Carleton University, 82.583, Fire Dynamics II, Winter 2003, Lecture # 10 1 Fire Dynamics II Lecture...

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

1

Fire Dynamics IIFire Dynamics II

Lecture # 10Lecture # 10

Pre-flashover FirePre-flashover FireJim MehaffeyJim Mehaffey

82.58382.583


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Pre-flashover FirePre-flashover Fire

OutlineOutline

• Develop a model to predict:Develop a model to predict:

– Upper layer temperature (function of time)Upper layer temperature (function of time)

– required for flashoverrequired for flashover

– Time to flashoverTime to flashover

Q


3

Predicting Pre-flashover Fire TemperaturesPredicting Pre-flashover Fire Temperatures

• In principle, solve complex set of equations presented In principle, solve complex set of equations presented in Lecture 7 in Lecture 7 Heat Transfer in Enclosure FiresHeat Transfer in Enclosure Fires for: for:– location of neutral planelocation of neutral plane– time-dependent mass flow ratestime-dependent mass flow rates– time dependent hot gas temperaturestime dependent hot gas temperatures– time dependent surface temperaturestime dependent surface temperatures

• An approximate solution developed in 1981 provides a An approximate solution developed in 1981 provides a simple alternative which is useful for:simple alternative which is useful for:– Understanding roles of variables in pre-flashover fireUnderstanding roles of variables in pre-flashover fire– Design purposes in simple applicationsDesign purposes in simple applications– Developing “first cut” designs in complex applicationsDeveloping “first cut” designs in complex applications– Forensic investigations: “simple” cases or “first cut”Forensic investigations: “simple” cases or “first cut”


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McCaffrey, Quintiere & Harkleroad (1981)McCaffrey, Quintiere & Harkleroad (1981)• Assumed only two-zones with TAssumed only two-zones with Thh uniform in hot upper layer uniform in hot upper layer

and Tand Too uniform in cool lower layer uniform in cool lower layer

• Developed correlation for average temperature of hot layerDeveloped correlation for average temperature of hot layer• Not interested in smoke filling but flashoverNot interested in smoke filling but flashover


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• First Step:First Step: Simplify energy balance eqn for hot layer Simplify energy balance eqn for hot layer by neglecting radiant heat loss through openingsby neglecting radiant heat loss through openings

Eqn (10-Eqn (10-1)1)

= heat release rate of fire (kW)= heat release rate of fire (kW)

= mass flow rate of hot gas out vent (kg s= mass flow rate of hot gas out vent (kg s -1-1))

ccpp = specific heat of hot gas (kJ kg = specific heat of hot gas (kJ kg -1-1 K K-1-1))

TThh = temperature of hot gas (K) = temperature of hot gas (K)

= net heat loss: hot layer to room boundaries (kW)= net heat loss: hot layer to room boundaries (kW)

LOSSPqTTcmQ ohh

Q

hm

LOSSq


6

• Second Step:Second Step: Develop approximation for Develop approximation for

• Assume surface temperature of boundaries equals Assume surface temperature of boundaries equals temperature of hot layer, so heat loss to boundaries is temperature of hot layer, so heat loss to boundaries is governed by heat conduction through boundaries andgoverned by heat conduction through boundaries and

Eqn (10-Eqn (10-2)2)

hhkk = effective heat transfer coefficient (kW m = effective heat transfer coefficient (kW m -2-2 K K-1-1))

AATT = total surface area of enclosure boundaries (m = total surface area of enclosure boundaries (m22))

• Note: no dependence on TNote: no dependence on Tss (boundary surface temp) (boundary surface temp)

• Note: Eqn is linearized no TNote: Eqn is linearized no Thh44 or T or Tss

44

LOSSq

OTLOSS TTA hq

hk


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• Third Step:Third Step: Develop expressions for h Develop expressions for hkk

• The quasi steady-state approximationThe quasi steady-state approximation::

• For long times or thin boundaries assume Fourier’s For long times or thin boundaries assume Fourier’s law applies to heat conduction across the boundarieslaw applies to heat conduction across the boundaries

Eqn (10-Eqn (10-3) 3)

= heat flux through the boundary (kW m= heat flux through the boundary (kW m-2-2))

k = thermal conductivity of the boundary (kW mk = thermal conductivity of the boundary (kW m -1-1KK-1-1))

