modeling of turbulent wall fires - stanford university · 2012. 7. 19. · ¾impact of smoke layer:...
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Slide 1
Modeling of Turbulent Wall Fires
Arnaud Trouvé
Department of Fire Protection EngineeringUniversity of Maryland, College Park, MD 20742 (USA)
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Slide 2
• OutlineOverview of Compartment Fire Dynamics
Multi-physics problemRole of wall flames
Laminar Wall FiresAnalytical solution of a canonical wall flame problem – the Emmons problem (non-spreading; constant wall temperature; no thermal radiation)
Turbulent Wall FiresLarge eddy simulation of a canonical wall fire problem (non-spreading; vertical wall)
Modeling of Turbulent Wall Fires
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Slide 3
Compartment Fires
• Example: Station Nightclub Fire, 02/20/03, Rhode IslandSequence of events: music band on stage using pyrotechnics; ignition of the insulation foam lining walls and ceiling around stage; rapid fire spread over dance floor (no sprinkler system); egress blocked bycrowding at main entrance; 100 dead peopleTechnical investigation conducted by the National Institute of Standards and Technology (Final Report published in June 2005)
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Slide 4
• Example: Station Nightclub Fire, 02/20/03, Rhode Island
Compartment Fires
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Slide 5
• Main features: fire is an unusual combustion process in which the fuel supply corresponds to a large list of flammable objectsand materials, usually in solid or liquid form
solids (wood, plastics, foams, fabric, linings, etc)liquids (engine fuels, LNG, melted solids, etc)
Compartment Fires
Liquid fuel Gaseous fuelSolid fuel FIREFIRE
ENGINE
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Slide 6
• Main features: fire is an unusual combustion process in which the fuel supply is unknown
Typical production of flammable vapors in a fire:• Consider a flammable solid object/material that is a potential fuel
source• At ambient temperature, the fuel is in solid form, the oxygen (from
air) in gaseous form, and there is no combustion• At moderately elevated temperatures (typically 200-400 degrees
Celsius), a complex thermal degradation process is initiated in the solid object/material, that corresponds to a phase change and produces fuel in gaseous form. This gasification process is called pyrolysis.
Compartment Fires
HeatGaseousfuel mass
Solid Fuel
Ambient air
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Slide 7
• Main features: fire is an unusual combustion process in which the fuel supply is unknown
Typical production of flammable vapors in a fire:• The fuel gasification rate is determined by a heat feedback
mechanismFuel gasification is an endothermic process and heat comes from the gas-to-solid heat transferThe fuel gasification rate is controlled by the rate of gas-to-solid heat transfer
Compartment Fires
netpyroF qHm ′′≈Δ′′ &&Fm&
Fuel gasificationrate
Heat releaserate fireQ&
Temperaturedistribution
Heat flux tofuel surface
Heat
Gaseousfuel mass
PyrolysisEvaporation
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Slide 8
• Main features: fire is an unusual combustion process in which the fuel supply is unknown
Typical production of flammable vapors in a fire:
Compartment Fires
The gas-to-solid thermal feedback controls the fuel mass loss rate and thereby the overall fire sizeThe fraction of energy fed back to the fuel source is typically a small fraction of the energy released by combustion:
The thermal feedback has 2 components corresponding to convective and radiativeheat transfer
10.001.0 −≈Δ
Δ≈
comb
pyrofeedback H
Hχ
D
radq ′′& convq ′′&
FuelFm& ′′
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Slide 9
• Main features: fire is a buoyancy-driven, relatively-slow, non-premixed combustion process
Example: pool fire configurationFuel source velocity is small (a few cm/s)Buoyancy effects accelerate the flow up to several m/s; flow regime corresponds to moderate turbulence intensitiesFlame corresponds to diffusion combustion and to a thin reaction sheet where fuel and air meet in stoichiometric proportionsSlow velocities and long residence times promote soot formation and radiant losses
Compartment Fires
Fuel
DiffusionFlame
air air
Plumeoverfireregion
underfireregion
D
%35~)/( combradrad QQ &&=χ
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Slide 10
• Main features: fire is a buoyancy-driven, relatively-slow, non-premixed combustion process
Example: pool fire configurationFlame height scales with Froude number
Compartment Fires
FFFp
comb
FF
f
stFF
FrdgdTc
gdTT
ZuFr
~
])()[(
)(
2,
*
2/12/1
2/3
∞∞∞
∞∞
=
Δ=
ρ
ρρ
&&
FFrQ ~*&
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Slide 11
• Main features: fire is a buoyancy-driven, relatively-slow, non-premixed combustion process
Example: pool fire configuration
Compartment Fires
)/( Ff dL
B M
M
1)/(,5,105* >>>> Fff dLFrQ&
B
)1()/(,5,105* OdLFrQ Fff =<<&
Buoyancy-driven flame regime:low velocities, large diameters
Momentum-driven flame regime:high velocities, small diameters
FIRE
ENGINE
