Fire plumes and jets

J. G. QuintiereDepartment of Fire Protection Engineering

University of Marylandjimq@umd.edu

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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 Moencmoen@sandia.gov

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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