Dissertation defense given at UC San Diego on May 21, 2012.

1. Studies on Upward Flame Spread
PhD Defense of
Michael J. Gollner
University of California, San Diego
Professor Forman A. Williams, Chair
July 24, 2012 1
May 21, 2012 PhD Defense: Studies on Upward Flame Spread 1

2. Motivation
Flame Spread Theory
1. Corrugated Cardboard Flame Spread
2. Inclined Flame Spread
3. Discrete Fuel Flame Spread
Conclusions
July 24, 2012
Acknowledgements 2
May 21, 2012 PhD Defense: Studies on Upward Flame Spread 2

3. Why Study Fire?
NFPA, 2009
July 24, 2012 3
$362 billion, or 2.5 % of the US GDP
May 21, 2012 PhD Defense: Studies on Upward Flame Spread 3

4. Motivation
Industrial Fires The Built Environment
July 24, 2012 4
Wildfires Cable Trays
May 21, 2012 PhD Defense: Studies on Upward Flame Spread 4

5. Review:
UPWARD FLAME SPREAD
THEORY
July 24, 2012 5
May 21, 2012 PhD Defense: Studies on Upward Flame Spread 5

6. Upward Flame Spread
Thermal Boundary Layer
g
Excess
SOLID FUEL
1. Thermal Boundary Layer Pyrolyzate
2. Heat Flux to the Fuel yf xf Flame Height
3. Buoyancy

q f ( x, t )
Vp
y  xp Pyrolysis Height
July 24, 2012 qp
6
x 
m f H c ~ HRR
Diffusion Flame
May 21, 2012 PhD Defense: Studies on Upward Flame Spread 6

7. Flame Spread Models

q Constant

q Constant
July 24, 2012 One of few models with q(x) [1]
7
1. Sibulkin and Kim, Comb. Sci. Tech. vol. 17, 1977
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8. Results of Upward Spread Theories
2
 Annamalai & Sibulkin: x f ~ A1 ( B1 t ) (Laminar)
t
 Saito, Quintiere, Williams: x f ~ A2e (Turbulent)
 Sibulkin & Kim: x f ~ A3t 2 (Laminar)
x f ~ B3e t (Turbulent)
Where A, B, and α are constants
NOTE: All results for non-charring fuels.
July 24, 2012 8
1. Annamalai, K. and Sibulkin, M., Combust. Sci. Tech., 1979, vol. 19, pp. 167-183.
2. Saito, J.G. Quintiere, and F.A. Williams, Fire Safety Science, vol.1, 1985, pp. 75-86.
3. Sibulkin and Kim, Comb. Sci. Tech. vol. 17, 1977
May 21, 2012 PhD Defense: Studies on Upward Flame Spread 8

9. Industrial Fires
Part I:
UPWARD FLAME SPREAD OVER
CORRUGATED CARDBOARD
July 24, 2012 9
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10. Cardboard Spread Experiments
• Uniform ignition at
base by Heptane wick
• Insulated board above
sample
• Sample filled with
plastics, but this study only addresses the
behavior before these plastics ignite
July 24, 2012 10
Gollner, M.J., Overholt, K., et al., Fire Saf. J., 46(6), 2011, pp. 305-316.
Overholt, K., Gollner, M.J, et al., Fire Saf. J., 46(6), 2011, pp 317-329.
Gollner, M.J., Williams, F.A., and Rangwala, A.S. Combust. Flame, 158(7), 2011.
May 15, 2012
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11. Flame Height Observations
x f ~ t 3/2 fits x f ,max
50
Observed Trend
40
Why does the pyrolysis front and flame height x f ,avg
Height (cm)
30
grow SLOWER than what current theories
would predict? x p ,avg
20
10
0
0
July 24, 2012 10 20 30 40 50
11
Time from Ignition (s)
Gollner, M.J., Williams, F.A., and Rangwala, A.S. Combust. Flame, 158(7), 2011.
May 15, 2012
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12. July 24, 2012 12

