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

2. Carleton University, 82.583, Fire Dynamics II, Winter 2003, Lecture # 11 2 Post-flashover Fire Outline Ventilation controlled firesVentilation controlled fires Fuel-surface controlled firesFuel-surface controlled fires Model: Hot gas temperature (function of time)Model: Hot gas temperature (function of time) Fire resistance testFire resistance test Characterizing fire severityCharacterizing fire severity Design for resistanceDesign for resistance

3. Carleton University, 82.583, Fire Dynamics II, Winter 2003, Lecture # 11 3 Post-flashover Fire Assumptions- Well-stirred reactorAssumptions- Well-stirred reactor - T h uniform throughout enclosure - T h uniform throughout enclosure

4. Carleton University, 82.583, Fire Dynamics II, Winter 2003, Lecture # 11 4 Post-flashover Fires Wood Cribs, Pallets & Stacked Furniture Harmathy (1972) identified two burning regimes for room fires involving wooden cribs: ventilation controlled & fuel-surface controlledHarmathy (1972) identified two burning regimes for room fires involving wooden cribs: ventilation controlled & fuel-surface controlled = mass loss rate of fuel (kg s -1 ) = mass loss rate of fuel (kg s -1 )  = ventilation parameter (kg s -1 )  = ventilation parameter (kg s -1 ) = A f = exposed surface area of fuel (m 2 )A f = exposed surface area of fuel (m 2 )

5. Carleton University, 82.583, Fire Dynamics II, Winter 2003, Lecture # 11 5 Post-flashover Fires Involving Wooden Cribs

6. Carleton University, 82.583, Fire Dynamics II, Winter 2003, Lecture # 11 6 Example Calculation of Equivalence Ratio Post-flashover Fires Involving Wooden Cribs Post-flashover fire is ventilation-controlled ifPost-flashover fire is ventilation-controlled if  / A f < 0.63 kg m -2 s -1 Eqn (11-1) Eqn (11-1) Fuel mass loss rate isFuel mass loss rate is Eqn (11-2) Eqn (11-2)

7. Carleton University, 82.583, Fire Dynamics II, Winter 2003, Lecture # 11 7 What do we know about ventilation-controlled post-flashover fires involving wooden cribs, pallets or stacked furniture? Fuel mass loss rate isFuel mass loss rate is Eqn (11-2) Eqn (11-2) Rate of entry of air into room isRate of entry of air into room is Eqn (11-3) Eqn (11-3) Rate of exit of hot gas from room isRate of exit of hot gas from room is Eqn (11-4) Eqn (11-4)

8. Carleton University, 82.583, Fire Dynamics II, Winter 2003, Lecture # 11 8 Ventilation-controlled post-flashover fires involving wooden cribs, pallets or stacked furniture Equivalence ratio isEquivalence ratio is  ~ 0.92 Eqn (11-5) The rate of heat release of the fire isThe rate of heat release of the fire is Eqn (11-6) Eqn (11-6) The mass flow rate of soot out of the enclosure isThe mass flow rate of soot out of the enclosure is Eqn (11-7) Eqn (11-7) (Important for assessment of visibility outside the room)

9. Carleton University, 82.583, Fire Dynamics II, Winter 2003, Lecture # 11 9 Ventilation-controlled post-flashover fires involving wooden cribs, pallets or stacked furniture The mass flow rate of CO out of the enclosure isThe mass flow rate of CO out of the enclosure is Eqn (11-8) Eqn (11-8) Concentration of CO in hot gas leaving enclosure isConcentration of CO in hot gas leaving enclosure is Eqn (11-9) Eqn (11-9) (Important for assessment of toxicity outside the room) (This is a very high and dangerous concentration)

10. Carleton University, 82.583, Fire Dynamics II, Winter 2003, Lecture # 11 10 Ventilation-controlled post-flashover fires involving wooden cribs, pallets or stacked furniture The mass flow rate of CO 2 out of the enclosure isThe mass flow rate of CO 2 out of the enclosure is Eqn (11-10) Eqn (11-10) Concentration of CO 2 in hot gas leaving enclosure isConcentration of CO 2 in hot gas leaving enclosure is Eqn (11-11) Eqn (11-11) This would cause significant increased CO uptake due to hyperventilation. See slide 3-32 in Fire Dynamics I.

