fire storms and large scale modelling derek bradley university of leeds ukelg 50th anniversary...

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.