13. July 24, 2012 13

14. July 24, 2012 14

15. July 24, 2012 15

16. July 24, 2012 16

17. July 24, 2012 17

18. July 24, 2012 18

19. July 24, 2012 19

20. 1/3
y~x
July 24, 2012 20

21. Boundary-Layer Extension
Traditional Boundary Hypothesized Modified
Layer Boundary layer
y~x 1/4 y ~ x1/3

q ~ 1/ x1/4 
q ~ 1/ x1/3
x
y
Curled
July 24, 2012 21
Cardboard
May 15, 2012 Buoyancy Effects on Burning Behavior and Flame Spread 21

22. How Would this Affect xp & xf?
Temperature of a thick fuel with time-dependent heat flux [1,2]:
t
1 
q
T T0 dt
k c 0 t t
Assuming material pyrolyses at fixed Tp, substitute τ=t/t’, integral becomes a
constant dependent on material properties:
1

q t
I d
0 1
Assuming a new q(x) power-law variation based on boundary layer extension:

q C / x1/3
The time, t of arrival of pyrolysis front will obey:
xp At 3/2
Assuming  
x f ~ m ~ x p , where m is the burning rate per unit width:
xf Bt 3/2
July 24, 2012 recover what was observed in experiments!
You 22
1. H.E. Mitler, Proc. Combust. Inst., 23 (1991), pp. 1715–1721
2. Conduction of heat in solids, Carslaw, H. S.; Jaeger, J. C. Oxford: Clarendon Press, 1959, 2nd ed.
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23. Corrugated Cardboard Applications
Early-stage ignition and spread
Rack storage test, UL Laboratories
HVLS Fan, NFPA FPRF Study
Photo Taken while at Schirmer Eng.
July 24, 2012 23
Tupperware Warehouse Fire (NFPA)
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24. The Built Environment Wildfires
Part II:
INCLINED FLAME SPREAD
July 24, 2012 24
May 21, 2012 PhD Defense: Studies on Upward Flame Spread 24

25. Burning & Spread over a Solid Fuel
g
y
July 24, 2012 25
x
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26. Burning & Spread over a Solid Fuel
• Modify Heat Flux Profiles
g 
• Will Modify V p and m f

q ( x, t , )

q f ( x, t ) f ~ xn
yf

qp
Vp

mf 
HcQ xf
y'
July 24, 2012 26
x' xp
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27. Experimental setup
July 24, 2012 27
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28. Effects of orientation
July 24, 2012 28
*Video is shown at 5 times actual speed
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29. 0.0
Spread Velocity
Spread Rate (cm/s)
0.0
0.0
0.09
0.0
0.08
Underside measurements
(-60 to 0 ) have not been 0.0
0.07 reported before
0.0
Spread Rate, Vp (cm/s)
0.06
0.05
The peak velocity appears
0.04
between 0 and -30
0.03
Vp (This study, w=10cm)
0.02 Pizzo (model)
Pizzo (exp, w=20cm)
0.01 Drydale and Macmillian (w=6cm)
Xie and DesJardin (model)
0
-60 -45 -30 0 30 45 60
Angle of Inclination,
July 24, 2012 29
1. Y. Pizzo, J.L. Consalvi, B. Porterie, Comb. Flame. 156 (2009) 1856-1859.
2. D. Drysdale, A. Macmillan. Fire Safety J. 18, no. 3 (1992): 245-254.
3. W. Xie, P. Desjardin, Comb. Flame. 156 (2009) 522-530.
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30. Mass-loss Rate per unit Area
Steady rates from larger gas
burner is qualitatively similar
Steady rates from smaller
PMMA samples are parabolic
Steady rates averaged 800-1000
seconds after uniform ignition
Spreading rates measured when
xp reaches top of sample
July 24, 2012 30
1. H. Ohtani, K. Ohta, Y. Uehara, Fire Mat. 18 (1991) 323-193.
2. de Ris, J, L. Orloff. Proc. Comb. Inst. 15 (1975) 175-182.
Burning of Inclined FuelStudies on Upward Flame Spread
May 21, 2012
July 24, 2012 PhD Defense: Surfaces WSS/CI Spring Meeting ASU 30

31. Radiant-Flux Estimates
July 24, 2012 31
Slide name - conference -
July 24, 2012 31
May 24, 2012
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location
Burning of Inclined Fuel Surfaces WSS/CI Spring Meeting ASU 31
31

