Fire Dynamics II

1
Fire Dynamics II

• Lecture 3
• Accumulation or Smoke Filling
• Jim Mehaffey
• 82.583 or CVG

2

• Accumulation or Smoke Filling
• Outline
• 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)

3

• Development of a Hot Smoke Layer
• Immediately after ignition enclosure is not
  important
• Fire characterized by free-burn heat release rate
  

4

• Development of a Hot Smoke Layer
• Fire plume is established enclosure is not
  important
• Fire plume entrains air
• Fire characterized by free-burn heat release rate

5

• Development of a Hot Smoke Layer
• Ceiling jet is established height of ceiling is
  important
• Heat transfer to ceiling // Ceiling exerts
  frictional force
• Fire plume entrains air ceiling jet entrains
  some air
• Fire characterized by free-burn heat release rate

6

• Development of a Hot Smoke Layer
• Wall alters ceiling jet flow causing downward
  wall jet
• Wall jet impeded by buoyancy ? air entrainment
• Heat transfer to wall // wall exerts frictional
  force
• Wall jet activates wall-mounted detectors
  sprinklers?
• Fire characterized by free-burn heat release rate

7

• Development of a Hot Smoke Layer
• Upper layer forms beneath ceiling wall jets
• Plume, ceiling jet wall jet dynamics
  (correlations) change

8

• Development of a Hot Smoke Layer
• Detectors sprinklers likely activated (small
  rooms)
• Upper layer may threaten life property safety
• Life threatening criteria layer above face
  elevation
• Radiant heat dangerous to skin (25 kW m-2 or
  upper layer temperature 200C). (Too low to
  cause flashover or significant increase in
  )
• Life threatening criteria layer at face
  elevation
• Reduced visibility
• High temperatures
• High CO levels
• At high temperatures potential for flashover

9

• Wall Flow from Hot Smoke Layer
• Second form of wall flow can develop as layer
  drops
• Gas in contact with wall cools drops (buoyancy)
• Seen in corridors Large perimeter to height
  ratio

10

• Model for Enclosure Smoke Filling
• Need for Models
• To predict ASET (available safe egress time)
• To provide input required for smoke management
• Desired Predictions
• Upper layer temperature and species
  concentrations as a function of time
• Upper layer depth as a function of time
• Volumetric or mass flow rate into upper layer

11

• Model for Enclosure Smoke Filling
• Modelling Considerations
• Consider fire in a single closed enclosure
• Fire located at elevation zf 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 - ?1) of heat released causes
  heating and expansion of gases in the enclosure

12

• Model for Enclosure Smoke Filling
• Modelling Considerations (Continued)
• The ceiling jet can be neglected
• 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 time
• Air is entrained from the lower layer into the
  plume
• Smoke (hot gas soot) is transported into upper
  layer by the plume

13

• Model for Enclosure Smoke Filling
• Modelling Considerations (Continued)
• Assume leakage relieves pressure in enclosure
• Once 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 layer

14

• Pressure Rise in Sealed Enclosures
• Global Modelling
• Neglect smoke layer and treat entire enclosure as
  a control volume with uniform properties
  throughout
• Energy balance for enclosure control volume
• Eqn (3-1)
• U total internal energy (kJ)
• net rate of heat addition (kW)
• P pressure in enclosure (Pa)
• V volume (m3)

15

• Pressure Rise in Sealed Enclosures
• Global Modelling
• mass flow rate into enclosure (kg s-1)
• hi specific enthalpy of air (kJ kg-1)
• mass flow rate out of enclosure (kg
  s-1)
• hO specific enthalpy of hot gas (kJ kg-1)

16

• Net Rate of Heat Addition
• Eqn (3-2)
• Cooper (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
  ratios
• Values 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)

17

• Pressure Rise in Sealed Enclosures
• In a sealed enclosure
• Define u specific internal energy (kJ kg-1) so
  that
• U ? V u
• ? density of gas (kg m-3)
• For a sealed enclosure, Eqn (3-1) simplifies to

18

• Pressure Rise in Sealed Enclosures
• 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 finds
• Eqn (3-3)

