Prsentation PowerPoint

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NANCY 09-06-05
D. Calogine K .Chetehouna E. Lamorlette J.
Margerit S. Ramezani N. Rimbert O. Séro-Guillaume
Modèles de Combustion en milieux
poreux Caractérisation de la végétation Modèles
de propagation à grande échelle Modélisation de
la lutte par largage
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INTRODUCTION
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The Scales
Scale of Combustion Flames above
vegetation Convection Radiation
The wood is a porous medium with several phases
and several components
The vegetation is a porous medium with two phases
Scale of chemical reactions Pyrolysis Drying
Scale of Combustion Convection Radiation
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The modeling at different scales
10 lt Re lt 104
Mesoscopic scale
Porous medium combustion model
Macroscopic scale
107lt Re
Gigascopicc scale
Propagation model
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VEGETATION MODEL
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Vegetation Model
CIRAD Software A.M.A.P.
Dedicated to virtual Agronomy
Vegetation has been considered as fractal
Not well suited for computational purposes
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Vegetation Model
Construction by Iterated Functions Systems I.F.S.
Barnsley, Hutchinson
Deterministic
Probabilistic
pi probabilites
Probability
is pi
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Vegetation Model
Calogine et al. 1998
Example
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Vegetation Model
Other Types of Vegetals
Model 3 Order 5
Model 1 Order 7
Model 2 Order 4
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Vegetation Model
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Vegetation Model
Automatic generation of the mesh
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Vegetation Model
Automatic generation of the mesh
h10m
7 millions cells
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Vegetation Model
z
y
x
écoulement
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Vegetation Model
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FIGHTING MODEL
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Dropping model
Continuous Eulerian model

• New equation for Interfacial area density
• New closure for Interfacial velocity

Averaging procedure
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Dropping model
Stochastic approach
Figure 1 fitting of the drop spray p.d.f. VSL
0.041 m/s VSG 35 m/s. From left to right the
p.d.f. are log-stable p.d.f., Upper-limit Evans
p.d.f. , log-normal p.d.f. and log-Weibull p.d.f.
Log-Levy stable distributions are better
distributions than the usual ones
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Dropping model
Transport Equation for the interfacial density

• It can be shown that
• Where Sc is a source related to curvature
• Se is a surface stretching term
• Sfc is a term related to fragmentation and
  coalescence

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Dropping model
Two Fluids Model
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Dropping Model
4.8 million cells used for the atomisation stage
A 850,000 cells grid used in the dispersion stage
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Dropping Model
velocity field around the cloud of retardant in
the airplane frame of reference t 0.5 s
isosurface a 0.5 (2 gum mass percentage)
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Dropping Model
The results of part I are initial conditions for
part II
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Dropping model
Dropping Simulations
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A 3D DETAILED MODELOFCOMBUSTION
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Homogenized Medium
First Step Extension of the equations
Write all equations at Microscopic scale using
distribution theory, so that boundary conditions
are included in the equations.
Albini Model at microscopic level (1985)
Example Mass Balance in the gaseous phase
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Homogenized Medium
Second Step Average procedure
Convolute the equations with a compact support
kernel of size h denoted m.
In the gaseous phase Balance of Mass Balance
of momentum Balance of Energy
In the vegetal phase Balance of Mass Balance
of Energy
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Homogenized Medium
For example
From the Balance of Momentum in the gaseous phase
we obtain the relation
And we define the following Average Quantities
Is the porosity
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Homogenized Medium
Third Step Closure operation
At Step 2 several new quantities has been
defined. They must be related to average
variables It is the Closure operation.
Equations for these new quantities are obtained
by writing that the entropy production is
positive.
We used Rational Extended Thermodynamics
(R.E.T.) Or Extended Irreversible Thermodynamics
(E.I.T.)
Jou, Casas-Vazquez, Lebon
Müller, Ruggeri
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Homogenized Medium
The obtained model is very general and has the
following characteristics
1) Two Temperatures, one for each phases with a
modified Fourier law
2) Contains a model of pyrolysis for the
vegetal with relaxation times
3) The vegetal phase has an internal
structure with possible modelling of chemical
actions of retardant
4) Extended Navier Stokes equation, with memory
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Homogenized Medium
Several Simplifications can be Made
Instantaneous momentum Transfer between Phases
...
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Homogenized Medium
Simplified 3D Model
PHASE W AS WOOD
Energy Balance
Mass Balance
Solid Constituents
Mass Transfer Between Phases wood and air
Liquid Constituent
Gaseous Constituent
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Homogenized Medium
3D Model Continued
PHASE F (AS FLUID) GAS
Energy Balance
Mass Balance
Mass Transfer Between Phases wood and air
Balance of Momentum
Thermodynamics Relations Radiative Transfer
Equation
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Numerical experiment in fire tunnels
1m/s
9m
25cm
6m
15m
Heat flux
Distribution exponentielle de porosité
DH
litière
Bilan de quantité de mouvement Phase gazeuse
Bilan dénergie LitièreGaz
Cinétique Chimique Litière Gaz
Bilans de masse Litièregaz
Équation du transfert radiatif LitièreGaz
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Numerical experiment in fire tunnels
AVI
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A 2D PROPAGATION MODEL
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Propagation Modeling
Hypotheses
Vegetation Height d small compared to the
gigascopic scale
Gigascopic Scale L
Flow Almost Parallel to the ground
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Propagation Modeling