32. Radiant-Flux Estimates
Total Heat Flux (estimated from
mass-loss rates)
Maximum heat flux in
combusting plume
Estimated radiant contribution
(from heat flux gauges)
qJuly 24,2012 m H p
 p q rr  32

q rr Tp 4 6.1 kW/m2
Burning of Inclined FuelStudies on Upward Flame Spread
May 21, 2012
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33. Flame Standoff Distance
July 24, 2012 33
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33

34. Flame-Standoff Distance
July 24, 2012 34
Burning of Inclined FuelStudies on Upward Flame Spread
May 21, 2012
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35. Flame Shape
July 24, 2012 35
Burning of Inclined FuelStudies on Upward Flame Spread
May 21, 2012
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36. Width Effects
July 24, 2012 36
Burning of Inclined FuelStudies on Upward Flame Spread
May 21, 2012
July 24, 2012 PhD Defense: Surfaces WSS/CI Spring Meeting ASU 36

37. Heat-Flux Profiles
15
10
5
 
-60o
  
2
-45o

q 1 -30o

0o
0.5
30o
0.25 45o
60o
1.2 1.4 1.6 1.8 2 2.2
 
 
x / xp
July 24, 2012 37
n
Power-law fit: 
q f ( x) A( x / x p )
Burning of Inclined FuelStudies on Upward Flame Spread
May 21, 2012
July 24, 2012 PhD Defense: Surfaces WSS/CI Spring Meeting ASU 37

38. Inclined Flame Spread & Burning
Flame Spread Steady Burning
0.09 10
          
0.08 9
  
Gas Burner, 65 cm [5]
     2  
0.07
8
Spread Rate, Vp Vp (cm/s)
0.06
Mass-loss Rate (g/m s)
Spread Rate, (cm/s)
7
0.05
0.09
6
0.04
0.08 PMMA, Steady Burning
5

0.03
0.07
Vp (This study, w=10cm)
4

0.02 Pizzo (model)
0.06
PMMA, Spreading
Spread Rate (cm/s)
Pizzo (exp, w=20cm)
0.01 Drydale and Macmillian (w=6cm) 3
0.05
Xie and DesJardin (model)
0
0.04
2
-60 -45 -30 0 30 45 60 -60 -45 -30 0 30 45 60
Angle of Inclination, θ
Angle of Inclination,   of  
Angle Inclination, θ
    
  
0.03
Vp (This Study, w=10cm)
0.02
Pizzo (Model)
Pizzo (Exp, w=20cm)
0.01
Drydale and Macmillian (w=6cm)
Xie and DesJardin (Model)
July -80 2012-40
0 24, -60 -20 0 20 40 60 80 38
Angle of Inclination,
1. Y. Pizzo, J.L. Consalvi, B. Porterie, Comb. Flame. 156 (2009) 1856-1859. 4. H. Ohtani, K. Ohta, Y. Uehara, Fire Mat. 18 (1991) 323-193.
2. D. Drysdale, A. Macmillan. Fire Safety J. 18, no. 3 (1992): 245-254. 5. de Ris, J, L. Orloff. Proc. Comb. Inst. 15 (1975) 175-182.
3. W. Xie, P. Desjardin, Comb. Flame. 156 (2009) 522-530.
May 15, 2012
21, 2012 BuoyancyDefense: Studies onBehavior Flame Spread
PhD Effects on Burning Upward and Flame Spread 38

39. Inclined Flame Spread Applications
Large, inclined atria ceiling
ASTM E108 (Roof Fire Test, Top)
Future KEPKO Headquarters
(Korea)
July 24, 2012 39
Flame spread on slopes ASTM E108 (Roof Fire Test, Bottom)
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21, 2012 BuoyancyDefense: Studies onBehavior Flame Spread
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40. Cable Trays Industrial Fires Wildfires
Part III:
DISCRETE FUEL FLAME SPREAD
July 24, 2012 40
May 15, 2012
May 15, 2012
21, 2012 BuoyancyDefense: Studies onBehavior Flame Flame Spread
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40

