8.3 - firefoam
TRANSCRIPT
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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
– ……..
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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
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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
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