Fire Dynamics II
Lecture # 11
Post-flashover Fire
Jim Mehaffey
82.583
Carleton University, 82.583, Fire
Dynamics II, Winter 2003, Lecture #
1
Post-flashover Fire
Outline
• Ventilation controlled fires
• Fuel-surface controlled fires
• Model: Hot gas temperature (function of time)
• Fire resistance test
• Characterizing fire severity
• Design for resistance
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Post-flashover Fire
• Assumptions
- Well-stirred reactor
- Th uniform throughout enclosure
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Post-flashover Fires
Wood Cribs, Pallets & Stacked Furniture
• Harmathy (1972) identified two burning regimes for
room fires involving wooden cribs:
ventilation controlled & fuel-surface controlled

• R  m = mass loss rate of fuel (kg s-1)
•  = ventilation parameter (kg s-1)
=  O A g h  3.76 A h
• Af = exposed surface area of fuel (m2)
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Post-flashover Fires Involving Wooden Cribs
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Example Calculation of Equivalence Ratio
Post-flashover Fires Involving Wooden Cribs
• Post-flashover fire is ventilation-controlled if
 / Af < 0.63 kg m-2 s-1
A h A f  0.07 m
1/2
Eqn (11-1)
• Fuel mass loss rate is

m  0.0236  kg s

1
m  0.09 A h kg s
1
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Eqn (11-2)
6
What do we know about ventilation-controlled
post-flashover fires involving wooden cribs,
pallets or stacked furniture?
• Fuel mass loss rate is

m  0.09 A h
kg s 1
Eqn (11-2)
• Rate of entry of air into room is

ma  0.45 A h
kg s
1
Eqn (11-3)
• Rate of exit of hot gas from room is

mh  0.54 A h
kg s
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1
Eqn (11-4)
7
Ventilation-controlled post-flashover fires involving
wooden cribs, pallets or stacked furniture
• Equivalence ratio is
 ~ 0.92
Eqn (11-5)
• The rate of heat release of the fire is

Q  1,050 A h (kW)
Eqn (11-6)
• The mass flow rate of soot out of the enclosure is

mS  1.5 A h (g s )
-1
Eqn (11-7)
(Important for assessment of visibility outside the room)
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Ventilation-controlled post-flashover fires involving
wooden cribs, pallets or stacked furniture
• The mass flow rate of CO out of the enclosure is

mCO  18 A h (g s 1 )
Eqn (11-8)
• Concentration of CO in hot gas leaving enclosure is
VCO  3.4%  34,200 ppm
Eqn (11-9)
(Important for assessment of toxicity outside the room)
(This is a very high and dangerous concentration)
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Ventilation-controlled post-flashover fires involving
wooden cribs, pallets or stacked furniture
• The mass flow rate of CO2 out of the enclosure is

mCO2  113 A h (g s-1 )
Eqn (11-10)
• Concentration of CO2 in hot gas leaving enclosure is
VCO2  13.7%  137,000 ppm
Eqn (11-11)
This would cause significant increased CO uptake due to
hyperventilation. See slide 3-32 in Fire Dynamics I.
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Ventilation-controlled post-flashover fires involving
wooden cribs, pallets or stacked furniture
• The mass flow rate of N2 out of the enclosure is

mN2  339 A h (g s )
1
Eqn (11-12)
• Concentration of N2 in hot gas leaving enclosure is
VN2  64.8%
Eqn (11-13)
On a molar basis, air is 78% N2 and the hot gas is 65% N2.
Since molecular wt of N2 is 28, molecular wt of air and the
hot gas is close to 28. Therefore, the value 28.95 can be
use for air and the hot gas with confidence.
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Fuel-Surface Controlled: Post-flashover Fires
• T.Z. Harmathy 1972 // wood cribs (cellulosic)
• Post-flashover fire is fuel-surface controlled if
 / Af  0.63 kg m-2 s-1
A h A f  0.07 m
1/2
Eqn (11-14)
• Fuel mass loss rate is
1
m  0.0062 A f kg s