11. Carleton University, 82.583, Fire Dynamics II, Winter 2003, Lecture # 11 11 Ventilation-controlled post-flashover fires involving wooden cribs, pallets or stacked furniture The mass flow rate of N 2 out of the enclosure isThe mass flow rate of N 2 out of the enclosure is Eqn (11-12) Eqn (11-12) Concentration of N 2 in hot gas leaving enclosure isConcentration of N 2 in hot gas leaving enclosure is Eqn (11-13) Eqn (11-13) On a molar basis, air is 78% N 2 and the hot gas is 65% N 2. Since molecular wt of N 2 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.

12. Carleton University, 82.583, Fire Dynamics II, Winter 2003, Lecture # 11 12 Fuel-Surface Controlled: Post-flashover Fires T.Z. Harmathy 1972 // wood cribs (cellulosic)T.Z. Harmathy 1972 // wood cribs (cellulosic) Post-flashover fire is fuel-surface controlled ifPost-flashover fire is fuel-surface controlled if  / A f  0.63 kg m -2 s -1 Eqn (11-14) Eqn (11-14) Fuel mass loss rate isFuel mass loss rate is Eqn (11-15) Eqn (11-15) G = Quantity of wood in room (kg)  = A f / G = specific area of wood (m 2 kg -1 )

13. Carleton University, 82.583, Fire Dynamics II, Winter 2003, Lecture # 11 13 The Rate of Burning of Fuel-Surface Controlled: Post-flashover Fires Rate of mass loss / unit surface area of fuel isRate of mass loss / unit surface area of fuel is Eqn (11-16) Eqn (11-16) Douglas fir:Douglas fir: –Assume  = 550 kg m -3. –Assume 80% converted to volatiles and 20% to char –Rate of advance of char front: V c = 0.85 mm min -1

14. Carleton University, 82.583, Fire Dynamics II, Winter 2003, Lecture # 11 14 Some Comparisons For massive timbers in standard fire resistance testFor massive timbers in standard fire resistance test V c = 0.6 mm min -1 Rate of char advance in wood cribs is (slide 8-36)Rate of char advance in wood cribs is (slide 8-36) V c = 2.2 x 10 -6 D -0.6 (m s -1 ) Sticks of square cross and side D (m)Sticks of square cross and side D (m) D (mm) V c (mm / min) 38 0.94 38 0.94 45 0.85 45 0.85 80 0.60 80 0.60

15. Carleton University, 82.583, Fire Dynamics II, Winter 2003, Lecture # 11 15  - Specific Area of Wood For Douglas fir:  = 550 kg m -3For Douglas fir:  = 550 kg m -3 Dimensional lumber (4 sides exposed)Dimensional lumber (4 sides exposed) –2x2 (38 mm x 38 mm)   = 0.191 m 2 kg -1 –2x4 (38 mm x 89 mm)   = 0.136 m 2 kg -1 –2x12 (38 mm x 286 mm)   = 0.108 m 2 kg -1 Heavy timber column (4 sides exposed)Heavy timber column (4 sides exposed) –8x8 (191 mm x 191 mm)   = 0.038 m 2 kg -1 Plywood (1 side exposed)Plywood (1 side exposed) –1/2” = 12.7 mm thick   = 0.143 m 2 kg -1 –1/4” = 6.4 mm thick   = 0.286 m 2 kg -1

16. Carleton University, 82.583, Fire Dynamics II, Winter 2003, Lecture # 11 16  - Specific Area of Wood Harmathy’s correlation for fuel-surface controlled burning derived from experimental data for wood cribsHarmathy’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 layerCorrelation 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 m 2 kg -1 Eqn (11-17)For such items assume  ~ 0.13 m 2 kg -1 Eqn (11-17) Harmathy’s correlation for fuel-surface controlled burning and  ~ 0.13 m 2 kg -1 are not appropriate for scenarios involving large exposed wooden surfaces like wall panellingHarmathy’s correlation for fuel-surface controlled burning and  ~ 0.13 m 2 kg -1 are not appropriate for scenarios involving large exposed wooden surfaces like wall panelling

17. Carleton University, 82.583, Fire Dynamics II, Winter 2003, Lecture # 11 17 G - Quantity of Fuel (kg) Quantity of fuel in a room is commonly expressed in terms of a calorifically equivalent quantity of woodQuantity 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 areaMany surveys have been conducted to determine mass of fuel / floor area Definition: L = specific fire load (kg m -2 )Definition: L = specific fire load (kg m -2 ) = mass of fuel / floor area G = L x (floor area) Eqn (11-18) G = L x (floor area) Eqn (11-18)

