Transcript Fire Dynamics I - Carleton University

Fire Dynamics II
Lecture # 10
Pre-flashover Fire
Jim Mehaffey
82.583
Carleton University, 82.583, Fire
Dynamics II, Winter 2003, Lecture #
1
Pre-flashover Fire
Outline
• Develop a model to predict:
– Upper layer temperature (function of time)

– Q required for flashover
– Time to flashover
Carleton University, 82.583, Fire
Dynamics II, Winter 2003, Lecture #
2
Predicting Pre-flashover Fire Temperatures
• In principle, solve complex set of equations presented
in Lecture 7 Heat Transfer in Enclosure Fires for:
–
–
–
–
location of neutral plane
time-dependent mass flow rates
time dependent hot gas temperatures
time dependent surface temperatures
• An approximate solution developed in 1981 provides a
simple alternative which is useful for:
–
–
–
–
Understanding roles of variables in pre-flashover fire
Design purposes in simple applications
Developing “first cut” designs in complex applications
Forensic investigations: “simple” cases or “first cut”
Carleton University, 82.583, Fire
Dynamics II, Winter 2003, Lecture #
3
McCaffrey, Quintiere & Harkleroad (1981)
• Assumed only two-zones with Th uniform in hot upper layer
and To uniform in cool lower layer
• Developed correlation for average temperature of hot layer
• Not interested in smoke filling but flashover
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4
• First Step: Simplify energy balance eqn for hot layer
by neglecting radiant heat loss through openings
Q  m h c P Th  To   q LOSS



Eqn (10-1)

Q = heat release rate of fire (kW)

m h = mass flow rate of hot gas out vent (kg s-1)
cp = specific heat of hot gas (kJ kg-1 K-1)
Th = temperature of hot gas (K)

q LOSS = net heat loss: hot layer to room boundaries (kW)
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5

• Second Step: Develop approximation for q LOSS
• Assume surface temperature of boundaries equals
temperature of hot layer, so heat loss to boundaries is
governed by heat conduction through boundaries and
q LOSS  h k A T Th  TO 

Eqn (10-2)
hk = effective heat transfer coefficient (kW m-2 K-1)
AT = total surface area of enclosure boundaries (m2)
• Note: no dependence on Ts (boundary surface temp)
• Note: Eqn is linearized no Th4 or Ts4
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6
• Third Step: Develop expressions for hk
• The quasi steady-state approximation:
• For long times or thin boundaries assume Fourier’s
law applies to heat conduction across the boundaries

q" 

k

Th  To 
Eqn (10-3)
q" = heat flux through the boundary (kW m-2)
k = thermal conductivity of the boundary (kW m-1K-1)
 = thickness of the boundary (m)
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7
• The quasi steady-state approximation:
• From Eqns (10-2) and (10-3) one can conclude that
hk 
k

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Dynamics II, Winter 2003, Lecture #
Eqn (10-4)
8
• The transient approximation:
• For short times or thick boundaries (Slides 6-10 & 6-11)

q"LOSS
Semi-finite solid
x
• Assume solid is initially at To

• For t  0, heat flux q"LOSS (W m-2) absorbed at surface
• Solve Eqn (5-9) of Fire Dynamics I subject to initial
condition & two boundary conditions
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Dynamics II, Winter 2003, Lecture #
9

q"LOSS  q
Transient Conduction with
• Solution for surface temperature is Ts
T
S
•
 TO  
2

q
t
kc
Eqn (10-5)
kc = thermal inertia (kJ m-2 s1/2 K-1)
• Solving Eqn (10-5) for heat flux from upper layer to
boundaries yields

q"LOSS 

2
kc
Th  TO 
t
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Dynamics II, Winter 2003, Lecture #
Eqn (10-6)
10
• The transient approximation:
• From Eqns (10-2) and (10-6) one can conclude that
kc
hk 
t
Eqn (10-7)
kc = thermal inertia of boundaries (kJ m-2 s-1/2 K-1)
t = duration of exposure (s)
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11
• The transient approximation:
kc
hk 
t
Eqn (10-7)
• The quasi steady-state approximation:
hk 
k