= thickness of the boundary (m)= thickness of the boundary (m)

ohTT

k"q

"q


8


• From Eqns (10-2) and (10-3) one can conclude thatFrom Eqns (10-2) and (10-3) one can conclude that

Eqn (10-Eqn (10-4) 4)

kh

k


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• The transient approximationThe transient approximation::

• For short times or thick boundaries For short times or thick boundaries (Slides 6-10 & 6-11)(Slides 6-10 & 6-11)

Semi-finite solidSemi-finite solid

xx

• AssumeAssume solid is initially at Tsolid is initially at Too

• For t For t 0, heat flux (W m 0, heat flux (W m-2-2) absorbed at surface) absorbed at surface

• Solve Eqn (5-9) of Fire Dynamics I subject to initial Solve Eqn (5-9) of Fire Dynamics I subject to initial condition & two boundary conditionscondition & two boundary conditions

LOSS"q

LOSS"q


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Transient Conduction withTransient Conduction with

• Solution for surface temperature is TSolution for surface temperature is Tss

Eqn (10-Eqn (10-5)5)

• = thermal inertia (kJ m= thermal inertia (kJ m-2-2 s s1/21/2 K K-1-1))

• Solving Eqn (10-5) for heat flux from upper layer to Solving Eqn (10-5) for heat flux from upper layer to boundaries yieldsboundaries yields

Eqn (10-Eqn (10-6) 6)

ck

q"qLOSS

ck

tq

2TT

OS

OLOSS

TTt

ck

2"q

h


11


• From Eqns (10-2) and (10-6) one can conclude thatFrom Eqns (10-2) and (10-6) one can conclude that

Eqn (10-Eqn (10-7)7)

= thermal inertia of boundaries (kJ m= thermal inertia of boundaries (kJ m-2-2 s s-1/2-1/2 K K--

11))

t = duration of exposure (s)t = duration of exposure (s)

t

ckh

k

ck


12


Eqn (10-Eqn (10-7)7)


Eqn (10-Eqn (10-4)4)

• The larger of the two governs. The transient approx The larger of the two governs. The transient approx holds from the beginning of the fire until the quasi holds from the beginning of the fire until the quasi steady-state approx takes over. steady-state approx takes over.

t

ckh

k

k

hk


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Transition from transient approximation toTransition from transient approximation to

quasi steady-state approximation occurs whenquasi steady-state approximation occurs when

or whenor when

Eqn (10-Eqn (10-8)8)

• ttpp can be thought of as a thermal penetration time can be thought of as a thermal penetration time

t

ckk

2

p k

ctt


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• If there are several boundary materials, compute hIf there are several boundary materials, compute hkk for for

each material separately, then compute an effective each material separately, then compute an effective hhkk as the area-weighted average as the area-weighted average

Eqn (10-Eqn (10-9)9)

T

EFF A

hA h

i ik,ik


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• Fourth Step:Fourth Step: Solve conservation of energy equation Solve conservation of energy equation to find temperature to find temperature

• Substitute Eqn (10-2) into Eqn (10-1) & solve for TSubstitute Eqn (10-2) into Eqn (10-1) & solve for Thh

Eqn (10-Eqn (10-10)10)

• Set Set TThh = T = Thh - T - To o & introduce dimensionless variables& introduce dimensionless variables

Eqn (10-Eqn (10-11)11)

TPA hmc

QTT

khoh

h

k

ho

o

h

mc

A h1

mTc

Q

T

T

P

T

P


16

• Fifth Step:Fifth Step: Simplify description of Simplify description of

• Substituting zSubstituting zhh = h - z = h - zoo into Eqn (4-23) yields into Eqn (4-23) yields

• For pre-flashover fires: 373 K < TFor pre-flashover fires: 373 K < Thh < 873 K < 873 K

• page 4-44 page 4-44

• page 4-38 page 4-38

hm

2/3

3/2

h

z-1 g

T

T1

T

T 2 h b Cm o

h

o

h

oh o

3

2

0.46 ~ T

T1

T

T

h

o

h

o

0.41 ~ h

z-1

3/2

o


17

• Consequently one can writeConsequently one can write

)s (kg h gA m 1h

o


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• Sixth Step:Sixth Step: Seek a solution in terms of dimensionless Seek a solution in terms of dimensionless variables of the formvariables of the form

Eqn (10-Eqn (10-12)12)

yx

OO

h gAc

A h

h gATc

QCT

P

Tk

OP

Th

releaseheat of rate essdimensionl~h gATc

Q

OP

O

boundaries tolossheat of rate essdimensionl~h gAc

A h

P

Tk

O


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• Seventh Step:Seventh Step: determine x, y and C determine x, y and CTT by correlating by correlating

with data from 100 experiments. with data from 100 experiments.

