

soot

j

itsoot

i

sooti

i

soot

N

n

xScxV

N

n

xN

nu

xN

n

t

x

Y

ScxVY

xYu

xY

t

,,

,

,,,

,

))(()()()(

)()()()(

Flame Modeling

• Thermal radiation transport model: non-scattering, gray gasassumption; Discrete Transfer Method (Lockwood & Shah, 1981)

Radiative transfer equation

Mean absorption coefficient [m-1]

• ap,i is the Planck mean absorption coefficient for species i [m-1 atm-1]and is obtained from tabulated data (TNF Workshop web site)

• ksoot is the soot mean absorption coefficient [m-1]

AbsorptionEmission

4 )/( ITds

dI

sootCOCOOHOH axaxp )(2222

-1-1Km1817sootCTYCTfC sootsootsootvsootsoot )/(

• Classical activation energy asymptotic (AEA) analysis

Mass density variations handled with Howarth transformation

Mixture fraction equation and solution (a is strain rate)

Flame structure given by flamelet equations (in mixture fraction space)

x

dx0

2 )/(

st

F

p

Fst

c

H

dZ

Td

)(

2 2

2

AEA Analysis

)/2

(erf2

1

2

1

2

DZ

2

2

2

d

ZdD

d

dZ

Fla

me

• Classical decomposition into inner/outer layers

Perform asymptotic expansion in terms of small parameter e

Inner layer problem

AEA Analysis

)exp(])1(

[][

)(;)()(

2

2

221,

q

st

stp

st

p

FFst

Z

Z

d

d

OZZOc

YHTT

(d is a reduced Damkohler number)

)()(1

1,

2

FF

p

a

st

YH

c

T

T

Ze

)1/()/(;1)/( stst ZZdddd

• AEA flame structure with thermal radiation

Temperature decomposition (outer layer problem)

Governing equation for temperature deficit due to radiant cooling

Green’s function solution

Consider that chemical reaction zone is thin compared to characteristicradiation length scale ( ): inner layer problem is essentiallyunchanged

AEA Analysis

TTT adBS

p

rad

c

qT

d

dDT

d

d

)()(

2

2

2

1)( reaction

*** ),()()(

dg

c

qT

p

rad

• AEA flame structure with thermal radiation

Green’s function solution

Emitting/absorbing medium (spectrally-averaged gray)

Planck mean aborption coefficient:

Analytical expression for G (as a function of optical depth t):

AEA Analysis

)4( 4 GTqrad

*** ),()()(

dg

c

qT

p

rad

TfCaxaxp vsootOHOHCOCO )(2222

]')'()'(')'()'(

)()([2

10

1

22,21,

R

dEIdEI

EIEIG

bb

Rbb

• AEA flame structure with soot

Two-equations model for ssot mass fraction and soot number density(Moss et al., Lindstedt et al. )

Soot formation and oxidation rates (C2H2-air combustion)

AEA Analysis

soot

soot

n

A

soott

A

soott

Y

soottsoot

t

N

n

d

Vd

N

n

d

dV

Yd

Vd

d

dYV

)()()(

)(

22

3/13/2

2

)()exp()(

)()exp()(

)exp()()exp()(

2

A

sootFn

sootsootOO

O

sootFFY

N

nTc

T

TXTcc

nYT

T

T

Xc

nT

TXTc

T

TXTc

soot

soot

• AEA flame structure with soot

External soot loading: a mechanism to simulate non-local effectsobserved in multi-dimensional flames in a one-dimensional framework

Soot loading from the flame air side

AEA Analysis

Flam

e

Soot

injection

FuelAir Air

Flame

Soot region

Laminar Counter-Flow Flames

Flam

e

Dx = 60 mmvariable Dy

• Reference counter-flow diffusion flame configuration

Flamelet perspective: steady flame structure obtained as a function offlame stretch, ranging from ultra-high to ultra-low values

