1. Fire Dynamics II Lecture # 10 Pre-flashover Fire Jim Mehaffey 82.583
Carleton University, , Fire Dynamics II, Winter 2003, Lecture # 10

2. Pre-flashover Fire Outline
Develop a model to predict:
Upper layer temperature (function of time)
required for flashover
Time to flashover
Carleton University, , Fire Dynamics II, Winter 2003, Lecture # 10

3. 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, , Fire Dynamics II, Winter 2003, Lecture # 10

4. 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
Carleton University, , Fire Dynamics II, Winter 2003, Lecture # 10

5. = heat release rate of fire (kW)
First Step: Simplify energy balance eqn for hot layer by neglecting radiant heat loss through openings
Eqn (10-1)
= heat release rate of fire (kW)
= 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)
= net heat loss: hot layer to room boundaries (kW)
Carleton University, , Fire Dynamics II, Winter 2003, Lecture # 10

6. Second Step: Develop approximation for
Assume surface temperature of boundaries equals temperature of hot layer, so heat loss to boundaries is governed by heat conduction through boundaries and
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
Carleton University, , Fire Dynamics II, Winter 2003, Lecture # 10

7. 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
Eqn (10-3)
= heat flux through the boundary (kW m-2)
k = thermal conductivity of the boundary (kW m-1K-1)
 = thickness of the boundary (m)
Carleton University, , Fire Dynamics II, Winter 2003, Lecture # 10

8. The quasi steady-state approximation:
From Eqns (10-2) and (10-3) one can conclude that
Eqn (10-4)
Carleton University, , Fire Dynamics II, Winter 2003, Lecture # 10

9. For short times or thick boundaries (Slides 6-10 & 6-11)
The transient approximation:
For short times or thick boundaries (Slides 6-10 & 6-11)
Semi-finite solid x
Assume solid is initially at To
For t  0, heat flux (W m-2) absorbed at surface
Solve Eqn (5-9) of Fire Dynamics I subject to initial condition & two boundary conditions
Carleton University, , Fire Dynamics II, Winter 2003, Lecture # 10

10. Transient Conduction with Solution for surface temperature is Ts
Eqn (10-5)
= thermal inertia (kJ m-2 s1/2 K-1)
Solving Eqn (10-5) for heat flux from upper layer to boundaries yields
Eqn (10-6)
Carleton University, , Fire Dynamics II, Winter 2003, Lecture # 10

11. The transient approximation:
From Eqns (10-2) and (10-6) one can conclude that
Eqn (10-7)
= thermal inertia of boundaries (kJ m-2 s-1/2 K-1)
t = duration of exposure (s)
Carleton University, , Fire Dynamics II, Winter 2003, Lecture # 10

12. The transient approximation: Eqn (10-7)
The quasi steady-state approximation:
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, , Fire Dynamics II, Winter 2003, Lecture # 10

13. Transition from transient approximation to
quasi steady-state approximation occurs when
or when
Eqn (10-8)
tp can be thought of as a thermal penetration time
Carleton University, , Fire Dynamics II, Winter 2003, Lecture # 10

14. If there are several boundary materials, compute hk for each material separately, then compute an effective hk as the area-weighted average
Eqn (10-9)
Carleton University, , Fire Dynamics II, Winter 2003, Lecture # 10

15. Fourth Step: Solve conservation of energy equation to find temperature
Substitute Eqn (10-2) into Eqn (10-1) & solve for Th
Eqn (10-10)
Set Th = Th - To & introduce dimensionless variables
Eqn (10-11)
Carleton University, , Fire Dynamics II, Winter 2003, Lecture # 10

16. Fifth Step: Simplify description of
Substituting zh = h - zo into Eqn (4-23) yields
For pre-flashover fires: 373 K < Th < 873 K
page 4-44 
page 4-38 
Carleton University, , Fire Dynamics II, Winter 2003, Lecture # 10

17. Consequently one can write
Carleton University, , Fire Dynamics II, Winter 2003, Lecture # 10

18. Sixth Step: Seek a solution in terms of dimensionless variables of the form
Eqn (10-12)
Carleton University, , Fire Dynamics II, Winter 2003, Lecture # 10

19. Description of experiments Steady state and transient fires
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
Carleton University, , Fire Dynamics II, Winter 2003, Lecture # 10

20. Findings: x = N = 2/3 y = M = - 1/3 CT = 480 K Rewrite Eqn (10-12)
Carleton University, , Fire Dynamics II, Winter 2003, Lecture # 10

21. Carleton University, 82.583, Fire Dynamics II, Winter 2003, Lecture # 10

22. 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
Eqn (10-14)
Carleton University, , Fire Dynamics II, Winter 2003, Lecture # 10

23. McCaffrey, Quintiere & Harkleroad Correlation
Early in pre-flashover fire (if t < tp,i for each boundary)
Eqn (10-14)
Eqn (10-15)
Carleton University, , Fire Dynamics II, Winter 2003, Lecture # 10

24. McCaffrey, Quintiere & Harkleroad Correlation
Later in pre-flashover fire (if t > tp,i for each boundary)
Eqn (10-16)
Eqn (10-17)
Carleton University, , Fire Dynamics II, Winter 2003, Lecture # 10

25. 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:
4. Correlation based on data from experiments with fuel near centre of room // no combustible walls or ceilings
Carleton University, , Fire Dynamics II, Winter 2003, Lecture # 10

26. Comments: MQH Correlation
5. Correlation validated by MQH for T < 600°C
6. Correlation applies to steady-state as well as time-dependent fires, provided primary transient response is the wall conduction problem
Carleton University, , Fire Dynamics II, Winter 2003, Lecture # 10