• Description of experimentsDescription of experiments• Steady state and transient firesSteady state and transient fires• Cellulosic, plastic & gaseous fuelsCellulosic, plastic & gaseous fuels• Compartment height: 0.3 m < H < 2.7 mCompartment height: 0.3 m < H < 2.7 m• Floor area: 0.14 mFloor area: 0.14 m22 < area < 12.0 m < area < 12.0 m22 • Variety of window / door sizesVariety of window / door sizes


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• Findings:Findings:• x = N = 2/3x = N = 2/3• y = M = - 1/3y = M = - 1/3

• CCTT = 480 K = 480 K

• Rewrite Eqn (10-12)Rewrite Eqn (10-12)

Eqn (10-Eqn (10-13)13)

MN21Th

XXCT


21


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Correlation for TemperatureCorrelation for Temperature

• Substituting ambient valuesSubstituting ambient valuesoo = 1.2 kg m = 1.2 kg m-3-3

• g = 9.81 m sg = 9.81 m s-2-2

• ccpp = 1.05 kJ kg = 1.05 kJ kg-1 -1 KK-1-1

• TToo = 295 K = 295 K

Eqn (10-Eqn (10-14)14)

3/1

Tk

h Ah hA

Q6.85T

2


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McCaffrey, Quintiere & Harkleroad CorrelationMcCaffrey, Quintiere & Harkleroad Correlation

• Early in pre-flashover fire (if t < tEarly in pre-flashover fire (if t < tp,ip,i for each boundary) for each boundary)

Eqn (10-Eqn (10-14)14)

Eqn (10-Eqn (10-15)15)

3/1

ckA hA

tQ6.85T

T

h

2

iiii ickA ckA

T


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McCaffrey, Quintiere & Harkleroad CorrelationMcCaffrey, Quintiere & Harkleroad Correlation

• Later in pre-flashover fire (if t > tLater in pre-flashover fire (if t > tp,ip,i for each boundary) for each boundary)

Eqn (10-Eqn (10-16)16)

Eqn (10-Eqn (10-17)17)

3/1

)k/(A hA

Q6.85T

T

h

2

)/k(A )k/(Aiii iT


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Comments: MQH CorrelationComments: MQH Correlation

1. Heat release rate is input: Determined by experiment 1. Heat release rate is input: Determined by experiment or other modelsor other models

2. Not applicable to rapidly developing fires in large 2. Not applicable to rapidly developing fires in large enclosures in which significant fire growth occurs enclosures in which significant fire growth occurs before combustion products exit the compartment.before combustion products exit the compartment.

3.3. Heat release rate is limited by available ventilation:Heat release rate is limited by available ventilation:

4. Correlation based on data from experiments with fuel 4. Correlation based on data from experiments with fuel near centre of room // no combustible walls or ceilingsnear centre of room // no combustible walls or ceilings

(kW) hA 1,500Q


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Comments: MQH CorrelationComments: MQH Correlation

5. Correlation validated by MQH for T < 600°C5. Correlation validated by MQH for T < 600°C

6.6. Correlation applies to steady-state as well as time-Correlation applies to steady-state as well as time-dependent fires, provided primary transient response dependent fires, provided primary transient response is the wall conduction problemis the wall conduction problem


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Experiments: Mehaffey & Harmathy, 1985Experiments: Mehaffey & Harmathy, 1985• 32 room fire experiments32 room fire experiments

– Fuel: wooden cribsFuel: wooden cribs

– Fuel load: simulated hotel & office roomsFuel load: simulated hotel & office rooms

