a`1

Workshop
Mathematical Modelling and Numerical Simulation of
Forest Fire Propagation
Predicting Eruptive Fire
Behaviour
by
Domingos Xavier Viegas
Department of Mechanical Engineering, University of
Coimbra, Portugal
xavier.viegas@dem.uc.pt
Vigo, 29/30 November 2007
Contents
• Introduction
• Modeling Fire Behaviour
• Eruptive Fire Behaviour
• Case Studies
• Conclusion
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Introduction
• For many years we have observed that forest
fires can behave in an extreme way with a
sudden acceleration and reach very high
rates of spread.
• This sudden change in fire behaviour has
caught by surprise many fire fighters and has
been the cause of many fatal accidents.
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• Scientists and managers have tried to explain
and model this phenomenon in the past.
• Current fire behaviour models do not deal easily
with ROS values that change in orders of
magnitude.
• Several arguments have been proposed to
explain it, but in my opinion most of them are not
convincing.
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• This phenomenon is known in the literature
as “blow-up”.
• We prefer to call it a fire eruption.
• In this lecture we will deal with the problem of
sudden fire acceleration in forest fires and
propose an explanation for it and present a
model to predict fire behaviour.
• I hope that you will understand why this
phenomenon can not be called unpredictable.
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• This lecture is based on the research that is
carried out by my Group at the University of
Coimbra for the past 20 years in forest fire
propagation.
• I acknowledge the contribution given by my
co-workers and the support given to our
research program by several institutions.
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• Methodology:
– Analytical and numerical work
– Field and laboratory experiments
– Analysis of real cases.
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Forest Fire Research Laboratory
2004
Seoul
September 2007
8
Combustion wind tunnel
Túnel de-Combustão
Lousã
Portugal
Seoul
September 2007
9
Joint effect of slope and wind
Seoul
September 2007
10
Fire spread in canyons – Large Table
DE 4
Seoul
September 2007
11
Vertical Combustion
Tunnel
Seoul
September 2007
12
Experimental field of Gestosa
Lousã (Portugal)
Seoul
September 2007
13
Gestosa 2002
31st May 2002
Seoul
September 2007
14
Observation of real fires
Fundão, 30 Jul 03
Seoul
September 2007
15
Analysis of accidents
Seoul
September 2007
16
Modelling Fire Behaviour
• Fire spread regimes:
– Low intensity fire (Ground fire)
– Average intensity fire (Surface fire)
– High intensity fire
• Eruptive fire
• Crown fire
• Spot fire
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• Classical fire behaviour modelling is
based on various assumptions:
RB
SA
RB
A
UA
B
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Fu
ro l
teo
Me
el
Triangle of Fire Factors
y
og
Topography
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• Concept of rate of spread
Present fire behaviour modeling is based on the
concept of rate of spread ROS
R = φ (U, α, mf, Mc, σ, β, …)
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• Concept of rate of spread ROS:
– The movement of the fire front is
characterized by a ROS vector that is well
defined at each point of the fire front.
• Local independence:
– The ROS vector depends only on the local
properties at each point of the fire front.
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• Reference or Basic ROS
U=0 and α=0º
R=Ro
Ro = φ (mf, Mc, σ, β, …)
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Combustibility Table
Determination of Ro
Combustibility Table
Seoul
September 2007
23
Determination of Ro
Ro (cm/s)
0,5
0,4
P. Pin.
0,3
0,2
0,1
0,0
0
10
20
30
40
50
60
70
80
mf (%)
Seoul
September 2007
24
• Effect of wind or
slope
R
R' =
= φ' (U, α)
Ro
• Concept of elliptical growth
RB
SA
RB
A
UA
B
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3 - Eruptive Fire Behaviour
• Fires in steep slopes and in canyons
have a peculiar behaviour.