• Reference counter-flow flame configuration

Flamelet database: steady flame structure obtained as a function offlame stretch, ranging from ultra-high to ultra-low values

kineticextinctionlimit

radiationextinction

limit

ststT versus

-1, s61ULext-1

, s025.0LLext


DNS

AEA

• Reference counter-flow flame configuration

Flamelet database: steady flame structure obtained as a function offlame stretch, ranging from ultra-high to ultra-low values


stradcomb qq versusand stradcombrad qqΓ versus)/(

%70radΓ2/1)( st

constant~and)(~ 1/2radstcomb qq

radq

combq

• Extinction limits: correspond to critical value of Damköhler number

*

)1()1(162

)1(

1,

)1(

*

2)10()1(

)/exp(8cqp

st

q

O

p

Fqp

sta

q

s

qp

F

qp

st

ZeMMb

TTArY


• Extinction limits: correspond to critical value of Damköhler number

*

)1()1(162

)1(

1,

)1(

*

2)10()1(

)/exp(8cqp

st

q

O

p

Fqp

sta

q

s

qp

F

qp

st

ZeMMb

TTArY


st versus*adiabatic

soot-free

withsoot

with externalsoot loading

approximatecritical value

1* c

Extinction

Flammable

• Extinction limits

Flammability map with mixing rate and fuel-air flame temperature ascoordinates


stT

Extinction

st

1* cFlammable

Engineextinction event

Fireextinction event

• Simplified turbulent flame configuration

Two-dimensional (8×4 cm2); grid size: 1216×376 (uniform×stretched);prescribed inflow turbulent fluctuations (u = 1-2.5 m/s; Lt = 1.7 mm)

Turbulent Wall-Jet Flames

Air

FuelSolid Wall

2.5-5 m/s Dy 50 mmDx 66 mm

• Analysis of flame structure (case: Tw = 300 K; d = 0.5 cm; withsoot/radiation; Csoot = 7000 m-1K-1)


radiation cooling rate

soot mass fraction

Observations:

• radiative cooling regionis not thin

• soot region is not thin

• Weak flame eventscorrelated with soot massleakage across the flame

extinction

extinction

• Analysis of flame structure (case: Tw = 300 K; d = 0.5 cm; withsoot/radiation; Csoot = 7000 m-1K-1)


weak spots

sTst versus sversusst

weak flame events occur at low values offlame stretch (slow mixing limit)


Flammability map with mixing rate and fuel-air flame temperature ascoordinates

Flame weakest spots (e.g., locations that show soot mass leakage)correspond to weak burning conditions, not flame extinction


stT

Extinction

st

1* c

representative conditions offlame weakest spots in DNS

• Simplified laminar flame configuration

High air co-flow velocity, diffusive-driven incoming fuel stream, zero-g

Recirculation zone close to fuel surface, long residence times

Laminar Co-Flow Flames

Fuel

Air1 m/s

Air

1 m/s


Comparison between solutions with (left) and without radiation (right)

Flame tip temperatures differ by more than 700 K



Comparison between solutions with (left) and without radiation (right)

Both flames feature both large amounts of soot within the flameenvelope and soot mass leakage across the flame tip



Flammability map with flame temperature and mixing rate as coordinates

Flame tip (e.g., location that show soot mass leakage) corresponds toweak burning conditions, not flame extinction


stT

Extinction

st

1* c

conditions along flamesurface from base to tip

with radiation

without radiation

• AEA theory and DNS are used to make fundamentalobservations of extinction phenomena in non-adiabatic turbulentdiffusion flames

• In laminar counter-flow flames, two different sets of flameextinction conditions are observed: Kinetic extinction occurring under fast mixing conditions

Radiation extinction occurring under slow mixing conditions

• These 2 different modes correspond to the same extinction limit: AEA analysis suggests that all extinction limits may be described by a

single criterion corresponding to a critical value of the Damköhler number

Soot has a significant impact on the extinction limit

• In laminar co-flow flames and in turbulent flames, it is found thatsoot mass leakage events do not correspond to radiationextinction events

Conclusions

• Intermediate stretch rate: cst = 5 s-1

Flame temperature versus distance normal to the flame

Weak radiation effects

1)( outer


• Low stretch rate: cst = 0.045 s-1

Flame temperature versus distance normal to the flame

Strong radiation effects

)1()( Oouter


radiationdrivenextinctioninfires

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