Fire Safety Engineering & Structures in Fire
Workshop at Indian Institute of Science
9-13 August, 2010
Bangalore
India
Fundamentals of Fire Dynamics
Session JT3 to JT8
Organisers:
CS Manohar and Ananth Ramaswamy
Indian Institute of Science
Speakers:
Jose Torero, Asif Usmani and Martin Gillie
The University of Edinburgh
Funding and
Sponsorship:
Evacuation
te = tde + tpre+ tmov
♦
♦
♦
♦
te – total egress time
tde – detection time
tpre – pre-movement time
tmov – movement or displacement time
Movement
♦ Egress is formulated on the basis of
displacement velocities
V [m/seg]
1 [m/seg]
D [people/m2]
Movement time(tmov)
♦ Calculations are based on empirical data (SFPE Handbook of Fire
Protection Engineering)
Pre-Movement (tpre)
♦ Purely statistical
♦ Large error bars
♦ Could potentially be the longest time
Detection time (tde)
♦ Calculated as a function of:
– Technology used
– Growth of the fire
– Compartment geometry
Detection
♦ Obvious alarm mechanism
♦ Types of detectors:
– Smoke detectors (ionization, photoelectric)
– CO Detectors
– Temperature detectors
– Multiple inputs (Artificial Intelligence)
– etc.
Movement time
♦ Empirical results are available for:
– Doors: (q) Personas/m.seg – Act like valves
Q= w.q
• Where w is the width of the door and Q the total flow rate
–
–
–
–
Stairs: (q) Personas/m.seg – Act like pipes
Ramps: (q) Personas/m.seg – Act like pipes
Corridors: (q) Personas/m.seg – Act like pipes
Open spaces: (V) velocity in m/s as a function of the
density (N – people/m2)
– Etc.
Simple Systems
♦ Egress time is the
displacement time + time to
go through a door: Required
Safe Egress Time (RSET)
♦ Untenable conditions give
the Available Safe Egress
Time (ASET)
♦ Codes transform these times
into a maximum
displacement distance + a
required minimum door
width
Maximum Egress Distance
♦ Egress Time (te) (RSET)
te= td + tp
♦ td=dMax/Ve
♦ tp= W.Ve,p
♦ W, dMax given by codes
More Complex Scenarios
♦ Maximum egress distances can not be achieved
– Safe areas need to be generated with fire
rated walls, doors, etc.
– Example: Stairs in high rise buildings
– The design of these safe areas has to
withstand a fire longer than the RSET
♦ Egress is directed to safe areas
Complex Systems
Street Level
16.4%
♦ Generally are multiple
entry, multiple exit
systems
♦ Requires more
complex calculations
Restaurant + Coffee shop
♦ But the principles are
8.1%
the same
Waiting Area
37.9%
Train Platform
37.6%
Complete Problem
♦ To be able to analyze such a system all
components must be understood
♦ It is necessary to calculate tf, te y ts
♦ Uncertainty needs to be established
The Fire Time (tf)
♦ To calculate the characteristic fire times it is
essential to understand compartment fire
dynamics
Introduction
♦ Smoke inhalation is responsible for most of the
deaths in a fire
♦ What do we need to know to determine the amount of
smoke produced by a fire?
♦ What is in that smoke?
♦ How is the smoke going to migrate from the room of origin
to the rest of the building?
♦ What has to be done to control smoke migration?
♦ How do we use the smoke for warning? - Detection
The Pre-flashover Fire
)
“The Front Room Fire”
(BRE Video)
The Pre-flashover Fire
)
)
The Pre-flashover Fire
)
)
)
The Pre-flashover Fire
The Compartment Fire
H
VS
TU
VS
TS
S
m
 a,o
m
Ta
e
m
e
m
f
m
 a,i
m
The Pre-flashover Fire
)
)
Flashover
The Fire
♦ Temperatures in
Two Zone Fires are
controlled by fuel
burning rates (Fuel
Limited)
♦ Temperatures in
fully developed fires
are controlled by
ventilation
(Ventilation Limited)
Timeline
Ventilation Limited
A (Floor Area)
H0
A0: Opening Area
H0: Opening Height
Ventilation
~3 m
12-18.5 m
♦ A~ 3000 m2
♦ A0~ 100 m2
♦ H0~ 3 m
♦ Ventilation Factor: A/A0H01/2~20
The Temperatures
• Empirical Data can be
used to estimate fire
temperatures
2
Mass Loss Rate per uint Total Area, g/m
♦ Depending on the
average compartment
temperature a mass
loss rate can be
established
♦ Total consumption of
the fuel defines the
longest possible fire
duration
-s
Duration of the Fire
80
70
60
Wood cribs
PU cribs
PMMA pools
PMMA pools, Vent-lim.
50
40
30
20
10
0
0
200
400
600
800
1000
Compartment Ceiling Gas Temperature (
1200
o
C)
 f
m
kg / m .s
2
♦ Fuel Load
M f
kg / m 
2
♦ Duration of the fire
M f
tf 
 f
m
2
Mass Loss Rate per uint Total Area, g/m
C.I.B.
♦ Fuel consumption per
unit area per unit time
-s
Duration of the Fire
80
70
60
Wood cribs
PU cribs
PMMA pools
PMMA pools, Vent-lim.
50
40
30
20
10
0
0
200
400
600
800
1000
Compartment Ceiling Gas Temperature (
1200
o
C)
Simplest Approach
Temperature:C.I.B.
Slope is defined by losses
through the walls (resistance
method)
7oC/min (t>60 min)
10oC/min (t<60 min)
tf
Resistance Method
h r  104  725
W / m2K
(500 o C  1200 o C)
1/Ahr
1/Ahr
Ta
Tf
1/Ahk
1/Ahc
k
h C  Nu g
H
1/Ahc
hK 
 kC
4 t
Fuel Limited (Growth-PreFlashover)
♦ Zone Model – Divides the room into two well
defined zones
– Upper Layer – Hot combustion products
– Lower Layer – Cold air
♦ Implies strong simplifications but help
understand the dynamics of the problem
Initial Stages of a Compartment Fire
H
VS
– Upper Layer The parameters
that need to be
evaluated are:
TU
VS
TS
S
m
 a,o
m
Ta
e
m
e
m
f
m
 a,i
m
• The temperature
of the upper layer:
Tu
• The velocity at
which the Upper
Layer descends:
VS 
dH
dt
Initial Stages of a Compartment Fire
♦ These parameters can be obtained from, the ideal
gas law and conservation of mass and energy in
the Upper Layer
P  RT u

