fireFoam表面火蔓延模型

⎛ ⎛ νt ρ D + ⎜ ⎜ ⎜ Prt ⎝ ⎝ ⎞ ∂Z ⎟ ⎠ ∂x j
⎛ ⎛ ν ρ⎜D+ t ⎜ ⎜ Prt ⎝ ⎝
T = ho Y h + ∑ f ,k k ∫ ∑ Cpk (τ )Yk dτ k T0 k

(
)
Chemical enthalpy
Sensible enthalpy
Validation 2: Fire Plumes
• B. J. McCaffrey,1979 • 30 cm x 30 cm square burner • 5 Methane flames (scaling)
Q [kW] Q* 14 0.19 22 0.29 23 0.44 45 0.60 58 0.77
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
Centerline Mean Temperature Velocity
β c ΔTc = 9.4 F
0.5
2/3 0
( y − y0 )
−5/3
/g
2.0 1.8 1.6 1.4 1.2
Vc = 3.4 F01/ 3 ( y − y0 )
−1 / 3
FireFOAM Exp S & G
FireFOAM Exp S & G
• 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)
βΔT/βcΔTc
V/Vc
-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3
0.6
0.6
0.4
0.4
0.2
0.2
0.0
0.0 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3
r/y
r/y
Self-similarity: Reynolds Stress
0.35 0.30 0.25 0.25 0.20
ν k = c k Δk 1 / 2
ε = cε k 3 / 2 Δ−1
Diffusion Combustion Model
• Single mixture fraction based • Infinite fast chemistry • Beta PDF for SGS mixture fraction
1 Yk = ∫ Yk ( Z ) Pdf ( Z )dZ 0
1.0
0.8
Fuel Oxidizer
Mass fraction
0.6
0.4
0.2
Yk ( Z )
0.2 0.4 0.6 0.8 1.0
Pdf ( Z )
0.0 0.0
M ixture fraction Z
Validation 1: Thermal Plume
• Code platform: OpenFOAM
Why OpenFOAM Platform
• Open source CFD toolbox /openfoam/index.html • Object-Oriented Programming (C++) • State-of-the-art CFD techniques
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)
• • • • • Buoyant turbulent diffusion flame Soot and radiation: (Chatterjee et. al. S30P2) Pyrolysis (Chaos et. al. S11P1) Water droplet transport FireFOAM Surface water film flow Combustion
0.01 0.00 -0.01 -0.3 -0.2 -0.1 0.0 0.1
0.3
0.2
0.3
8D 12D -0.06 16D -0.3 -0.2 Exp S&G
-0.05
-0.1
0.0
0.1
0.2
0.3
r/y
trms / ΔTc
r/y
0.2
0.1
0.0
-0.1 -0.4
-0.3
-0.2
-0.1
0.0
y/D
Radial Self-Similarity Profile: T and V
β ΔT = e −68( r / y ) β c ΔTc
1.2
2
V − 58 ( r / y ) 2 =e Vc
8D 12D 16D Exp S&G
1.2
1.0
1.0
8D 12D 16D Exp S&G
0.8
0.8
LES SGS Closure
• SGS stress tensor – eddy viscosity model • Turbulent flux – gradient diffusion model
– One equation model
∂ρ k k ) = ∇ ⋅ ( ρν k ∇k ) + P − ε + ∇ ⋅ ( ρu ∂t
FireFOAM: Governing Equations
Mass Momentum Total Enthalpy Mixture Fraction j ∂ρ ∂ρ u + =0 ∂t ∂x j i u j i ∂ρ u ∂ρ u ∂p ∂ + =− + ∂t ∂x j ∂xi ∂x j Dp ∂ ∂ρ u jh ∂ρ h + = + Dt ∂x j ∂t ∂x j ∂ρ u jZ ∂ρ Z ∂ + = ∂t ∂x j ∂x j ⎛ ⎛ ∂u j 2 ∂u i ∂u k ⎞ ⎞ + − δ ⎟ + ρ gi ⎜ ρ (ν +ν t ) ⎜ ⎜ ∂x j ∂xi 3 ∂xk ij ⎟ ⎟⎟ ⎜ ⎝ ⎠⎠ ⎝ ⎞ ∂h ⎟ ⎠ ∂x j ⎞ ⎟ ⎟ ⎠ ⎞ ⎟ ⎟ ⎠
– – – – – Massive parallel Unstructured mesh Numerical schemes Physical models ……..
FireFOAM
• Solver based on OpenFOAM for fire modeling
– – Industrial scale fire growth and suppression – Platform for fire related submodels
0.1
0.2
0.3
0.4
r/y
Correlation Coefficient v ' T ' / v '2 T '2
1.0
1.0
v' t' correlation coefficient
0.8
0.9 0.8 0.7
8D 12D 16D
<v'T'> / <v'><T'>
0.6
<v'T'> / <v'><T'>
0.4
V [m/s]
0 2 4 6 8 10 12 14 16 18
0.3
ΔT / T
1.0 0.8 0.6
0.2
0.1
0.4 0.2
0.0
0.0 0 2 4 6 8 10 12 14 16 18
y/D
y/D
Centerline Turbulent Fluctuations
0.55 0.50 0.45
0.6 0.5 0.4 0.3 0.2
0.4
0.2
Centerline
0.0 2 4 6 8 10 12 14 16 18
Radial
-0.1 0.0 0.1 0.2
0.1 0.0 -0.2
y/D
r/y
Experimental (S&G, 1994, George et al. 1977) value: 0.67-0.7
0.10 0.09 0.08 0.07 0.06
0.05
8D 12D 16D Exp S&G
0.04 0.03 0.02 0.01
8D 12D 16D Exp S&G
vt / VcΔTc
0.05 0.04 0.03 0.02
0.5
ut / VcΔTc
0.4
0.00 -0.01 -0.02 -0.03 -0.04
LES of Thermal and Fire 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
8D 12D 16D Exp S&G
0.35 0.30
8D 12D 16D Exp S&G
urms / Vc
0.20 0.15 0.10 0.10 0.05 0.00 -0.4 -0.3 -0.2 -0.1 0.0
0.04 0.03
vrms / Vc
0.15
0.05 0.00 0.2 0.3 0.4 -0.4
Flame spread in parallel panel (Krishnomoorthy et al. S25P3)
Soot/Radiation Pyrolysis
Outline
• FireFOAM gas phase solver • Thermal plume validation • Fire plume validation
r/y
0.1 0.02
0.01
8D 12D 16D -0.3 -0.2 Exp S&G
-0.1
0.0
0.1
0.2
0.3
0.4
r/y
uv / Vc
2
0.00 -0.01 -0.02 -0.03 -0.04 -0.4
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
0.4
r/y
Self-similarity: Turbulent Heat Flux
Background
• FM Global research program
– To develop CFD fire modeling capability for large-scale fires including fire growth and extinguishment, which will help FM Global to reduce the number of required large-scale tests
Numerical Method
• Pressure based segregated solver (SIMPLE/PISO) • 2nd order implicit Finite Volume discretization • Unstructured polyhedral mesh • Massive parallelization
* = Q
Q
ρ∞ c pT∞ gDD 2
Case Setup
• Mesh:
– 389k unstructured mesh – 24 cells across burner
• Domain: 3m x 3m x 3m • Average time: 13 seconds • Assumptions:
Exp: 36%-42% (jet 18%)
T' / (T-T0) v' / Vc u' / Vc
T' / (T - T0), v' / V and u' / V
0.40 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00 2 4 6 8 10 12 14 16 18
Exp: 25%-33%