The document is a thesis proposal for examining flame spread over various fuels. It begins by introducing the theory of flame spread and how heat transfer from the flame leads to pyrolysis and propagation. Previous work on upward flame spread over corrugated cardboard is summarized, finding flame and pyrolysis heights grow more slowly than models predict. The non-homogeneity of cardboard's corrugated structure is hypothesized to extend the thermal boundary layer, slowing growth. Future work is proposed on inclined flame spread over homogeneous PMMA at various angles to systematically vary the heat flux profile. Understanding heat flux is critical for flame spread models.

1. University Senate Exam for
Michael Gollner
Adviser:
Professor Forman A. Williams
Supported by: Society of Fire Protection Engineers
Educational and Scientific Foundation Grant 1

2. Outline
I. Introduction
I. Theory of Flame Spread
II. Flame Spread Over Inhomogeneous Fuels
I. Upward Spread: Corrugated Cardboard
III. Flame Spread Over Homogenous Fuels
I. Inclined Flame Spread: PMMA
IV. Conclusion
2

3. I. Introduction
Theory of Flame Spread
3

4. 1. Thermal boundary layer
Fire Spread 2. Heat flux from flame to virgin fuel
3. Influence of orientation
g
q ( x, t )
f  f ~ xn
Excess Vp
Pyrolyzate
yf
q
p

m  HcQ
f
y  xf
x
xp
Fire spread occurs because of a transfer of thermal energy from a burning
region to a region of virgin fuel 4

5. xp
xp
“Wall Fire”
xp xp
xp
xp
xp
“Ceiling Fire” “Pool Fire” 5

6. Motivation
 The rate of fire spread is central to fire safety design –
it describes the rate a fire will grow and hence its fire
hazard
 Flame spread is still not well understood for:
 Forest fires (e.g. inclined slopes)
 Warehouse fires
 Undersides of burning roofs
6

7. Objectives
 Understand the influence of the following parameters
on the rate of fire spread, Vp,
 Non-homogeneity of fuels (modifying the thermal
boundary layer, δf)
 Fuel orientation angles, θ
 Heat flux profiles ahead of the flame, q ( x, t )
f
7

8. II. Flame Spread Over
Inhomogeneous Fuels:
Upward Spread: Corrugated Cardboard
(Previous Work)
8

9. Previous Work
 Upward flame spread over Corrugated Cardboard
 What influence does the non-homogeneity of the fuel
have on the flame spread rate?
 Motivations
 Upward flame spread is the initial stage in warehouses, where
later stages involve more material (plastics)
 Motivation: The smallest amount of suppressant necessary to
extinguish any fire occurs at early times (fire involves less
material, lower burning rate or HRR)
Gollner, M.J., Williams, F.A., and Rangwala, A.S. Upward flame spread over corrugated
cardboard. Combustion and Flame. DOI: 10.1016/j.combustflame.2010.12.005
9

10. Upward Flame Spread
 For upward flame spread
 Heat transfer is by radiation and convection from the
flame to virgin fuel
 On continuous fuels, flame spread is unsteady and
extremely rapid
10

11. Upward Flame Spread - Laminar
• Flame height <25 cm
Boundary layer
Buoyant Plume
Plume Radiative +
Convective Heat Transfer
Combusting Plume
Excess Flame Radiative +
Pyrolyzate Convective Heat Transfer
Pyrolysis Zone flame xf
 
mF (~ 20 to 25 cm Laminar
xp Flame Propagation)
Y-axis
Fuel
• Study important because it provides physical understanding
of the problem 11

12. Upward Flame Spread - Turbulent
Buoyant Plume
Plume Radiative +
Boundary Convective Heat Transfer
layer
flame
Combusting Plume
Flame Radiative +
Convective Heat Transfer
Excess
Pyrolyzate
 
mF
Pyrolysis
Zone xp xf
• Flame height >25 cm (Turbulent flame height >25 cm)
• Realistic fire situation
• Cardboard still intact Y-axis
Fuel 12

