Fire Dynamics II

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Fire Dynamics II

• Lecture 11
• Post-flashover Fire
• Jim Mehaffey
• 82.583

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• Post-flashover Fire
• Outline
• Ventilation controlled fires
• Fuel-surface controlled fires
• Model Hot gas temperature (function of time)
• Fire resistance test
• Characterizing fire severity
• Design for resistance

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• Post-flashover Fire
• Assumptions - Well-stirred reactor
• - Th uniform throughout enclosure

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• Post-flashover Fires
• Wood 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)

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• Post-flashover Fires Involving Wooden Cribs

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• Example Calculation of Equivalence Ratio
• Post-flashover Fires Involving Wooden Cribs
• Post-flashover fire is ventilation-controlled if
• ? / Af lt 0.63 kg m-2 s-1
• Eqn (11-1)
• Fuel mass loss rate is
• Eqn (11-2)

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• What do we know about ventilation-controlled
  post-flashover fires involving wooden cribs,
  pallets or stacked furniture?
• Fuel mass loss rate is
• 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)

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• 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)

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• Ventilation-controlled post-flashover fires
  involving wooden cribs, pallets or stacked
  furniture
• 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)

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• Ventilation-controlled post-flashover fires
  involving wooden cribs, pallets or stacked
  furniture
• 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.

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• Ventilation-controlled post-flashover fires
  involving wooden cribs, pallets or stacked
  furniture
• 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.

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• 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)
• Fuel mass loss rate is
• Eqn (11-15)
• G Quantity of wood in room (kg)
• ? Af / G specific area of wood (m2 kg-1)

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• 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 char
• Rate of advance of char front
• Vc 0.85 mm min-1

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• Some Comparisons
• For massive timbers in standard fire resistance
  test
• Vc 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

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• ? - 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-1
• 2x4 (38 mm x 89 mm) ? ? 0.136 m2 kg-1
• 2x12 (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-1
• 1/4 6.4 mm thick ? ? 0.286 m2 kg-1

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• ? - 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

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• 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)

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• L - Specific Fire Load (kg m-2)
• L is random variable mean standard
  deviation ?L
• Harmathy recommendations (old data)
• Assuming L follows a normal distribution
• Eqn (11-19)

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• Duration of a Post-flashover Fire
• Assume 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 is
• MT 0.8 G (kg) Eqn (11-20)
• Duration of post-flashover phase is
• Eqn (11-21)

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• Duration of a Post-flashover Fire
• For a fuel-surface controlled fire
• Eqn (11-22)
• For a ventilation controlled fire
• Eqn (11-23)

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• Duration of Post-flashover Fire

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• Kemano

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• Time-averaged Temperatures in Room Fires
• Experimental data from SFPE handbook

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• Post-flashover Fires Involving Wood, PMMA PE

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• Burning 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)
• Heat release rate still can be ventilation-control
  led

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• 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

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• Physical Model - Post-flashover Fire
• The Fire Resistance Test
• Physical (as opposed to mathematical) model of a
  post-flashover fire
• Initial development 1908
• Standard Fire Resistance Tests
• CAN/ULC-S101, Standard methods of fire endurance
  tests of building construction materials
• CAN/ULC-S101 ASTM E119
• (Determination of loads is different)
• ISO 834 international standard

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

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• Performance Requirements
• Separating Element
• 1. Specimen remains in place
• 2. No passage of hot gas / flame
• 3. ?T lt 140C (average unexposed side)
• ?T lt 180C (single point, unexposed side)
• 4. Hose-stream Test
• Load-bearing Element
• 1. Specimen supports design load
• Fire-resistance Rating
• Time specimen meets performance requirements

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• Principle for Establishing Fire Resistance
  Requirements for Buildings

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• Principle for Establishing Fire Resistance
  Requirements for Buildings

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• NBCC Requirements
• Compartmentation
• Fire separations often must be fire rated
• Fire 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 hour
• Structural Fire Protection
• Floors and structural elements supporting floors
  often must be rated
• In small buildings fire-resistance rating of 3/4
  or 1 h
• In large buildings fire-resistance rating of 2 h

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• Performance-based Design for Fire Resistance
• Design Fire Scenarios
• Buildings with High Degree of Compartmentation
• Examples Apartment office buildings
• Scenario Post-flashover fire (no suppression)
• Design Fire A credible but severe post-flashover
  fire
• Buildings with Large Open Spaces
• Examples Warehouses Factories
• Scenario Localized fire (diffusion flame)
• Design Fire A credible but severe localized fire

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• Model for Post-flashover Fire Severity
• Japanese 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 t0
• Fuel Load Total fuel load is consumed

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• Japanese Parametric Model
• for 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)

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• 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)

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• Duration of post-flashover fire tD (s)
• Eqn (11-26)
• L fuel load (kg m-2)
• AF area of the floor (m2)

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• Japanese Parametric Model
• 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?

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• 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)
• Eqn (11-27)
• For ISO 834 ? 230 K s-1/6
• For ASTM E119 ? 229 K s-1/6

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• 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
  acceptable
• Advantage 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 load

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• Design Considerations
• Fuel Load
• Use 95th percentile in fuel load distribution
  Eqn (11-19)
• Ventilation
• Assume unprotected openings are open
• Assume fire-rated closures remain intact
• If several vents at approximately the same
  elevation
• Eqn (11-29)
• Compartment Boundaries
• Boundaries do not include internal partitions
• If there is more than one boundary material

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• 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 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

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• Ventilation Window breaks door remains
  intact
• Compartment boundaries
• ceiling walls - ventsgypsum
  bd
• floorn.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

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• Japanese Parametric Model
• 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

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• Japanese Parametric Model
• 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 / 2303/2 x 23.5 min 47.2 min