Carleton University, 82.583, Fire Dynamics II, Winter 2003, Lecture # 11 1 Fire Dynamics II Lecture # 11 Post-flashover Fire Jim Mehaffey 82.583

Fire Dynamics IILecture # 11Post-flashover FireJim Mehaffey

82.583

Carleton University, 82.583, Fire Dynamics II, Winter 2003, Lecture # 11

Post-flashover FireOutline

Ventilation controlled fires

Fuel-surface controlled fires

Model: Hot gas temperature (function of time)

Fire resistance test

Characterizing fire severity

Design for resistance


Post-flashover Fire

Assumptions- Well-stirred reactor - Th uniform throughout enclosure


Post-flashover FiresWood Cribs, Pallets & Stacked Furniture

Harmathy (1972) identified two burning regimes for room fires involving wooden cribs: ventilation controlled & fuel-surface controlled

= mass loss rate of fuel (kg s-1)

= ventilation parameter (kg s-1)

=

Af = exposed surface area of fuel (m2)


Post-flashover Fires Involving Wooden Cribs


Example Calculation of Equivalence RatioPost-flashover Fires Involving Wooden Cribs

Post-flashover fire is ventilation-controlled if

/ Af < 0.63 kg m-2 s-1

Eqn (11-1)

Fuel mass loss rate is

Eqn (11-2)


What do we know about ventilation-controlled post-flashover fires involving wooden cribs, pallets or stacked furniture?


Eqn (11-2)

Rate of entry of air into room is

Eqn (11-3)

Rate of exit of hot gas from room is

Eqn (11-4)


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

Eqn (11-6)

The mass flow rate of soot out of the enclosure is

Eqn (11-7)

(Important for assessment of visibility outside the room)



The mass flow rate of CO out of the enclosure is

Eqn (11-8)

Concentration of CO in hot gas leaving enclosure is

Eqn (11-9)(Important for assessment of toxicity outside the room)(This is a very high and dangerous concentration)



The mass flow rate of CO2 out of the enclosure is

Eqn (11-10)

Concentration of CO2 in hot gas leaving enclosure is

Eqn (11-11)This would cause significant increased CO uptake due to hyperventilation. See slide 3-32 in Fire Dynamics I.



The mass flow rate of N2 out of the enclosure is

Eqn (11-12)

Concentration of N2 in hot gas leaving enclosure is

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.


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

Eqn (11-14)


Eqn (11-15)

G = Quantity of wood in room (kg) = Af / G = specific area of wood (m2 kg-1)


The Rate of Burning of Fuel-Surface Controlled: Post-flashover Fires

Rate of mass loss / unit surface area of fuel is

Eqn (11-16)

Douglas fir:Assume = 550 kg m-3. Assume 80% converted to volatiles and 20% to charRate of advance of char front:

Vc = 0.85 mm min-1


Some Comparisons

For massive timbers in standard fire resistance testVc = 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) Vc (mm / min) 38 0.94 45 0.85 80 0.60


- 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-12x4 (38 mm x 89 mm) = 0.136 m2 kg-12x12 (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-11/4 = 6.4 mm thick = 0.286 m2 kg-1


- Specific Area of Wood

Harmathys 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)

Harmathys 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


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) Eqn (11-18)


L - Specific Fire Load (kg m-2)

L is random variable: mean & standard deviation LHarmathy recommendations (old data)

Assuming L follows a normal distribution

Eqn (11-19)


Occupancy

(kg m-2 )

(L (kg m-2 )

Dwelling

30.1

4.4

Office

24.8

8.6

School

17.5

5.1

Hospital

25.1

7.8

Hotel

14.6

4.2

_1109767839.unknown

Duration of a Post-flashover Fire

Assume volatiles released in post-flashover phaseLittle mass loss in pre-flashover phaseDominantly 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

Eqn (11-21)


Duration of a Post-flashover Fire

For a fuel-surface controlled fire

Eqn (11-22)

For a ventilation controlled fire

Eqn (11-23)


Duration of Post-flashover Fire


Test

G

kg

Af

m2

V C

or

F S C

Duration

test

min

Duration

theory

min

1

0.92

130

16.9

0.054

VC

18.5

20.9

2

0.92

130

16.9

0.054

VC

21

20.9

3

0.92

234

30.4

0.030

VC

28

37.7

4

1.42

234

30.4

0.047

VC

24

24.4

5

2.13

234

30.4

0.070

VC?

