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MINISTERO DELL’INTERNO
DIPARTIMENTO DEI VIGILI DEL FUOCO,
DEL SOCCORSO PUBBLICO E DELLA DIFESA CIVILE
DIREZIONE CENTRALE PER LA FORMAZIONE
An Application In Fire Safety Engineering
C. Barbera, A. Bascià, G. Di Salvo, A. Galfo, R. Lala,
S. Lucidi, D. Maisano, G. Mancini, V. Puccia, F. Vorraro
I e II Corso Direttori Antincendi
Istituto Superiore Antincendi Roma
Fire Service College Moreton-in-Marsh
FIRE SAFETY
Deterministic Approach
Laws and regulations
Fire Engineering Approach
Fire Models
FIRE ENGINEERING APPLICATIONS
• In absence of specific laws and regulations
• When specific laws and regulations can’t be complied with
• Fire investigation
• High risk activities (safety report)
FIRE ENGINEERING: OPERATIVE VS. NUMERICAL MODELS
Fitted parameters models (or operative models or zone models)
• They solve exactly a set of simplified semi – empirical equations
(momentum, energy, mass)
• The computational domain is divided into mixed zones, where intensive
properties (i.e., P, T, concentrations) are assumed to be homogeneous
• They yield temperature and gases and smoke concentration in each zone
Distributed parameters models (or numerical models or field models)
• They solve numerically (i.e., approximately) a set of exact balance
equations (momentum, energy, mass)
• The computational domain is meshed by means of a calculation grid,
whose refinement affects the accuracy of the result
• They yield temperature and concentration profiles as a function of time
and space
AN OPERATIVE MODEL: CFAST
Hypotheses
• Confined fires
• Two mixed volumes: upper layer (hot layer) + lower layer (cold layer)
ventilation controlled fire
• tcomb << t = V / Q
Controlling parameters
SmA
• 
equivalence factor
me
• Ventilation factor,
• Heat Release Rate (HRR)
 S: stoichiometric ratio air / fuel
 m: specific combustion rate [=] kg m-2 s-1
 A: compartment section [=] m-2
 me: air mass flow rate [=] kg s-1
Correlation equation
X  X 0 [1   / exp (/ ) - ]
 X: output variable
 X0 : X evaluated in unconfined fires
 , , : correlation parameters
AN OPERATIVE MODEL: CFAST
Equations
dmi
 m i
dt
dP   1  

hL  hU
dt
V

mass equation

pressure equation
dEi 1 
dP
 (hi  Vi
)
dt 
dT
energy equation
dVi
1
dP
 ((  1)hi  Vi
)
dt P
dT
volume equation
d i
V dP
1