m  0.0062  G kg s 1
Eqn (11-15)
G = Quantity of wood in room (kg)
 = Af / G = specific area of wood (m2 kg-1)
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The Rate of Burning of
Fuel-Surface Controlled: Post-flashover Fires
• Rate of mass loss / unit surface area of fuel is


m"  m
Af
 0.0062 kg m -2 s 1  6.2 g m -2 s 1
Eqn (11-16)
• Douglas fir:
– Assume  = 550 kg m-3.
– Assume 80% converted to volatiles and 20% to char
– Rate of advance of char front:
Vc = 0.85 mm min-1
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Some Comparisons
• For massive timbers in standard fire resistance test
Vc = 0.6 mm min-1
• Rate of char advance in wood cribs is (slide 8-36)
Vc = 2.2 x 10-6 D-0.6
(m s-1)
• Sticks of square cross and side D (m)
D (mm)
38
45
80
Vc (mm / min)
0.94
0.85
0.60
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 - Specific Area of Wood
• For Douglas fir:  = 550 kg m-3
• Dimensional lumber (4 sides exposed)
– 2x2 (38 mm x 38 mm)   = 0.191 m2 kg-1
– 2x4 (38 mm x 89 mm)   = 0.136 m2 kg-1
– 2x12 (38 mm x 286 mm)   = 0.108 m2 kg-1
• Heavy timber column (4 sides exposed)
– 8x8 (191 mm x 191 mm)   = 0.038 m2 kg-1
• Plywood (1 side exposed)
– 1/2” = 12.7 mm thick   = 0.143 m2 kg-1
– 1/4” = 6.4 mm thick   = 0.286 m2 kg-1
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 - Specific Area of Wood
• Harmathy’s correlation for fuel-surface controlled
burning derived from experimental data for wood cribs
• Correlation is likely okay for wood cribs, stacked wood
pallets & stacked wood furniture where most surfaces
are shielded from radiation from hot upper layer
• For such items assume  ~ 0.13 m2 kg-1 Eqn (11-17)
• Harmathy’s correlation for fuel-surface controlled
burning and  ~ 0.13 m2 kg-1 are not appropriate for
scenarios involving large exposed wooden surfaces
like wall panelling
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G - Quantity of Fuel (kg)
• Quantity of fuel in a room is commonly expressed in
terms of a calorifically equivalent quantity of wood
• Many surveys have been conducted to determine
mass of fuel / floor area
• Definition:
L = specific fire load (kg m-2)
= mass of fuel / floor area
G = L x (floor area)
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Eqn (11-18)
17
L - Specific Fire Load (kg m-2)
• L is random variable: mean L & standard deviation L
• Harmathy recommendations (old data)
Occupancy
Dwelling
Office
School
Hospital
Hotel
L
-2
(kg m )
30.1
24.8
17.5
25.1
14.6
L
-2
(kg m )
4.4
8.6
5.1
7.8
4.2
• Assuming L follows a normal distribution
80th percentile L80  L  0.84  L
95th percentile L95  L  1.64  L
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Eqn (11-19)
18
Duration of a Post-flashover Fire
• Assume volatiles released in post-flashover phase
– Little mass loss in pre-flashover phase
– Dominantly glowing char in decay phase
• Assume total mass loss during post-flashover phase is
MT = 0.8 G
(kg)
Eqn (11-20)
• Duration of post-flashover phase is

MT

Eqn (11-21)
m
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Duration of a Post-flashover Fire
• For a fuel-surface controlled fire
0.8 G

 990 s  16.5 min
0.0062  G
Eqn (11-22)
• For a ventilation controlled fire
0.8 G
8.89 G