A(Tu )H( t )  m S
t



 SCp TS
A(Tu )H( t )Cp Tu  m
t
Conservation of Energy
S m
 f m
e
m



 SCp TS
A(Tu )H( t )Cp Tu  m
t
♦ Unknowns:
QP
f
m
e
m
 SCp (TS  Ta )
Qm
P
Correlations
♦ The “Energy Release Rate”
f
Q  HCm
♦ Mass of air entrained
1/ 3
 g 

 Q1/ 3 (H 0  H( t )) 5 / 3
m e  0.20
 C P Ta 
2
a
♦ Mass Burning Rate: Generally obtained from empirical
correlations
 f  f (D, Q,Fuel )
m
References
♦ Different engineering correlations are proposed in
the literature
– SFPE Handbook of Fire Protection Engineering
– NFPA-The Fire Protection Handbook
– Karlsson and Quintiere, “Enclosure Fire Dynamics,” CRC
Press, 2000.
– Drysdale, “An Introduction to Fire Dynamics,” John Wiley
and Sons, 1999
– Cox, “Combustion Fundamentals of Fire,” Academic
Press, 1995
– etc., etc., etc….
The “Energy Release Rate, Q”
Q
♦ The effective energy
release rate that will be
transferred to the
combustion products is
unknown.
♦ The effective energy used
to gasify the fuel is
unknown.
P
Qr
Q
QF
f
m
aQ
QC
QS,r
Assumptions
♦ Total Energy:
♦ Feedback is generally
assumed to be small
♦ Radiation is assumed to
be a fraction of the total
energy released
Q  QP  QF  Qr
QF  0
Qr  Q
  0.3
QP  (1 )Q  0.7Q
Simplifications
♦ Under these
assumptions we can
correlate everything
with “Q”
♦ There is no need to
“calculate” QP directly
♦ How do we calculate
“Q”?
f
Q  HCm
1/ 3
 g 

