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2016 | OriginalPaper | Buchkapitel

13. Fire Plumes, Flame Height, and Air Entrainment

verfasst von : Gunnar Heskestad

Erschienen in: SFPE Handbook of Fire Protection Engineering

Verlag: Springer New York

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Abstract

Practically all fires go through an important, initial stage in which a coherent, buoyant gas stream rises above a localized volume undergoing combustion into surrounding space of essentially uncontaminated air. This stage begins at ignition, continues through a possible smoldering interval, into a flaming interval, and may be said to end prior to flashover. The buoyant gas stream is generally turbulent, except when the fire source is very small. The buoyant flow, including any flames, is referred to as a fire plume.

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Vorheriges Kapitel Fundamentals of Premixed Flames

Nächstes Kapitel Ceiling Jet Flows

Defined in Equation 13.6 (m⋅kW^–2/5)

Buoyancy flux defined in Equation 13.15 (m⁴⋅s⁻³)

Plume radius (m)

b ΔT

Plume radius to point where ΔT/ΔT ₀ = 0.5 (m)

b u

Plume radius to point where u/u ₀ = 0.5 (m)

b um

b _u at level of maximum gas velocity near flame tip (m)

Adjustable constant, Equation 13.35

c p

Specific heat of air at constant pressure (kJ/kg⋅K)

Diameter (m)

Function (c _p, T _∞, ρ_∞, g); see Equation 13.31 (m⋅kW^–2/5)

Frequency (s⁻¹)

Acceleration due to gravity (m/s²)

H c

Actual lower heat of combustion (kJ/kg)

ΔH O

Tewarson’s [44] lower heat of combustion per unit mass of oxygen consumed (kJ/kg)

Intermittency

Ratio of specific heats, constant-pressure versus constant-volume

Mean flame height above base of fire (m)

L B

Buoyancy controlled flame height (m)

L I

Intermittency length scale

L M

Momentum controlled flame height (m)

ṁ ent

Entrained mass flow rate in plume (kg/s)

ṁ ent,L

ṁ _ent at the mean flame height, L(kg/s)

ṁ f

Mass burning rate (kg/s)

Nondimensional parameter defined in Equation 13.4

p s

Pressure in source gas discharge stream (Pa)

p s0

Pressure in source gas reservoir (Pa)

\( \dot{Q} \)

ṁ _f H _ctotal heat release rate (kW)

\( {\dot{Q}}_c \)

Convective heat release rate (kW)

\( {\dot{Q}}^{*} \)

Radiative heat release rate (kW)

\( {\dot{Q}}^{*} \)

Nondimensional parameter defined in 13.1

Radius (m)

Actual mass stoichiometric ratio, air to fuel volatiles

R M

Momentum parameter defined in Equation 13.8

Mean temperature (K)

T 0

Mean centerline temperature in plume (K)

T ∞

Ambient temperature (K)

T ′

rms temperature fluctuation (K)

T a (z)

Ambient temperature at level z (K)

T a1

Ambient temperature at source level (K)

T L

T ₀ at mean flame height (K)

ΔT

T − T _∞, mean temperature rise above ambient (K)

ΔT 0

Value of ΔT on plume centerline (K)

ΔT L

T _L − T _∞(K)

Time (s)

t g

Growth time; see Equation 13.49 (s)

t R

Rise time of plume front (s)

t R *

Nondimensional rise time of plume front, see 13.62

Mean axial velocity (m/s)

u 0

Mean axial velocity on centerline (m/s)

u 0m

Maximum value of u ₀, near flame tip (m/s)

u′

rms velocity fluctuation in axial direction (m/s)

W f

Fire perimeter (m)

Height above base of fire (m)

z 0

Height of virtual origin above base of fire (m)

z m

Maximum vertical penetration of plume fluid in stratified ambient (m)

Entrainment coefficient

Nondimensional parameter defined in Equation 13.26

v m

Kinematic viscosity of flame gases at maximum flame temperature (m² ⋅ s⁻¹)

Mean density (kg/m³)

ρa1

Ambient density at source level (kg/m³)

ρ fe

Mean density in flames (kg/m³)

ρ s

Density of source gas discharge stream (kg/m³)

ρs0

Density of source gas in reservoir (kg/m³)

ρs∞

Density of source gas at ambient temperature and pressure (kg/m³)

ρ∞

Ambient density (kg/m³)

Δρ

ρ_∞ − ρ, mean density deficiency (kg/m³)

σΔT

Plume radius to point where ΔT/ΔT ₀ = e⁻¹ (m)

σ u

Plume radius to point where u/u ₀ = e⁻¹ (m)

As a further aid in assessing variations in A, Tewarson [44], in his Table 3–4.12, lists values of ΔH _O for complete combustion of many fuels, the lower heat of combustion per unit mass of oxygen consumed. From these values, H _c /r (kJ/kg) can be easily calculated, the lower heat of combustion per unit mass of air (of standard composition) consumed and, hence, the coefficient A.

For normal atmospheric conditions (T _∞ = 293 K, g = 9.81 m/s², c _p = 1.00 kJ/kg K, ρ_∞ = 1.2 kg/m³), the factor \( 9.1{\left[{T}_{\infty }/\left(\Big(,g{c}_p^2\ {p}_{\infty}^2\right)\right]}^{1/3} \) has the numerical value 25.0 K m^5/3 kW^–2/3, and the factor 3.4[g/(c _pρ_∞ T _∞)]^1/3 has the numerical value 1.03 m^4/3 s⁻¹ kW^–1/3.

A ratio L/D = 0.02 can be calculated from Equation 13.7 assuming H _c/r = 3470 kJ/kg, an average for silicone oils from values reported by Tewarson [63] and assuming a convective heat fraction \( {\dot{Q}}_c/\dot{Q}=0.7 \). If a value of H _c/r near the bottom of the reported range [63] is selected, 3230 kJ/kg, the observed value L/D = 0.14 is reproduced; slight changes in the assumed convective fraction will also reproduce the measured value.

Without specific knowledge, \( {\dot{Q}}_c/\dot{Q} \) may usually be assumed at 0.7. However, methyl alcohol produces a fire of low luminosity and radiation, for which \( {\dot{Q}}_c/\dot{Q}=0.8 \) is a good estimate.

In addition to convective heating, which depends on gas temperature and velocity, radiative heating would also be important in such cases and might even dominate over convective heating if the structure is immersed in flames.

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Titel: Fire Plumes, Flame Height, and Air Entrainment
verfasst von: Gunnar Heskestad
Verlag: Springer New York
Buch: SFPE Handbook of Fire Protection Engineering
Print ISBN: 978-1-4939-2564-3

Electronic ISBN: 978-1-4939-2565-0

Copyright-Jahr: 2016
DOI: https://doi.org/10.1007/978-1-4939-2565-0_13

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