• Their rate of spread increases
continuously and in the limit they
produce a “fire eruption”
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Eruptive processes in Nature
Forest fires
Volcanoes
Monte de Santa Helena
Seoul
Incêndio de Thirtymile, 10 Julho 2001
September 2007
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Monte de Santa Helena
Loop Fire 1966
Seoul
September 2007
Staff Ride
28
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DE 3
Canyon shaped Table
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30
Point ignition in a canyon
Fuelbed of pinus pinaster
16
14
R'in
R'med
12
R'fin
δ=40º
R/Ro
10
8
6
4
2
0
-45
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0
α º
15
30
45
31
Fire spread with wind
R1
U’o
L’
Uo
R
R’
D
D’
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The Square of Fire:
Time
Vegetation
Meteorology
Topography
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Jan. 2002
DE 2
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Δt=20”
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250
s1
200
20º
150
a=0º
a=10º
100
a=20º
a=30º
50
a=40º
0
0
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200
300
400
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600
700
37
16
ds1/dt
14
Rate of spread
cm/s
Velocidade
de propagação
12
10
8
a=0º
a=10º
6
a=20º
a=30º
20º
a=40º
4
2
0
0
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200
300
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400
500
600
t (s)
38
700
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A m2
1600
25000
1400
Área
Area(m2)
Perimeter(m)
Perímetro
20000
1200
1000
15000
800
600
10000
400
5000
200
0
00:00
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10:00
15:00
20:00
25:00
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35:00
0
40:00
41
P m
1800
30000
Mathematical model
• Based on the laboratory experiments we
developed a mathematical model for this
phenomena.
• This is a semi-empirical model based on two
assumptions that takes into account the
feedback between the fire and the
surrounding flow.
Viegas, 2005
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First assumption:
• There is a univocal relationship between the
surrounding flow velocity and the rate of
spread (ROS):
• R=f(U)
R
b1
R' =
= 1 + a1U
Ro
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Combustion tunnel
Lousã - Portugal
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R/Ro
25
Wind effect
20
Exp.
15
2R’=1+1.10 U
2.02
10
5
Pine needles
0
0
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4
U m/s
5
45
Second assumption:
• The instantaneous wind velocity is modified
by the flow induced by the fire:
U=Ua+ΔUf
• This induced wind velocity change is
univocally related to the Rate of Spread:
ΔUf= g(R). dt
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• The fire induced flow velocity increase
during time step dt is given by the
following function of ROS:
dU = a 2R' .dt
b2
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Combining the two previous equations we can
eliminate the flow velocity variable U between
them to obtain a differential of the rate of
spread (ROS) as an explicit function of time:
df
df
dR
dR =
.dU =
.g.dt =
.dt
dU
dU
dt
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In the present case the development is the following:
b1
R ' = 1 + a1.U
⎡ (R'−1) ⎤
U=⎢
⎥
⎣ a1 ⎦
dU =
1
1
1 1b1
ba
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b1
(R'−1)
1
−1
b1
.dR'
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b2
dU = a 2 .R' .dt
49
Differential equation of the model
1
1−
b1
1
dR'
= a1b1 a 2b1(R'−1)
dt
R'
b2
dR
R − Ri = ∫
.dt
t i dt
t
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Non-dimensional form
• Reference parameters
– Ro
– to
– Uo
Basic rate of spread
Residence or reaction time
Reference wind velocity
(Uo=1 m/s)
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a’1=a1Uob =a1
1
a’2=a2.to
R’=R/Ro
t’=t/to
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Non-dimensional equations
R’=1+a’1U’b1
dU’=a’2R’b2.dt’
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• Combining both equations we obtain:
1
1−
b1
1
dR'
= a'1b1 a'2 b1(R'−1)
dt'
1
dR'
= a1b1 a 2b1(R'−1)
dt
1−
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1
b1
R'
R'
b2
b2
54
Determination of a’2 and b2
1
−1
b1
dR' (R'−1)
Y = a' 2 R ' =
.