17

16.5

_1110028394.unknown

_1110028524.unknown

Kemano


S-987

Chart1

2012.3111.47

0.2092515.0411.74

0.375783333315.7312.45

0.542466666718.2114.08

0.709833333322.2614.76

0.876066666724.7416.5

12426.316.63

1.209366666723.6616.71

1.376483333325.5518.57

1.542716666724.7219.37

1.709833333331.1320.89

1.876216666728.5420.84

22731.9320.46

2.209816666735.2621.69

2.376233333341.4624.03

2.5425556.7628.48

2.709833333382.6334.11

2.8760833333128.3141.26

33119056.56

3.2096166667358.07161.46

3.3760833333458.12319.02

3.5424666667764.53471.01

3.7093833333885.03794.41

3.8758333333853.09793.87

434718.69620.7

4.2094166667662.63567.08

4.3764333333697.9699.13

4.5428333333765.8722.51

4.7091166667749.35856.6

4.87625726.91806.35

538732.64785.88

5.2096666667760.73839.49

5.3762333333725.54794.96

5.5425166667668.39697.06

5.7095833333687.98713.11

5.8758666667732.67808.66

571757.93784.29

6.2094666667738.53734.6

6.3759666667751.46788.84

6.5424833333753.91825.56

6.7095833333739.29761.04

6.87585734.52756.35

604760.12797.28

7.20945780.08785.59

7.3757833333797.58791.54

7.5430333333830.61817.94

7.7095333333840.41829.27

7.8760166667850.01845.02

638907.31894.69

8.2097166667820.4817.83

8.3760833333924.27902.86

8.5426333333966.93943.78

8.7098166667923.15904.69

8.8761166667959.31940.9

671986958.75

9.20956666671004.51975.42

9.37591006.24976.73

9.54246666671015.8984.78

9.70993333331023.46991.88

9.87631666671020.6992.63

7041032.26996.74

10.20941035.58999.31

10.37583333331030.02991.73

10.54311051.571006.35

10.70958333331052.511008.4

10.876051071.241019.46

7151082.451026.24

11.20983333331082.021030.61

11.376151073.521020.54

11.54273333331085.151026.12

11.70931666671083.021027.02

11.87601666671085.41025.87

7261084.891029.37

12.20966666671083.581025.79

12.37606666671095.21035.56

12.54248333331085.261034.39

12.70978333331081.631035.33

12.87626666671081.161040.08

7381083.651042.63

13.20971666671077.761040.5

13.37616666671073.961039.59

13.542451080.221040.04

13.70991080.671041.59

13.87638333331070.531034.59

7491069.831032.71

14.20981666671065.421028.58

14.37643333331072.791028.36

14.542851071.211027.58

14.709451057.561019.48

14.87578333331067.291022.18

7601055.11014.58

15.20968333331039.571003.01

15.37583333331031.47997.06

15.542851028.45991.5

15.70971017.06975.99

15.87651666671008.51975.68

7671009.78980.06

16.20968333331000.48974.8

16.3759999.03969.8

16.5428166667995.43970.1

16.7091166667992.1966.02

16.8761981.81957.5

774981.14955.27

17.2095968.85948.87

17.3763333333962.87943.61

17.5424833333951.98934.99

17.70945944.43928.85

17.8762833333935.85920.47

781929.2915.52

18.2095166667918.27904.91

18.3763333333910.08898.89

18.5424666667903.74892.23

18.70945892.48883.72

18.8765333333880.88870.69

788841.12830.05

19.209633333366.4667.89

19.375866666760.3360.01

19.542583333355.4152.9

19.709566666745.2145.06

19.875933333337.0539.37

79538.1939.74

20.20936666673940.35

20.3764540.0240.11

800.22121

805.42222

810.62323

815.82424

8212525

825.42626

829.82727

834.22828

838.62929

8433030

846.83131

850.63232

854.43333

858.23434

8623535

865.23636

868.43737

871.63838

874.83939

8784040

880.84141

883.64242

886.44343

889.24444

8924545

894.64646

897.24747

899.84848

902.44949

9055050

907.25151

909.45252

911.65353

913.85454

9165555

918.25656

920.45757

922.65858

924.85959

9276060

Living Room Fires - Duplex

ASTM E 119 & CAN/ULC-S101

Time (min)

Temperature (oC)