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Slide 12
• Main features: flow confinement and buoyancy forces lead to the formation of a ceiling-level smoke layer
Compartment Fires
time
Ignition andearly growth
Smokefilling
Quasi-steadyregime
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Slide 13
• Main features: flow confinement and buoyancy forces lead to the formation of a ceiling-level smoke layer
Smoke layer composition: hot combustion products mixed with ambient air; depending on fuel type and combustion conditions, may contain significant amounts of soot
Compartment Fires
Soot particlesProduct of incomplete combustionPhase: solidChemical composition: primarily made of carbon atomsParticle size distribution: from a few nanometers (10-9 m) to several microns (10-6 m)Particles geometry: complex shapes (agglomerates of elementary spherical particles)
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Slide 14
• Main features: flow confinement and buoyancy forces lead to the formation of a ceiling-level smoke layer
Smoke layer depth: depends on fire size and vent flow rates
Compartment Fires
Accumulation of smokenear ceiling
Fast fire growth andsmoke descent to floor
Smoke filling andloss of visibility
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Slide 15
• Main features: flow confinement and buoyancy forces lead to the formation of a ceiling-level smoke layer
Impact of smoke layer: increases (radiation-driven) heat feedback to fuel sources
Compartment Fires
Heat Fuel
Solid Fuel
Upper layer (UL)),,(, ,,, 22 ULvULCOULOHUL fxxT
Flame
{ {
{ { {
{
))()((
))exp(1(
componentsoot
,
component gas
,,
coef absorptionmeanPlanck
lengthbeammean
coef absorptionmeanPlanck emissivity
4
emissivitypower emissive
2222
43421
444444 3444444 21
ULULvsoot
COULCOOHULOHUL
ULULUL
ULULUL
TfC
TaxTaxp
d
TG
+
+=
×−−=
=
κ
κε
σε
ULG
often dominant
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Slide 16
• Main features: flow confinement and buoyancy forces lead to the formation of a ceiling-level smoke layer
Impact of smoke layer: increases heat feedback to fuel sources, therefore increases fuel gasification rate and heat release rate
Compartment Fires
time
Fire spread
Fire growth
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Slide 17
• Main features: flow confinement and buoyancy forces lead to the formation of a ceiling-level smoke layer
Impact of smoke layer: increases heat feedback to fuel sources, therefore increases fuel gasification rate and heat release rate (fire growth and fire spread)Possible transition to flashover (rapid series of ignition events involving all flammable objects/materials present in the fire room)
Compartment Fires
Small fire
Flammableobjects
Flashover !
time
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Slide 18
• Main features: flow confinement and buoyancy forces lead to the formation of a ceiling-level smoke layer
Possible transition to flashover: may trigger in turn a transition to under-ventilated combustion
Compartment Fires
Flames extending out of the compartment of fire origin
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Slide 19
• Main features: flow confinement and buoyancy forces lead to the formation of a ceiling-level smoke layer
Possible transition to under-ventilated combustionFlame location: (1) near the fuel source; (2) near the vents
Compartment Fires
(1) Over-ventilated combustion, Vent
AirFuel
Flame Smoke
(2) Under-ventilated combustionVent
AirFuel
Flame
Smoke
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Slide 20
• Main features: flow confinement and buoyancy forces lead to the formation of a ceiling-level smoke layer
Possible transition to under-ventilated combustionClassical Burke-Schumann problem (1928): 2 possible regimes
Compartment Fires
FuelAir
Walls
Air
Laminar flame-flow configuration
Flameover-ventilated
flame
under-ventilatedflame
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Slide 21
• Main features: flow confinement and buoyancy forces lead to the formation of a ceiling-level smoke layer
Possible transition to under-ventilated combustionSmoke layer composition: (1) products of complete combustion mixed with air; (2) products of incomplete combustion
Compartment Fires
(1) Over-ventilated combustion, Vent
AirFuel
Flame Smoke
(2) Under-ventilated combustionVent
AirFuel
Flame
Smoke
CO2, H2OExcess air
CO2, H2OCO, uHCsoot
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Slide 22
Vent
AirFuel
Flame
• Main features: flow confinement and buoyancy forces lead to the formation of a ceiling-level smoke layer
Impact of smoke layer: air vitiation as the compartment fire system evolves from well-ventilated to under-ventilated combustionAir vitiation reduces the flame intensity and promotes flame extinction
Compartment Fires
Fuel
Flame
Oxidizer∞∞22
, OO TY∞∞FF TY ,
airO
airOO
TT
YY
≥
≤∞
∞
2
22 ,
Air vitiation
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Slide 23
• Main features: flow confinement and buoyancy forces lead to the formation of a ceiling-level smoke layer
Reduced-scale compartment fire experiments (Utiskul & Quintiere)Vent size: variable width and heightFuel pan: variable diameter
Compartment Fires
Heat Flux Gauge
Heat Flux Gauge
