8.3 - firefoam

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LES of Thermal andFire Plumes

Y. Wang, P. Chatterjee, J. de Ris

FM Global, Research Division

Norwood, MA, USA

6th International Seminar on Fire and Explosion Hazards, April 2010, Leeds, UK

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Background• FM Global research program

– To develop CFD fire modelingcapability for large-scale fires

including fire growth and

extinguishment, which will help FM

Global to reduce the number of

required large-scale tests

• Code platform: OpenFOAM

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Why OpenFOAM Platform• Open source CFD toolbox

http://www.opencfd.co.uk/openfoam/index.html• Object-Oriented Programming (C++)

• State-of-the-art CFD techniques

– Massive parallel

– Unstructured mesh

– Numerical schemes – Physical models

– ……..

http://www.opencfd.co.uk/openfoam/index.html

http://www.opencfd.co.uk/openfoam/index.html

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FireFOAM• Solver based on OpenFOAM for fire modeling

– http://code.google.com/p/firefoam-dev – Industrial scale fire growth and suppression

– Platform for fire related submodels

• Buoyant turbulent diffusion flame• Soot and radiation: (Chatterjee et. al. S30P2)

• Pyrolysis (Chaos et. al. S11P1)

• Water droplet transport• Surface water film flow

Flame spread in parallel panel(Krishnomoorthy et al. S25P3)

FireFOAM

Combustion

Soot/Radiation

Pyrolysis

http://code.google.com/p/firefoam-dev

http://code.google.com/p/firefoam-dev

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Outline• FireFOAM gas phase solver

• Thermal plume validation

• Fire plume validation

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FireFOAM: Governing Equations

0 j

j

u

t x

ρ ρ ∂∂+ =

∂ ∂

Pr

j t

j j t j

u Z Z Z Dt x x x

ρ ν ρ ρ

⎛ ⎞∂ ⎛ ⎞∂ ∂ ∂

+ = +⎜ ⎟⎜ ⎟⎜ ⎟∂ ∂ ∂ ∂⎝ ⎠⎝ ⎠

( ) 2

3

i j ji i k t ij i

j i j j i k

u u uu u u pg

t x x x x x x

ρ ρ ρ ν ν δ ρ

⎛ ⎞⎛ ⎞∂ ∂∂ ∂ ∂∂ ∂+ = − + + + − +⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟∂ ∂ ∂ ∂ ∂ ∂ ∂⎝ ⎠⎝ ⎠

Pr

j t

j j t j

u hh Dp h Dt x Dt x x

ρ ν ρ ρ ⎛ ⎞∂ ⎛ ⎞∂ ∂ ∂+ = + +⎜ ⎟⎜ ⎟⎜ ⎟∂ ∂ ∂ ∂⎝ ⎠⎝ ⎠

Momentum

TotalEnthalpy

Mass

Mixture

Fraction

( )0

, ( )T

o

f k k k k T

k k

h h Y Cp Y d τ τ = +∑ ∑∫

Sensible enthalpyChemical enthalpy

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Numerical Method• Pressure based segregated solver

(SIMPLE/PISO)• 2nd order implicit Finite Volume discretization

• Unstructured polyhedral mesh

• Massive parallelization

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LES SGS Closure• SGS stress tensor – eddy viscosity model

• Turbulent flux – gradient diffusion model

– One equation model

( ) ( )k

k k k P

t

ρ ρ ρν ε

∂+ ∇ ⋅ = ∇ ⋅ ∇ + −

∂u

2/1k ck k Δ=ν 12/3 −Δ= k cε ε

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Diffusion Combustion Model• Single mixture fraction based

• Infinite fast chemistry• Beta PDF for SGS mixture fraction

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

M a s s f r a c t i o n

Mixture fraction Z

Fuel

Oxidizer

1

0( ) ( )

k k Y Y Z Pdf Z dZ =

∫

( )k Y Z ( )Pdf Z

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Validation 1: Thermal Plume• Shabbir & George (JFM, 1994)