19

• Pressure Rise in Sealed Enclosures
• Qo,v ?ocvToV is the ambient internal energy of
  the enclosure space
• Po and To are ambient temperature pressure
• For air (diatomic molecules) cp/cv ? 7/5
  1.4 so that cv cp / ? 1.0 kJ kg-1 K-1 / 1.4
  0.714 kJ kg-1 K-1
• ?ocvTo 1.2 kg m-3 x 0.714 kJ kg-1 K-1 x 293 K
  251 kJ m-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 sealed
• A concern for fires in submarines space ships
• A 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 leakage

21

• Leaky Enclosures
• Global Modelling
• Neglect 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 paths
• Assume gas escapes through leakage paths but
  cannot enter against the pressure
• For leaky enclosure fires, ?P / Po 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 prevails

22

• Leaky Enclosures
• Energy balance for enclosure control volume
• Eqn (3-4)
• ho cp Te where Te is temp of escaping gas
• and
• so that Eqn (3-5)

23

• Leaky Enclosures
• Solving Eqn (3-5) for the volumetric flow rate of
  gases from the enclosure
• Eqn (3-6)
• At constant pressure ?ecpTe ?ocpTo
• 1.2 kg m-3 x 1.0 kJ kg-1 K-1 x 293 K 352 kJ
  m-3

24

• Comparison with Vent Flow Theory
• Lecture 4 Volumetric flow rate of gas from
  enclosure and pressure rise within enclosure are
  related as
• Eqn (3-7)
• Where Cd 0.6 (vent flow coefficient)
• Combining Eqns (3-6) and (3-7) yields
• Eqn (3-8)
• Eqn (3-8) is useful to determine whether ?P ltlt Po

25

• Leaky Enclosures
• Global Modelling of Temperature Rise
• Neglect 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 pressure
• Substituting into Eqn (3.4) yields
• Eqn (3-9)

26

• Leaky Enclosures
• Global Modelling of Temperature Rise
• For an ideal gas at constant pressure ? ?oTo /
  T so
• Eqn (3-10)
• Substituting Eqn (3-10) into Eqn (3-9) yields
• Eqn (3-11)
• Qo,p ?ocpToV is the ambient enthalpy of
  enclosure space at constant pressure

27

• Leaky Enclosures
• Global Modelling of Temperature Rise
• Rearranging Eqn (3-11) and integrating yields
• Integrating one finds
• Eqn (3-12)
• Permits hand calculation of global temperature
  rise
• If elevated fire source compute V between source
  ceiling

28

• Leaky Enclosures
• Global Modelling of Oxygen Depletion
• Limit to how much heat released in an enclosure
  because finite amount of O2 in air in enclosure
• Since O2 cannot enter enclosure due to pressure,
  fire must eventually die down due to O2 depletion
• Limit to heat that can be released is
• Eqn (3-13)

29

• Leaky Enclosures
• Global Modelling of Oxygen Depletion
• Limiting temperature rise associated with
  oxygen-limited heat release is
• Eqn (3-14)
• ?o2,lim fraction of O2 that can be consumed
  before extinction. Given in terms of Xo2 molar
  fraction of O2 as
• Eqn (3-15)

30

• Leaky Enclosures
• Global Modelling of Oxygen Depletion
• Under ambient conditions Xo2,O 0.21
• At extinction (room T P) Xo2,lim 0.13
• Using Eqn (3-15), ?o2,lim 0.4
• HC heat of combustion per kg of fuel (kJ / kg)
• For most fuels, HC / rair 3,000 kJ / kg
• cp 1.0 kJ kg-1 K-1

31

• Leaky Enclosures
• Consequences of Eqn (3-14)
• For a heat loss fraction ?1 0.9, ?Tg,lim
  120 K
• For a heat loss fraction ?1 0.6, ?Tg,lim
  480 K
• Significant 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 O2 and
  escalation of fire intensity

32

• Smoke Filling in Leaky Enclosures
• Assume an Upper Lower Layer
• 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

• Smoke Filling in Leaky Enclosures
• Mass Balance on Lower Layer (Labelled 1)
• Case 1 Leakage near floor
• Eqn (3-16)
• Case 2 Leakage near ceiling
• Eqn (3-17)

34

• Smoke Filling in Leaky Enclosures
• Volumetric Growth Rate of Upper Layer (Labelled
  u)
• Substituting dVu - dV1 into Eqns (3-16)
  (3-17) and dividing through by ?1 (which is
  constant)
• Case 1 Leakage near floor
• Eqn (3-18)
• Case 2 Leakage near ceiling
• Eqn (3-19)