• Asymptotic Expansion

The Ratio ed/Lltlt 1, Small parameter
L can be the size of the fire or the distance to
the fire front
Quantities are continuous across the vegetation
toward ambient air Use of Matched Asymptotic
Expansion on the Whole Domain z gt 0 (vegetation
ambient air)
Inner Part of the Asymptotic Expansion Propagati
on Model
Outer Part of the Asymptotic Expansion
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Propagation Modeling
Model I Only for phase W Propagation Model
Energy Balance
Mass Balance for the cellulose
Mass Balance for the water
Mass Balance for the char
Are quantities deduced from experiments outer
expansion
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Propagation Modeling
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Modélisation de la Propagation
Takes into account Drying, Pyrolysis, Wind, Slope
Radiative flux
with
K is the extinction function
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Propagation Modeling
Highly non linear 5 free boundaries
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Propagation Modelling
Occupation density 0.5
Moisture 0.07
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Propagation Modelling
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Propagation Modelling
Wind effect, 30 mn, 45 mn, 1h15, 1h50
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Propagation Modelling
Under a certain value of the occupation density
the fire will not propagate
Percolation Density
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FIGHTING MODEL
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PESPECTIVES
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Travail en cours
Caractérisation de la végétation comme milieu
poreux. Thermique et Radiatif
Modèle de flamme dans le modèle de propagation
Rendre opérationnel le modèle de propagation à
très grande échelle. Amélioration de la
convection.
Pris en compte de leffet du retardant sur la
propagation
Modèle simplifié de largage
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NANCY 09-06-05
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Travail en cours
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Level Set or V.O.F. Formulation
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Level Set or V.O.F. Formulation
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Control on the initial density
What happens if the initial density is decreased ?
Simulation
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3 QUESTIONSOF OPTIMIZATION AND CONTROL
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Control on the initial density
What happens if the initial density is decreased ?
Simulation
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Propriétés à basse densité
Au dessous dune valeur critique de de la
densité doccupation le feu ne se propage plus.
Densité de Percolation
Expérience de Propagation-Percolation Fractalité
du front ?? Mécanismes mis en jeu ??
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Fire Front Reconstruction Data Assimilation
Question 1
Is it possible to find a initial distribution of
vegetation and a Tgt0 such that
Prevention
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Control on the retardant distribution
Aerial fighting by indirect attack
The dropped fluid Water Ammonium Phosphate
Gum
The Ammonium Phosphate decreases the activation
energy in the pyrolysis law
Simulation
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Fire Front Reconstruction Data Assimilation
height
tilt angle
The flame is defined by
emitted power
rate of spread
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Fire Front Reconstruction Data Assimilation
2) Que se passe-t-il si la densité de
combustible tend vers 0 ?
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Fire Front Reconstruction Data Assimilation
Extinction line
Fire line
Flux meters positions
Data from satellite?
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1 QUESTIONOF STABILITY AND UNICITY
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Uniqueness and stability.
Let c the characteristic function of the burning
zone
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Uniqueness and stability.

• For homogeneous conditions of vegetation the
  straight line seems to be the only stable
  solution
• (Depend on wind and slope)

• The direction of propagation seems to be along
  the line of maximum rate of spread

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Rate of spread.
Rate of spread is solution of the non linear
egeinvalue problem
Problème qui peut avoir plusieurs solutions ou
pas du tout
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Rate of spread.
Dimensional analysis
Small parameter
We look for a series solution
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Rate of spread.
is the unique solution of
Radius of convergence of the series and
uniqueness ?
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Conclusion
1) Much more questions than answers
2) Mathematicians are welcome
3) Thank you
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TYPOLOGIE DES MODELES
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Modèles Géométriques
Méthode de Enveloppes
Hypothèse sur la forme géométrique du feu
Méthode de construction du front à t dt
Méthode qui marche bien mais fournit des
solutions très régulières
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Modèles empiriques
Modèle de Rothermel
s surface spécifique, d épaisseur couverture
végétale
C charge ducombuxtible sec, r masse vol. sec.
DH chaleur contenue dans la particule sèche
Chaque partie du front est déplacée avec la
vitesse normale R
V vitesse du vent à mi hauteur
tanj pente
Front à linstant t
Hu Humidité des particules de combustible
He Humidité dextinction
Hypothèse
R f( s, d, r, tanj, DH, V, Hu, He)
P
n
R vitesse de propagation
Front à linstant tdt
PRndt
Méthode qui marche bien mais fournit des
solutions très régulières
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Modèles Physiques
Modèle de Réaction diffusion
Equation seule (1)
Système dEquations (2) Réactions
chimiques Dynamiques des populations
Prototype
Modèles dits Physiques ont la structure
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COMPARAISON DES MODELES
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Résultat des Courses
Réaction- Diffusion
Rothermel
Modèles de Réaction diffusion peuvent faire aussi
bien que les modèles denveloppe et de Rothermel
Les modèles denveloppe se comportent très mal à
basse densité ?
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Conclusions partielles
Conclusions
1) Les modèles de propagation dits de
Réaction-Diffusion pourraient fournir plus
dinformation que les modèles semi empiriques.
2) Théoriquement ils peuvent faire au moins
autant que les modèles denveloppe ou de type
Rothermel.
3) Ils sont plus faciles à calibrer
Questions
4) Peuvent ils faire plus ? Et rendre compte de
comportements très irréguliers du front de flamme
5) Si oui quelle stratégie de modélisation ?
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Stratégie de Modélisation
Modèle Détaillé
Réduction
Spécifications Echelle Objectifs
Modèle Souhaité
Complexification