– D = 0.0635 m, V = 0.98 m/s – T = 295 C, T0 = 25 C

– Re = 1300

– Fr = 1.5

– Synthetic turbulent inlet BC used – Long-time average for statistics (10-30s)

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Mesh – Domain: 15D * 20D

– Mesh: 400k cells

• 32 across nozzle, (0.2cm)

• 60 radial cells outside nozzle (3.5% stretch ratio)

• Azimuthal 48 cells, axial 120 cells (1cm)

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Centerline Mean Temperature Velocity( ) 3/1

0

3/1

04.3 −

−= y yF V c( ) 5/32/3

0 09.4 /c cT F y y g β −

Δ = −

0 2 4 6 8 10 12 14 16 180.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

V [ m / s ]

y / D

FireFOAM

Exp S & G

0 2 4 6 8 10 12 14 16 180.0

0.1

0.2

0.3

0.4

0.5

T / T

y / D

FireFOAM

Exp S & G

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2 4 6 8 10 12 14 16 180.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0.55

T ' / ( T

- T 0 ) , v ' / V

a n d u ' / V

y / D

T' / (T-T0)

v' / Vc

u' / Vc

Centerline Turbulent Fluctuations

Exp: 36%-42% (jet 18%)

Exp: 25%-33%

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Radial Self-Similarity Profile: T and V

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

0.0

0.2

0.4

0.6

0.8

1.0

1.2

T /

c

T c

r/y

8D

12D

16D

Exp S&G

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

0.0

0.2

0.4

0.6

0.8

1.0

1.2

V / V

c

r/y

8D

12D

16D

Exp S&G

268( / )r y

c c

T e

T

β

β

−Δ=

Δ

258 ( / )r y

c

V e

V

−=

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Self-similarity: Reynolds Stress

-0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35 8D

12D

16D

Exp S&G

u r m s

/ V

c

r/y-0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35 8D

12D

16D

Exp S&G

v r m s

/ V

c

r/y

-0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4-0.04

-0.03

-0.02

-0.01

0.00

0.01

0.02

0.03

0.04

8D

12D

16D

Exp S&G

u v / V

c 2

r/y

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Self-similarity: Turbulent Heat Flux

-0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4-0.1

0.0

0.1

0.2

0.3

0.4

0.5

t r m s

/

T c

r/y

8D

12D

16D

Exp S&G-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3-0.01

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.10

8D

12D

16D Exp S&G

v t / V

c

T c

r/y

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3-0.06

-0.05

-0.04

-0.03

-0.02

-0.01

0.00

0.01

0.02

0.03

0.04

0.05

8D

12D

16D Exp S&G

u t / V

c

T c

r/y

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2 4 6 8 10 12 14 16 180.0

0.2

0.4

0.6

0.8

1.0

< v ' T ' > / < v ' > < T ' >

y / D

v' t' correlation coefficient

Correlation Coefficient

Experimental (S&G, 1994, George et al. 1977) value: 0.67-0.7

2 2

' ' / ' 'v T v T

-0.2 -0.1 0.0 0.1 0.20.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

8D 12D

16D

< v ' T ' > / < v ' > < T ' >

r/y

Centerline Radial

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Thermal Plume: Summary• FireFOAM capable of model buoyancy-driven

turbulent – Centerline temperature and velocity follow

theoretical decay rate

– High turbulent fluctuations captured – Self-similarity observed in both mean and

fluctuation quantities

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Validation 2: Fire Plumes• B. J. McCaffrey,1979

• 30 cm x 30 cm square burner • 5 Methane flames (scaling)

*

2 p

QQ

c T gDD ρ ∞ ∞

=

Q [kW] 14 22 23 45 58

Q* 0.19 0.29 0.44 0.60 0.77

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Case Setup• Mesh:

– 389k unstructured mesh – 24 cells across burner

• Domain: 3m x 3m x 3m

• Average time: 13 seconds

• Assumptions:

– Fixed radiation fraction 20%

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0 0.5 1 1.5 2 2.5 3

-60

-40

-20

0

20

40

60

Y [ m ]

