Fire Storms and Large Scale Modelling
Derek BradleyUniversity of Leeds
UKELG 50TH ANNIVERSARY DISCUSSION MEETING
“Explosion Safety – Assessment and Challenges”
9th to 11th July 2013Cardiff University
Fire Storms ?
•
The Buoyant Plume
Conditions for a Fire Storm
• High column of burned gas
• Large spillage and favourable topology
• Turbulence generation at base
• Rich aerosol mixture topped by lighter fractions
• Large turbulent length scales
• (Turbulence, buoyancy and aerosols give positive feed-back)
Atmospheric Turbulenceu m/s u′ m/s l m
zo = .05 m zo = 1 m zo = .05 m zo = 1 m
3 (light breeze)
0.57 1.30 59.8 26.1
15 (near gale)
2.83 6.51 59.8 26.1
31 (violent storm)
5.85 13.46 59.8 26.1
Turbulent Explosion
Turbulent Burning Correlation
U = ut /u' K =0.25(u'/uℓ)2Rl-0.5
Cellular Laminar Explosion
Laminar Instability Inner and Outer Cut-offs
Flame area ratio
= (ns/nl)D-2
Fractal Dimension,D = 7/3
Spillage Magnitudes
Spillage at Explosion
(tonnes)
Spillage Area (m2)
Mean height at lean flammability limit (m)
Donnellson
(1978)
300 304,000 24
Ufa
(1989)
4,500 2,500,000 140
Atmospheric Turbulenceu m/s u′ m/s l m
zo = .05 m zo = 1 m zo = .05 m zo = 1 m
3 (light breeze)
0.57 1.30 59.8
K=0.0004
26.1
K=0.0019
15 (near gale)
2.83 6.51 59.8
K=0.0041
26.1
K=0.022
31 (violent storm)
5.85 13.46 59.8
K=0.012
26.1
K=0.064
Turbulent Burning Correlation
U = ut/u' K =0.25(u'/uℓ)2Rl-0.5
0.01 0.1 10
2
4
6
8 Masr
-23 -19 3
Flame stretchdominant regime
Flame Instabilitiesdominant regime
U
K
Regime of Peak Turbulence-Instability Interaction
Influence of ls/lG on U
0
1
2
3
4
5
6
7
0 0.02 0.04 0.06 0.08
K
U
0
10
20
30
40
50
60
ls /lG
U
l s /lG 2128 Kll ss G
Masr = -23 Masr = 3
Estimated Donnellson Burning Velocity
Ufa
X
Ufa Topography
Ufa Ignition Source
The Buoyant Plume
Ufa Topography
Ufa and Donnellson Burning Velocities Compared
23
Congestion:Flame and Shock Wave in a Duct
aA
Flame Shock wave
The Maximum Turbulent Burning Velocity
Maximum Turbulent Burning Velocity
Influence of Venting Ratio, A/a
0
5
10
15
20
25
0 0.5 1 1.5 2
u t /a 1
P2/
P1
1
2
3
4
5
6
T2/T
1
A/a = 3
A/a = 1.44
g = 1.4
0
10
20
30
40
50
0 5 10 15 20 25
x
B
DEVELOPING DETONATION
P
e
x u
x l
N2
K2
S E
65.2
33.7
48.4
0
10
20
30
40
50
0 5 10 15 20 25
x
B
DEVELOPING DETONATION
P
e
x u
x l
N2
K2
S E
65.2
33.7
48.4
Strong, Stable, Detonations require Low (ξε), or (τi /τe)
Problems of Large Scale Modelling
• Uncertain discharge composition, mixing, and circumstances of ignition.
• Uncertain physico-chemical data (Ma, extinction stretch rates, burning velocities, (τi /τe).
• Complexity of congestions,venting, shock wave reflection and refraction.
• Uncertainties in rate of change of heat release rate.
References
• G.M. Makhviladze, S.E. Yakush, (2002) “Large Scale Unconfined Fires and Explosions,” Proceedings of the Combustion Institute 29: 195-210.
•
• D. Bradley, M. Lawes, K. Liu, M.S. Mansour, (2013) “Measurements and Correlations of Turbulent Burning Velocities over Wide Ranges of Fuels and Elevated Pressures,” Proceedings of the Combustion Institute 34: 1519-1526.
• D. Bradley, M. Lawes, Kexin Liu, (2008) “Turbulent flame speeds in ducts and the deflagration/detonation transition,” Combust. Flame 154 96-108.
• D. Bradley, (2012) “Autoignitions and detonations in engines and ducts,” Philosophical Transactions of the Royal Society a-Mathematical Physical and Engineering Sciences, 370, no. 1960: 689–714.
Top Related