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Fire plumes and jets
J. G. QuintiereDepartment of Fire Protection Engineering
University of [email protected]
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With permission from John Wiley & sons, Ltd.
And from M. G. Zabetakis, “Flammability characteristics of combustible gases and vapors”,
Bul. 627, Bur. Of Mines, 1965.
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Scope• Integral theory• Phenomena
– Evaporation & burning– Buoyant plumes and jets– Flame extent– Transients
• H2 characteristics From Chris [email protected]
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H2 Scenarios
• Spill of liquid, release of vapor– Evaporation rate– Buoyant plume– Flammability issue
• Burning of liquid or vapor
– Fireball– Flame height
– Jet– Temperature
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Evaporation of Liquid H2
Mass and Energy for Liquid
mc dTdt
= 0 = Ý q − Ý m h fg
Convection onlyÝ q = Ahc (Ta − T)Claussius Eq.dpH 2
dT=
h fg M H 2 pH 2
RT 2
Dalton's Law pH 2 = paYH 2Ma / M H 2
Mass Transfer
Ý m = A hc (YH 2 − 0)c p
Heat from all surroundings
Liquid boiling
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Evaporation Rates10
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2
RegressionRate
In/min Liquid H2 on paraffin
Time, s
From Zabetakis
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Fire Plume Topics�• Buoyancy• Entrainment• Wind blown• Jet flames
• Turbulent flow• Flame Height• Temperature• Fireballs
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Buoyant Flow• Temperature rise gives a decrease in density• For H2, evaporation gives low density• Potential energy converted in to kinetic energy
Unit volume at plume gas at density ρ and temperature T
Unit volume of air at density ρaand temperature Ta
Z
V
D
Buoyant plume
ρT = ρaTa , ρminρa
≈ 0.30
ρH 2ρa
≈ 0.07
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ρv 2 = ρa − ρ( )gz = ρa 1−Ta
T⎛ ⎝ ⎜
⎞ ⎠ ⎟ gz, ⇒
v 2
T − Ta
Ta
⎛
⎝ ⎜
⎞
⎠ ⎟ gz
= 2 ≈1.6, experimentsBernoulli:
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Turbulent Entrainment
• Engulfment of air into the fire plume
• Eddies: fluctuating and rotating balls of fluid, large scale rolling-up fluid motion on the edge of the plume.
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Shedding Frequency of Eddies)• f is the frequency in hertz or cycles/sec• D is the diameter of the pool fire in m
Df 5.1
=
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Turbulent Fire Plume• Very low initial fuel velocity• Entrainment and Flame Height controlled by Buoyancy
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Theory of Non-Combusting Plume -- Point source
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Governing Equationsentrainment
mass
momentum
energy
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Combusting PlumeAll the oxygen is burned, but mixing is inefficient. Requires about 10 x stoichiometric.
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Fire Plume Centerline Temperature
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Large Fire Flame Temperatures
ºC
(m)
D (m)• Increases as Xr
(Radiation Fraction) decreases.
• Increases as Dincreases.
• Is not significant function of fuel.
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Mean Turbulent Temperature
Xr
H2
CT,f = 0.50
Tf − T∞ ≈1450 ºC for Xr = 0
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Flame Height Mechanism
• Flame ends where all O2 is burned
• About 10 x stoichiometric air is needed
• Flame height fluctuates
zf [m]
D [m]
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Flame Height Formula
zf [m]
D [m]
From Heskestad. SFPE Handbook:
zf = 0.23Q2/5-1.02D
where Q is in kW.
.
.
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Formula and Data
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Jet Flames at Q* ~ 106
Q* ≡Ý Q
ρacpTa gD5 / 2
FirepowerFlow Energy
z f
D≈18.5 ρF
ρa
⎛
⎝ ⎜
⎞
⎠ ⎟
1/ 2
r,
r is the stoichometric air/fuel
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Turbulent Jet Diffusion Flame• Entrainment controlled by high initial fuel velocity • For a given inlet diameter, the flame height is
constant for a fully turbulent jet flame.
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Flame Height and Diameter for two fuels
0
1
2
3
4
5
0.01 0.1 1 10 100
SP4 Flame Geometry
Heptane GrovePMMA GroveHeptane HeskestadPMMA Heskestad
Z f / D
D (m)
Heptane
4160 kW/m2
PMMA
484 kW/m2
H2 = 2400 kW/m2
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Wind-blown Flames
θ
cos θ( )=vwind
g Ý ′ ′ m fuelD /ρa( )1/ 3
⎡
⎣
⎢ ⎢
⎤
⎦
⎥ ⎥
−0.49
Thomas
From Beyler, SFPE
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Starting Plume
From Tanaka
Rise of H2 Plume
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Spillage of 3 liters of liquid hydrogen
On Macadam surfaceIn quiescent air at 15ºC
HEIGHTFT
10
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Fireball
D
H
Flame burns to D and H based on initial fuel
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Fireball Correlations
From Fay and Lewis,For Propane
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Summary
• Buoyancy and entrainment• Turbulent flame temperatures• Flame height• Fireball• H2 distinctions