Transcript Fire Dynamics I - Carleton University
Fire Dynamics II
Lecture # 3 Accumulation or Smoke Filling
Jim Mehaffey 82.583 or CVG****
Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 1
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) Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 2
Development of a Hot Smoke Layer
• Immediately after ignition: enclosure is not important • Fire characterized by free-burn heat release rate Q (t) Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 3
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
Q
Q RAD
Q CONV
Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 4
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 Q (t) Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 5
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 Q (t) Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 6
Development of a Hot Smoke Layer
• Upper layer forms beneath ceiling & wall jets • Plume, ceiling jet & wall jet dynamics (correlations) change Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 7
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 ~ 200 °C). (Too low to Q • Life threatening criteria: layer at “face” elevation – Reduced visibility – High temperatures – High CO levels • At high temperatures potential for flashover Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 8
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 Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 9
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 Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 10
Model for Enclosure Smoke Filling Modelling Considerations
• Consider fire in a single “closed” enclosure • Fire located at elevation z f is represented as a point source Q • A fraction ( 1 ) of heat released is lost by heat transfer to boundaries of enclosure or to other surfaces within enclosure. Clearly 1 Q (t) Q (t) RAD • A fraction (1 1 ) of heat released causes heating and expansion of gases in the enclosure Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 11
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 Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 12
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 Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 13
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: dU dt Q NET m i h i m O h O P dV dt Eqn (3-1)
U = total internal energy (kJ)
Q NET
= net rate of heat addition (kW) P = pressure in enclosure (Pa) V = volume (m 3 )
Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 14
Pressure Rise in Sealed Enclosures Global Modelling
m
i
= mass flow rate into enclosure (kg s -1 ) h i
m O
= specific enthalpy of air (kJ kg -1 ) = mass flow rate out of enclosure (kg s -1 ) h O = specific enthalpy of hot gas (kJ kg -1 )
Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 15
Net Rate of Heat Addition
Q NET Q 1 1 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 ) Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 16
Pressure Rise in Sealed Enclosures
• In a sealed enclosure m i m O dV dt d dt 0 • 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 V du dt Q NET Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 17
Pressure Rise in Sealed Enclosures
• Assuming constant specific heat (at constant volume) (true for an ideal gas) c V V dT Q NET dt • Solving for the temp rise at time t and employing the ideal gas law one finds
P P O
T T O
0
t Q O c V NET dt T O V
Q NET Q O
,
V
Eqn (3-3) Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 18
Pressure Rise in Sealed Enclosures
• Q 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 & pressure • • For air (diatomic molecules) c p /c v that c v = c p / = 1.0 kJ kg -1 K -1 = = 7/5 = 1.4 so / 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
Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 19
Pressure Rise in Sealed Enclosures
P P O
T T O
0
t Q O c V NET dt T O V
Q NET Q O
,
V
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 Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 20
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 / 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 prevails Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 21
Leaky Enclosures
• Energy balance for enclosure control volume: Q NET m O h O Eqn (3-4) • h o = c p T e where T e is temp of escaping gas • and
m O
e V
e
• so that Q NET e c p T e V
e
Eqn (3-5) Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 22
Leaky Enclosures
• Solving Eqn (3-5) for the volumetric flow rate of gases from the enclosure:
V
e
(
m
3 /
s
)
Q
e c NET p T e
Q NET (kW) 352 (kJ/m 3 ) Eqn (3-6) • 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
Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 23
Comparison with Vent Flow Theory
• Lecture 4: Volumetric flow rate of gas from enclosure and pressure rise within enclosure are related as: V e C d A leak 2 P
e
Eqn (3-7) • Where C d ~ 0.6 (vent flow coefficient) • Combining Eqns (3-6) and (3-7) yields
P
1 2
e
e c Q p T e
NET C d A leak
2 Eqn (3-8) • Eqn (3-8) is useful to determine whether P << P o Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 24
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
m O
d
dt V
V d
dt
• Substituting into Eqn (3.4) yields Q NET m O h O c p T V
d
dt
Eqn (3-9) Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 25
Leaky Enclosures Global Modelling of Temperature Rise
• For an ideal gas at constant pressure = o T o / T so
d
dt
O T O T
2
dT dt
Eqn (3-10) • Substituting Eqn (3-10) into Eqn (3-9) yields
Q NET
O c p T O V
1
T dT dt
Q O
,
p
1
T dT dt
Eqn (3-11) • Q o,p = o c p T o V is the ambient enthalpy of enclosure space at constant pressure Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 26
Leaky Enclosures Global Modelling of Temperature Rise
• Rearranging Eqn (3-11) and integrating yields 0 t
Q NET Q O
,
p dt
T O T g dT T
• Integrating one finds
T g T O
exp
Q NET Q O
,
p
1 Eqn (3-12) • Permits hand calculation of “global” temperature rise •
If elevated fire source compute V between source & ceiling
Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 27
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 enclosure • Since 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 is
Q
lim 1
Q O
,
p
1 ln 1
O V Q O
,
p H C r air
O
2 , lim ( 1 1 ) Eqn (3-13) Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 28
Leaky Enclosures Global Modelling of Oxygen Depletion
• Limiting temperature rise associated with oxygen limited heat release is
T g
, lim
H C r air
O
2 , lim 1 1
c p
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
X O
2 ,
O
X O
2 , lim
X O
2 ,
O
Eqn (3-15) Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 29
Leaky Enclosures Global Modelling of Oxygen Depletion
• Under ambient conditions: X o 2,O = 0.21
• At extinction (room T & P): X o 2,lim = 0.13
• Using Eqn (3-15), o 2 ,lim = 0.4
• H C = heat of combustion per kg of fuel (kJ / kg) • For most fuels, H C / r air = 3,000 kJ / kg • c p = 1.0 kJ kg -1 K -1 Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 30
Leaky Enclosures Consequences of Eqn (3-14)
• For a heat loss fraction 1 = 0.9, T g,lim = 120 K • For 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 flashover • However, global temperature rise may cause fracture & collapse of ordinary plate glass windows allowing introduction of O 2 and escalation of fire intensity Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 31
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.
Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 32
Smoke Filling in Leaky Enclosures Mass Balance on Lower Layer (Labelled 1)
•
Case 1: Leakage near floor
d
1
dt
1
dV
1
dt
m pl
m e
Eqn (3-16) •
Case 2: Leakage near ceiling
d
1
dt
1
dV
1
dt
m pl
Eqn (3-17) Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 33
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)
Case 1: Leakage near floor
dV dt U
m pl
1
m e
V
pl
V
e
Case 2: Leakage near ceiling
dV U dt
m pl
1
V
pl
Eqn (3-18) Eqn (3-19) Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 34
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 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 time
Q
n t n
Eqn (3-20) Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 35
Smoke Filling in Leaky Enclosures
• Classical axisymmetric plume entrainment theory V
pl
k V
1 / 3
Q CONV z
5 / 3 Eqn (3-21) • Substitute Eqns (3-20) & (3-21) into Eqn (3-21), for n=0, an analytical solution exists for
Case 2 (ceiling)
z u H
1 1 2
t
3
V
3 / 2 Eqn (3-22)
V
V
V pl
,
H
k V A H
1 / 3
Q CONV
2
H
4 / 3 Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 Eqn (3-23) 36
Smoke Filling in Leaky Enclosures
• Observing Eqn (3-18), it is evident that Eqns (3-22) & (3-23) apply to
Case 1 (floor)
provided
V
pl
V
e
Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 37
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 volume
Case 1: Leakage near floor
T u
(
t
)
T O
0
t
(
V
pl
0
t V
pl V
dt e
)
dt
Case 2: Leakage near ceiling
T u
(
t
)
O T O
0
t
(
O V
0
t V
pl
pl dt
u V
e
)
dt
Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 Eqn (3-24) Eqn (3-25) 38
Smoke Filling in Leaky Enclosures Oxygen Prediction
• Similar expressions can be derived for concentration (mass fraction) of O 2 in smoke layer (see Mowrer) Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 39
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 numerically • Computer models exist (ASET or ASET-B) and spreadsheet models (Mowrer) Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 40
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 t 2 for 60 s and levels off at 186 kW – Radiative fraction = 0.35
• Characteristics of model – Not reported ( 1 = ? and k V = ?) Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 41
Comparison: Spreadsheet vs Experiment Experiment 1
: Hagglund et al.
Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 42
Smoke Filling in Leaky Enclosures Comparison: Spreadsheet vs Experiment
•
Experiment 2
: Yamana and Tanaka (BRI) • Enclosure: Floor area = 720 m 2 . Height = 26.3 m • Characteristics 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 model – 1 = 0.50 (low heat loss since low radiative loss) – Not reported (k V = ?) Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 43
Comparison: Spreadsheet vs Experiment Experiment 2
: Yamana and Tanaka (BRI) Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 44
•
Smoke Filling in Leaky Enclosures Estimation: Hand Calculations - Steady Fire Depth of smoke layer: Eqn (3-22)
z u H
1 1 2
t
3
V
3 / 2 •
Global Temperature: Eqn (3-12)
T T O g
exp
Q NET Q O
,
p
1 •
Upper Layer Temperature, T u :
H T g = T u z u - T o (H-z u ) Eqn (3-26) Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 45
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)
Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 46
Smoke Filling in an Atrium
• For Q (t) Q 0 (kW) z i H 1.11
0.28
ln H t Q 1/3 0 4/3 (AH 2 ) Eqn (3-27) • For Q (t) t 2 1000 t t g 2 (kW) z i H 0.91
H 4/5 t t A g H 2/5 2 3/5 1.45
Eqn (3-28) Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 47
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) Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 48
Estimation of Temperature of Smoke Layer
• The heat release rate of the fire can be written
Q
Q RAD
Q CONV
• •
Assumptions
Q RAD
is radiated away from the fire below smoke layer
Q CONV
is convected into smoke layer • No heat loss from smoke layer to atrium boundaries Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 49
Estimation of Temperature of Smoke Layer
• Energy balance for upper layer
h
c p T h T a A (H z i ) 0 t Q CONV dt 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
1
T a T h
into Eqn (3-**). Get upper limit for T h
0
t Q CONV
a c p T a A
(
H dt
z i
) Eqn (3-30) Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 50
Estimation of Concentration of Chemical Species in Smoke Layer
• The total mass of fuel consumed is given by m fuel H ch 0 t Q dt • 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 Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 51
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 Carleton University, 82.583 (CVG****), Fire Dynamics II, Winter 2003, Lecture # 3 52