• Room DimensionsRoom Dimensions

– Floor: 2.4 m x 3.6 mFloor: 2.4 m x 3.6 m

– Ceiling height: 2.4 mCeiling height: 2.4 m

• Ventilation openingVentilation opening

– Open throughout testOpen throughout test

• Purpose of experimentsPurpose of experiments

– Assess thermal response of room boundaries exposed Assess thermal response of room boundaries exposed to post-flashover firesto post-flashover fires


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Impact of boundary (thermal properties) Impact of boundary (thermal properties)


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Impact of boundary (thermal properties) Impact of boundary (thermal properties) • Fuel: wooden cribs: 15 kg mFuel: wooden cribs: 15 kg m-2-2 (hotel) (hotel)• Window: area = 9% area of floorWindow: area = 9% area of floor

– b =0.7 m; h =1.2 m; = 0.92 mb =0.7 m; h =1.2 m; = 0.92 m5/25/2

• Post-flashover fire: ventilation controlledPost-flashover fire: ventilation controlled

– rate of heat release = 970 kW ~ 1 MWrate of heat release = 970 kW ~ 1 MW

• . . . . “Standard fire” CAN4-S101 (ASTM E119). . . . “Standard fire” CAN4-S101 (ASTM E119)

hA

Room ck (J m-2 s-1/2 K-1)kc (kJ2 m-4 s-1 K-2)1 868 0.7532 334 0.112


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Thermal PropertiesThermal PropertiesAt elevated temperatures associated with fireAt elevated temperatures associated with fire


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Impact of size of openings Impact of size of openings


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Impact of size of openings Impact of size of openings • Fuel: wooden cribs: 27 kg mFuel: wooden cribs: 27 kg m-2-2 (office) (office)• Thermal inertia of room boundariesThermal inertia of room boundaries

– = 666 J m-2 s-1/2 K-1

– kc = 0.444 kJ2 m-4 s-1 K-2

• Post-flashover fire: ventilation controlledPost-flashover fire: ventilation controlled

• . . . . “Standard fire” CAN4-S101 (ASTM E119). . . . “Standard fire” CAN4-S101 (ASTM E119)

ck

Roomb (m)h (m) hA (m5/2)

Q (kW)30.71.20.9297040.71.61.421,49050.72.12.132,240


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ExampleExample• Room with dimensions: 3.0 m x 3.0 m x 2.4 m (high)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 mDoor (open) with dimensions: 0.8 m x 2.0 m

– = 2.26 m= 2.26 m5/25/2

• Walls & ceiling: fire-rated gypsum boardWalls & ceiling: fire-rated gypsum board– Surface area (gypsum) = ASurface area (gypsum) = A11

– AA1 1 = {3 x 3 + 4 x 3 x 2.4 - 0.8 x 2} m= {3 x 3 + 4 x 3 x 2.4 - 0.8 x 2} m22 = 36.2 m = 36.2 m22

• Floor: woodFloor: wood– Surface area (wood) = ASurface area (wood) = A22

– AA2 2 = 3 x 3 m= 3 x 3 m22 = 9 m = 9 m22

• Total area of surface boundaries:Total area of surface boundaries:– AAT T = A= A1 1 + A+ A2 2 = 36.2 m= 36.2 m22 + 9 m + 9 m22 = 45.2 m = 45.2 m22

hA


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ExampleExample• Walls & ceiling: fire-rated gypsum board (1layer each Walls & ceiling: fire-rated gypsum board (1layer each

side of studs)side of studs)• k = 0.27 x 10k = 0.27 x 10-3-3 kW m kW m-1-1KK-1-1

= 680 kg m= 680 kg m-3-3 • c = 3.0 kJ kgc = 3.0 kJ kg-1 -1 KK-1-1

= 2 x 12.7 mm = 0.0254 m= 2 x 12.7 mm = 0.0254 m• Walls & ceiling: thermal penetration timeWalls & ceiling: thermal penetration time

• Walls & ceiling: thermal inertiaWalls & ceiling: thermal inertia

= 0.742 kJ m= 0.742 kJ m-2-2 s s1/21/2 K K-1-1

min 3.81s 4880k

ct 2

p,1

ck


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ExampleExample• Floor: woodFloor: wood

