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.