41. Discrete Fuel Spread & Burning
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May 15, 2012
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41

42. Matchstick Spread & Burning
Pyrolysis Spread Burnout Time
xp ~ t1.6 to t1.7
x p ~ t 3/2
S
xp ~ t
xp tb
(cm)
S 0
t (s) x (cm)
u ~ gx ~ Re ~ Nu
July 24, 2012 42
Gollner, M.J., Xie, Y., Lee, M., Nakamura, Y., and Rangwala,
A.S., 2012, In Press, Comb. Sci. Tech.
May 15, 2012
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42

43. Calculating Ignition Time for Spread
• Flame spread is a sequence of ignitions
• Matchsticks assumed to be thermally thin1, so
the pyrolysis or ignition time can be reduced
to tp s c p , s d (Tp

T )/q
• Simple heat transfer correlations can be used

to determine q for two limiting cases:
S 0 S 0
July 24, 2012 43
1Matchstick thickness 
less than thermal thickness, lth ~ ks (Tig T ) / q
May 15, 2012
May 15, 2012
21, 2012 BuoyancyDefense: Studies onBehavior Flame Flame Spread
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43

44. Heat Transfer, S = 0
S 0
• Primarily convection-driven heat transfer from
burning matchsticks below to wall above2
• Correlation for flow over a wall can be used1
Nu x 059(Grx Pr)1/4
• Where Gr ( g (T T ) x ) / is the Grashof number,
x s
3 3
Pr / t is the Prandtl number and Nu d hd / k is
g
the Nusselt number
July 24, 2012 44
1.F. P. Incropera and D. P. DeWitt. Introduction to Heat Transfer, Fifth Edition. John Wiley & Sons, New York, 2002.
2. G. F. Carrier, F. E. Fendell, and M. F. Wolf., Combust. Sci. Technol., 75(1-3):3151, 1991.
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44

45. Heat Transfer, S > 0
S 0
• Primarily convection-driven heat transfer from
burning matchstick below to stick above
• Correlation for flow over a cylinder can be used [1]
Nu d 0.344Re0.56
d
• Assuming the buoyant velocity follows ug gx , the
Reynolds number, Re u d/ can be calculated d g g g
• The average rate of heat transfer, q can be calculated

from the Nusselt number for each matchstick
July 24, 2012 45

q h (Ts T )
1. F. A. Albini and E. D. Reinhardt. Int. J. Wildland Fire, 5(2):8191, 1995.
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21, 2012 BuoyancyDefense: Studies onBehavior Flame Flame Spread
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45

46. Matchstick Spread & Burning
Pyrolysis Spread Burnout Time
xp ~ t1.6 to t1.7
x p ~ t 3/2
S 0
xp ~ t
xp tb
(cm)
S
t (s) x (cm)
u ~ gx ~ Re ~ Nu
• Predictions suggest the spread
process 24, 2012
July is dominated by convection 46
Gollner, M.J., Xie, Y., Lee, M., Nakamura, Y., and Rangwala,
A.S., 2012, In Press, Comb. Sci. Tech.
May 15, 2012
May 15, 2012
21, 2012 BuoyancyDefense: Studies onBehavior Flame Flame Spread
Buoyancy Effects on BurningUpward and Flame Spread
PhD Effects on Burning Behavior and Spread 46
46

47. Burnout Time Prediction
• We again analyze two limiting cases, S 0 and S
• For S 0 , heating from the flame to the solid occurs
as conduction from the flame to the fuel surface:

q kg (Tf Ts ) / y f
• If the fuel is thermally thin and yf is uniform along
the side of the fuel, a balanced equation of energy is
tb Tf Ts c (Ts T )d
s p ,s H pd s
kg dt
0 yf 2
• Integrating and solving for the burnout time
yf s d [c p ,s (Ts T ) Hp]
tb
2k g (T f Ts )
S 0
July 24, 2012 47 47
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PhD Effects on Burning Behavior and Spread 47
47