18. Carleton University, 82.583, Fire Dynamics II, Winter 2003, Lecture # 11 18 L - Specific Fire Load (kg m -2 ) L is random variable: mean & standard deviation  LL is random variable: mean & standard deviation  L Harmathy recommendations (old data)Harmathy recommendations (old data) Assuming L follows a normal distributionAssuming L follows a normal distribution Eqn (11-19) Eqn (11-19)

19. Carleton University, 82.583, Fire Dynamics II, Winter 2003, Lecture # 11 19 Duration of a Post-flashover Fire Assume volatiles released in post-flashover phaseAssume 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 isAssume total mass loss during post-flashover phase is M T = 0.8 G (kg) Eqn (11-20) Duration of post-flashover phase isDuration of post-flashover phase is Eqn (11-21) Eqn (11-21)

20. Carleton University, 82.583, Fire Dynamics II, Winter 2003, Lecture # 11 20 Duration of a Post-flashover Fire For a fuel-surface controlled fireFor a fuel-surface controlled fire Eqn (11-22) Eqn (11-22) For a ventilation controlled fireFor a ventilation controlled fire Eqn (11-23) Eqn (11-23)

21. Carleton University, 82.583, Fire Dynamics II, Winter 2003, Lecture # 11 21

22. Carleton University, 82.583, Fire Dynamics II, Winter 2003, Lecture # 11 22

23. Carleton University, 82.583, Fire Dynamics II, Winter 2003, Lecture # 11 23 Duration of Post-flashover Fire

24. Carleton University, 82.583, Fire Dynamics II, Winter 2003, Lecture # 11 24Kemano

25. Carleton University, 82.583, Fire Dynamics II, Winter 2003, Lecture # 11 25 Time-averaged Temperatures in Room Fires Experimental data from SFPE handbook

26. Carleton University, 82.583, Fire Dynamics II, Winter 2003, Lecture # 11 26 Post-flashover Fires Involving Wood, PMMA & PE

27. Carleton University, 82.583, Fire Dynamics II, Winter 2003, Lecture # 11 27 Burning rate in post-flashover fires involving fuels with exposed surfaces is enhanced by radiationBurning 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)Large burning rates inhibit inflow of air so increase equivalence ratio  reduced heat release (inside) Heat release rate still can be ventilation-controlledHeat release rate still can be ventilation-controlled

28. Carleton University, 82.583, Fire Dynamics II, Winter 2003, Lecture # 11 28 Traditional Design for Fire Resistance Basic Objective: Provide sufficient time for escapeBasic Objective: Provide sufficient time for escape Strategy # 1 - Compartmentation: Inhibit fire spread: enclose compartments with fire resistant separationsStrategy # 1 - Compartmentation: Inhibit fire spread: enclose compartments with fire resistant separations Strategy # 2 - Structural Fire Protection: Delay collapse of structure: make elements fire resistantStrategy # 2 - Structural Fire Protection: Delay collapse of structure: make elements fire resistant Functional Requirement: Assemblies must perform acceptably when exposed to design fire & design loadFunctional 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 fireAcceptance Criterion (Not clearly stated): Fire separations & structural members must perform intended functions for duration of fire

29. Carleton University, 82.583, Fire Dynamics II, Winter 2003, Lecture # 11 29 Physical Model - Post-flashover Fire The Fire Resistance Test Physical (as opposed to mathematical) model of a post-flashover firePhysical (as opposed to mathematical) model of a post-flashover fire Initial development ~ 1908Initial development ~ 1908 Standard Fire Resistance Tests CAN/ULC-S101, Standard methods of fire endurance tests of building construction materialsCAN/ULC-S101, Standard methods of fire endurance tests of building construction materials CAN/ULC-S101 = ASTM E119CAN/ULC-S101 = ASTM E119 (Determination of loads is different) ISO 834 = international standardISO 834 = international standard

30. Carleton University, 82.583, Fire Dynamics II, Winter 2003, Lecture # 11 30

31. Carleton University, 82.583, Fire Dynamics II, Winter 2003, Lecture # 11 31 Standard Temperature-time Curve: CAN/ULC-S101 or ASTM E119

32. Carleton University, 82.583, Fire Dynamics II, Winter 2003, Lecture # 11 32 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 requirementsTime specimen meets performance requirements