1
dt' b a' b1
b2
1
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δ=11º
δ=20º
δ=32º
δ=40º
α=0º
α=10º
α=20º
α=30º
α=40º
Configurations tested in the basic program
Viegas and Pita, 2004
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Dead litter of Pinus pinaster
a1=1.10
b1=2.02
to=80s
0.22 cm/s<Ro<0.34 cm/s
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Ref.
α
δ
Ref.
α
δ
501
10º
40º
512
20º
20º
502
20º
40º
513
30º
20º
503
30º
40º
514
40º
20º
506
10º
32º
516
10º
11º
507
20º
32º
517
20º
11º
508
30º
32º
518
30º
11º
509
40º
32º
531
40º
0º
511
10º
20º
532
30º
0º
Test cases
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Validation
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0,20
0,15
Outliers
533
518
531
512
514
508
506
502
Y
516
0,10
0,05
0,00
0
5
10
15
R'
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For pine needles
a’2=0. 496 and b2=1.16
Using R’i=1.1 we integrate the
differental equation.
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15
Model
517
519
511
10
513
507
R'
509
501
503
5
0
0
50
100
150
200
250
300
t (s)
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• Particular case of b1=b2=1
R’=1+a1U
dU=a2R’dt
dR'
= a1a 2 .dt
R'
R'
a1a 2 .t
=e
R'i
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dR’=a1.dU
[ln R']
R'
R 'i
= a1a 2 .t
Exponential growth of ROS
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Model parameters
Ro
Basic rate of spread
to
Residence time of the fire in the fuelbed
a1
Wind law coefficient
b1
Wind law exponent
a2
Induced velocity coefficient
b2
Induced velocity exponent
R1
Initial value of the ROS
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Extension to other fuels
• Generalization of the model to other fuel
types besides the ones considered in
the experimental program.
• Field experiments and real cases.
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Common fuel types
•
•
•
•
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Herbaceous
Litter
Shrubs
Slash
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Range of variation of the model parameters
Herbaceous
Litter
Shrubs
Slash
Min
Max
Min
Max
Min
Max
Min
Max
Ro
0,001
0,01
0,001
0,01
0,001
0,01
0,001
0,01
a1
3
1
1,5
0,5
1
0,2
0,5
0,1
b1
2
3
2
2,5
1,5
2,5
1
1,5
a2
0,001
0,01
0,001
0,01
0,0001
0,001
0,00005
0,0005
b2
1,5
2
1
1,5
1
1,5
0,5
1
t0
10
50
30
100
100
2000
1000
10000
a'1
3
1
1,5
0,5
1
0,2
0,5
0,1
a'2
0,05
0,1
0,1
0,3
0,2
0,1
0,5
0,5
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Typical values of the parameters
Ro
HB
0,005
LT
0,002
SR
0,005
SL
0,001
a1
1,4
1
0,8
0,6
b1
2,3
2,2
2
1,13
a2
0,01
0,0062
0,0005
0,0001
b2
1,5
1,2
1,1
0,8
t0
30
80
1000
5000
a'1
1,4
1
0,8
0,6
a'2
0,3
0,496
0,5
0,5
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10,000
HB
LT
SR
SL
R (m/s)
1,000
0,100
0,010
0,001
1
10
100
1000
10000
100000
t (sec)
Viegas, 2006
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1000,00
X (m)
100,00
10,00
1,00
HB
LT
SR
0,10
SL
0,01
10
100
1000
10000
100000
t (sec)
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Same fuel with different moisture content values
10,000
R (m/s)
1,000
0,001
0,002
0,005
0,100
0,010
0,001
1
10
100
1000
t (sec)
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10,000
X (m)
1,000
0,001
0,002
0,005
0,100
0,010
0,001
1
10
100
1000
t (sec)
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Other models and explanations
• Complete mathematical models
• Empirical explanations
–
–
–
–
Topography
Fuels
Meteorology
Miscelaneous
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• Fuels
– Fuel dessication
– Thermal belt
– Fuel transition
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• Meteorology
–
–
–
–
–
–
–
–
Passage of a cold front (wind shift)
Venturi effect
Vertical instability of the atmosphere
Low altitude jet stream
Daily air temperature variations
Air turbulence
Air vorticity
Colapse of convection column
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• Miscelaneous
– Spot fires
– Radiation from one slope to another
– Air buble with volatile gases
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4 - Case Studies
• The eruptive fire behaviour is related to
many accidents with fatalities that have
occurred in forest fires.