E

n t h a l p y f l o w r a t e [ k W ]

h

hs

hc

h(0)-hc

Energy Conservation

total enthalpy

sensible enthalpy

chemical enthalpy

58kW fire, 20% radiant loss

20% loss

20% loss

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0.01 0.02 0.04 0.08 0.2 0.3 0.550

80

100

200

300400

500600

800

10001200

Y/Q2/5

[ m ⋅ kW-2/5

]

Δ T

[ K

]

14 kW

22 kW33 kW

45 kW

58 kW

McCaffrey

0.01 0.02 0.04 0.08 0.2 0.3 0.550

80

100

200

300400

500600

800

10001200

Y/Q2/5

[ m ⋅ kW-2/5

]

Δ T

[ K

]

14 kW

22 kW33 kW

45 kW

58 kW

McCaffrey

2

2/52 0.9

T k Y T

g Q

η

∞ ⎛ ⎞⎛ ⎞Δ = ⎜ ⎟⎜ ⎟

⎝ ⎠ ⎝ ⎠

0=η

1−=η

3/5−=η

Flame Intermittent Plume

Normalized Centerline Temperature

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0.01 0.02 0.04 0.08 0.2 0.3 0.5

0.3

0.4

0.5

0.6

0.8

1

2

Y/Q2/5

[ m ⋅ kW-2/5

]

V / Q

1 / 5

[ m ⋅ s - 1 ⋅

k W - 1 / 5

]

14 kW

22 kW33 kW

45 kW

58 kW

McCaffrey

0.01 0.02 0.04 0.08 0.2 0.3 0.5

0.3

0.4

0.5

0.6

0.8

1

2

Y/Q2/5

[ m ⋅ kW-2/5

]

V / Q

1 / 5

[ m ⋅ s - 1 ⋅

k W - 1 / 5

]

14 kW

22 kW33 kW

45 kW

58 kW

McCaffrey

1/5 2/5

V Y

k Q Q

η

⎛ ⎞=

⎜ ⎟⎝ ⎠

2/1=η

0=η

3/1−=η

Flame Intermittent Plume

Normalized Centerline Velocity

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10 20 30 40 50 600

0.5

1

1.5

HRR [ kW ]

F l a m e H e i g h

t [ m ]

Heskestad

Zukoski

Cox & ChittyDelichatsios

Current Simulations

10 20 30 40 50 600

0.5

1

1.5

HRR [ kW ]

F l a m e H e i g h

t [ m ]

Heskestad

Zukoski

Cox & ChittyDelichatsios

Current Simulations

0.08Q2/5

0.2Q2/5

Flame Zone

Plume Zone

Intermittent Zone

Flame Height

*2/53.7 1.02 f

H Q D D= −

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10 20 30 40 50 60-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

HRR [ kW ]

V i r t u a l O r i g i n [ m ]

Heskestad

Current Simulations

Virtual Origin

2/5

0 1.02 0.083 Z D Q= − +

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0 0.5 1 1.5 2 2.5 30

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Y [ m ]

14 kW22 kW

33 kW

45 kW

58 kW

Local Froude Number

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Entrainment

0 0.2 0.4 0.6 0.8 1 1.20

5

10

15

Y / Flame Height

1 / E q u i v a l e n c e R a t i o

14 kW

22 kW

33 kW45 kW

58 kW

10-12 times stoichiometric

air entrained at flame tip

Linear

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Conclusions• A LES solver – FireFOAM, has been developed

and validated in thermal and fire plumes – Conservation verified

– Buoyancy-driven turbulence captured

– Correct scaling in near/ far fields observed

– Flame height & entrainment

– Boundary treatment adequate• Inlet, entrainment and outlet

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Future Work for FireFOAM• Gas phase

– Validation for large fires and wall fires• SGS treatment for larger grid sizes

• SGS models with buoyancy effect

• Wall models

– Numerical enhancement

• Boundedness, conservation, efficiency, etc

– Gas phase extinction

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Acknowledgement• OpenCFD

– Henry Weller – Sergio Ferraris

• FM Global

– Sergey Dorofeev

– Regis Bauwens

– Yibing Xin – Franco Tamanini

8.3 - firefoam

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