35

• Smoke Filling in Leaky Enclosures
• Case 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 only
• If zu depth of upper layer (m), then rate of
  descent of upper layer can be derived from Eqns
  (3-18) (3-19) by substituting dVu A dzu where
  A is floor area (m2)
• Assume heat release rate follows a power law in
  time
• Eqn (3-20)

36

• Smoke Filling in Leaky Enclosures
• Classical axisymmetric plume entrainment theory
• Eqn (3-21)
• Substitute Eqns (3-20) (3-21) into Eqn (3-21),
  for n0, an analytical solution exists for Case 2
  (ceiling)
• Eqn (3-22)
• Eqn (3-23)

37

• Smoke Filling in Leaky Enclosures
• Observing Eqn (3-18), it is evident that Eqns
  (3-22) (3-23) apply to Case 1 (floor) provided

38

• Smoke Filling in Leaky Enclosures
• Temperature Prediction
• Ave temp in smoke layer, Tu, is calculated by
  noting ?uTu ?oTo ?u mass of upper layer /
  its volume
• Case 1 Leakage near floor
• Eqn (3-24)
• Case 2 Leakage near ceiling
• Eqn (3-25)

39

• Smoke Filling in Leaky Enclosures
• Oxygen Prediction
• Similar expressions can be derived for
  concentration (mass fraction) of O2 in smoke
  layer (see Mowrer)

40

• Smoke Filling in Leaky Enclosures
• Numerical Predictions
• With few exceptions, to compute upper layer
  depth, temperature and O2 concentration as
  functions of time, these equations must be solved
  numerically
• Computer models exist (ASET or ASET-B) and
  spreadsheet models (Mowrer)

41

• Smoke Filling in Leaky Enclosures
• Comparison Spreadsheet vs Experiment
• Experiment 1 Hagglund et al.
• Enclosure 5.62 m X 5.62 m x 6.15 m (high)
• Characteristics of fire
• 0.2 m above floor
• grows as ?t2 for 60 s and levels off at 186 kW
• Radiative fraction 0.35
• Characteristics of model
• Not reported (?1 ? and kV ?)

42

• Comparison Spreadsheet vs Experiment
• Experiment 1 Hagglund et al.

43

• Smoke Filling in Leaky Enclosures
• Comparison Spreadsheet vs Experiment
• Experiment 2 Yamana and Tanaka (BRI)
• Enclosure Floor area 720 m2. Height 26.3 m
• Characteristics of fire
• methanol pool fire (3.24 m2)
• grows as ?t2 for 60 s and levels off at 1.3 MW
• Radiative fraction 0.10
• Characteristics of model
• ?1 0.50 (low heat loss since low radiative
  loss)
• Not reported (kV ?)

44

• Comparison Spreadsheet vs Experiment
• Experiment 2 Yamana and Tanaka (BRI)

45

• Smoke Filling in Leaky Enclosures
• Estimation Hand Calculations - Steady Fire
• Depth of smoke layer Eqn (3-22)
• Global Temperature Eqn (3-12)
• Upper Layer Temperature, Tu
• H Tg Tu zu - To (H-zu) Eqn (3-26)

46

• Smoke Filling in an Atrium
• J.H. Klote J.A. Milke (1992)
• H Atrium height (m)
• A Atrium floor area (m2)
• zi Interface height (m)

47

• Smoke Filling in an Atrium
• For
• Eqn (3-27)
• For
• Eqn (3-28)

48

• Smoke Filling in an Atrium
• Correlations Eqns (3-27) (3-28) developed by
  comparison with experiment
• Valid for 0.2 ? zi / H ? 1.0
• Valid for 0.90 ? A H-2 ? 14.0
• Valid for unobstructed plume flow
• (Fire is far" from walls)

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

• Estimation of Temperature of Smoke Layer
• Energy balance for upper layer
• Eqn (3-29)
• cp specific heat of gas in smoke layer
• 1.0 kJ kg-1 K-1 _at_ T 293 K (air)
• 1.1 kJ kg-1 K-1 (smoke layer is mostly
  N2)
• Substitute ?hTh ?aTa into Eqn (3-). Get upper
  limit for Th
• Eqn (3-30)

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
• mco Yco mfuel
• The total mass mass of soot (S) generated is
• mS YS mfuel

52

• References
• 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