• As the ROS is initially very low the fire
fighters can be mislead by the
behaviour of the fire when attacking the
fire.
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• If the suppression of the fire is not
achieved in time the fire may erupt and
reach their position with great intensity.
• Unfortunately this has happened – and
continues to happen – too many times
in the past.
• Brief mention to some case studies.
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Freixo de Espada-a-Cinta
• The year 2003 was particularly bad in terms
of forest fires in Portugal. There were 21
persons killed in 18 fire related accidents.
• This case occurred in the North of Portugal
on the 5th of August of 2003.
• Two persons (a couple 50 and 40 years old)
were killed in this accident.
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Meteo station
Accident
Start of Fire
Start of blow-up
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5-8-03
2 Victims
Freixo de Espada à Cinta
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60
Freixo E C
50
5 Aug 03
Air temperature
Temperature
40
30
20
10
0
0:00
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12:00
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18:00
21:00
0:00
84
70
60
Relative humidity
50
40
30
20
10
0
0:00
3:00
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9:00
12:00
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18:00
21:00
0:00
85
360
315
Rumo
do vento
Wind
direction
270
225
180
135
90
45
0
0:00
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9:00
12:00
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18:00
21:00
0:00
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100
90
80
Average and
maximum
Wind
velocity Wind velocity
70
60
50
40
30
20
10
0
0:00
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6:00
9:00
12:00
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18:00
21:00
0:00
87
120
Model prediction
100
Modelo
Umax
U km/h
80
Uaver
60
40
20
0
0
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100
120
Minutos
88
• This case shows that the interaction
between the fire and the surrounding air
can modify dramatically both fire
behaviour properties and the
meteorological conditions.
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Mann Gulch
Fire
• USA 1949
• 13 Victims
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A Race that could not be Won
Rothermel, 1990
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Loop Fire
1st November 1966
12 Victims
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Loop Fire under the influence of the Santa Ana wind.
Staff Ride
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South
Canyon Fire
USA 1994
14 Victims
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1200
South Canyon
R'
1000
800
Observações
600
400
Modelo presente
200
Ro=0.166 cm/s
0
0
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600
900
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1200
1500
1800
96
t (s)
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Thirtymile Fire
10 July 2001
4 victims
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160
140
Thirty Mile Accident
120
R'
100
80
Model
60
Observ
40
20
0
0
1
2
3
4
5
6
7
8
t (h)
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Guadalajara
• This accident occurred on the 17th July
2005.
• 11 Firefighters were killed by a double
fire eruption.
• This accident raised great concerns in
Spain and is promoting many changes.
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Guadalajara
July
2005
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Guadalajara
17 de Julho de 2005
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Famalicão
• This accident occurred in Famalicão da
Serra (Guarda- Portugal) on the 9th
July 2006.
• Six fire fighters were killed in this
accident. Five of them were Chilean
citizens working as professionals in fire
suppression in Portugal.
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Famalicão da Serra
Julho de 2006
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Lição 7
Casos de Estudo 2
109
6 - Conclusion
• Eruptive fire behaviour is relatively
common in complex terrain and it is
associated to many fatal accidents in
forest fires.
• The sudden acceleration of the fire front
can be explained by the convective flow
induced by the fire itself.
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• A simple mathematical model was
proposed to explain and predict
eruptive fire behaviour.
• The parameters of the model can be
determined from experiments or from
field data.
• The model can be applied to a wide
range of situations.
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• I have the feeling that this is a piece of
fire behaviour science that everyone
dealing with forest fires should know.
• Yet we still find persons that know very
much about fires but are not aware of
this.
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