13. Mechanisms of Fire Spread
 Important quantity: heat flux ahead of pyrolysis region
q( x, t )

 Approximately, forward heat flux is all imparted over
combusting plume ( x f  xp )
 Therefore, flame height (xf) and pyrolysis height (xp)
become relevant parameters for study
13

14. Definition of Flame Height
Heat flux
imparted to fuel
q( x, t )

MOST heat flux
imparted to fuel
14

15. Results of Upward Flame Spread Theories*
 Annamalai & Sibulkin: x f ~ A1( B1  t ) 2
(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
1. Annamalai, K. and Sibulkin, M. Flame spread over combustible surfaces for laminar flow systems. Part I & II: Excess fuel and heat flux. 1979,
Combust. Sci. Tech., vol. 19, pp. 167-183.
2. Saito, J.G. Quintiere, and F.A. Williams, "Upward Turbulent Flame Spread," Fire Safety Science-Proceedings of the First International
Symposium, 1985, pp. 75-86.
3. The dependence of flame propagation on surface heat transfer II. Upward burning . Sibulkin and Kim, Comb. Sci. Tech. 1976
*NOTE: Results for non-charring fuels.
15

16. Cardboard Spread Experiments
 Cardboard ignited uniformly at
base by burning wick
 Flames propagate up
 Insulated board above sample
 Sample is filled with
plastics, but this study only
addresses the behavior before
these plastics ignite
Gollner, M.J., Williams, F.A., and Rangwala, A.S. Upward flame spread over corrugated
cardboard. Combustion and Flame. DOI: 10.1016/j.combustflame.2010.12.005 16

17. Flame Height Observations
x f ,max
50
40
x f ,avg
Height (cm)
30
x p ,avg
20
10
0
0 10 20 30 40 50
Time from Ignition (s)
Gollner, M.J., Williams, F.A., and Rangwala, A.S. Upward flame spread over corrugated
17
cardboard. Combustion and Flame. DOI: 10.1016/j.combustflame.2010.12.005

18. Flame Height Observations
2
x f ~ t fits x f ,max
50
Predicted using
current models
40
x f ,avg
Height (cm)
30
20
x p ,avg
10
0
0 10 20 30 40 50
Time from Ignition (s)
Gollner, M.J., Williams, F.A., and Rangwala, A.S. Upward flame spread over corrugated
18
cardboard. Combustion and Flame. DOI: 10.1016/j.combustflame.2010.12.005

19. Flame Height Observations
xf ~ t 3/2
fits x f ,max
50
Observed Trend
40
Why does the pyrolysis front and flame x f ,avg
Height (cm)
30
height grow SLOWER than what current
theories would predict? x p ,avg
20
10
0
0 10 20 30 40 50
Time from Ignition (s)
Gollner, M.J., Williams, F.A., and Rangwala, A.S. Upward flame spread over corrugated
19
cardboard. Combustion and Flame. DOI: 10.1016/j.combustflame.2010.12.005

20. Pyrolysis Height Observations
x p ~ t 3/2
Same trend
observed in
flame heights
Gollner, M.J., Williams, F.A., and Rangwala, A.S. Upward flame spread over corrugated
20
cardboard. Combustion and Flame. DOI: 10.1016/j.combustflame.2010.12.005

21. Burning-Rate Observations

Laminar Q  20kW / m
2

x f ~ (Q)4/3

Turbulent Q  20kW / m
2

x f ~ (Q)2/3
Observations are
expected.
What causes the
x~t3/2
dependence?
21

22. What is Corrugated Cardboard?
1. Grant, G. and Drysdale, D., Numerical Modeling of Early Flame Spread in Warehouse Fires. Fire Safety Journal, 1995. 24(3):
p. 247-278.
2. T. Jayaweera, H.Z. Yu, Water absorption in horizontal corrugated boards under water sprays, Fire Safety Journal. 41 (2006)
22
335–342.