 Q1/ 3 (H 0  H( t )) 5 / 3
m e  0.20
 C P Ta 
2
a
 f  f (D, Q,Fuel )
m
The Energy Release Rate
f
Q  HCm
Can be found in
tables but
generally only for
simple materials,
i.e. liquid fuels
Can be found for
some particular
conditions,
generally difficult
to generalize to
real scenarios
♦ Generally “Q” is evaluated empirically
Standard Test Methods
♦ The Cone Calorimeter
 Energy Release Rate obtained from Oxygen Consumption
– ASTM E 1354 Standard Test Method for Heat and Visible
Smoke Release Rates for Materials and Products Using an
Oxygen Consumption Calorimeter
– NFPA 264 Standard Method of Test for Heat and Visible
Smoke Release Rates for Materials and Products Using an
Oxygen Consumption Calorimeter
– ISO 5660 Rate of Heat Release of Building Products (Cone
Calorimeter)
♦ Ohio State University Calorimeter (OSUCalorimeter)
• Energy Release Rate obtained from temperature measurements
of the combustion products
– ASTM E906 Standard Test Method for Heat and Visible
Smoke Release Rates for Materials and Products
The Cone Calorimeter (ASTM E 1354 )
Fundamental Issues
♦ Heat Release Rate is obtained indirectly by
measuring O2 consumption
♦ Mass is obtained real-time allowing a true mass
loss rate to be obtained
♦ External Heat Fluxes of 0 to 100 kW/m2 may be
achieved simulating conditions from incipient
stages of a fire to post-flashover conditions
O2 Consumption
COMPLETE COMBUSTION
♦ Main simplifying assumptions:
– Energy release per unit mass of O2,constant
E = 13.1 MJ/kg of O2 consumed
– Ideal gas law applies
– O2 depletion factor assumes each mole of air
required for complete combustion is
replaced by 1.105 moles of products
nf  nair  np  1.105nair
Energy Released/kg of O2
[MJ/kg]
Energy Released per kg of O2
18
16
14
12
10
8
6
4
2
0
0
5
10
Carbon Atoms
15
Example
CH4  2(O2  3.76N2 )  CO2  2H2O  7.52N2
2  7.52  1  2  7.52  1.105nair  nP
♦ The assumption is reasonable but can be
improved by measuring CO, CO2, soot
concentration and reconstructing the
chemical reaction
O2 Consumption
To
Blower
 ex
m
Exhaust Duct
= control volume
 in
m
Plenum
Hood
f
m
Calculations
♦ Oxygen concentration is measured at the
exhaust
♦ Incoming oxygen concentration is that of
air
♦ Therefore oxygen consumed is given by:
O m
 O .in  m
 O .ex
m
2
2
2
Calculations
♦ Using this information, the energy release
rate can be calculated as:
O
Q  13.1 m
2
MJ
Calculations
2P
mex  cA 

o To

Texh
P
Density of the exhaust gas
Pressure differential across the exhaust orifice
A
Cross sectional area of the exhaust stack
c
Orifice coefficient
Solution
♦ How much smoke?
♦ How much time does it take? H(tO)=HO
♦ The following equations need to be solved:
P  RT u

A(Tu )H( t )  m S
t



 SCp TS
A(Tu )H( t )Cp Tu  m
t
Solution
1/ 3
 g 

 Q1/ 3 (H 0  H( t )) 5 / 3
m e  0.20
 C P Ta 
P  RT u
2
a

A(Tu )H( t )  m S
t
1.105nair  np
 S  f (m
 e)
m



 SCp TS
A(Tu )H( t )Cp Tu  m
t
 SCp (TS  Ta )  0.7Q
QP  m
Q comes from experimental data – Calorimetry
Experimental Results
♦ Ideal Scenario:
Q
m f
f
m
t
t
Kerosene
600
500
2
HRR (kW/m )
400
Series1
Series2
Series3
300
200
100
0
0
25
50
75
100
125
Time (s)
150
175
200
225
Gasoline
800
700
600
2
HRR (kW/m )
500
Series1
Series2
Series3
400
300
200
100
0
0
25
50
75
Time (s)
100
125
150
Naphthalene
1200
1000
2
HRR (kW/m )
800
Series1
Series2
Series3
600
400
200
0
0
25
50
75
Time (s)
100
125
The Real Scale Application
♦ Large Scale Calorimeters
– Factory Mutual
– Underwriters Laboratories
– BRE
Design Fire
♦ Simple representation of the HRR
  H m