Upper Gas Tube
Lower Gas TubeHeat Flux Gauge
Stand to Load Cell with Water Seal
Fuel Pan
Heat Flux Gauge
Center Thermocouple
Top Vent
Bottom Vent
Front Wall Thermocouples
Inner Size: 40x40x40 cm3
Adjustable Back Wall
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Slide 24
• Main features: flow confinement and buoyancy forces lead to the formation of a ceiling-level smoke layer
Reduced-scale compartment fire experiments (Utiskul & Quintiere)Steady under-ventilated fire (flame stabilized at the vents)
Compartment Fires
Vent
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Slide 25
Compartment Fires
• Role of wall flamesControl the ignition and fire growth/spread processes
Ignition and earlyvertical spread ofwall flames
Vertical wall flamesimpinging on ceiling
Horizontal spread
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Slide 26
Compartment Fires
• SummaryCompartment fires feature rich multi-physics dynamics
Buoyancy-driven, low-to-moderate Reynolds number turbulent flowNon-premixed combustionPyrolysis processesSoot formation/oxidationThermal radiation transport
Wall flames are an essential ingredient of the fire dynamics
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Slide 27
• OutlineOverview of Compartment Fire Dynamics
Multi-physics problemRole of wall fires
Laminar Wall FiresAnalytical solution of a canonical wall flame problem – the Emmons problem (non-spreading; constant wall temperature; no thermal radiation)
Turbulent Wall FiresLarge eddy simulation of a canonical wall fire problem (non-spreading; vertical wall)
Modeling of Turbulent Wall Fires
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Slide 28
• A variety of configurations:Solid wall material
Chemically inert (e.g., concrete)Flammable (e.g., plastic, wood, fabric)
Wall orientationFloor fire (pool fire)
Wall fire
Ceiling fire
Wall thicknessThermally thin
Thermally thick
Laminar Wall Fires
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Slide 29
• A variety of configurations:Propagation
Non-spreading wall flameBuoyancy-driven (u∞ small) or momentum-driven (u∞large) flow
Laminar Wall Fires
px
Gravity g
yx
flx
Free streamvelocity u∞
BoundaryLayer
Flame
Fuel
pxx ≤≤0
flxx ≤≤0
xx fl ≤
• Pyrolysis region
• Inert wall region
• Wall flame region
• Wall plume region
xxp ≤
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Slide 30
• A variety of configurations:Propagation
Spreading wall flame with upward spread (flow-aided, concurrent spread)
Laminar Wall Fires
px
Gravity g
yx
flx
ROS
BoundaryLayer
Flame
Fuelbox
• Pyrolysis region
• Inert wall regions
• Wall flame region
• Wall plume region
)()( txxtx pbo ≤≤
)()( txxtx flbo ≤≤
xtx fl ≤)(
x(t)x(t)xx pbo ≤≤ and
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Slide 31
• A variety of configurations:Propagation
Spreading wall flame with downward spread (flow-opposed spread)
Laminar Wall Fires
px
Gravity g
yx
flx
ROS
BoundaryLayer
Flame
Fuel
box
• Pyrolysis region
• Inert wall regions
• Wall flame region
• Wall plume region
)()( txxtx bop ≤≤
)()( txxtx flp ≤≤
xtx fl ≤)(
x(t)x(t)xx bop ≤≤ and
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Slide 32
• Emmons problemA canonical boundary layer combustion problem corresponding to a non-spreading laminar wall flame with forced convection (external flow)Assumptions:
Constant and uniform free stream conditionsNo gravityBoundary layer approximationInfinitely fast, single-step chemistry (mixture-fraction based combustion model)Constant wall temperatureNo thermal radiation
H.W. Emmons (1956) “The Film Combustion of Liquid Fuel”, Z. Angew. Math. Mech., 36:1 pp. 60-71.
Laminar Wall Fires
PrOrF ss )1(2 +→+
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Slide 33
• Flat (liquid or solid) fuel surface burning in a laminar gaseouscross-flow
Modified Blasius solution for the velocity field:Variable mass densityFinite normal velocity at the fuel surface
Infinitely-fast chemistry
Laminar Wall Fires
Flame
Liquid/solid Fuel
HeatFuel
HeatOxygen
Fuel side
Oxidizer sideFree streamvelocity u∞
0)0,( ≠xv),( yxρ
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Slide 34
• Emmons solutionGoverning equations for the flow field
Boundary conditions
)(
0)()(
yu
yyuv
xuu
vy
ux
∂∂
∂∂
=∂∂
+∂∂
=∂∂
+∂∂
μρρ
ρρ
∞=∞=
uxuxu
),(0)0,(
Laminar Wall Fires
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Slide 35
• Emmons solutionGoverning equations for the mixture composition
Laminar Wall Fires
combFpp
FsO
OOO
FF
FFF
HyT
yyTvc
xTuc
ry
YD
yyY
vx
Yu
yYD
yyYv
xYu
Δ+∂∂
∂∂
=∂∂
+∂∂
−∂
∂
∂∂
=∂
∂+
∂
∂
−∂∂
∂∂
=∂∂
+∂∂
ωλρρ
ωρρρ
ωρρρ
&
&
&
)(
)(
)(
2
2
22
DcDD pOF ===+ )/( 2
ρλ
PrOrF ss )1(2 +→+
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Slide 36
• Emmons solutionBoundary conditions at fuel surface (y = 0)
Total mass:
Fuel mass:
Oxygen mass:
Energy:
Laminar Wall Fires
wwF
wwwFww my
YDYv ′′=∂∂
− &
4444 34444 21gas
, )(ρρ
0,2=wOY
43421
&
gas
)( wwpyrow yTHm∂∂
=Δ′′ λ
{ www mv ′′= &gas
ρ
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Slide 37
• Emmons solutionMixture fraction formulation
where
Laminar Wall Fires
)(yZD
yyZv
xZu
∂∂
∂∂
=∂∂
+∂∂ ρρρ
∞
∞
∞∞
∞∞
∞
∞
−=
−Δ−
Δ−+−=
+
+−=
uuu
rYHTTcHTTcrYY
rYYrYrYY
Z
sOcombwp
FpsOO
sOwF
sOsOF
)/(/)(/)(/)(
)/()/()/(
,
,