33. Carleton University, 82.583, Fire Dynamics II, Winter 2003, Lecture # 11 33 Principle for Establishing Fire Resistance Requirements for Buildings

34. Carleton University, 82.583, Fire Dynamics II, Winter 2003, Lecture # 11 34 Principle for Establishing Fire Resistance Requirements for Buildings

35. Carleton University, 82.583, Fire Dynamics II, Winter 2003, Lecture # 11 35 NBCC Requirements Compartmentation Fire separations often must be fire ratedFire separations often must be fire rated Fire separations between public corridors & suites in small buildings require fire-resistance rating of 3/4Fire 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 hourFire 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 ratedFloors and structural elements supporting floors often must be rated In small buildings: fire-resistance rating of 3/4 or 1 hIn small buildings: fire-resistance rating of 3/4 or 1 h In large buildings: fire-resistance rating of 2 hIn large buildings: fire-resistance rating of 2 h

36. Carleton University, 82.583, Fire Dynamics II, Winter 2003, Lecture # 11 36 Performance-based Design for Fire Resistance Design Fire Scenarios Buildings with High Degree of Compartmentation Examples: Apartment & office buildingsExamples: Apartment & office buildings Scenario: Post-flashover fire (no suppression)Scenario: Post-flashover fire (no suppression) Design Fire: A credible but severe post-flashover fireDesign Fire: A credible but severe post-flashover fire Buildings with Large Open Spaces Examples: Warehouses & FactoriesExamples: Warehouses & Factories Scenario: Localized fire (diffusion flame)Scenario: Localized fire (diffusion flame) Design Fire: A credible but severe localized fireDesign Fire: A credible but severe localized fire

37. Carleton University, 82.583, Fire Dynamics II, Winter 2003, Lecture # 11 37 Model for Post-flashover Fire Severity Japanese Parametric Model Basic Assumptions Ventilation: Assume unprotected openings are openVentilation: Assume unprotected openings are open Assume fire-rated closures remain intact Assume fire-rated closures remain intact Heat Release: Heat released in post-flashover phaseHeat Release: Heat released in post-flashover phase Maximum possible value from t=0 Maximum possible value from t=0 Fuel Load: Total fuel load is consumedFuel Load: Total fuel load is consumed

38. Carleton University, 82.583, Fire Dynamics II, Winter 2003, Lecture # 11 38 Japanese Parametric Model for Ventilation Controlled Fires Temperature of fire gases: T h (t) (K)Temperature of fire gases: T h (t) (K) T h (t) - T o =  t 1/6 Eqn (11-24) where  = a constant (K s -1/6 ) t = time since ignition (s) t = time since ignition (s) Eqn (11-25) Eqn (11-25)

39. Carleton University, 82.583, Fire Dynamics II, Winter 2003, Lecture # 11 39 A = area of openings (windows) (m 2 ) h = height of openings (windows) (m) A T = total area of boundaries (m 2 ) 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 )

40. Carleton University, 82.583, Fire Dynamics II, Winter 2003, Lecture # 11 40 Duration of post-flashover fire: t D (s) Eqn (11-26) Eqn (11-26) L = fuel load (kg m -2 ) A F = area of the floor (m 2 )

41. Carleton University, 82.583, Fire Dynamics II, Winter 2003, Lecture # 11 41

42. Carleton University, 82.583, Fire Dynamics II, Winter 2003, Lecture # 11 42

43. Carleton University, 82.583, Fire Dynamics II, Winter 2003, Lecture # 11 43

44. Carleton University, 82.583, Fire Dynamics II, Winter 2003, Lecture # 11 44

45. Carleton University, 82.583, Fire Dynamics II, Winter 2003, Lecture # 11 45

46. Carleton University, 82.583, Fire Dynamics II, Winter 2003, Lecture # 11 46

47. Carleton University, 82.583, Fire Dynamics II, Winter 2003, Lecture # 11 47 Japanese Parametric Model Option 1: Response of Assembly Predicted Using Mathematical Model Fire characterized by temperature-time curve generated by Japanese parametric 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).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.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?Do fire separations and structural members meet the acceptance criteria?