Q


H
A
m
C
f
C
B
f
A B  r 2  (Vf t ) 2  (Vf2 ) t 2


2
2
2

 f  H C (Vf )m
 f t  at
Q  H C A B m
t2 parameters
Incipient heat release rate (Q*i)
Incipient period (to)
Growth time (tg)
Growth HRR(Q*o)
Peak HRR (Q*max)
Total HR (Q)
Burnout time (tbo)
RELEASE RATE
♦
♦
♦
♦
♦
♦
♦
1
2
3
4
Q max
tg
Q o
Q
Q i
to
tbo
TIME
Fire growth characterization
Q=at2
Loveseat
Loveseat
Qmax
Q=at2
Bunk bed
♦ Corner ignition of lower bunk
♦ Data from “Fire on the Web” (www.bfrl.nist.gov)
Mattress
HRR data resources
♦ BFRL / NIST - Fire on the Web
– www.bfrl.nist.gov
♦ Lund University - Report on initial fires
– www.brand.lth.se
♦ Many other scattered reports
♦ Some data included in fire model suites
– CFAST; FPETool
Initial Stages of a Compartment Fire
♦ With “Q” and the empirical correlations we
can come back and evaluate:
P  RT u

A(Tu )H( t )  m S
t



 SCp TS
A(Tu )H( t )Cp Tu  m
t
The Solution
♦ For most cases the solution to those three
simultaneous equations has to be achieved
numerically
♦ Several “codes” are available that will solve the
equations
♦ Always remember what the assumptions are and
where correlations were included
♦ Make sure that the assumptions and correlations
apply to your particular scenario
Smoke Movement
H
VS
TU
VS
TS
S
m
 a,o
m
Ta
e
m
e
m
f
m
 a,i
m
Objectives
♦ How much smoke?
♦ How much time will it take for the smoke to
come out of the room of origin?
♦ What is in the smoke?
Solution
♦ How much smoke?
♦ How much time does it take? H(tO)=HO
♦ The following equations need to be solved:
P  RT u

A(Tu )H( t )  m S
t



 SCp TS
A(Tu )H( t )Cp Tu  m
t
Solution
1/ 3
 g 

 Q1/ 3 (H 0  H( t )) 5 / 3
m e  0.20
 C P Ta 
P  RT u
2
a

A(Tu )H( t )  m S
t
1.105nair  np
 S  f (m
 e)
m



 SCp TS
A(Tu )H( t )Cp Tu  m
t
 SCp (TS  Ta )  0.7Q
QP  m
Q comes from experimental data – Calorimetry
Design Fire
♦ Simple representation of the HRR
  H m




Q


H
A
m
C
f
C
B
f
A B  r 2  (Vf t ) 2  (Vf2 ) t 2


2
2
2

 f  H C (Vf )m
 f t  at
Q  H C A B m
How do we calculate the area?
A B  r  (Vf t )  (V ) t
2
2
2
f
♦ A function of the flame spread
– Flame spread is a function of ignition
2
Ignition
q e
q ( L)
x
x=0
L
♦ Simplest case
– 1-D
– Constant heat
flux
Ignition Events
 F
m
q e
TFP
TfP
TP
0
♦
♦
♦
♦
Flash Point
Fire Point
Auto-Ignition
Piloted Ignition
♦ Piloted ignition
minimizes environmental
variables-preferred to
study the solid phase!
x
Standard Protocols to Assess the Solid
♦ Introduce many simplifications
♦ A standard methodology will be described
and all simplifications and assumptions
studied
The Lateral Ignition Flame Test (LIFT-ASTM-1321)
Ignition Test
Flame Spread Test
The Lateral Ignition and Flame Spread Test (LIFT)
t ig  t p  t m  t i
t ig  t p  t m  t i
t ig  t p
TP
T(x,t>tP)
 F (t  t P )
m
x
T(x,tP)
Ignition Delay Time
Ignition Delay Time [s]
1400
1200
1000
800
600
Critical Heat
Flux for
Ignition
400
200
0
0
5
10
15
20
25
30
2
External Heat Flux [kW/m ]
35
40
45
Results
♦ The experimental data is fitted to the theoretical predictions
and all characteristic values are extracted
♦ The total heat transfer coefficient is evaluated (hT)
♦ Material properties are evaluated (kC, Tig)
Assumptions
♦ Semi-Infinite Solid
♦ Linearized Total Heat Transfer Coefficient: hT=hC+hS,r
♦ Solid remains inert until ignition
Summary
2500
"
q
time [sec]
2000
0 ,ig
 h T (Tig  T )
1500
"
1
1000
t ig
500
0
0
10
Critical Heat Flux
for Ignition
q e
20
30
2
[kW/m ]
40