,,
,
2
22
2
22
![Page 38: Modeling of Turbulent Wall Fires - Stanford University · 2012. 7. 19. · ¾Impact of smoke layer: air vitiation as the compartment fire system evolves from well-ventilated to under-ventilated](https://reader036.vdocuments.mx/reader036/viewer/2022071418/6115964cf0478f4bad086bed/html5/thumbnails/38.jpg)
Slide 38
• Emmons solutionBoundary conditions for mixture fraction:
andwith
Laminar Wall Fires
0),(1)0,(=∞=
xZxZ
wwww myZDB ′′=∂∂
− &])([ ρ
pyro
combsOwp
wF
sOwF
HHrYTTc
YrYY
BΔ
Δ+−=
−
+= ∞∞∞ )/()(
1)/( ,
,
,, 22
(Spalding B number) Ratio of heat released by unit mass of oxidizer divided by heat required to gasify unit mass of fuel
![Page 39: Modeling of Turbulent Wall Fires - Stanford University · 2012. 7. 19. · ¾Impact of smoke layer: air vitiation as the compartment fire system evolves from well-ventilated to under-ventilated](https://reader036.vdocuments.mx/reader036/viewer/2022071418/6115964cf0478f4bad086bed/html5/thumbnails/39.jpg)
Slide 39
• Emmons solutionIntroduce a modified stream function
Look for a similarity solution
Re-formulate the problem as an ODE problem
Laminar Wall Fires
),( yxψ
xv
yu
∂∂
−=∂∂
=ψρψρ ;
)(1),( ; )(),(
)(),(
)(Re
)(),(00
ηη
ηη
ηνρψ
νρρ
ρρη
ddGyxZ
ddGuyxu
Gxuyx
xudy
xdyyx
yxy
−==
=
==
∞
∞∞∞
∞
∞
∞∞∫∫
02 =′′+′′′ GGG
1)(0)0(
0)0()0(2
=∞′=′
=+′′
GG
GGB
![Page 40: Modeling of Turbulent Wall Fires - Stanford University · 2012. 7. 19. · ¾Impact of smoke layer: air vitiation as the compartment fire system evolves from well-ventilated to under-ventilated](https://reader036.vdocuments.mx/reader036/viewer/2022071418/6115964cf0478f4bad086bed/html5/thumbnails/40.jpg)
Slide 40
• Emmons solutionFuel mass loss rate
Scaling
Laminar Wall Fires
BG
Gumx
w
offunction ))0((
))0((Re2=−
−=′′ ∞∞ρ&
∞′′
′′
um
xm
s
s
~
/1~
&
&
![Page 41: Modeling of Turbulent Wall Fires - Stanford University · 2012. 7. 19. · ¾Impact of smoke layer: air vitiation as the compartment fire system evolves from well-ventilated to under-ventilated](https://reader036.vdocuments.mx/reader036/viewer/2022071418/6115964cf0478f4bad086bed/html5/thumbnails/41.jpg)
Slide 41
• Emmons solution
Laminar Wall Fires
)5 m/s; 5.0 flow;(air ==∞ Bu
Streamwise velocity field Temperature field (Ts = 630 K)
![Page 42: Modeling of Turbulent Wall Fires - Stanford University · 2012. 7. 19. · ¾Impact of smoke layer: air vitiation as the compartment fire system evolves from well-ventilated to under-ventilated](https://reader036.vdocuments.mx/reader036/viewer/2022071418/6115964cf0478f4bad086bed/html5/thumbnails/42.jpg)
Slide 42
• Emmons solution
Laminar Wall Fires
)5 m/s; 5.0 flow;(air ==∞ Bu
Flame structure in y-direction (x = 0.5 m)
![Page 43: Modeling of Turbulent Wall Fires - Stanford University · 2012. 7. 19. · ¾Impact of smoke layer: air vitiation as the compartment fire system evolves from well-ventilated to under-ventilated](https://reader036.vdocuments.mx/reader036/viewer/2022071418/6115964cf0478f4bad086bed/html5/thumbnails/43.jpg)
Slide 43
• Emmons solutionFuel mass loss rate
Scaling: effect of material properties
Laminar Wall Fires
))0((~ Gmw −′′&
pyro
combsO
pyro
combsOwp
HHrY
HHrYTTc
BΔ
Δ≈
Δ
Δ+−= ∞∞∞ )/()/()( ,, 22
BG
Gumx
w
offunction ))0((
))0((Re2=−
−=′′ ∞∞ρ&
15.08.1)1(
BBLn +
Emmons solution
![Page 44: Modeling of Turbulent Wall Fires - Stanford University · 2012. 7. 19. · ¾Impact of smoke layer: air vitiation as the compartment fire system evolves from well-ventilated to under-ventilated](https://reader036.vdocuments.mx/reader036/viewer/2022071418/6115964cf0478f4bad086bed/html5/thumbnails/44.jpg)
Slide 44
• Emmons solution: provides a metric to evaluate fire risk associated with different materials
n-heptane (liquid fuel)
Polymethylmethacrylate (PMMA)
Wood (douglas fir)
Laminar Wall Fires
2.6;52.3 ;MJ/kg 48.0 ;MJ/kg 45 ≈=≈Δ≈Δ BrHH spyrocomb
45.1;92.1 ;MJ/kg 2 ;MJ/kg 24 ≈=≈Δ≈Δ BrHH spyrocomb
45.0;95.0 ;MJ/kg 8.6 ;MJ/kg 4.12 ≈=≈Δ≈Δ BrHH spyropyro
pyro
combsO
HHrY
BΔ
Δ≈ ∞ )/( ,2
![Page 45: Modeling of Turbulent Wall Fires - Stanford University · 2012. 7. 19. · ¾Impact of smoke layer: air vitiation as the compartment fire system evolves from well-ventilated to under-ventilated](https://reader036.vdocuments.mx/reader036/viewer/2022071418/6115964cf0478f4bad086bed/html5/thumbnails/45.jpg)
Slide 45
• Emmons solution: provides a metric to evaluate fire risk associated with different materials
n-heptane (liquid fuel)
Polymethylmethacrylate (PMMA)
Wood (douglas fir)
Laminar Wall Fires
13~HRRPUA
9.3~HRRPUA
1=HRRPUA
combcombw HB
BLnHmHRRPUA Δ+
Δ′′= 15.0
)1(~&
![Page 46: Modeling of Turbulent Wall Fires - Stanford University · 2012. 7. 19. · ¾Impact of smoke layer: air vitiation as the compartment fire system evolves from well-ventilated to under-ventilated](https://reader036.vdocuments.mx/reader036/viewer/2022071418/6115964cf0478f4bad086bed/html5/thumbnails/46.jpg)
Slide 46
• Emmons solution: extension to buoyancy-driven flowConsider a vertical solid flammable surfaceF. J. Kosdon, F. A. Williams & C. Buman (1969) “Combustion of vertical cellulosic cylinders in air”, Proc. Combust. Inst., 12:253-264.J. S. Kim, J. De Ris & F. William Kroesser (1971) “Laminar free-convective burning of fuel surfaces”, Proc. Combust. Inst., 13:949-961.