27. 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
Carleton University, , Fire Dynamics II, Winter 2003, Lecture # 10

28. Impact of boundary (thermal properties)
Carleton University, , Fire Dynamics II, Winter 2003, Lecture # 10

29. 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; = 0.92 m5/2
Post-flashover fire: ventilation controlled
rate of heat release = 970 kW ~ 1 MW
“Standard fire” CAN4-S101 (ASTM E119)
Carleton University, , Fire Dynamics II, Winter 2003, Lecture # 10

30. At elevated temperatures associated with fire
Thermal Properties
At elevated temperatures associated with fire
Carleton University, , Fire Dynamics II, Winter 2003, Lecture # 10

31. Impact of size of openings
Carleton University, , Fire Dynamics II, Winter 2003, Lecture # 10

32. Impact of size of openings
Fuel: wooden cribs: 27 kg m-2 (office)
Thermal inertia of room boundaries
= 666 J m-2 s-1/2 K-1
kc = kJ2 m-4 s-1 K-2
Post-flashover fire: ventilation controlled
“Standard fire” CAN4-S101 (ASTM E119)
Carleton University, , Fire Dynamics II, Winter 2003, Lecture # 10

33. 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
= 2.26 m5/2
Walls & ceiling: fire-rated gypsum board
Surface area (gypsum) = A1
A1 = {3 x x 3 x 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
Carleton University, , Fire Dynamics II, Winter 2003, Lecture # 10

34. 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 = m
Walls & ceiling: thermal penetration time
Walls & ceiling: thermal inertia
= kJ m-2 s1/2 K-1
Carleton University, , Fire Dynamics II, Winter 2003, Lecture # 10

35. 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 = m
Floor: thermal penetration time
Floor: thermal inertia
= kJ m-2 s1/2 K-1
Carleton University, , Fire Dynamics II, Winter 2003, Lecture # 10

36. Example The fire: Heat release rate is limited by ventilation:
Consider an upholstered chair that burns in the room for 4 minutes at a heat release rate of
Clealy t < tp,i for both boundary materials so
(36.2 x x 0.436) kJ s1/2 K-1
= kJ s1/2 K-1
Carleton University, , Fire Dynamics II, Winter 2003, Lecture # 10

37. Example The temperature is given by
Carleton University, , Fire Dynamics II, Winter 2003, Lecture # 10

38. Example The temperature is given by
Carleton University, , Fire Dynamics II, Winter 2003, Lecture # 10

39. 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
Eqn (10-17)
= minimum required for flashover (kW)
Carleton University, , Fire Dynamics II, Winter 2003, Lecture # 10

40. Rate of Heat Release Required for Flashover (MQH)
For t < tp,i (for each boundary) is minimum required for flashover in time t (s) & is given by
Eqn (10-18)
For t > tp,i (for each boundary) quasi steady-state heat flow is achieved so becomes absolute minimum required for flashover & is given by
Eqn (10-19)
Carleton University, , Fire Dynamics II, Winter 2003, Lecture # 10

41. Rate of Heat Release Required for Flashover Babrauskas
Theoretical maximum heat release rate is
Developed correlation using experimental data
33 room fires involving wood & polyurethane
Ventilation factor: 0.03 m5/2 < < 7.31 m5/2
Surface area: 9 m-1/2 < < 65 m-1/2
Finding:
Eqn (10-20)
Carleton University, , Fire Dynamics II, Winter 2003, Lecture # 10

42. Rate of Heat Release Required for Flashover Thomas
Heat balance for hot layer is
Assumptions at flashover:
mass flow rate
cp = kJ kg-1 K-1
Th = 600 K
Correlation with experimental data:
Finding:
Eqn (10-21)
Carleton University, , Fire Dynamics II, Winter 2003, Lecture # 10

43. Rate of Heat Release Required for Flashover
Example: Same room as in Slides to 10-38
Babrauskas
Thomas
MQH
= 610 (0.438 x 2.26)1/2 = 610 kW
Carleton University, , Fire Dynamics II, Winter 2003, Lecture # 10

44. Rate of Heat Release Required for Flashover
within 10 minutes = 600 s
MQH
= 610 (30.78 / x 2.26)1/2
= 1030 kW
Carleton University, , Fire Dynamics II, Winter 2003, Lecture # 10

45. Correlation for Temperature
Foote, Pagni & Alvares
Correlation for forced-ventilation fires
Eqn (10-22)
= 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: to kg s-1
Measured temperatures: 100 to 300°C
Carleton University, , Fire Dynamics II, Winter 2003, Lecture # 10

46. 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)
Carleton University, , Fire Dynamics II, Winter 2003, Lecture # 10

47. Cone Calorimeter (3) - ISO 5660 & ASTM E1354
Carleton University, , Fire Dynamics II, Winter 2003, Lecture # 10

48. Cone Calorimeter Data - Thermoset
Carleton University, , Fire Dynamics II, Winter 2003, Lecture # 10

49. Model for a Thermoset
Carleton University, , Fire Dynamics II, Winter 2003, Lecture # 10

50. Quintiere and Harkleroad, 1985
Opposed Flow Spread
Quintiere and Harkleroad, 1985
 = 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)
Carleton University, , Fire Dynamics II, Winter 2003, Lecture # 10

51. LIFT Apparatus
Carleton University, , Fire Dynamics II, Winter 2003, Lecture # 10

52. Karlsson Correlation Cone calorimeter results LIFT results
Time to flashover in ISO 9705 room test
Carleton University, , Fire Dynamics II, Winter 2003, Lecture # 10