48. Carleton University, 82.583, Fire Dynamics II, Winter 2003, Lecture # 11 48 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 )Heat absorbed by unit surface area of fire separations or structural members in post-flashover fire: q” (kJ m -2 ) Eqn (11-27) Eqn (11-27) For ISO 834:  = 230 K s -1/6For ISO 834:  = 230 K s -1/6 For ASTM E119:  = 229 K s -1/6For ASTM E119:  = 229 K s -1/6

49. Carleton University, 82.583, Fire Dynamics II, Winter 2003, Lecture # 11 49 Normalized Heat Load Concept (Harmathy & Mehaffey) Compartment fire of duration t D is equivalent in severity to an ISO 834 fire test of duration t eq in which same heat is absorbed per unit areaCompartment fire of duration t D is equivalent in severity to an ISO 834 fire test of duration t eq in which same heat is absorbed per unit area Eqn (11-28) Eqn (11-28) Assembly fire resistance rating  t eq is acceptableAssembly fire resistance rating  t eq is acceptable Advantage of Option 2: Existing fire resistance ratings can still be usedAdvantage 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 loadDrawback of Option 2: Fire-resistance ratings are determined using max load not actual design load

50. Carleton University, 82.583, Fire Dynamics II, Winter 2003, Lecture # 11 50

51. Carleton University, 82.583, Fire Dynamics II, Winter 2003, Lecture # 11 51 Design Considerations Fuel Load Use 95th percentile in fuel load distribution: Eqn (11-19)Use 95th percentile in fuel load distribution: Eqn (11-19)Ventilation Assume unprotected openings are openAssume unprotected openings are open Assume fire-rated closures remain intactAssume fire-rated closures remain intact If several vents at approximately the same elevationIf several vents at approximately the same elevation Eqn (11-29) Eqn (11-29) Compartment Boundaries Boundaries do not include internal partitionsBoundaries do not include internal partitions If there is more than one boundary materialIf there is more than one boundary material

52. Carleton University, 82.583, Fire Dynamics II, Winter 2003, Lecture # 11 52

53. Carleton University, 82.583, Fire Dynamics II, Winter 2003, Lecture # 11 53 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 m 2 Window Dimensions: 4.0 m x 1.5 m (height) Fuel Load: 95th percentile Eqn (11-19) L 95 = L + 1.64  L = (24.8 + 1.64 x 8.6) kg m -2 = 38.9 kg m -2 L 95 = L + 1.64  L = (24.8 + 1.64 x 8.6) kg m -2 = 38.9 kg m -2

54. Carleton University, 82.583, Fire Dynamics II, Winter 2003, Lecture # 11 54 Ventilation: Window breaks & door remains intact Compartment boundaries = [ceiling + walls - vents][gypsum bd] = [ceiling + walls - vents][gypsum bd] + [floor][n.w. concrete] + [floor][n.w. concrete] = [6x4 + 6x2.4x2 + 4x2.4x2 - 1.5x4] x 0.742 = [6x4 + 6x2.4x2 + 4x2.4x2 - 1.5x4] x 0.742 + [6 x 4] x [2.192] + [6 x 4] x [2.192] = 101.58 kJ s -1/2 K -1 = 101.58 kJ s -1/2 K -1

55. Carleton University, 82.583, Fire Dynamics II, Winter 2003, Lecture # 11 55 Japanese Parametric Model Temperature of fire gases: T h (t) (K)Temperature of fire gases: T h (t) (K) T h (t) - T o =  t 1/6 Eqn (11-24) where  (K s -1/6 ) characterises the fire Eqn (11-25) Eqn (11-25)  = 3 x 293 x [ 7.35 / 101.58 ] 1/3 = 366 K s -1/6   = 3 x 293 x [ 7.35 / 101.58 ] 1/3 = 366 K s -1/6

56. Carleton University, 82.583, Fire Dynamics II, Winter 2003, Lecture # 11 56 Japanese Parametric Model Duration of post-flashover fire: t D (s)Duration of post-flashover fire: t D (s) Eqn (11-26) Eqn (11-26) t D = 38.9 x 24 / [ 0.09 x 7.35 ] = 1411 s = 23.5 min  t D = 38.9 x 24 / [ 0.09 x 7.35 ] = 1411 s = 23.5 min Duration of equivalent fire resistance test: t eqDuration of equivalent fire resistance test: t eq Eqn (11-28) Eqn (11-28) t eq = [366 / 230] 3/2 x 23.5 min = 47.2 min  t eq = [366 / 230] 3/2 x 23.5 min = 47.2 min