23. 23

24. 24

25. 25

26. 26

27. 27

28. 28

29. 29

30. 30

31. 31

32. Heat Flux in Flame Spread Models
q  Constant

q = constant One of few models with q(x) [1]
1. Sibulkin and Kim, Comb. Sci. Tech. vol. 17, 1977 32

33. Heat Flux in Experiments
 Simplifications of the description of the spatial
dependence of q are prevalent, often q( x, t )  const

Transient measurement
of dynamic heat flux at
height xp < x < xf on a
sample of corrugated
cardboard
q( x, t )  20kW / m2

selected in their study
Grant, G. and Drysdale, D., Numerical Modeling of Early Flame Spread in Warehouse Fires. Fire Safety Journal, 1995.
24(3): p. 247-278. 33

34. ‘Constant’ Heat Flux in Models
Tsai, K. (2009). Width effect on upward flame spread. Fire Safety Journal, 44(7), 962-967.
34

35. 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
Cardboard
35

36. How would this affect xp & xf ?
Temperature of a thick fuel with time-dependent heat flux:
(Carslaw & Jager and Mitler et al.)
q
t
1 
T  T0 
 kc 
0 t  t
dt 
Assuming material pyrolyses at fixed Tp, substitute τ=t/t’, integral becomes
a constant dependent on material properties:
q t
1

I  d
0 1 
Assuming a new q(x) power-law variation based on boundary layer extension:
q  C / x1/3

H. Mitler, Predicting the spread rates of fires on vertical surfaces, Symposium (International) On
Combustion. 23 (1991) 1715-1721. 36

37. How would this affect xp & xf ?
The time, t of arrival of pyrolysis front will obey:
x p  At 3/2
Assuming x f ~ m ~ x p
 , where m is the burning rate per unit width:

x f  Bt 3/2
You recover what was observed in experiments!
Gollner, M.J., Williams, F.A., and Rangwala, A.S. Upward flame spread over corrugated
cardboard. Combustion and Flame. DOI: 10.1016/j.combustflame.2010.12.005 37

38. Critical Point
The heat flux ahead of the flame front,
q( x, t )

is critical toward understanding flame
spread phenomena
38

39. III. Flame Spread over
Homogenous Fuels
Inclined Flame Spread: PMMA
(Future Work)
39

40. Current Work
 Gravity-Assisted Flame Spread over PMMA at
various Angles of Inclination
 The heat flux profile can be consistently modified by
changing the buoyancy direction (tilting the sample)
 This introduces less uncertainties than changing
materials, which sometimes have less understood
properties
 A material, Polymethyl Methacrylate (PMMA) is
chosen to first be tested because its combustion
properties are well understood for fire problems.
40

41. Flame Inclinations
41

42. Average Burning Rates 3.5
Average Burning Rates at Angles
3
2.5 Numerical (Methanol, 11mm) [1]
Acetone (10cm) [2]
Aviation Fuel (10cm) [2]
Benzene (10cm) [2]
MLR / MLR(90,ceiling)
Kerosene (10cm) [2]
2 Methanol (10cm) [2]
Toluene (10cm) [2]
Gas (B=0.35,0.65m) [3]
Gas (B=0.7,0.65m) [3]
Gas (B=1,0.65m) [3]
1.5 PMMA (3cm) [4]
PMMA (4cm) [4]
PMMA (5cm) [4]
PMMA (6cm) [4]
PMMA (8cm) [4]
1 PMMA (10cm) [4]
0.5
0
-100 -80 -60 -40 -20 0 20 40 60 80 100
Angle of Inclination, (-90o = ceiling, 0 = wall, 90 = pool)
o o
42

43. Rates of Flame Spread
Spread Rate from Previous Studies
0.9
Pizzo Model [5]
Pizzo Experiment [5]
Drydale and Macmillian (6cm) [6]
0.8 Xie and DesJardin Model [7]
Drysdale Avg [6]
0.7
0.6
Spread Rate (cm/s)
0.5
0.4
0.3
0.2
0.1
0
-20 0 20 40 60 80 100
Angle of Inclination, (-90o = ceiling, 0 = wall, 90o = pool)
o
43