• k = 0.15 x 10k = 0.15 x 10-3-3 kW m kW m-1-1KK-1-1

= 550 kg m= 550 kg m-3-3 • c = 2.3 kJ kgc = 2.3 kJ kg-1 -1 KK-1-1

= 25.4 mm = 0.0254 m= 25.4 mm = 0.0254 m• Floor: thermal penetration timeFloor: thermal penetration time

• Floor: thermal inertiaFloor: thermal inertia

= 0.436 kJ m= 0.436 kJ m-2-2 s s1/21/2 K K-1-1ck

min 7.90s 5440k

ct 2

p,2


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ExampleExample• The fire: Heat release rate is limited by ventilation:The fire: Heat release rate is limited by ventilation:

• Consider an upholstered chair that burns in the room Consider an upholstered chair that burns in the room for 4 minutes at a heat release rate of for 4 minutes at a heat release rate of

• Clealy t < tClealy t < tp,ip,i for both boundary materials so for both boundary materials so

(36.2 x 0.742 + 9 x 0.436) kJ s(36.2 x 0.742 + 9 x 0.436) kJ s1/21/2 KK-1 -1

= 30.78 kJ s= 30.78 kJ s1/21/2 K K-1-1

kW 3,390 hA 1,500Q

kW 1,000 Q

iiii ickA ckA

T


37

ExampleExample• The temperature is given byThe temperature is given by

3/1

ckA hA

tQ6.85T

T

h

2

3/1

30.78 x 2.26

t)000,1(6.85T

2

h

1/6 t167Th


38

ExampleExample• The temperature is given byThe temperature is given by

1/6 t167Th

t (s) Th (C)0 030 29460 330

120 371180 397240 416


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Rate of Heat Release Required for Flashover Rate of Heat Release Required for Flashover McCaffrey, Quintiere & HarkleroadMcCaffrey, Quintiere & Harkleroad

• Conservative flashover criterion: Conservative flashover criterion: TThh = 500°C = 500°C

• Substitute Substitute TThh = 500°C into Eqn (10-14) & solve for = 500°C into Eqn (10-14) & solve for

Eqn (10-Eqn (10-17)17)

• = minimum required for flashover (kW)= minimum required for flashover (kW)

Q

1/2

TkFO hA A h 610Q

QFOQ


40

Rate of Heat Release Required for Flashover (MQH)Rate of Heat Release Required for Flashover (MQH)

• For t < tFor t < tp,ip,i (for each boundary) is minimum required (for each boundary) is minimum required

for flashover in time t (s) & is given byfor flashover in time t (s) & is given by

Eqn (10-18)Eqn (10-18)

• For t > tFor t > tp,ip,i (for each boundary) quasi steady-state heat flow (for each boundary) quasi steady-state heat flow

is achieved so becomes absolute minimum is achieved so becomes absolute minimum required for flashover & is given byrequired for flashover & is given by

Eqn (10-19)Eqn (10-19)

Q

QFOQ

FOQ

1/2

TEFF

ip,FO hA A t c)(k 610)t(tQ

1/2

TEFFip,FO hA A )(k/ 610)tt(Q


41

Rate of Heat Release Required for Flashover Rate of Heat Release Required for Flashover BabrauskasBabrauskas

• Theoretical maximum heat release rate isTheoretical maximum heat release rate is

• Developed correlation using experimental dataDeveloped correlation using experimental data• 33 room fires involving wood & polyurethane33 room fires involving wood & polyurethane• Ventilation factor: 0.03 mVentilation factor: 0.03 m5/25/2 < < 7.31 m < < 7.31 m5/25/2 • Surface area: 9 mSurface area: 9 m-1/2-1/2 < < < 65 m < 65 m-1/2-1/2

• Finding:Finding:

Eqn (10-Eqn (10-20) 20)

(kW) hA1,500QMAX

hAhAA

T

(kW) hA750QFO


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Rate of Heat Release Required for Flashover Rate of Heat Release Required for Flashover ThomasThomas

• Heat balance for hot layer isHeat balance for hot layer is

• Assumptions at flashover:Assumptions at flashover:• mass flow rate mass flow rate

• ccpp = 1.26 kJ kg = 1.26 kJ kg-1 -1 KK-1-1

TThh = 600 K = 600 K

• Correlation with experimental data:Correlation with experimental data:• Finding:Finding:

Eqn (10-Eqn (10-21) 21)