48. Burnout Time Prediction
• For S , we assume a match is nearly burning
free in the air
• Burning rate theory for a spherical fuel droplet
can be extended to a cylindrical geometry [1]
• Assuming a matchstick is nearly cylindrical with
initial radius ri d / 2 and unit length, the burning
rate becomes
d 2 drs

m ( s r )
s 2 rs s

m(rs ),
dt dt
Where rs is the radius of the cylinder at time t
July 24, 2012 48
1. C. K. Lee. Burning rate of fuel cylinders. Combust. Flame, 32:271276, 1978.
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21, 2012 BuoyancyDefense: Studies onBehavior Flame Flame Spread
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PhD Effects on Burning Behavior and Spread 48
48

49. Burnout Time Prediction
• The time necessary to deplete all fuel in the cylinder,
the burnout time is then
tb 2 rs s
tb dr .
0  (rs ) s
m
• Replacing m(r ) with the solution for the burning rate
 s
k
over a cylinder fuel surface, c ln(1 B) ln(r / r ) , where
2
g
p, g
f s
1
B c p (T f Ts ) / H p and integrating the burnout time is
c
s p, g ln(rf / rs )ri 2
tb .
4k g ln(1 B)
• The standoff distance ratio is estimated from a
correlation:
0.75
ln(rf / rs ) 02(d / 2)
July 24, 2012 49
1. C. K. Lee. Burning rate of fuel cylinders. Combust. Flame, 32:271276, 1978.
May 15, 2012
May 15, 2012
21, 2012 BuoyancyDefense: Studies onBehavior Flame Flame Spread
Buoyancy Effects on BurningUpward and Flame Spread
PhD Effects on Burning Behavior and Spread 49
49

50. Matchstick Spread & Burning
Pyrolysis Spread Burnout Time
xp ~ t1.6 to t1.7
x p ~ t 3/2
S 0
xp ~ t
xp tb
(cm)
S
t (s) x (cm)
u ~ gx ~ Re ~ Nu Analytical Predictions
c ln(rf / rs )ri 2
• Predictions suggest the spread
s p, g
tb .
S 4k g ln(1 B)
process 24, 2012
July is dominated by convection 50 s d[c p,s (Ts
yf T ) Hp]
Gollner, M.J., Xie, Y., Lee, M., Nakamura, Y., and Rangwala,
S 0 tb
2k g (T f Ts )
A.S., 2012, In Press, Comb. Sci. Tech.
May 15, 2012
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50

51. Discrete Fuel Spread Applications
Upward spread through cable trays/ wire arrays
July 24, 2012 51
Tranisition to crown fire behavior (especially important for controlled burns)
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52. Conclusions
• Even non-charring fuels can modify the boundary layer
- Corrugated cardboard delaminates (not in current models)
• The heat flux within the B.L. is crucial to understanding
both the flame-spread rate and steady burning
• Discontinuous fuels can achieve spread rates faster than
continuous fuel beds
- Important for transition in wildfires & spread in cable trays
• Flame-spread rates were found to be greatest in near-
vertical orientations while burning rates are maximized in
near-horizontal orientations.
July 24, 2012 52
- Worst-case scenario important for small-scale flammability tests
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52

53. Acknowledgements
• Jonathan Perricone, Garner Palenske and all my colleagues at
Schirmer Engineering for introducing me to this field
• UCSD Graduate Students: Xinyan Huang, Ulrich Niemann and
Ryan Ghemlich for their contributions to laboratory
experiments
• UCSD Undergraduate Students: Jeanette Cobian, Mario Zuniga
and Alexander Marcacci for their contributions to laboratory
experiments
• Worcester Polytechnic Institute Students and staff: Simon Xie,
Minkyu Lee, Randy Harris, Kris Overholt and Todd Hetrick
July 24, 2012 by:
Supported
53
Society of Fire Protection Engineers
Educational and Scientific Foundation
May 15, 2012
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53

54. Acknowledgements
• John de Ris, Jose Torero, Adam Cowlard and Yuji
Nakamura for valuable discussions
• The faculty and staff of the UCSD MAE dept.
• Outstanding advisors: Professors Forman A. Williams
and Ali S. Rangwala
• The support of all my family and friends
July 24, 2012 by:
Supported
54
Society of Fire Protection Engineers
Educational and Scientific Foundation
May 15, 2012
May 15, 2012
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55. July 24, 2012 55