44. Previous Literature
1. S.M. Ali, V. Raghavan, A. Rangwala, A numerical study of quasi-steady burning characteristics of a
condensed fuel: effect of angular orientation of fuel surface, Combustion Theory and Modelling. 14
(2010) 495-518.
2. P.L. Blackshear, M.A. Kanury, Some effects of size, orientation, and fuel molecular weight on the
burning of fuel-soaked wicks, Symposium (International) On Combustion. 11 (1967) 545-552.
3. de Ris, J, and L. Orloff. “The role of buoyancy direction and radiation in turbulent diffusion flames on
surfaces.” Symposium (International) on Combustion 15, no. 1 (1975): 175-182.
4. H. Ohtani, K. Ohta, Y. Uehara, Effect of orientation on burning rate of solid combustible, Fire and
Materials. 18 (1991) 323-193.
5. Y. Pizzo, J.L. Consalvi, B. Porterie, A transient pyrolysis model based on the B-number for gravity-
assisted flame spread over thick PMMA slabs, Combustion and Flame. 156 (2009) 1856-1859.
6. Drysdale, D, and a Macmillan. “Flame spread on inclined surfaces.” Fire Safety Journal 18, no. 3 (1992):
245-254.
7. W. Xie, P. Desjardin, An embedded upward flame spread model using 2D direct numerical
simulations, Combustion and Flame. 156 (2009) 522-530.
Relevant but not plotted:
1. Y. Wu, H.J. Xing, G. Atkinson, Interaction of fire plume with inclined surface, Fire Safety Journal 35
(2000) 391-403
2. ITO, A, and T KASHIWAGI. “Characterization of flame spread over PMMA using holographic
interferometry sample orientation effects.” Combustion and Flame 71, no. 2 (February 1988): 189-204.
44

45. Gaps in Existing Data
 No previous data on spreading flames under inclined
angles has been performed (only steady)
 Hazards at underside angles has not been assessed
experimentally and may have a wide application for
future flammability tests and standards
 Measurements of heat flux profiles and standoff
distances ahead of the flame front have not been
performed
 Critical to finding critical mechanisms and development
of analytical theories. Only performed for wall fires (0°)
45

46. Apparatus
46

47. Apparatus
Insulation Board
Thin-Skin Calorimeters
Side-View DSLR Camera
Rear
View
PMMA Sample Camera
(7 Surface Thermocouples)
Load Cell
Data Acquisition System
Not Shown: Front Video Camera, Optional IR Camera
47

48. Test Run
48

49. Non-Uniformity in Heat Flux
Preliminary test on
PMMA at 30 degrees
Increasing
time and xp
49

50. Acknowledgements
 Most of all, Prof. Forman Williams and Ali Rangwala
for their advice and guidance
 Kristopher Overholt (WPI), Simon Xie (WPI), Todd
Hetrick (WPI), Cecelia Florit(WPI), Xinyan Huang
(UCSD) and Chuck Marcacci (UCSD) for their
assistance in the laboratory
 Prof. Jose Torero (Edinburgh), Dr. Adam Cowlard
(Edinburgh), Jonathan Perricone and many others for
their advice, assistance and hospitality
50

51. IV. Conclusion
51

52. Next Steps
 Running tests at -60,-45,-30,0,30,45,60 degrees
 Will analyze
 Heat flux profiles
 Flame Standoff Distance
 Burning Rates
 Flame Spread Rates
 Look at influence of heat flux profile on spread and
burning rates
52