 16.5 min
0.09 A h
A h
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Eqn (11-23)
20
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Duration of Post-flashover Fire
A h
Test
1
2
3
4
5
m
5/2
0.92
0.92
0.92
1.42
2.13
G
Af
kg
2
m
130
130
234
234
234
16.9
16.9
30.4
30.4
30.4
A h /A f
m 1/2
0.054
0.054
0.030
0.047
0.070
VC
or
FSC
VC
VC
VC
VC
VC?
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Duration Duration
test
theory
min
min
18.5
21
28
24
17
20.9
20.9
37.7
24.4
16.5
23
Kemano
F ire Exposures
1200 .0
Liv ing R oom F ire s - D uplex
1000 .0
AST M E 119 & CAN/UL C-S1 01
o
Tempe ra ture ( C)
800 .0
600 .0
400 .0
200 .0
0 .0
0 .0
10 .0
20 .0
30 .0
Time (min)
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40 .0
50 .0
60 .0
S -987
24
Time-averaged Temperatures in Room Fires
Experimental data from SFPE handbook
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Post-flashover Fires Involving Wood, PMMA & PE
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• Burning rate in post-flashover fires involving fuels with
exposed surfaces is enhanced by radiation
• Large burning rates inhibit inflow of air so increase
equivalence ratio  reduced heat release (inside)
• Heat release rate still can be ventilation-controlled
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Traditional Design for Fire Resistance
• Basic Objective: Provide sufficient time for escape
• Strategy # 1 - Compartmentation: Inhibit fire spread:
enclose compartments with fire resistant separations
• Strategy # 2 - Structural Fire Protection: Delay
collapse of structure: make elements fire resistant
• Functional Requirement: Assemblies must perform
acceptably when exposed to design fire & design load
• Acceptance Criterion (Not clearly stated): Fire
separations & structural members must perform intended
functions for duration of fire
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Physical Model - Post-flashover Fire
The Fire Resistance Test
• Physical (as opposed to mathematical) model of a
post-flashover fire
• Initial development ~ 1908
Standard Fire Resistance Tests
• CAN/ULC-S101, Standard methods of fire endurance
tests of building construction materials
• CAN/ULC-S101 = ASTM E119
(Determination of loads is different)
• ISO 834 = international standard
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Standard Temperature-time Curve: CAN/ULC-S101 or ASTM E119
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Performance Requirements
Separating Element
1. Specimen remains in place
2. No passage of hot gas / flame
3. T < 140°C (average unexposed side)
T < 180°C (single point, unexposed side)
4. Hose-stream Test
Load-bearing Element
1. Specimen supports design load
Fire-resistance Rating
• Time specimen meets performance requirements
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Principle for Establishing Fire Resistance
Requirements for Buildings
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Principle for Establishing Fire Resistance
Requirements for Buildings
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NBCC Requirements
Compartmentation
• Fire separations often must be fire rated
• Fire separations between public corridors & suites in
small buildings require fire-resistance rating of 3/4
• Fire separations between public corridors & suites in
large buildings require fire-resistance rating of 1 hour
Structural Fire Protection
• Floors and structural elements supporting floors often
must be rated
• In small buildings: fire-resistance rating of 3/4 or 1 h
• In large buildings: fire-resistance rating of 2 h
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Performance-based Design for Fire Resistance
Design Fire Scenarios
Buildings with High Degree of Compartmentation
• Examples: Apartment & office buildings
• Scenario: Post-flashover fire (no suppression)
• Design Fire: A credible but severe post-flashover fire
Buildings with Large Open Spaces
• Examples: Warehouses & Factories
• Scenario: Localized fire (diffusion flame)
• Design Fire: A credible but severe localized fire
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Model for Post-flashover Fire Severity
Japanese Parametric Model
Basic Assumptions
• Ventilation: Assume unprotected openings are open
Assume fire-rated closures remain intact
• Heat Release: Heat released in post-flashover phase
Maximum possible value from t=0

Q  1,500 A h (kW)
• Fuel Load: Total fuel load is consumed
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Japanese Parametric Model
for Ventilation Controlled Fires
• Temperature of fire gases: Th(t) (K)
Th(t) - To =  t1/6
where
Eqn (11-24)
 = a constant (K s-1/6)
t = time since ignition (s)
1/ 3
 A h


  3.0 TO 
 AT k  c 
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Eqn (11-25)
38
A = area of openings (windows) (m2)
h = height of openings (windows) (m)
AT = total area of boundaries (m2)
k = thermal conductivity boundaries (kW m-1 K-1)
 = density of boundaries (kg m-3)
c = specific heat of boundaries (kJ K-1 kg-1)
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Duration of post-flashover fire: tD (s)
L AF
tD 
0.09 A h
Eqn (11-26)
L = fuel load (kg m-2)
AF = area of the floor (m2)
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Japanese Parametric Model
Model Validation
Test
G = L AF
(kg)
Ah
5/2
(m )
AT
2
(m )
kc
-2 -1/2
-1
(kJ m s K )

