1 / 52

Fire Dynamics II

Fire Dynamics II. Lecture # 10 Pre-flashover Fire Jim Mehaffey 82.583. Pre-flashover Fire Outline Develop a model to predict: Upper layer temperature (function of time) required for flashover Time to flashover. Predicting Pre-flashover Fire Temperatures

bonner
Download Presentation

Fire Dynamics II

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

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

  5. 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, 82.583, 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, 82.583, 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, 82.583, 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, 82.583, Fire Dynamics II, Winter 2003, Lecture # 10

  9. 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, 82.583, 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, 82.583, 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, 82.583, 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, 82.583, 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, 82.583, 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, 82.583, 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, 82.583, 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, 82.583, Fire Dynamics II, Winter 2003, Lecture # 10

  17. Consequently one can write Carleton University, 82.583, 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, 82.583, Fire Dynamics II, Winter 2003, Lecture # 10

  19. 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, 82.583, Fire Dynamics II, Winter 2003, Lecture # 10

  20. Findings: • x = N = 2/3 • y = M = - 1/3 • CT = 480 K • Rewrite Eqn (10-12) Eqn (10-13) Carleton University, 82.583, 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, 82.583, 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, 82.583, 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, 82.583, 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, 82.583, 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, 82.583, 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, 82.583, Fire Dynamics II, Winter 2003, Lecture # 10

  28. Impact of boundary (thermal properties) Carleton University, 82.583, 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, 82.583, Fire Dynamics II, Winter 2003, Lecture # 10

  30. Thermal Properties At elevated temperatures associated with fire Carleton University, 82.583, Fire Dynamics II, Winter 2003, Lecture # 10

  31. Impact of size of openings Carleton University, 82.583, 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 = 0.444 kJ2 m-4 s-1 K-2 • Post-flashover fire: ventilation controlled • . . . . “Standard fire” CAN4-S101 (ASTM E119) Carleton University, 82.583, 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 3 + 4 x 3 x 2.4 - 0.8 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, 82.583, 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 = 0.0254 m • Walls & ceiling: thermal penetration time • Walls & ceiling: thermal inertia = 0.742 kJ m-2 s1/2 K-1 Carleton University, 82.583, 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 = 0.0254 m • Floor: thermal penetration time • Floor: thermal inertia = 0.436 kJ m-2 s1/2 K-1 Carleton University, 82.583, 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 0.742 + 9 x 0.436) kJ s1/2 K-1 = 30.78 kJ s1/2 K-1 Carleton University, 82.583, Fire Dynamics II, Winter 2003, Lecture # 10

  37. Example • The temperature is given by Carleton University, 82.583, Fire Dynamics II, Winter 2003, Lecture # 10

  38. Example • The temperature is given by Carleton University, 82.583, 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, 82.583, 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, 82.583, 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, 82.583, 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 = 1.26 kJ kg-1 K-1 • Th = 600 K • Correlation with experimental data: • Finding: Eqn (10-21) Carleton University, 82.583, Fire Dynamics II, Winter 2003, Lecture # 10

  43. Rate of Heat Release Required for Flashover Example: Same room as in Slides 10-33 to 10-38 Babrauskas Thomas MQH = 610 (0.438 x 2.26)1/2 = 610 kW Carleton University, 82.583, Fire Dynamics II, Winter 2003, Lecture # 10

  44. Rate of Heat Release Required for Flashover within 10 minutes = 600 s MQH = 610 (30.78 / 24.5 x 2.26)1/2 = 1030 kW Carleton University, 82.583, 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: 0.110 to 0.325 kg s-1 • Measured temperatures: 100 to 300°C Carleton University, 82.583, 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, 82.583, Fire Dynamics II, Winter 2003, Lecture # 10

  47. Cone Calorimeter (3) - ISO 5660 & ASTM E1354 Carleton University, 82.583, Fire Dynamics II, Winter 2003, Lecture # 10

  48. Cone Calorimeter Data - Thermoset Carleton University, 82.583, Fire Dynamics II, Winter 2003, Lecture # 10

  49. Model for a Thermoset Carleton University, 82.583, Fire Dynamics II, Winter 2003, Lecture # 10

  50. 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, 82.583, Fire Dynamics II, Winter 2003, Lecture # 10

More Related