1. Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 1 Fire Dynamics II Lecture # 3 Accumulation or Smoke Filling Jim Mehaffey 82.583 or CVG****

2. Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 2 Accumulation or Smoke Filling Outline Models for rate of descent of the hot layer (sealed & leaky enclosures)Models for rate of descent of the hot layer (sealed & leaky enclosures) Models to predict the properties of the hot layer (temperature, gas & soot concentrations)Models to predict the properties of the hot layer (temperature, gas & soot concentrations)

3. Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 3 Development of a Hot Smoke Layer Immediately after ignition: enclosure is not importantImmediately after ignition: enclosure is not important Fire characterized by free-burn heat release rateFire characterized by free-burn heat release rate

4. Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 4 Development of a Hot Smoke Layer Fire plume is established: enclosure is not importantFire plume is established: enclosure is not important Fire plume entrains airFire plume entrains air Fire characterized by free-burn heat release rateFire characterized by free-burn heat release rate

5. Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 5 Development of a Hot Smoke Layer Ceiling jet is established: height of ceiling is importantCeiling jet is established: height of ceiling is important Heat transfer to ceiling // Ceiling exerts frictional forceHeat transfer to ceiling // Ceiling exerts frictional force Fire plume entrains air; ceiling jet entrains some airFire plume entrains air; ceiling jet entrains some air Fire characterized by free-burn heat release rateFire characterized by free-burn heat release rate

6. Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 6 Development of a Hot Smoke Layer Wall alters ceiling jet flow causing downward wall jetWall alters ceiling jet flow causing downward wall jet Wall jet impeded by buoyancy  air entrainmentWall jet impeded by buoyancy  air entrainment Heat transfer to wall // wall exerts frictional forceHeat transfer to wall // wall exerts frictional force Wall jet activates wall-mounted detectors & sprinklers?Wall jet activates wall-mounted detectors & sprinklers? Fire characterized by free-burn heat release rateFire characterized by free-burn heat release rate

7. Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 7 Development of a Hot Smoke Layer Upper layer forms beneath ceiling & wall jetsUpper layer forms beneath ceiling & wall jets Plume, ceiling jet & wall jet dynamics (correlations) changePlume, ceiling jet & wall jet dynamics (correlations) change

8. Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 8 Development of a Hot Smoke Layer Detectors & sprinklers likely activated (small rooms)Detectors & sprinklers likely activated (small rooms) Upper layer may threaten life & property safetyUpper layer may threaten life & property safety Life threatening criteria: layer above “face” elevationLife threatening criteria: layer above “face” elevation –Radiant heat dangerous to skin (~25 kW m -2 or upper layer temperature ~ 200°C). (Too low to cause flashover or significant increase in ) Life threatening criteria: layer at “face” elevationLife threatening criteria: layer at “face” elevation –Reduced visibility –High temperatures –High CO levels At high temperatures potential for flashoverAt high temperatures potential for flashover

9. Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 9 Wall Flow from Hot Smoke Layer Second form of wall flow can develop as layer dropsSecond form of wall flow can develop as layer drops Gas in contact with wall cools & drops (buoyancy)Gas in contact with wall cools & drops (buoyancy) Seen in corridors: Large perimeter to height ratioSeen in corridors: Large perimeter to height ratio

10. Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 10 Model for Enclosure Smoke Filling Need for Models To predict ASET (available safe egress time)To predict ASET (available safe egress time) To provide input required for smoke managementTo provide input required for smoke management Desired Predictions Upper layer temperature and species concentrations as a function of timeUpper layer temperature and species concentrations as a function of time Upper layer depth as a function of timeUpper layer depth as a function of time Volumetric or mass flow rate into upper layerVolumetric or mass flow rate into upper layer

11. Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 11 Model for Enclosure Smoke Filling Modelling Considerations Consider fire in a single “closed” enclosureConsider fire in a single “closed” enclosure Fire located at elevation z f with heat release rate is represented as a point sourceFire located at elevation z f with heat release rate is represented as a point source A fraction (  1 ) of heat released is lost by heat transfer to boundaries of enclosure or to other surfaces within enclosure. Clearly  1 A fraction (  1 ) of heat released is lost by heat transfer to boundaries of enclosure or to other surfaces within enclosure. Clearly  1  A fraction (1 -  1 ) of heat released causes heating and expansion of gases in the enclosureA fraction (1 -  1 ) of heat released causes heating and expansion of gases in the enclosure

12. Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 12 Model for Enclosure Smoke Filling Modelling Considerations (Continued) The ceiling jet can be neglectedThe ceiling jet can be neglected Assume there are two distinct layers: an upper hot layer (smoke) and a lower cool layer (air)Assume there are two distinct layers: an upper hot layer (smoke) and a lower cool layer (air) Assume upper layer has uniform temperature and species concentrations which vary with timeAssume upper layer has uniform temperature and species concentrations which vary with time Air is entrained from the lower layer into the plumeAir is entrained from the lower layer into the plume Smoke (hot gas + soot) is transported into upper layer by the plumeSmoke (hot gas + soot) is transported into upper layer by the plume

13. Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 13 Model for Enclosure Smoke Filling Modelling Considerations (Continued) Assume leakage relieves pressure in enclosureAssume leakage relieves pressure in enclosure Once smoke layer descends to elevation of fire source entrainment of fresh air from lower layer ceasesOnce smoke layer descends to elevation of fire source entrainment of fresh air from lower layer ceases Smoke layer may continue to descend due to expansion, but intensity of fire may diminish due to oxygen depletion in upper layerSmoke layer may continue to descend due to expansion, but intensity of fire may diminish due to oxygen depletion in upper layer

14. Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 14 Pressure Rise in Sealed Enclosures Global Modelling Neglect smoke layer and treat entire enclosure as a “control volume” with uniform properties throughoutNeglect smoke layer and treat entire enclosure as a “control volume” with uniform properties throughout Energy balance for enclosure control volume:Energy balance for enclosure control volume: Eqn (3-1) U = total internal energy (kJ) = net rate of heat addition (kW) = net rate of heat addition (kW) P = pressure in enclosure (Pa) V = volume (m 3 )

15. Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 15 Pressure Rise in Sealed Enclosures Global Modelling = mass flow rate into enclosure (kg s -1 ) = mass flow rate into enclosure (kg s -1 ) h i = specific enthalpy of air (kJ kg -1 ) = mass flow rate out of enclosure (kg s -1 ) = mass flow rate out of enclosure (kg s -1 ) h O = specific enthalpy of hot gas (kJ kg -1 )

16. Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 16 Net Rate of Heat Addition Eqn (3-2) Eqn (3-2) Cooper (developer of ASET)   1 = 0.6 to 0.9Cooper (developer of ASET)   1 = 0.6 to 0.9 Values near 0.6 are appropriate for spaces with smooth ceilings & large ceiling area to height ratiosValues near 0.6 are appropriate for spaces with smooth ceilings & large ceiling area to height ratios Values near 0.9 are appropriate for spaces with irregular ceiling shapes, small ceiling area to height ratios & where fires are located against wallsValues near 0.9 are appropriate for spaces with irregular ceiling shapes, small ceiling area to height ratios & where fires are located against walls Temp predictions are sensitive to selection of (1 -  1 )Temp predictions are sensitive to selection of (1 -  1 )

17. Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 17 Pressure Rise in Sealed Enclosures In a sealed enclosureIn a sealed enclosure Define u = specific internal energy (kJ kg -1 ) so thatDefine u = specific internal energy (kJ kg -1 ) so that U =  V u  = density of gas (kg m -3 )  = density of gas (kg m -3 ) For a sealed enclosure, Eqn (3-1) simplifies toFor a sealed enclosure, Eqn (3-1) simplifies to

18. Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 18 Pressure Rise in Sealed Enclosures Assuming constant specific heat (at constant volume) (true for an ideal gas)Assuming constant specific heat (at constant volume) (true for an ideal gas) Solving for the temp rise at time t and employing the ideal gas law one findsSolving for the temp rise at time t and employing the ideal gas law one finds Eqn (3-3)

19. Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 19 Pressure Rise in Sealed Enclosures Q o,v =  o c v T o V is the ambient internal energy of the enclosure spaceQ o,v =  o c v T o V is the ambient internal energy of the enclosure space P o and T o are ambient temperature & pressureP o and T o are ambient temperature & pressure For air (diatomic molecules) c p /c v =  = 7/5 = 1.4 so that c v = c p /  = 1.0 kJ kg -1 K -1 / 1.4 = 0.714 kJ kg -1 K -1For air (diatomic molecules) c p /c v =  = 7/5 = 1.4 so that c v = c p /  = 1.0 kJ kg -1 K -1 / 1.4 = 0.714 kJ kg -1 K -1  o c v T o = 1.2 kg m -3 x 0.714 kJ kg -1 K -1 x 293 K = 251 kJ m -3  o c v T o = 1.2 kg m -3 x 0.714 kJ kg -1 K -1 x 293 K = 251 kJ m -3

20. Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 20 Pressure Rise in Sealed Enclosures Eqn (3-3) Eqn (3-3) demonstrates how quickly enclosure boundaries would fail due to over-pressurization if boundaries were fact hermetically sealedEqn (3-3) demonstrates how quickly enclosure boundaries would fail due to over-pressurization if boundaries were fact hermetically sealed A concern for fires in submarines & space shipsA concern for fires in submarines & space ships A concern for pre-mixed fires: rapid heat release rate, slow loss of heat to boundaries & slow leakageA concern for pre-mixed fires: rapid heat release rate, slow loss of heat to boundaries & slow leakage But for typical fires in typical buildings there is leakageBut for typical fires in typical buildings there is leakage

21. Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 21 Leaky Enclosures Global Modelling Neglect smoke layer and treat entire enclosure as a “control volume” with uniform properties throughoutNeglect smoke layer and treat entire enclosure as a “control volume” with uniform properties throughout Assume pressure rise caused by release of energy is relieved through available leakage pathsAssume pressure rise caused by release of energy is relieved through available leakage paths Assume gas escapes through leakage paths but cannot enter against the pressureAssume gas escapes through leakage paths but cannot enter against the pressure For leaky enclosure fires,  P / P o = 10 -3 to 10 -5. This causes significant flow through leakage paths, but is negligible as far as energy conservation is concernedFor leaky enclosure fires,  P / P o = 10 -3 to 10 -5. This causes significant flow through leakage paths, but is negligible as far as energy conservation is concerned So assume constant atmospheric pressure prevailsSo assume constant atmospheric pressure prevails

22. Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 22 Leaky Enclosures Energy balance for enclosure control volume:Energy balance for enclosure control volume: Eqn (3-4) h o = c p T e where T e is temp of escaping gash o = c p T e where T e is temp of escaping gas andand so that Eqn (3-5)so that Eqn (3-5)

23. Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 23 Leaky Enclosures Solving Eqn (3-5) for the volumetric flow rate of gases from the enclosure:Solving Eqn (3-5) for the volumetric flow rate of gases from the enclosure: Eqn (3-6) At constant pressure  e c p T e =  o c p T o =At constant pressure  e c p T e =  o c p T o = 1.2 kg m -3 x 1.0 kJ kg -1 K -1 x 293 K = 352 kJ m -3

24. Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 24 Comparison with Vent Flow Theory Lecture 4: Volumetric flow rate of gas from enclosure and pressure rise within enclosure are related as:Lecture 4: Volumetric flow rate of gas from enclosure and pressure rise within enclosure are related as: Eqn (3-7) Eqn (3-7) Where C d ~ 0.6 (vent flow coefficient)Where C d ~ 0.6 (vent flow coefficient) Combining Eqns (3-6) and (3-7) yieldsCombining Eqns (3-6) and (3-7) yields Eqn (3-8) Eqn (3-8) is useful to determine whether  P << P oEqn (3-8) is useful to determine whether  P << P o

25. Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 25 Leaky Enclosures Global Modelling of Temperature Rise Neglect smoke layer and treat entire enclosure as a “control volume” with uniform properties throughoutNeglect smoke layer and treat entire enclosure as a “control volume” with uniform properties throughout Assume gas escapes through leakage paths but cannot enter against the pressureAssume gas escapes through leakage paths but cannot enter against the pressure Substituting into Eqn (3.4) yieldsSubstituting into Eqn (3.4) yields Eqn (3-9)

26. Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 26 Leaky Enclosures Global Modelling of Temperature Rise For an ideal gas at constant pressure  =  o T o / T soFor an ideal gas at constant pressure  =  o T o / T so Eqn (3-10) Eqn (3-10) Substituting Eqn (3-10) into Eqn (3-9) yieldsSubstituting Eqn (3-10) into Eqn (3-9) yields Eqn (3-11) Eqn (3-11) Q o,p =  o c p T o V is the ambient enthalpy of enclosure space at constant pressureQ o,p =  o c p T o V is the ambient enthalpy of enclosure space at constant pressure

27. Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 27 Leaky Enclosures Global Modelling of Temperature Rise Rearranging Eqn (3-11) and integrating yieldsRearranging Eqn (3-11) and integrating yields Integrating one findsIntegrating one finds Eqn (3-12) Eqn (3-12) Permits hand calculation of “global” temperature risePermits hand calculation of “global” temperature rise If elevated fire source compute V between source & ceilingIf elevated fire source compute V between source & ceiling

28. Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 28 Leaky Enclosures Global Modelling of Oxygen Depletion Limit to how much heat released in an enclosure because finite amount of O 2 in air in enclosureLimit to how much heat released in an enclosure because finite amount of O 2 in air in enclosure Since O 2 cannot enter enclosure due to pressure, fire must eventually die down due to O 2 depletionSince O 2 cannot enter enclosure due to pressure, fire must eventually die down due to O 2 depletion Limit to heat that can be released isLimit to heat that can be released is Eqn (3-13) Eqn (3-13)

29. Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 29 Leaky Enclosures Global Modelling of Oxygen Depletion Limiting temperature rise associated with oxygen- limited heat release isLimiting temperature rise associated with oxygen- limited heat release is Eqn (3-14) Eqn (3-14)  o 2,lim fraction of O 2 that can be consumed before extinction. Given in terms of X o 2 molar fraction of O 2 as  o 2,lim fraction of O 2 that can be consumed before extinction. Given in terms of X o 2 molar fraction of O 2 as Eqn (3-15) Eqn (3-15)

30. Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 30 Leaky Enclosures Global Modelling of Oxygen Depletion Under ambient conditions: X o 2,O = 0.21Under ambient conditions: X o 2,O = 0.21 At extinction (room T & P): X o 2,lim = 0.13At extinction (room T & P): X o 2,lim = 0.13 Using Eqn (3-15),  o 2,lim = 0.4Using Eqn (3-15),  o 2,lim = 0.4 H C = heat of combustion per kg of fuel (kJ / kg)H C = heat of combustion per kg of fuel (kJ / kg) For most fuels, H C / r air = 3,000 kJ / kgFor most fuels, H C / r air = 3,000 kJ / kg c p = 1.0 kJ kg -1 K -1c p = 1.0 kJ kg -1 K -1

31. Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 31 Leaky Enclosures Consequences of Eqn (3-14) For a heat loss fraction  1 = 0.9,  T g,lim = 120 KFor a heat loss fraction  1 = 0.9,  T g,lim = 120 K For a heat loss fraction  1 = 0.6,  T g,lim = 480 KFor a heat loss fraction  1 = 0.6,  T g,lim = 480 K Significant from thermal injury or damage standpoint, but temp rise of 580 K required for flashoverSignificant from thermal injury or damage standpoint, but temp rise of 580 K required for flashover However, global temperature rise may cause fracture & collapse of ordinary plate glass windows allowing introduction of O 2 and escalation of fire intensityHowever, global temperature rise may cause fracture & collapse of ordinary plate glass windows allowing introduction of O 2 and escalation of fire intensity

32. Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 32 Smoke Filling in Leaky Enclosures Assume an Upper & Lower Layer Consider two leakage scenarios:Consider two leakage scenarios: –Case 1: Leakage near floor: Expansion of gas in upper layer causes expulsion of air from lower layer until smoke layer descends to floor. Then smoke is expelled. Considered in ASET computer model. –Case 2: Leakage near ceiling: Expansion of gas in upper layer causes expulsion of gas from upper layer. Not considered in ASET computer model.

33. Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 33 Smoke Filling in Leaky Enclosures Mass Balance on Lower Layer (Labelled 1) Case 1: Leakage near floorCase 1: Leakage near floor Eqn (3-16) Eqn (3-16) Case 2: Leakage near ceilingCase 2: Leakage near ceiling Eqn (3-17) Eqn (3-17)

34. Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 34 Smoke Filling in Leaky Enclosures Volumetric Growth Rate of Upper Layer (Labelled u) Substituting dV u = - dV 1 into Eqns (3-16) & (3-17) and dividing through by  1 (which is constant)Substituting dV u = - dV 1 into Eqns (3-16) & (3-17) and dividing through by  1 (which is constant) Case 1: Leakage near floorCase 1: Leakage near floor Eqn (3-18) Eqn (3-18) Case 2: Leakage near ceilingCase 2: Leakage near ceiling Eqn (3-19) Eqn (3-19)

35. Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 35 Smoke Filling in Leaky Enclosures Case 1: Leakage near floor: Upper layer volumetric growth due to plume entrainment & gas expansionCase 1: Leakage near floor: Upper layer volumetric growth due to plume entrainment & gas expansion Case 2: Leakage at ceiling: Upper layer volumetric growth due to plume entrainment onlyCase 2: Leakage at ceiling: Upper layer volumetric growth due to plume entrainment only If z u = depth of upper layer (m), then rate of descent of upper layer can be derived from Eqns (3-18) & (3-19) by substituting dV u = A dz u where A is floor area (m 2 )If z u = depth of upper layer (m), then rate of descent of upper layer can be derived from Eqns (3-18) & (3-19) by substituting dV u = A dz u where A is floor area (m 2 ) Assume heat release rate follows a power law in timeAssume heat release rate follows a power law in time Eqn (3-20) Eqn (3-20)

36. Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 36 Smoke Filling in Leaky Enclosures Classical axisymmetric plume entrainment theoryClassical axisymmetric plume entrainment theory Eqn (3-21) Eqn (3-21) Substitute Eqns (3-20) & (3-21) into Eqn (3-21), for n=0, an analytical solution exists for Case 2 (ceiling)Substitute Eqns (3-20) & (3-21) into Eqn (3-21), for n=0, an analytical solution exists for Case 2 (ceiling) Eqn (3-22) Eqn (3-22) Eqn (3-23) Eqn (3-23)

37. Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 37 Smoke Filling in Leaky Enclosures Observing Eqn (3-18), it is evident that Eqns (3-22) & (3-23) apply to Case 1 (floor) providedObserving Eqn (3-18), it is evident that Eqns (3-22) & (3-23) apply to Case 1 (floor) provided

38. Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 38 Smoke Filling in Leaky Enclosures Temperature Prediction Ave temp in smoke layer, T u, is calculated by noting  u T u =  o T o &  u = mass of upper layer / its volumeAve temp in smoke layer, T u, is calculated by noting  u T u =  o T o &  u = mass of upper layer / its volume Case 1: Leakage near floorCase 1: Leakage near floor Eqn (3-24) Eqn (3-24) Case 2: Leakage near ceilingCase 2: Leakage near ceiling Eqn (3-25) Eqn (3-25)

39. Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 39 Smoke Filling in Leaky Enclosures Oxygen Prediction Similar expressions can be derived for concentration (mass fraction) of O 2 in smoke layer (see Mowrer)Similar expressions can be derived for concentration (mass fraction) of O 2 in smoke layer (see Mowrer)

40. Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 40 Smoke Filling in Leaky Enclosures Numerical Predictions With few exceptions, to compute upper layer depth, temperature and O 2 concentration as functions of time, these equations must be solved numericallyWith few exceptions, to compute upper layer depth, temperature and O 2 concentration as functions of time, these equations must be solved numerically Computer models exist (ASET or ASET-B) and spreadsheet models (Mowrer)Computer models exist (ASET or ASET-B) and spreadsheet models (Mowrer)

41. Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 41 Smoke Filling in Leaky Enclosures Comparison: Spreadsheet vs Experiment Experiment 1: Hagglund et al.Experiment 1: Hagglund et al. Enclosure 5.62 m X 5.62 m x 6.15 m (high)Enclosure 5.62 m X 5.62 m x 6.15 m (high) Characteristics of fireCharacteristics of fire –0.2 m above floor –grows as  t 2 for 60 s and levels off at 186 kW –Radiative fraction = 0.35 Characteristics of modelCharacteristics of model –Not reported (  1 = ? and k V = ?)

42. Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 42 Comparison: Spreadsheet vs Experiment Experiment 1: Hagglund et al.

43. Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 43 Smoke Filling in Leaky Enclosures Comparison: Spreadsheet vs Experiment Experiment 2: Yamana and Tanaka (BRI)Experiment 2: Yamana and Tanaka (BRI) Enclosure: Floor area = 720 m 2. Height = 26.3 mEnclosure: Floor area = 720 m 2. Height = 26.3 m Characteristics of fireCharacteristics of fire –methanol pool fire (3.24 m 2 ) –grows as  t 2 for 60 s and levels off at 1.3 MW –Radiative fraction = 0.10 Characteristics of modelCharacteristics of model –  1 = 0.50 (low heat loss since low radiative loss) –Not reported (k V = ?)

44. Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 44 Comparison: Spreadsheet vs Experiment Experiment 2: Yamana and Tanaka (BRI)

45. Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 45 Smoke Filling in Leaky Enclosures Estimation: Hand Calculations - Steady Fire Depth of smoke layer: Eqn (3-22)Depth of smoke layer: Eqn (3-22) Global Temperature: Eqn (3-12)Global Temperature: Eqn (3-12) Upper Layer Temperature, T u :Upper Layer Temperature, T u : H T g = T u z u - T o (H-z u ) Eqn (3-26)

46. Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 46 Smoke Filling in an Atrium J.H. Klote & J.A. Milke (1992) H = Atrium height (m) A = Atrium floor area (m 2 ) z i = Interface height (m)

47. Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 47 Smoke Filling in an Atrium For Eqn (3-27) For Eqn (3-28)

48. Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 48 Smoke Filling in an Atrium Correlations {Eqns (3-27) & (3-28)} developed by comparison with experiment –Valid for 0.2  z i / H  1.0 –Valid for 0.90  A H -2  14.0 –Valid for unobstructed plume flow (Fire is ”far" from walls)

49. Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 49 Estimation of Temperature of Smoke Layer The heat release rate of the fire can be written Assumptions is radiated away from the fire below smoke layer is convected into smoke layer No heat loss from smoke layer to atrium boundaries

50. Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 50 Estimation of Temperature of Smoke Layer Energy balance for upper layer Eqn (3-29) c p = specific heat of gas in smoke layer ~ 1.0 kJ kg -1 K -1 @ T = 293 K (air) ~ 1.1 kJ kg -1 K -1 (smoke layer is mostly N 2 ) Substitute  h T h =  a T a into Eqn (3-**). Get upper limit for T h Eqn (3-30)

51. Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 51 Estimation of Concentration of Chemical Species in Smoke Layer The total mass of fuel consumed is given by The total mass mass of CO generated is m co = Y co m fuel The total mass mass of soot (S) generated is m S = Y S m fuel

52. Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 52References F.W. Mowrer, Fire Safety Journal, Volume 33, pp 93-114 (1999) J.H. Klote & J.A. Milke, Design of Smoke Management Systems ASHRAE & SFPE, 1992, pp. 107-108