Fire Exposures

Sheet1

0.020.012.3111.471010.586

0.215.0411.741020.555

0.415.7312.451030.547

0.518.2114.081040.548

0.722.2614.761050.59

0.924.7416.51060.564

1.0124.026.316.631070.59

1.223.6616.711080.562

1.425.5518.571090.589

1.524.7219.371100.563

1.731.1320.891110.59

1.928.5420.841120.573

2.0227.031.9320.461130.553

2.235.2621.691140.589

2.441.4624.031150.574

2.556.7628.481160.553

2.782.6334.111170.59

2.9128.3141.261180.565

3.0331.019056.561190.55

3.2358.07161.461200.577

3.4458.12319.021210.565

3.5764.53471.011220.548

3.7885.03794.411230.563

3.9853.09793.871240.55

4.0434.0718.69620.71250.579

4.2662.63567.081260.565

4.4697.9699.131270.586

4.5765.8722.511280.57

4.7749.35856.61290.547

4.9726.91806.351300.575

5.0538.0732.64785.881310.559

5.2760.73839.491320.58

5.4725.54794.961330.574

5.5668.39697.061340.551

5.7687.98713.111350.575

5.9732.67808.661360.552

6.0571.0757.93784.291370.589

6.2738.53734.61380.568

6.4751.46788.841390.558

6.5753.91825.561400.549

6.7739.29761.041410.575

6.9734.52756.351420.551

7.0604.0760.12797.281430.583

7.2780.08785.591440.567

7.4797.58791.541450.547

7.5830.61817.941460.582

7.7840.41829.271470.572

7.9850.01845.021480.561

8.0638.0907.31894.691490.547

8.2820.4817.831500.583

8.4924.27902.861510.565

8.5966.93943.781520.558

8.7923.15904.691530.589

8.9959.31940.91540.567

9.0671.0986958.751550.55

9.21004.51975.421560.574

9.41006.24976.731570.554

9.51015.8984.781580.548

9.71023.46991.881590.596

9.91020.6992.631600.579

10.0704.01032.26996.741610.582

10.21035.58999.311620.564

10.41030.02991.731630.55

10.51051.571006.351640.586

10.71052.511008.41650.575

10.91071.241019.461660.563

11.0715.01082.451026.241670.554

11.21082.021030.611680.59

11.41073.521020.541690.569

11.51085.151026.121700.564

11.71083.021027.021710.559

11.91085.41025.871720.561

12.0726.01084.891029.371730.549

12.21083.581025.791740.58

12.41095.21035.561750.564

12.51085.261034.391760.549

12.71081.631035.331770.587

12.91081.161040.081780.576

13.0738.01083.651042.631790.568

13.21077.761040.51800.583

13.41073.961039.591810.57

13.51080.221040.041820.547

13.71080.671041.591830.594

13.91070.531034.591840.583

14.0749.01069.831032.711850.579

14.21065.421028.581860.589

14.41072.791028.361870.586

14.51071.211027.581880.571

14.71057.561019.481890.567

14.91067.291022.181900.547

15.0760.01055.11014.581910.55

15.21039.571003.011920.581

15.41031.47997.061930.55

15.51028.45991.51940.571

15.71017.06975.991950.582

15.91008.51975.681960.591

16.0767.01009.78980.061970.561

16.21000.48974.81980.581

16.4999.03969.81990.554

16.5995.43970.12000.569

02016.7992.1966.022010.547

1123.616.9981.81957.52020.566

2227.217.0774.0981.14955.272030.547

3330.817.2968.85948.872040.57

4434.417.4962.87943.612050.58

553817.5951.98934.992060.549

6571.217.7944.43928.852070.567

7604.417.9935.85920.472080.577

8637.618.0781.0929.2915.522090.591

9670.818.2918.27904.912100.571

1070418.4910.08898.892110.58

11715.218.5903.74892.232120.548

12726.418.7892.48883.722130.567

13737.618.9880.88870.692140.592

14748.819.0788.0841.12830.052150.567

1576019.266.4667.892160.578

1676719.460.3360.012170.552

1777419.555.4152.92180.555

1878119.745.2145.062190.574

1978819.937.0539.372200.556

2079520.0795.038.1939.742210.584

21800.220.23940.352220.562

22805.420.440.0240.112230.587

23810.621800.2

24815.822805.4

2582123810.6

26825.424815.8

27829.825821

28834.226825.4

29838.627829.8

3084328834.2

31846.829838.6

32850.630843

33854.431846.8

34858.232850.6

3586233854.4

36865.234858.2

37868.435862

38871.636865.2

39874.837868.4

4087838871.6

41880.839874.8

42883.640878

43886.441880.8

44889.242883.6

4589243886.4

46894.644889.2

47897.245892

48899.846894.6

49902.447897.2

5090548899.8

51907.249902.4

52909.450905

53911.651907.2

54913.852909.4

5591653911.6

56918.254913.8

57920.455916

58922.656918.2

59924.857920.4

6092758922.6

59924.8

60927

Sheet2

Sheet3

Sheet4

Time-averaged Temperatures in Room FiresExperimental data from SFPE handbook


Post-flashover Fires Involving Wood, PMMA & PE


Burning rate in post-flashover fires involving fuels with exposed surfaces is enhanced by radiationLarge burning rates inhibit inflow of air so increase equivalence ratio reduced heat release (inside)Heat release rate still can be ventilation-controlled