Eqn (10-4)
• The larger of the two governs. The transient approx
holds from the beginning of the fire until the quasi
steady-state approx takes over.
Carleton University, 82.583, Fire
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12
Transition from transient approximation to
quasi steady-state approximation occurs when
kc


t
k
or when
t  tp 
c
k

2
Eqn (10-8)
• tp can be thought of as a thermal penetration time
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13
• If there are several boundary materials, compute hk for
each material separately, then compute an effective
hk as the area-weighted average
h k 
EFF

i A i h k,i
AT
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Eqn (10-9)
14
• Fourth Step: Solve conservation of energy equation
to find temperature
• Substitute Eqn (10-2) into Eqn (10-1) & solve for Th



Q

Th  To   
 cP mh  h AT 


k
Eqn (10-10)
• Set Th = Th - To & introduce dimensionless variables

Q
 c T m h 
P o
Th



To
 h AT

k

1 



c
m
h


P

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Eqn (10-11)
15

• Fifth Step: Simplify description of m h
• Substituting zh = h - zo into Eqn (4-23) yields

2
m h  C b h 3/2  o
3
3/ 2


To  To   z o 
2 1   g 1 - 
Th  Th   h 
• For pre-flashover fires: 373 K < Th < 873 K
• page 4-44 
• page 4-38 
To  To 
1   ~ 0.46

Th  Th 
 zo 
1 - 
 h
3/2
~ 0.41
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• Consequently one can write

mh   A g h
(kg s 1 )
o
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17
• Sixth Step: Seek a solution in terms of dimensionless
variables of the form


Q

Th  CT 
 c P TO  O A g h 



x
 h k AT 


 cP O A g h 
y
Eqn (10-12)


Q

 ~ dimensionl ess rate of heat release
 c P TO  O A g h 



 h k AT 

 ~ dimensionl ess rate of heat loss to boundaries
 cP O A g h 
Carleton University, 82.583, Fire
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18
• Seventh Step: determine x, y and CT by correlating
with data from 100 experiments.
• Description of experiments
• Steady state and transient fires
• Cellulosic, plastic & gaseous fuels
• Compartment height: 0.3 m < H < 2.7 m
• Floor area: 0.14 m2 < area < 12.0 m2
• Variety of window / door sizes
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• Findings:
• x = N = 2/3
• y = M = - 1/3
• CT = 480 K
• Rewrite Eqn (10-12)
Th  CT X1  X 2 
N
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M
Eqn (10-13)
20
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21
Correlation for Temperature
• Substituting ambient values
• o = 1.2 kg m-3
• g = 9.81 m s-2
• cp = 1.05 kJ kg-1 K-1
• To = 295 K
1/ 3


Q


Th  6.85

A
h
h
A

k
T 



2
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Eqn (10-14)
22
McCaffrey, Quintiere & Harkleroad Correlation
• Early in pre-flashover fire (if t < tp,i for each boundary)
1/ 3


Q t


Th  6.85

A
h
A
k

c


T



2
AT kc  i Ai k i i ci
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Eqn (10-14)
Eqn (10-15)
23
McCaffrey, Quintiere & Harkleroad Correlation
• Later in pre-flashover fire (if t > tp,i for each boundary)
1/ 3


Q


Th  6.85
 A h A T (k/ ) 


Eqn (10-16)
A T (k/ )  i A i (k i / i )
Eqn (10-17)

2
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Comments: MQH Correlation
1. Heat release rate is input: Determined by experiment
or other models
2. Not applicable to rapidly developing fires in large
enclosures in which significant fire growth occurs
before combustion products exit the compartment.
3. Heat release rate is limited by available ventilation:

Q  1,500 A h
(kW)
4. Correlation based on data from experiments with fuel
near centre of room // no combustible walls or ceilings
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Comments: MQH Correlation
5. Correlation validated by MQH for T < 600°C
6. Correlation applies to steady-state as well as timedependent fires, provided primary transient response
is the wall conduction problem
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26
Experiments: Mehaffey & Harmathy, 1985
• 32 room fire experiments
– Fuel: wooden cribs
– Fuel load: simulated hotel & office rooms
• Room Dimensions
– Floor: 2.4 m x 3.6 m
– Ceiling height: 2.4 m
• Ventilation opening
– Open throughout test
• Purpose of experiments
– Assess thermal response of room boundaries exposed
to post-flashover fires
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Impact of boundary (thermal properties)
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Impact of boundary (thermal properties)
• Fuel: wooden cribs: 15 kg m-2 (hotel)
• Window: area = 9% area of floor
– b =0.7 m; h =1.2 m; A h = 0.92 m5/2
• Post-flashover fire: ventilation controlled
– rate of heat release = 970 kW ~ 1 MW
• . . . . “Standard fire” CAN4-S101 (ASTM E119)
Room
1
2
kc (J m-2 s-1/2 K-1)
868
334
2
-4
-1
-2
kc (kJ m s K )
0.753
0.112
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Thermal Properties
At elevated temperatures associated with fire
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Impact of size of openings
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31
Impact of size of openings
• Fuel: wooden cribs: 27 kg m-2 (office)
• Thermal inertia of room boundaries
–
kc = 666 J m-2 s-1/2 K-1
– kc = 0.444 kJ2 m-4 s-1 K-2
• Post-flashover fire: ventilation controlled
• . . . . “Standard fire” CAN4-S101 (ASTM E119)
5/2
Room
b (m)
h (m)
A h (m )
3
4
5
0.7
0.7
0.7
1.2
1.6
2.1
0.92
1.42
2.13
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
Q (kW)
970
1,490
2,240
32
Example
• Room with dimensions: 3.0 m x 3.0 m x 2.4 m (high)
• Door (open) with dimensions: 0.8 m x 2.0 m
– A h = 2.26 m5/2
• Walls & ceiling: fire-rated gypsum board
– Surface area (gypsum) = A1
– A1 = {3 x 3 + 4 x 3 x 2.4 - 0.8 x 2} m2 = 36.2 m2
• Floor: wood
– Surface area (wood) = A2
– A2 = 3 x 3 m2 = 9 m2
• Total area of surface boundaries:
– AT = A1 + A2 = 36.2 m2 + 9 m2 = 45.2 m2
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33
Example
• Walls & ceiling: fire-rated gypsum board (1layer each
side of studs)
• k = 0.27 x 10-3 kW m-1K-1
•  = 680 kg m-3
• c = 3.0 kJ kg-1 K-1
•  = 2 x 12.7 mm = 0.0254 m
• Walls & ceiling: thermal penetration time
c 2
t p,1    4880 s  81.3 min
k
• Walls & ceiling: thermal inertia
kc = 0.742 kJ m-2 s1/2 K-1
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Example
• Floor: wood
• k = 0.15 x 10-3 kW m-1K-1
•  = 550 kg m-3
• c = 2.3 kJ kg-1 K-1
•  = 25.4 mm = 0.0254 m
• Floor: thermal penetration time
c 2
t p,2    5440 s  90.7 min
k
• Floor: thermal inertia
kc = 0.436 kJ m-2 s1/2 K-1
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35
Example
• The fire: Heat release rate is limited by ventilation:

Q  1,500 A h  3,390 kW
• Consider an upholstered chair that burns in the room
for 4 minutes at a heat release rate of

Q  1,000 kW
• Clealy t < tp,i for both boundary materials so
AT kc  i Ai k i i ci  (36.2 x 0.742 + 9 x 0.436) kJ s1/2 K-1
= 30.78 kJ s1/2 K-1
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Example
• The temperature is given by
1/ 3


Q t


Th  6.85
 A h A T kc 



2
1/ 3
 (1,000) t 

Th  6.85
 2.26 x 30.78 
2
Th  167 t
1/6
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Example
• The temperature is given by
Th  167 t
1/6
t (s)
0
30
60
120
180
240
Th (C)
0
294
330
371
397
416
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38
Rate of Heat Release Required for Flashover
McCaffrey, Quintiere & Harkleroad
• Conservative flashover criterion: Th = 500°C

• Substitute Th = 500°C into Eqn (10-14) & solve for Q


QFO  610 h k AT A h


1/2
Eqn (10-17)

