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Direction Générale Technique
Calcul Scientifique en
Aérodynamique
Université Paris XIII - Calcul Intensif Distribué dans l’Industrie
Villetaneuse - Mercredi 22 Janvier 2014
VA OÙ TON RÊVE TE PORTE
Chercheurs de l’équipe
Modélisation et Méthodes
Numériques









Frédéric Chalot
Franck Dagrau
Laurent Daumas
Steven Kleinveld
Vincent Levasseur
Michel Mallet
Gilbert Rogé
Van Tien Dung
+ PostDocs, Thésards, Stagiaires
page : 3
Civil > 50 %
Rafale
Falcon 7X
Spatial
UAV
NEURON
page : 4
Simulation numérique
 Mécanique des fluides numériques et conception
automatique de formes aérodynamiques.
 Aéroélasticité, aéroacoustique, contrôle des équations
aux dérivées partielles, électromagnétisme,
optimisation multidisciplinaire.
Plan de l’exposé
 Problématiques (calcul des performances
aérodynamiques, …)
 Modélisation (équations de Navier-Stokes,
modèles de turbulence, …)
 Analyse Numérique (Éléments Finis, …)
 Moyens de calcul (supercalculateurs, …)
 Illustration par des résultats récents
 Travail en équipe, MDO, collaboration avec
les Centres de Recherche
 Les axes de Recherche actuels
(taille, rayon d'action, poids, ...)
Calculs de bilans et performance
Avant-Projets
(N1)
Optimisation
Conception Préliminaire
(N2)
Calculs Eléments Finis en
aéro, structure, E.M
Conception Détaillée
(N3)
Maquette Numérique
(CATIA)
Essais soufflerie+structuraux+
E.M
niveau 3
Missions (exigences du marché )
niveau 2
niveau 1
Conception Multi-niveaux
Essais Sol et Vol
Exemple
Structure
Turbulence modeling for complex flows
What RANS can do well
Mach 0.80
Cryotechnic test of generic
Falcon shape in ETW
Mach 0.85
•Full aircraft Navier-Stokes simulations are used at
all stages of design
•Very good validation is obtained at cruise conditions
•Design for cruise conditions is based on CFD
•Wind tunnel tests can be limited to intermediate
and final check-out if sufficient validation is
obtained at flight Reynolds number
Modélisation du bang sonique
Sonic Boom computation process
Source term:
starting from the model geometry and
flight conditions, generation of a mesh
for CFD simulations or determination of
the Whitham’s F-function (including
shape and lift effects)
nearfield
farfield
Propagation to the ground:
use of a ray tracing code that can
account for maneuvers and
meteorological effects.
=>
The ground signature is determined
(pressure variations levels and location
of the sonic boom carpet)
Ground signature
Signal treatment
30
20
Conversion of the signal in
Sonic boom loudness metrics:
dBA, dBC, PL*
10
0
-10
-20
-30
-40
0
50
100
150
Time duration (ms)
200
dB
(dB)
Noise level
Overpressure (Pa)
40
100
50
0
-50
-100
1
10
100
F(Hz)
1000
Frequency (Hz)
Direction Générale Technique
10000
*Perceived Level,
Stevens Mark VII method
N. Héron, HISAC Sonic Boom tasks logic, 22/5/2007
Ce document est la propriété intellectuelle de DASSAULT AVIATION. Il ne peut être utilisé, reproduit, modifié ou communiqué sans son autorisation. DASSAULT AVIATION Proprietary Data.
8
Interaction Fluide –Structure
Développement : CFD linéarisées
CFD non-linéaire
Une forme
X0
Un champ aérodynamique CFD
C p X 0 
CFD linéarisée fréquentielle
Un déplacement
Une variation de champ aéro.
C p  X 0 
dX
Instationnaire temporel
X t 
C p t 
Instationnaire fréquentiel
it
dX .e
X
dC p .ei (t  )
9
Temps de retour du linéarisé fréquentiel par rapport au non linéaire
temporel : facteur 100
Résolution difficile des systèmes linéarisés complexes
algorithme GMRes, préconditionnement BSOR , nombreux second-membres,
…
Modélisations aérodynamiques adaptées aux phénomènes physiques étudiés
(Euler/Navier-Stokes, temporel/fréquentiel, …)
Aéroélasticité dynamique : Prédiction de
l’aérodynamique instationnaire pour le
couplage Flexion - Torsion
flutter
Maquette (empennage
isolé)
Mise en défaut de la modélisation Euler –
défaut de prédiction de la dynamique du choc
Prise en compte des effets visqueux
Prise en compte de la variation des
effets turbulents
10
Instable
• Essais dans le domaine transsonique
• Essais d’aérodynamique instationnaire
• Essais de flottement
Expe
Singularités
Euler linéarisé
NS linéarisé
NS non lin. Temporel
Stable
Derivatives 1 and 2 validation
aoa=1 deg
CDp
Full modelization
Taylor 2
Taylor 1
Thinner airfoil
RELATIVE THICKNESS
Thicker airfoil
11
But …gradient of turbulence mandatory
aoa=2.79 deg
Pressure Drag
Frozen turbulence
Taylor 2
Taylor 1
Full modelization
Relative Thickness
12
Simulation for aeroacoustics
Introduction
• Objective : reduced environmental impact → low noise footprint
• Engine noise shielding → innovative aircraft configurations
• Reduced engine noise → need to reduce airframe noise
• Prediction tools with sufficient level of accuracy are required
Simulation for aeroacoustics
Example : detailed evaluation of turbine
noise with shielding
Navier Stokes
Aerodynamics
computation of
coaxial jet
Local propagation with
influence of jet
High order linearized Euler
in frequency domain
RANS solution projected on isotropic
mesh
Farfield signal
- Kirchhoff
- BEM/FMM
Directivity
Optimization Process
Volume mesh displacement
Baseline
volume
mesh
Volume mesh
deformation
Adjoint
Volume mesh
deformation
Adjoint
CFD solver
Modified
volume mesh
CFD solver
Aerodynamic
observations
Aerodynamic
observations
gradient
Modified surface
mesh & gradient
Aerodynamic
variables
CAD Modeler
Cost - Gradient
Baseline
geometry
Objective &
constraints
Optimizer
design variables
Cost, constraints &
gradients
Starting point
E ( ,W ( ))  0
 State equation
j ( )  J ( ,W ( ))
g ( )  G( ,W ( ))

