1. Fire Storms and Large Scale Modelling Derek Bradley University of Leeds UKELG 50TH ANNIVERSARY DISCUSSION MEETING “Explosion Safety – Assessment and Challenges” 9th to 11th July 2013 Cardiff University

2. Fire Storms ?

4. The Buoyant Plume

5. 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)

6. Atmospheric Turbulence u m/su′ m/sl m z o =.05 mz o = 1 mz o =.05 mz o = 1 m 3 (light breeze) 0.571.3059.826.1 15 (near gale) 2.836.5159.826.1 31 (violent storm) 5.8513.4659.826.1

7. Turbulent Explosion

8. Turbulent Burning Correlation U = u t /u' K =0.25(u'/u ℓ ) 2 R l -0.5

9. Cellular Laminar Explosion

10. Laminar Instability Inner and Outer Cut-offs = (n s /nl) D-2 Flame area ratio = (n s /n l ) D-2 Fractal Dimension, D = 7/3

11. Spillage Magnitudes Spillage at Explosion (tonnes) Spillage Area (m 2 ) Mean height at lean flammability limit (m) Donnellson (1978) 300304,00024 Ufa (1989) 4,5002,500,000140

12. Atmospheric Turbulence u m/su′ m/sl m z o =.05 mz o = 1 mz o =.05 mz o = 1 m 3 (light breeze) 0.571.3059.8 K=0.0004 26.1 K=0.0019 15 (near gale) 2.836.5159.8 K=0.0041 26.1 K=0.022 31 (violent storm) 5.8513.4659.8 K=0.012 26.1 K=0.064

13. Turbulent Burning Correlation U = u t /u' K =0.25(u'/u ℓ ) 2 R l -0.5

14. Regime of Peak Turbulence- Instability Interaction

15. Influence of l s /l G on U Masr = -23Masr = 3

16. Estimated Donnellson Burning Velocity

17. Ufa X

18. Ufa Topography

19. Ufa Ignition Source

20. The Buoyant Plume

21. Ufa Topography

22. Ufa and Donnellson Burning Velocities Compared

23. 23 Congestion:Flame and Shock Wave in a Duct a A Flame Shock wave

24. The Maximum Turbulent Burning Velocity

25. Maximum Turbulent Burning Velocity

26. Influence of Venting Ratio, A/a

27. Strong, Stable, Detonations require Low (ξε), or (τ i /τ e )

28. Problems of Large Scale Modelling Uncertain discharge composition, mixing, and circumstances of ignition. Uncertain physico-chemical data (Ma, extinction stretch rates, burning velocities, (τ i /τ e ). Complexity of congestions,venting, shock wave reflection and refraction. Uncertainties in rate of change of heat release rate.

29. 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.