LOSSPqTTcmQ ohh

hA0.5~mh

Tloss A 7.8~q

(kW) A 7.8hA 378QTFO


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Rate of Heat Release Required for FlashoverRate of Heat Release Required for Flashover

Example: Example: Same room as in Slides 10-33 to 10-38Same room as in Slides 10-33 to 10-38

BabrauskasBabrauskas

ThomasThomas

MQHMQH

= 610 (0.438 x 2.26)= 610 (0.438 x 2.26)1/21/2 = 610 kW = 610 kW

kW 1,7002.26 x 750 hA750QFO

kW 1,21045.2 x 7.82.26 x 378 A 7.8hA 378QTFO

1/2

TEFFFO hA A )(k/ 610Q


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Rate of Heat Release Required for FlashoverRate of Heat Release Required for Flashover

within 10 minutes = 600 swithin 10 minutes = 600 s

MQHMQH

= 610 (30.78 / 24.5 x 2.26)= 610 (30.78 / 24.5 x 2.26)1/21/2

= 1030 kW= 1030 kW

1/2

TEFF

ip,FO hA A t c)(k 610)t(tQ


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Correlation for TemperatureCorrelation for Temperature

Foote, Pagni & AlvaresFoote, Pagni & Alvares• Correlation for forced-ventilation firesCorrelation for forced-ventilation fires

Eqn (10-Eqn (10-22)22)

• = mass supply rate (kg s= mass supply rate (kg s-1-1))• Correlation developed using experimental dataCorrelation developed using experimental data

• Methane gas burner: 150 to 490 kWMethane gas burner: 150 to 490 kW• Room: 6 m x 4 m & height of 4.5 mRoom: 6 m x 4 m & height of 4.5 m• Air supply rate: 0.110 to 0.325 kg sAir supply rate: 0.110 to 0.325 kg s-1-1

• Measured temperatures: 100 to 300°CMeasured temperatures: 100 to 300°C

36.072.0

PO

Tk

OPOO

h

c m

A h

Tc m

Q 0.63

T

T

Om


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Time to Flashover in a Room with Time to Flashover in a Room with Combustible Linings (Wall & Ceiling)Combustible Linings (Wall & Ceiling)

• Theory developed by Karlsson, 1989Theory developed by Karlsson, 1989

• Predicts time to flashover in room-fire test (ISO 9705)Predicts time to flashover in room-fire test (ISO 9705)

• Depends on data generated in small-scale testsDepends on data generated in small-scale tests– Cone calorimeter (characterizes heat release rate)Cone calorimeter (characterizes heat release rate)– LIFT apparatus (characterizes lateral flame-spread)LIFT apparatus (characterizes lateral flame-spread)


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Cone Calorimeter (3) - Cone Calorimeter (3) - ISO 5660 & ASTM E1354ISO 5660 & ASTM E1354


48

Cone Calorimeter Data - ThermosetCone Calorimeter Data - Thermoset


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Model for a ThermosetModel for a Thermoset

Eigmax"qon depend and t,"Q


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Opposed Flow SpreadOpposed Flow Spread

• Quintiere and Harkleroad, 1985Quintiere and Harkleroad, 1985

= = flame-heating parameter (kWflame-heating parameter (kW22 m m-3-3) {material property}) {material property}

• Provided no dripping, this model holds forProvided no dripping, this model holds for– downward flame spread (wall)downward flame spread (wall)– lateral flame spread (wall)lateral flame spread (wall)– horizontal flame spread (floor) horizontal flame spread (floor)

, k, kc and Tc and Tigig - measured (LIFT apparatus) - measured (LIFT apparatus)

• TTss - depends on scenario (external flux) - depends on scenario (external flux)

2 Sig

TT ckv


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LIFT ApparatusLIFT Apparatus


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Karlsson CorrelationKarlsson Correlation

• Cone calorimeter resultsCone calorimeter results

• LIFT resultsLIFT results

• Time to flashover in ISO 9705 room testTime to flashover in ISO 9705 room test

2

EmaxmkW 30"qat and "Q

ck

0.52

MAX

11.037.00.755

FO)"Q(c)(k 10 x 3.08t

Carleton University, 82.583, Fire Dynamics II, Winter 2003, Lecture # 10 1 Fire Dynamics II Lecture...

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