Laminar Wall Fires
![Page 47: Modeling of Turbulent Wall Fires - Stanford University · 2012. 7. 19. · ¾Impact of smoke layer: air vitiation as the compartment fire system evolves from well-ventilated to under-ventilated](https://reader036.vdocuments.mx/reader036/viewer/2022071418/6115964cf0478f4bad086bed/html5/thumbnails/47.jpg)
Slide 47
• Emmons solutionFuel mass loss rate
Scaling
Laminar Wall Fires
4/1/1~ xmw′′&
BG
Gx
Grm xwww
offunction ))0((
))0(()(2
3 4/1
=−
−=′′νρ
&( )
∞
∞−=
TxTTgGr
w
wx 2
3
)(ν
![Page 48: Modeling of Turbulent Wall Fires - Stanford University · 2012. 7. 19. · ¾Impact of smoke layer: air vitiation as the compartment fire system evolves from well-ventilated to under-ventilated](https://reader036.vdocuments.mx/reader036/viewer/2022071418/6115964cf0478f4bad086bed/html5/thumbnails/48.jpg)
Slide 48
• Emmons solution
Laminar Wall Fires
)5( =B
Streamwise velocity field Temperature field (Ts = 630 K)
Gravity gGravity g
![Page 49: Modeling of Turbulent Wall Fires - Stanford University · 2012. 7. 19. · ¾Impact of smoke layer: air vitiation as the compartment fire system evolves from well-ventilated to under-ventilated](https://reader036.vdocuments.mx/reader036/viewer/2022071418/6115964cf0478f4bad086bed/html5/thumbnails/49.jpg)
Slide 49
• Limitations of Emmons solutionAssumes laminar flowNeglects role of thermal radiation
Laminar Wall Fires
wwpyrow yTHm )(∂∂
=Δ′′ λ& radwwwpyrow qyTHm ,)( ′′+∂∂
=Δ′′→ && λ
combHΔ combrad HΔ−→ )1( χ
![Page 50: Modeling of Turbulent Wall Fires - Stanford University · 2012. 7. 19. · ¾Impact of smoke layer: air vitiation as the compartment fire system evolves from well-ventilated to under-ventilated](https://reader036.vdocuments.mx/reader036/viewer/2022071418/6115964cf0478f4bad086bed/html5/thumbnails/50.jpg)
Slide 50
• Limitations of Emmons solutionNeglects role of pyrolysis processes occurring inside condensed phase
Laminar Wall Fires
wwpyrow yTHm )(∂∂
=Δ′′ λ& radwwwws
wspyrow qyT
yTHm ,, )()( ′′+
∂∂
=∂∂
+Δ′′→ && λλ
p
pyrocombsOw c
HBHrYTT
Δ−Δ+= ∞
∞
)/( ,2 constant≠→ wT
∫ Δ−′′′=′′→
0),( dxtxm gw ω&&
in-depth processes (rather than surface processes)
![Page 51: Modeling of Turbulent Wall Fires - Stanford University · 2012. 7. 19. · ¾Impact of smoke layer: air vitiation as the compartment fire system evolves from well-ventilated to under-ventilated](https://reader036.vdocuments.mx/reader036/viewer/2022071418/6115964cf0478f4bad086bed/html5/thumbnails/51.jpg)
Slide 51
• Pyrolysis modeling: description of fuel mass loss rateFinite-rate chemistry model: explicit treatment of thermal decomposition chemistryThermal degradation across flammable solid described by a local one-dimensional problem in the direction normal to the exposed surface
Laminar Wall Fires
43421&
43421&
flow gasby transportconvectiveongasificatiby
consumedenergy
)(xTcmH
xTk
xtTc s
ggpyrogs
ss
ss ∂∂′′−Δ′′′−
∂∂
∂∂
=∂∂ ωρ
G
44 344 214444 34444 214434421 convectionradiation
44
n)(conductiointerior wallflux toheat
)),0(()),0((),0( ∞∞ −+−+−=∂∂
− TtThTtTGtxTk ss
ss εσε
![Page 52: Modeling of Turbulent Wall Fires - Stanford University · 2012. 7. 19. · ¾Impact of smoke layer: air vitiation as the compartment fire system evolves from well-ventilated to under-ventilated](https://reader036.vdocuments.mx/reader036/viewer/2022071418/6115964cf0478f4bad086bed/html5/thumbnails/52.jpg)
Slide 52
• Pyrolysis modeling: description of fuel mass loss rateFinite-rate chemistry model: explicit treatment of thermal decomposition chemistryThermal degradation across flammable solid described by a local one-dimensional problem in the direction normal to the exposed surface
Laminar Wall Fires
ggg
gs
xm
t
t
ωρ
ωρ
′′′=∂
′′∂+
∂
∂
′′′−=∂∂
&&
& mass conservation(solid phase)
mass conservation(gas phase)
{ccg ηηη
charvolatilessolidvirgin 1kg 1
+→−=4342143421
)/exp(0svsg RTEAx
vs−=′′′ ρω&
G
∫ Δ−′′′=′′
0),()( dxtxtm gf ω&&
![Page 53: Modeling of Turbulent Wall Fires - Stanford University · 2012. 7. 19. · ¾Impact of smoke layer: air vitiation as the compartment fire system evolves from well-ventilated to under-ventilated](https://reader036.vdocuments.mx/reader036/viewer/2022071418/6115964cf0478f4bad086bed/html5/thumbnails/53.jpg)
Slide 53
J/kg 0J/mol 101.256E
1/s 105.250A
0.9
K-J/kg 2520
kg/m 133