53. Papers and Current Projects
Peer-Reviewed Publications
1. Gollner, M.J., Williams, F.A., and Rangwala, A.S. Upward flame spread over corrugated
cardboard. Combustion and Flame. DOI: 10.1016/j.combustflame.2010.12.005
Publications Under Review and in Preparation
1. Gollner, M.J., Overholt, K., Williams, F.A., Rangwala, A.S. and Perricone, J., Warehouse commodity
classification from fundamental principles. Part I: commodity and burning rates, Under
Review, Fire Safety Journal. 2010.
2. Overholt, K., Gollner, M.J., Williams, F.A., Rangwala, A.S. and Perricone, J., Warehouse commodity
classification from fundamental principles. Part II: flame height prediction. Under Review,
Fire Safety Journal. 2010.
3. Gollner, M.J., Xie, Y., Lee, M., Nakamura, Y., Rangwala, A.S., Burning behavior of vertical
matchstick arrays, In Preparation for Combustion Science and Technology
Current Projects
1. Tilting Flame Spread – Apparatus at UCSD. Advising Graduate Student, Xinyan Huang
2. Influence of backing on upward flame spread over corrugated cardboard – Advising 2 undergraduate
students at WPI for their Senior Project: Amanda Keller and Ben Travis.
53

54. Questions?
54

55. Additional Slides
55

56. Additional Applications of Work
 Comparing measuring B-number with both the mass-
loss rate and standoff distance methods [1,2]
 Determine the worst-case angles for flame spread
 Implications to design of buildings and small-scale
“worst-case scenario” testing
 Development of analytical upward (and tilted) flame
spread models that use a variable heat flux profile
1. Gollner, M.J., Overholt, K., Williams, F.A., Rangwala, A.S. and Perricone, J., Warehouse commodity classification from
fundamental principles. Part I: commodity and burning rates, Under Review, Fire Safety Journal. 2010.
2. A.S. Rangwala, S.G. Buckley, J.L. Torero, Analysis of the constant B-number assumption while modeling flame spread,
Combustion and Flame. 152 (2008) 401-414. 56

57. Measurement of Heat Flux
Thin-Skin Calorimeter
Combined heat flux from calorimeter
(accounting for losses)
qi  qc  qr  qsto  qc,st qi
qc
qr
qc,st
qsto
American Society of Testing and Materials, Standard ASTM E 459-97 57

58. Cardboard Experimental Setup
 Standard Group-A Plastic Commodity
 Polystyrene cups in compartmented cardboard carton 58

59. Previous Literature
1. de Ris, J, and L. Orloff. “The role of buoyancy direction and radiation in turbulent diffusion flames on
surfaces.” Symposium (International) on Combustion 15, no. 1 (1975): 175-182.
2. H. Ohtani, K. Ohta, Y. Uehara, Effect of orientation on burning rate of solid combustible, Fire and
Materials. 18 (1991) 323-193.
3. P.L. Blackshear, M.A. Kanury, Some effects of size, orientation, and fuel molecular weight on the
burning of fuel-soaked wicks, Symposium (International) On Combustion. 11 (1967) 545-552.
4. Y. Wu, H.J. Xing, G. Atkinson, Interaction of fire plume with inclined surface, Fire Safety Journal 35
(2000) 391-403
5. S.M. Ali, V. Raghavan, A. Rangwala, A numerical study of quasi-steady burning characteristics of a
condensed fuel: effect of angular orientation of fuel surface, Combustion Theory and Modelling. 14
(2010) 495-518.
6. W. Xie, P. Desjardin, An embedded upward flame spread model using 2D direct numerical
simulations, Combustion and Flame. 156 (2009) 522-530.
7. ITO, A, and T KASHIWAGI. “Characterization of flame spread over PMMA using holographic
interferometry sample orientation effects.” Combustion and Flame 71, no. 2 (February 1988): 189-204.
8. Drysdale, D, and a Macmillan. “Flame spread on inclined surfaces.” Fire Safety Journal 18, no. 3 (1992):
245-254.
9. Y. Pizzo, J.L. Consalvi, B. Porterie, A transient pyrolysis model based on the B-number for gravity-
assisted flame spread over thick PMMA slabs, Combustion and Flame. 156 (2009) 1856-1859.
59