-1/6
(K s )
tD
(s)
1
130
0.92
45.24
0.868
252
1570
2
130
0.92
45.24
0.334
346
1570
3
233
0.92
45.24
0.666
275
2814
4
233
1.42
44.96
0.666
318
1823
5
233
2.13
44.61
0.666
365
1215
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Japanese Parametric Model
Option 1: Response of Assembly Predicted Using
Mathematical Model
• Fire characterized by temperature-time curve
generated by Japanese parametric model.
• Load carried by structural members taken directly from
structural analysis (Part 4 of the NBCC).
• A fire-resistance model is used to predict thermal and
structural response of each assembly.
• Do fire separations and structural members meet the
acceptance criteria?
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Japanese Parametric Model
Option 2: Response of Assembly Predicted Using
Physical Model
• Heat absorbed by unit surface area of fire separations
or structural members in post-flashover fire: q” (kJ m-2)
3
q" ( t D) 
2
• For ISO 834:
• For ASTM E119:
k  c t 2D / 3
Eqn (11-27)
 = 230 K s-1/6
 = 229 K s-1/6
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Normalized Heat Load Concept
(Harmathy & Mehaffey)
• Compartment fire of duration tD is equivalent in
severity to an ISO 834 fire test of duration teq in which
same heat is absorbed per unit area
  

t eq  
 230 
3/ 2
tD
Eqn (11-28)
• Assembly fire resistance rating  teq is acceptable
• Advantage of Option 2: Existing fire resistance ratings
can still be used
• Drawback of Option 2: Fire-resistance ratings are
determined using max load not actual design load
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Design Considerations
Fuel Load
• Use 95th percentile in fuel load distribution: Eqn (11-19)
Ventilation
• Assume unprotected openings are open
• Assume fire-rated closures remain intact
• If several vents at approximately the same elevation
A h  A1 h1  A 2 h 2  A 3 h 3  ...
Eqn (11-29)
Compartment Boundaries
• Boundaries do not include internal partitions
• If there is more than one boundary material
A T kc  A T,1 k1 1c1  A T,2 k 2  2 c 2  A T,3 k 3 3c3  ...
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Example - Design for Fire Resistance
Prevent Fire Spread from an Office Suite
Room Dimensions: 6.0 m x 4.0 m x 2.4 m (height)
Floor Area: 6.0 m x 4.0 m = 24 m2
Window Dimensions: 4.0 m x 1.5 m (height)
Fuel Load: 95th percentile Eqn (11-19)
L95 = L + 1.64 L = (24.8 + 1.64 x 8.6) kg m-2 = 38.9 kg m-2
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Ventilation: Window breaks & door remains intact
A h  4.0 m x 1.5 m 1.5 m  7.35 m5/2
Compartment boundaries
A T kc  A T,1 k1 1c1  A T,2 k 2  2 c 2
= [ceiling + walls - vents][gypsum bd]
+ [floor][n.w. concrete]
= [6x4 + 6x2.4x2 + 4x2.4x2 - 1.5x4] x 0.742
+ [6 x 4] x [2.192]
= 101.58 kJ s-1/2 K-1
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Japanese Parametric Model
• Temperature of fire gases: Th(t) (K)
Th(t) - To =  t1/6
Eqn (11-24)
where  (K s-1/6) characterises the fire
1/ 3
 A h


  3.0 TO 
 AT k  c 
Eqn (11-25)
\  = 3 x 293 x [ 7.35 / 101.58 ]1/3 = 366 K s-1/6
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Japanese Parametric Model
• Duration of post-flashover fire: tD (s)
L AF
tD 
0.09 A h
Eqn (11-26)
\ tD = 38.9 x 24 / [ 0.09 x 7.35 ] = 1411 s = 23.5 min
• Duration of equivalent fire resistance test: teq
  

t eq  
 230 
3/ 2
tD
Eqn (11-28)
\ teq = [366 / 230]3/2 x 23.5 min = 47.2 min
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