kg/m 663
K- W/m126.0
,
5
7
00
30
30
00
=Δ×=
×=
=
==
=
=
==
gvH
cc
kk
cvs
c
vs
cvs
ε
ρ
ρ
Back surface (Δ = 2.5 cm): adiabaticComputational grid: Δx = 200 μm
MLR (kg/s/m2)
time (s)
2kW/m 25=G
MLR
secondMLR peak
initialMLR peak
• Pyrolysis modeling: description of fuel mass loss rateExample: particle board (Novozhilov, Moghtaderi, Fletcher & Kent, Fire Safety J. 27 (1996) 69-84)
Laminar Wall Fires
![Page 54: Modeling of Turbulent Wall Fires - Stanford University · 2012. 7. 19. · ¾Impact of smoke layer: air vitiation as the compartment fire system evolves from well-ventilated to under-ventilated](https://reader036.vdocuments.mx/reader036/viewer/2022071418/6115964cf0478f4bad086bed/html5/thumbnails/54.jpg)
Slide 54
• SummaryWall fires are characterized by a strong coupling between gas and solid phase processes
the gas-to-solid heat transfer drives pyrolysisthe solid-to-gas fuel mass transfer drives combustion
The Emmons solution identifies the B number as the main parameter to compare and rank different materials
Laminar Wall Fires
![Page 55: Modeling of Turbulent Wall Fires - Stanford University · 2012. 7. 19. · ¾Impact of smoke layer: air vitiation as the compartment fire system evolves from well-ventilated to under-ventilated](https://reader036.vdocuments.mx/reader036/viewer/2022071418/6115964cf0478f4bad086bed/html5/thumbnails/55.jpg)
Slide 55
• OutlineOverview of Compartment Fire Dynamics
Multi-physics problemRole of wall fires
Laminar Wall FiresAnalytical solution of a canonical wall flame problem – the Emmons problem (non-spreading; constant wall temperature; no thermal radiation)
Turbulent Wall FiresLarge eddy simulation of a canonical wall fire problem (non-spreading; vertical wall)
Modeling of Turbulent Wall Fires
![Page 56: Modeling of Turbulent Wall Fires - Stanford University · 2012. 7. 19. · ¾Impact of smoke layer: air vitiation as the compartment fire system evolves from well-ventilated to under-ventilated](https://reader036.vdocuments.mx/reader036/viewer/2022071418/6115964cf0478f4bad086bed/html5/thumbnails/56.jpg)
Slide 56
• Experimental database: simplifiedvertical wall flame configuration (J.L. de Ris, FM Global 1999)
Porous burners with gaseous fuel (prescribed fuel mass loss rate); use different fuels (propylene, ethylene, ethane, methane) and different fuel injection ratesQuasi two-dimensional configurationMain diagnostics: total wall heat flux (water cooling system); radiative wall heat flux (radiometers); soot layer thickness (soot deposition on glass rod); temperature profiles (thermocouples)
Turbulent Wall Fires
• Ongoing large eddy simulation study (N. Ren, S. Vilfayeau, Y. Wang, A. Trouvé)
![Page 57: Modeling of Turbulent Wall Fires - Stanford University · 2012. 7. 19. · ¾Impact of smoke layer: air vitiation as the compartment fire system evolves from well-ventilated to under-ventilated](https://reader036.vdocuments.mx/reader036/viewer/2022071418/6115964cf0478f4bad086bed/html5/thumbnails/57.jpg)
Slide 57
• Experimental database (J.L. de Ris, FM Global 1999)
Temperature profiles for different values of MLR
Convective/radiative/total wallheat fluxes at different elevations
totalwq ,′′&
radwq ,′′&
cwq ,′′&
fm ′′& increasing
Turbulent Wall Fires
![Page 58: Modeling of Turbulent Wall Fires - Stanford University · 2012. 7. 19. · ¾Impact of smoke layer: air vitiation as the compartment fire system evolves from well-ventilated to under-ventilated](https://reader036.vdocuments.mx/reader036/viewer/2022071418/6115964cf0478f4bad086bed/html5/thumbnails/58.jpg)
Slide 58
FireFOAM
• Open-source fire model supported by FM Global, USA• Based on OpenFOAM: OpenFOAM is a general-purpose
advanced CFD solver developed by OpenCFD, UK (http://www.opencfd.co.uk)
• Main featuresLibrary of solvers: LES approach for turbulence; compressible flow formulationAdvanced physical models for LES, turbulent combustion, heat transferNumerical methods: finite volume scheme (2nd order in space); implicittime integration (2nd order in time)Advanced meshing capabilities: structured or unstructured (polyhedral) computational grid (built-in mesh generation capability)Software engineering: public domain (http://code.google.com/p/firefoam-dev/); open source (object-oriented C++ environment); Linux OS; massively parallel capability (MPI-based)Post-processing: third-party visualization with ParaView (open source)