(( hi  c p m i Ti )  i
)
dt
c p Ti Vi
  1 dT
density equation
dTi
1
dP

(( hi  c p m i Ti )  Vi
)
dt
c p  i Vi
dT
temperature equation
AN OPERATIVE MODEL: CFAST
Inputs
• Geometry (compartment dimension, ventilation surface, etc.)
• Material properties (thermal conductivities, etc.)
• Fire geometry and position
• HRR vs. time curve
Outputs
• Average temperature in both layers
• height of layer interfacies
• O2 concentration
• CO concentration
• visibility index
• mass and enthalpy exchange rates
A NUMERICAL MODEL: FDS (Fire Dynamics Simulator)
Hypotheses
• Both confined and unconfined fires
• Rate of Heat Release (HRR) not depending on O2 concentration
Equations
•
•
•
•
•
Mass conservation
Momentum conservation (three scalar equations)
Constitutive law (nine scalar equations)
Energy conservation
Chemical species conservation
A NUMERICAL MODEL: FDS (Fire Dynamics Simulator)
Inputs
• Geometry (compartment dimension, ventilation surface, etc.)
• Material properties (thermal conductivities, etc.)
• Position and characteristics of ignition sources
• Rate of Heat Release (HRR): depends on fuel and combustion conditions
Outputs
• Pressure, temperature, velocity and chemical species concentrations as
a function of time and space
• Fluxes and exchange rates
COMPUTATIONAL DOMAIN (D.M. 16/2/1982 All.I – act. 87)
Plan
Cross Section
North View
South View
COMPUTATIONAL DOMAIN (D.M. 16/2/1982 All.I – act. 87)
• Geometry
Two compartments
Ventilation surfaces (2 windows + 1 external door + 1 internal door)
• Material properties
Concrete walls ( = 2100 kg m-3; cp = 0.88 kJ kg-1 K-1; kT = 1 W m-1 K-1)
• Fire geometry and position
7 cellulosic material stacks
• Heat Release Rate (HRR):
depends on fuel and combustion conditions
CFAST NUMERICAL RUNS
HRR [=] MW
HRR    t 2
t0
Run 1:
sensitivity
analysis on the
role of 
t1
t2
t [=] s
t3
Runs
1
0.0029
kW s-2
2
0.0049
kW s-2
3
0.0069
kW s-2
4
0.009
kW s-2
5
0.011
kW s-2
6
0.02
kW s-2
HRRmax (MW)
27.55
32.83
36.90
40.22
42.97
52.39
t0 (s)
0
0
0
0
0
0
t1 (s)
3080
2585
2300
2110
1975
1620
t2 (s)
9240
7755
6900
6330
5925
4860
t3 (s)
12320
10340
9200
8440
7900
6480
A TYPICAL CFAST OUTPUT WINDOW
Profiles
Values
 = 0.0069 kW s-2
 = 0.009 kW s-2
 = 0.011 kW s-2
 = 0.02 kW s-2
OUTPUTS OF CFAST RUN 1
Run 1
1
0.0029
kW s-2
2
0.0049
kW s-2
3
0.0069
kW s-2
4
0.009
kW s-2
5
0.011
kW s-2
6
0.02
kW s-2
h1 (m)
1.21
1.21
1.21
1.21
1.21
1.21
h2 (m)
0.89
0.88
0.87
0.86
0.86
0.86
Tu1 (°C)
670
654
643
636
630
610
Tl1 (°C)
585
567
554
546
538
514
Tu2 (°C)
289
282
278
275
272
265
Tl2 (°C)
61
60
59
59
58.7
58
 h1: interfacies height in compartment 1
 h2: interfacies height in compartment 2
 Tu1: maximum temperature in the upper layer in compartment 1
 Tl1: maximum temperature in the lower layer in compartment 1
 Tu2: maximum temperature in the upper layer in compartment 2
 Tl2: maximum temperature in the lower layer in compartment 2
CFAST NUMERICAL RUNS
Run 2: sensitivity analysis on the role of ventilation factor
OUTPUTS OF CFAST RUN 2
Run 2
(6 = 0.02)
Vf1
0.031
Vf2
0.034
Vf3
0.0366
Vf4
0.046
t600 (min)
77.8
56.2
46.3
28.1
h1 (m)
1.21
1.21
1.22
1.27
h2 (m)
0.86
0.92
0.99
1.11
Tu1 (°C)
610
665
704
813
Tl1 (°C)
514
564
596
707
Tu2 (°C)
265
271
273
282
Tl2 (°C)
58
54
50
44
 t600: t corresponding to Tu = 600 °C
FDS NUMERICAL RUNS
Operative assumptions
Distributed parameters model
Fire load can be splitted!
7 stacks with HRR = HRRmax / 7
Fire starts from stack 1
Each stack burns when T ≥ 200°C (ignition temperature)
Run1: without sprinklers
Run 2: with sprinklers
OUTPUTS OF FDS RUN 1
Ceiling temperature
Ceiling temperature vs. time
t (T1max) = 338 s
Ceiling temperature distribution at
t = 338 s
OUTPUTS OF FDS RUN 1
Smoke propagation:
even though at t = 180 s only one stack burns, smoke invades both the
compartments.
t = 60 s
t = 120 s
t = 180 s
t = 338 s
FDS NUMERICAL RUN 2
Sprinklers lay-out
Sprinklers characteristics
• Operating pressure: 0.483 bar
• K: 79 l min-1 bar -1/2
• Activation temperature: 74°C
• RTI (Response Time Index): 110 (m·s)1/2
OUTPUTS OF FDS RUN 2
Ceiling temperature
700
370,00
320,00
Synoptic
Tc1
Tc1
Tc2
600
no sprinkler
sprinkler
Tc3
Tc4
Tc5
270,00
500
Temperature [°C]
Temperature [°C]
Tc6
Tc7
220,00
170,00
400
300
120,00
200
70,00
100
20,00
0,00
0
100,00
200,00
300,00
400,00
500,00
600,00
0
100
200
Tim e [s]
400
500
600
300
300
Tc4
250
no sprinkler
Tc7
250
sprinkler
no sprinkler
sprinkler
200
200
Temperature [°C]
Temperature [°C]
300
Tim e [s]
150
100
150
100
50
50
0
0
0
100
200
300
Tim e [s]
400
500
600
0
100
200
300
Tim e [s]
400
500
600
OUTPUTS OF FDS RUN 2
Smoke propagation and sprinkler activation:
the first sprinkler activates
at t = 111.6 s…
… and the last one at t = 330 s
CONCLUSIONS…
• Zone models are very sensitive to ventilation factor and HRR vs. time
curve (controlling parameters): they are quick and simple
• Field models allow a more realistic and flexible problem description:
accurate input estimation is required and simulations are very time
expensive
• T vs. t curves yielded by the two models are different but similarly
shaped
… AND FURTHER INVESTIGATIONS
• A set of numerical runs has to be carried out in order to gain a deeper
insight in T vs. t curves
• A comparison between model prediction and deterministic approach
results can be performed