2

1
q
kc Tig  T 
i
Ignition Properties
1
t ig
Material

Tig [oC]
q
"
2
1

kc Tig  T

e

kC
[s.kW2/m4K2]
Douglas Fir
Cedar
Iroko
Polyisocianurate
Polyurethane
PMMA
Acrilic
382
402
410
445
390
378
300
0.94
1.22
1.30
0.02
0.30
1.02
0.42
Critical
Heat Flux [kW/m2]
16
18
17
21
16
15
10
Flame Spread
♦ Propagation Rates
are controlled by
orientation
♦ Propagation
defines the
evolution in size
with time of the fire
Forward
Propagation
Flame
Opposed
Propagation
Lateral
Propagation
Opposed Flame Spread
T
g
Cp,g
lg
VF
TF
S C P ,S Vf (TP  T ) d T  q g d S
U
Vf 
T
-x
dg
q g d S
 S C P ,S (TP  T ) d T
e
x
T
S
Cp,S
lS
dT
L
Thermally Thick
dT 
TP
l S (TP  T )
q g
Thermally Thin
T
dS
x
dT  L
Thermally Thick
♦ Solution
Vf 
q g
S
l SS C P ,S (TP  T ) 2
♦ Flame Spread Parameter
♦ Solution
d
2
  q g  d S

Vf 
l SS C P,S (TP  T ) 2
2
LIFT Test - Flammability Diagram
1400
0.0045
0.004
1200
F*
Vf 
[ q 0,ig  q e ] 2
0.003
800
tig (s)
0.0025
Flame
Spread
Data
600
0.002
Ignition Data
0.0015
400
q "o ,ig  11
kW
m2
0.001
200
0.0005
0
0
0
10
20
30
40
50
Incident Heat Flux (kW/m2)
60
70
Vf (m/s)
1000
0.0035
Flame Spread Properties
F*
Vf 
[ q 0,ig  q e ] 2
Material
Minimum Flux
[kW/m2]
Douglas Fir
Cedar
Particle Board
Polyurethane
Acrilic
PMMA
6.0
9.0
5.7
0.0
2.0
0.0
F*
[kW2/s.m3]
2.3
1.2
2.1
11.7
9.9
14.4
Design Fire
♦ Simple representation of the HRR
  H m




Q


H
A
m
C
f
C
B
f
A B  r 2  (Vf t ) 2  (Vf2 ) t 2


2
2
2

 f  H C (Vf )m
 f t  at
Q  H C A B m
Smouldering
♦ Smouldering leads to propagation rates 100
times slower than flaming fires
♦ Therefore is important to establish if the fire
originated in smouldering
Smouldering Limits
1600
Exposure Time (s)
1400
1200
1000
800
600
400
ignition
no ignition
200
0
5.9
6
6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9
kW/m2
What is inside the smoke?
♦ Generally defined by yields (Yp)
♦ A yield is the fraction of the total mass that
corresponds to the specific product
♦ The mass of the specific product is given by:
 CO  YCOm
S
m
Typical Yields
Irritants
Compound
Formaldehyde
Acetaldehyde
Acetone
Phenol
Xylene
Styrene
Pyrolysis Yield
(%)
0
0
0
0
0.61
0.56
Oxidation Yield
(%)
3.32
3.50
3.84
1.16
0.02
0.40
Threshold Value
(ppm)
2
100
750
5
From Purser, SFPE Handbook,
1995
These values vary from fuel to fuel and from
burning conditions to burning condition
Carbon Monoxide (I)
Flaming Combustion
Material
PVC
Methane
Propane
Polyester
Rayon
Polyurethane
Paper
Wood (red oak)
CO Yield
(%)
Well Ventilated
11
0.1
0.1
1.5
4.3
1
0.3
0.4
CO Yield
(%)
Under-Ventilated
42
10
12
From Tewarson, SFPE Handbook,
1995
♦ CO yields for smoldering tend to be much higher,
i.e. 6% for polyurethane foam
Carbon Monoxide (II)
3
Heavy Work
Light Work
Sitting
2.5
%CO2
2
1.5
1
0.5
0
0
10
20
minutes
30
40
From Purser, SFPE Handbook,
1995
♦ Time to incapacitation because of CO
inhalation
Carbon Monoxide (III)
♦ It is necessary to know the concentration of CO
within the smoke
♦ An additional differential equation has to be
incorporated for each species

AYCO, u(Tu )H( t )  m CO  YCOm S
t
♦ The CO concentration is a direct function of the
fire size