![Page 59: Modeling of Turbulent Wall Fires - Stanford University · 2012. 7. 19. · ¾Impact of smoke layer: air vitiation as the compartment fire system evolves from well-ventilated to under-ventilated](https://reader036.vdocuments.mx/reader036/viewer/2022071418/6115964cf0478f4bad086bed/html5/thumbnails/59.jpg)
Slide 59
• LES computational grid design (wall-resolved LES)Two characteristic length scalesBoundary layer thicknessViscous sub-layer thickness
Momentum-driven flow
Buoyancy-driven flow
BLδ
VSLδ
(Hölling & Herwig, J. Fluid Mech., 2005)
BLδ
yVSLδ
Temperature orvertical flow velocity
Turbulent Wall Fires
mm 2.0)/( 2/1 ≈≈
ww
wVSL ρτ
νδ
mm 5.0
)()/(Pr)/(
4/14/1,,
4/3
≈
′′≈
wwpwcw
wVSL gcq βρ
νδ&
![Page 60: Modeling of Turbulent Wall Fires - Stanford University · 2012. 7. 19. · ¾Impact of smoke layer: air vitiation as the compartment fire system evolves from well-ventilated to under-ventilated](https://reader036.vdocuments.mx/reader036/viewer/2022071418/6115964cf0478f4bad086bed/html5/thumbnails/60.jpg)
Slide 60
• Numerical configurationBaseline case(propylene fuel C3H6; )(isothermal wall; Tw = 348 K)Block-structured grid (0.9 million cells)Near-wall resolutionΔy1 = 2 mm
Turbulent Wall Fires
2g/s/m 17=′′fm&
mm 55.2 1 =Δ×=Δ=Δ yxz
![Page 61: Modeling of Turbulent Wall Fires - Stanford University · 2012. 7. 19. · ¾Impact of smoke layer: air vitiation as the compartment fire system evolves from well-ventilated to under-ventilated](https://reader036.vdocuments.mx/reader036/viewer/2022071418/6115964cf0478f4bad086bed/html5/thumbnails/61.jpg)
Slide 61
• Modeling choices (FireFOAM v.1.7.x)
Turbulence: dynamic k-equation eddy viscosity model coupled with WALE modelCombustion: Eddy Dissipation Concept modelSoot: mixture-fraction-based flameletcorrelationRadiation: RTE solver; finite volume model (angular space discretized using 64 solid angles)
Turbulent Wall Fires
![Page 62: Modeling of Turbulent Wall Fires - Stanford University · 2012. 7. 19. · ¾Impact of smoke layer: air vitiation as the compartment fire system evolves from well-ventilated to under-ventilated](https://reader036.vdocuments.mx/reader036/viewer/2022071418/6115964cf0478f4bad086bed/html5/thumbnails/62.jpg)
Slide 62
• Modeling choices (FireFOAM v.1.7.x)
Turbulence: dynamic k-equation eddy viscosity model coupled with WALE model (Nicoud & Ducros 1999)
Turbulent Wall Fires
( )
( ) ( )( ) ( ) 4/52/5
2/32
21 ,
21
31
dij
dijijij
dij
dij
wsgs
i
j
j
iij
i
j
j
iij
mnmnmnmnijkjikkjikdij
SSSS
SSC
xu
xu
xu
xuS
SSSSS
+Δ=
⎟⎟⎠
⎞⎜⎜⎝
⎛
∂
∂−
∂∂
=Ω⎟⎟⎠
⎞⎜⎜⎝
⎛
∂
∂+
∂∂
=
ΩΩ−−ΩΩ+=
ρμ
δ
![Page 63: Modeling of Turbulent Wall Fires - Stanford University · 2012. 7. 19. · ¾Impact of smoke layer: air vitiation as the compartment fire system evolves from well-ventilated to under-ventilated](https://reader036.vdocuments.mx/reader036/viewer/2022071418/6115964cf0478f4bad086bed/html5/thumbnails/63.jpg)
Slide 63
• Modeling choices (FireFOAM v.1.7.x)
Combustion: Eddy Dissipation Concept model (Magnussen & Hjertager1976)
Turbulent Wall Fires
( )ddEDCt
sOFF CC
rYY/ ,/min)/~;~min(
2
ττρω ×=′′′&
)/( and )/( where 22/1thdsgst Dk Δ=Δ= ττ
PrOrF ss )1(2 +→+
![Page 64: Modeling of Turbulent Wall Fires - Stanford University · 2012. 7. 19. · ¾Impact of smoke layer: air vitiation as the compartment fire system evolves from well-ventilated to under-ventilated](https://reader036.vdocuments.mx/reader036/viewer/2022071418/6115964cf0478f4bad086bed/html5/thumbnails/64.jpg)
Slide 64
• Modeling choices (FireFOAM v.1.7.x)
Radiation: RTE solver; finite volume model (angular space discretizedusing 64 solid angles)
Turbulent Wall Fires
{AbsorptionEmission
4 )/( ITdsdI κπσκ −=
43421
),,( zyx
sr
ΩdPlanck mean absorption coefficient [m-1]
where:ap,i is the Planck mean absorption coefficient
for species i [m-1 atm-1] and is obtained fromtabulated dataκsoot is the soot mean absorption coefficient [m-1]
TfC vsootsoot ×=κ
sootCOCOOHOH axaxp κκ ++= )(2222
![Page 65: Modeling of Turbulent Wall Fires - Stanford University · 2012. 7. 19. · ¾Impact of smoke layer: air vitiation as the compartment fire system evolves from well-ventilated to under-ventilated](https://reader036.vdocuments.mx/reader036/viewer/2022071418/6115964cf0478f4bad086bed/html5/thumbnails/65.jpg)