• Q FO = minimum Q required for flashover (kW)
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39
Rate of Heat Release Required for Flashover (MQH)


• For t < tp,i (for each boundary) Q FO is minimum Q
required for flashover in time t (s) & is given by
1/2
 (kc)EFF
 Eqn (10-18)
QFO (t  t p,i )  610 
AT A h 
t



• For t > tp,i (for each boundary)
quasi steady-state heat

flow
is achieved so Q FO becomes absolute minimum

Q required for flashover & is given by


Q FO ( t  t p,i )  610 (k/ ) EFF A T A h
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
1/2
Eqn (10-19)
40
Rate of Heat Release Required for Flashover
Babrauskas
• Theoretical maximum heat release rate is

QMAX  1,500 A h
(kW)
• Developed correlation using experimental data
• 33 room fires involving wood & polyurethane
• Ventilation factor: 0.03 m5/2 < A h< 7.31 m5/2
• Surface area: 9 m-1/2 < A T A h < 65 m-1/2
• Finding:

QFO  750 A h
(kW)
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Eqn (10-20)
41
Rate of Heat Release Required for Flashover
Thomas
• Heat balance for hot layer is
Q  m h c P Th  To   q LOSS



• Assumptions at flashover:

• mass flow rate m h ~ 0.5 A h
• cp = 1.26 kJ kg-1 K-1
• Th = 600 K

• Correlation with experimental data: q loss ~ 7.8 AT
• Finding:

QFO  378 A h  7.8 AT
(kW)
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Eqn (10-21)
42
Rate of Heat Release Required for Flashover
Example: Same room as in Slides 10-33 to 10-38
Babrauskas

QFO  750 A h  750 x 2.26  1,700 kW
Thomas

QFO  378 A h  7.8 AT  378 x 2.26  7.8 x 45.2  1,210 kW
MQH


QFO  610 (k/ ) EFF AT A h

1/2
= 610 (0.438 x 2.26)1/2 = 610 kW
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43
Rate of Heat Release Required for Flashover
within 10 minutes = 600 s
MQH
 (kc)EFF

QFO (t  t p,i )  610 
AT A h 
t



1/2
= 610 (30.78 / 24.5 x 2.26)1/2
= 1030 kW
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44
Correlation for Temperature
Foote, Pagni & Alvares
• Correlation for forced-ventilation fires
 Q 
Th

 0.63  
 mO c T 
TO

P O 

0.72
h A 
 k T

m

O c

P 
0.36
Eqn (10-22)

• mO = mass supply rate (kg s-1)
• Correlation developed using experimental data
•
•
•
•
Methane gas burner: 150 to 490 kW
Room: 6 m x 4 m & height of 4.5 m
Air supply rate: 0.110 to 0.325 kg s-1
Measured temperatures: 100 to 300°C
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45
Time to Flashover in a Room with
Combustible Linings (Wall & Ceiling)
• Theory developed by Karlsson, 1989
• Predicts time to flashover in room-fire test (ISO 9705)
• Depends on data generated in small-scale tests
– Cone calorimeter (characterizes heat release rate)
– LIFT apparatus (characterizes lateral flame-spread)
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46
Cone Calorimeter (3) - ISO 5660 & ASTM E1354
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Cone Calorimeter Data - Thermoset
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Model for a Thermoset


Q"max , t ig and  depend on q"E
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49
Opposed Flow Spread
• Quintiere and Harkleroad, 1985

v
2
kc Tig  TS 
•  = flame-heating parameter (kW2 m-3) {material property}
• Provided no dripping, this model holds for
– downward flame spread (wall)
– lateral flame spread (wall)
– horizontal flame spread (floor)
• , kc and Tig - measured (LIFT apparatus)
• Ts - depends on scenario (external flux)
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50
LIFT Apparatus
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Karlsson Correlation
• Cone calorimeter results


Q"max and  at q"E  30 kW m
2
• LIFT results


kc
• Time to flashover in ISO 9705 room test
t FO  3.08 x 10 (kc) 
5
0.75
0.37
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
 (Q"MAX )
0.11
0.52
52