60. Previous Literature – Thick Fuels
 Steady Burning Experiments
 de Ris and Orloff (-90 to +90) [1]
 Ohtani et al. (-90 to +90) [2]
 Blackshear and Kanury (-90, 0, +90) [3]
 Wu et al. [4]
 Numerical Simulations
 Ali et al. (-90 to +90) (Steady) [5]
 Xie and DesJardin (0 to +90) (Spreading) [6]
 Spreading Fires
 Ito and Kashiwagi (-90 to +90) (Small Sample Width) [7]
 Drysdale and Macmillan (0 to +90) [8]
 Pizzo et al. (0 to +90) [9]
60

61. Picture of Experimental Setup
WPI, Summer 2008
TC wires
Heat flux sensors
Back View Front View
61

62. Commodities Used in Testing
Class II Class III Class Group A Plastic
IV/Group B
Commodities Used in Reality
62

63. Commodity Test Results
30 s 92 s 100 s 132 s 150 s
Front Face of Cardboard Plateau PS Cups & Cardboard
Burning Burning
Stage I Stage II Stage III
63

64. The B-number
B
impetuses i.e. heat of combustion for burning
resistances i.e. heat of vaporization to the process
“Thermodynamic Driving Force”
(1   )(HcYO , ) / s  C p , (Tp  T )
B B-number
Hg  Q
χ = Fraction of radiation lost [-] T∞ = Ambient temperature [K]
∆Hc = Heat of combustion [kJ/kg] L = Latent heat of vaporization [kJ/kg]
YO,∞ = Mass fraction of oxygen in ambient [-] ∆Hc = Heat of gasification [kJ/kg]
νs = Oxygen-fuel mass stoichiometric ratio [-] Cp,f = Specific heat of the fuel [kJ/kg-K]
Cp,∞ = Specific heat of ambient air [kJ/kg-K] Q = L + Cp,f(TB-TR) [kJ/kg]
Tp = Pyrolysis temperature of the fuel
[1] Kanury, A. M. An Introduction to Combustion Phenomena. s.l. : Gordon & Breach Science Publishers, Inc, 1977. 64

65. Experimentally-Measured B
•Solving for B and using Nu correlation for the heat-transfer coefficient:
 m''
f 
B  exp  1
   0.13[GrPr]1/ 3 

 g g 
•Formula for average B-number based on measured rate of mass loss
•Applies in regimes dominated by convective heat transfer, as found in
many small-scale experiments.
•Effective B-number derived by same formula with radiation included
Kanury, A. M. An Introduction to Combustion Phenomena. Gordon & Breach Science Publishers, Inc, 1977. 65

66. Stage 3 – Mixed Case
• Flame height >25 cm
• Realistic fire situation
• Cardboard breaks
66

67. Preliminary Spread Rates
Spread Rate as Function of Angle)
4.5
4
3.5
Spread Rate (cm/s)
Topside
3
2.5
Underside
2
1.5
-60 -40 -20 0 20 40 60
Angle
Only 1 test per point (Preliminary tests, not perfect material)
Points toward potential interesting results for underside flame spread! 67

68. Conclusions
Increasing Costs
Bench B-number Small Large
Scale Scale Scale
Tests Ys Tests Tests
68

69. Burning Rates
69

70. Material Flammability
70

71.  Sibulkin & Kim
Yo ,
YF vs
x f  0.64(r / B)2/3 xp
Convection
Convection +
Radiation
Sibulkin and Kim, Comb. Sci. Tech. vol. 17, 1977 71

72. Sprinkler Spray 2. Sprinkler Flow
Characterization
3. Flow Interaction
PLUME
1. Classification
FIRE of Commodity
72

73. Upward flame spread over Group A Plastic Commodity. 1.89 X’s original speed,
73

74. Xf and Xp Relationship
74