Slide 65
• Modeling choices (FireFOAM v.1.7.x)
Laminar-to-turbulent flow transition:Flame at the base of the wall is laminar Laminar region is over-estimated in the LES simulationsForce transition by using a forcing scheme acting on the fuel flow rate at the base of the wall
Turbulent Wall Fires
Constantflow rate
Perturbedflow rate
![Page 66: Modeling of Turbulent Wall Fires - Stanford University · 2012. 7. 19. · ¾Impact of smoke layer: air vitiation as the compartment fire system evolves from well-ventilated to under-ventilated](https://reader036.vdocuments.mx/reader036/viewer/2022071418/6115964cf0478f4bad086bed/html5/thumbnails/66.jpg)
Slide 66
Turbulent Wall Fires
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Slide 67
• ResultsWall heat flux versus elevation z
Turbulent Wall Fires
totalwq ,′′&
radwq ,′′&
cwq ,′′&
Experimental data
FMG Model
FMG Model
Solid lines: LES laminar turbulent
![Page 68: Modeling of Turbulent Wall Fires - Stanford University · 2012. 7. 19. · ¾Impact of smoke layer: air vitiation as the compartment fire system evolves from well-ventilated to under-ventilated](https://reader036.vdocuments.mx/reader036/viewer/2022071418/6115964cf0478f4bad086bed/html5/thumbnails/68.jpg)
Slide 68
• ResultsWall-normal profile of mean temperature
Turbulent Wall Fires
Comparison between raw (uncorrected) thermocouple measurements and LES “thermocouple data”LES thermocouple (TC) data are obtained from a virtual instrumentmodel:
( ) ( )TCgasTCTC
TC
TC
TCTCTC
TThTG
dtdT
AVC
−+−
=
4 σε
ρ
Experimental data
LES
cm 77=z
![Page 69: Modeling of Turbulent Wall Fires - Stanford University · 2012. 7. 19. · ¾Impact of smoke layer: air vitiation as the compartment fire system evolves from well-ventilated to under-ventilated](https://reader036.vdocuments.mx/reader036/viewer/2022071418/6115964cf0478f4bad086bed/html5/thumbnails/69.jpg)
Slide 69
• ResultsEvaluation of self-similarity in wall-normal profiles of mean temperature
Turbulent Wall Fires
Experimental data LES
![Page 70: Modeling of Turbulent Wall Fires - Stanford University · 2012. 7. 19. · ¾Impact of smoke layer: air vitiation as the compartment fire system evolves from well-ventilated to under-ventilated](https://reader036.vdocuments.mx/reader036/viewer/2022071418/6115964cf0478f4bad086bed/html5/thumbnails/70.jpg)
Slide 70
• ResultsEvaluation of self-similarity in wall-normal profiles of mean z-velocity
Turbulent Wall Fires
gzw 2/~ ><
δ/z
LES
![Page 71: Modeling of Turbulent Wall Fires - Stanford University · 2012. 7. 19. · ¾Impact of smoke layer: air vitiation as the compartment fire system evolves from well-ventilated to under-ventilated](https://reader036.vdocuments.mx/reader036/viewer/2022071418/6115964cf0478f4bad086bed/html5/thumbnails/71.jpg)
Slide 71
• Results: grid convergence studyWall heat flux versus elevation z
FireFOAM Results
cwq ,′′&
mm 41 =Δymm 31 =Δymm 21 =Δy
radwq ,′′&
FMG ModelFMG Model
![Page 72: Modeling of Turbulent Wall Fires - Stanford University · 2012. 7. 19. · ¾Impact of smoke layer: air vitiation as the compartment fire system evolves from well-ventilated to under-ventilated](https://reader036.vdocuments.mx/reader036/viewer/2022071418/6115964cf0478f4bad086bed/html5/thumbnails/72.jpg)
Slide 72
• Results: grid convergence studyWall-normal profile of mean temperature and z-velocity
FireFOAM Results
><T~ >< w~
mm 41 =Δymm 31 =Δymm 21 =Δy
Expt data
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Slide 73
• SummaryFirst step in a model development/validation strategy: wall-resolved LES of a simplified configuration (non-spreading vertical wall flame; prescribed fuel flow rate)
Features: low (transition) Reynolds number conditions; laminar base region and a weakly turbulent downstream regionResults are encouraging. But: the size of the laminar base region is overestimated in the simulations; and the LES combustion and radiation models lack accuracy under laminar-like conditions
The experimental database is limited to first-order statistical moments and there is a need to extend the scope and quality of experimental data (velocity measurements, second-order moments, etc)
Conclusion