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


Physical Model - Post-flashover Fire

The Fire Resistance Test

Physical (as opposed to mathematical) model of a post-flashover fireInitial development ~ 1908

Standard Fire Resistance Tests

CAN/ULC-S101, Standard methods of fire endurance tests of building construction materialsCAN/ULC-S101 = ASTM E119(Determination of loads is different)ISO 834 = international standard


Standard Temperature-time Curve: CAN/ULC-S101 or ASTM E119


Performance RequirementsSeparating Element1. Specimen remains in place2. No passage of hot gas / flame3. T < 140C (average unexposed side)T < 180C (single point, unexposed side)4. Hose-stream Test

Load-bearing Element1. Specimen supports design load

Fire-resistance RatingTime specimen meets performance requirements


Principle for Establishing Fire Resistance Requirements for Buildings


NBCC RequirementsCompartmentationFire separations often must be fire ratedFire separations between public corridors & suites in small buildings require fire-resistance rating of 3/4Fire separations between public corridors & suites in large buildings require fire-resistance rating of 1 hour

Structural Fire ProtectionFloors and structural elements supporting floors often must be ratedIn small buildings: fire-resistance rating of 3/4 or 1 hIn large buildings: fire-resistance rating of 2 h


Performance-based Design for Fire ResistanceDesign Fire Scenarios

Buildings with High Degree of CompartmentationExamples: Apartment & office buildingsScenario: Post-flashover fire (no suppression)Design Fire: A credible but severe post-flashover fire

Buildings with Large Open SpacesExamples: Warehouses & FactoriesScenario: Localized fire (diffusion flame)Design Fire: A credible but severe localized fire


Model for Post-flashover Fire SeverityJapanese 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

Fuel Load: Total fuel load is consumed


Japanese Parametric Modelfor Ventilation Controlled Fires

Temperature of fire gases: Th(t) (K)

Th(t) - To = t1/6 Eqn (11-24)

where = a constant (K s-1/6) t = time since ignition (s)

Eqn (11-25)


_1110109404.unknown

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)


Duration of post-flashover fire: tD (s)

Eqn (11-26)

L = fuel load (kg m-2)

AF = area of the floor (m2)


_1110109956.unknown


Japanese Parametric Model

Model Validation

Test

G = L AF

(kg)

Ah

(m5/2)

AT

(m2)

kc

(kJ m-2 s-1/2 K-1)

(K s-1/6)

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


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?



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)

Eqn (11-27)

For ISO 834: = 230 K s-1/6 For ASTM E119: = 229 K s-1/6


_1110114384.unknown

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

Eqn (11-28)Assembly fire resistance rating teq is acceptableAdvantage of Option 2: Existing fire resistance ratings can still be usedDrawback of Option 2: Fire-resistance ratings are determined using max load not actual design load


_1110114718.unknown

Design ConsiderationsFuel LoadUse 95th percentile in fuel load distribution: Eqn (11-19)VentilationAssume unprotected openings are openAssume fire-rated closures remain intactIf several vents at approximately the same elevation Eqn (11-29)

Compartment BoundariesBoundaries do not include internal partitionsIf there is more than one boundary material


Example - Design for Fire ResistancePrevent 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


Ventilation: Window breaks & door remains intact

Compartment boundaries

= [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



Temperature of fire gases: Th(t) (K)

Th(t) - To = t1/6 Eqn (11-24)

where (K s-1/6) characterises the fire

Eqn (11-25)

\ = 3 x 293 x [ 7.35 / 101.58 ]1/3 = 366 K s-1/6


_1110109404.unknown


Duration of post-flashover fire: tD (s)

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

Eqn (11-28)

\ teq = [366 / 230]3/2 x 23.5 min = 47.2 min


_1110109956.unknown

_1110114718.unknown

Documents

Carleton University, 82.583, Fire Dynamics II, Winter 2003, Lecture # 11 1 Fire Dynamics II Lecture # 11 Post-flashover Fire Jim Mehaffey 82.583