 Cost function
 Constraints functions
 Minimizing
while respecting constraints
We observe



Set
with l = aerodynamic parameters
and  = geometric parameters (CAD modeler)
j( )
PDE control theory
J-L Lions
Dunod, 1968
gi ( )  0
f ( )  F ( ,W ( ))  J ( ,W ( )), G( ,W ( )) 
  ( , l )
page : 16
Gradients calculation : introduction
Taking into account surface displacements
 CAD modeler :
  d ( )
 Either we model d( ) by transpiration conditions (Hadamard,
Lighthill)
 Either we extend it to volume mesh :

(laplacian like operator)
L(d ( ), D( ))  0
Gradients calculation
 Our goal is
 to estimate :
df (  )
dF (  ,W (  ))
f 
  
 
d
d
F W
F W
F
F
f 
 l 
    l   
W l
W 
l

 thanks to the state equation

and then
E ( ,W ( ))  0
E
E
E ( ,W ( )) 
 W     0
W

L(d ( ), D( ))  0
L
L
L(d ( ), D( ))   d   D  0
d
D
 and thanks to the mesh deformation equation

and then
Mesh deformation approach in adjoint mode
We evaluate variations of the lagrangian:
f *  f  ( )T E  ( )T L
 E

 F
T
with : 
l , D( ), W ( )  ( )    ,W ( ) 
 W

 W

T
and
F
T E
T L
l , D( ),W ( )   l , D( ),W ( )   d ( ), D( )
D
D
D
 dF F
T  E 
 dl  l    l 

 
to obtain : 
 dF   T  L d 
 d  
 d


Supersonic cruise wing optimization
• Supersonic cruise: free stream Mach number = 1.8
• Design point: heavy cruise lift coefficient CL prescribed
• Cost function
1
2
j  C D 
2
• “Glider” configuration: aircraft without lateral nacelle
• Wing-body intersection frozen
• Angle of attack (aoa)
• Level 1 planform parameters (surface, aspect ratio, taper
ratio, thickness) given
• Leading edge radius fixed
• Twist angles, leading edge camber
Mesh + CAD (symmetric wing)
symmetric airfoil
0 .0 1
3D view
0 .0 0 5
Z/C
0
- 0 .0 0 5

- 0 .0 1
- 0 .0 1 5
0
page : 21
z/c
number of vertices: 133239
number of tetrahedral elements: 750773
number of triangle boundary elements: 33198
optimized
airfoil
x/c
0 .0 2 5
0 .0 5
0 .0 7 5
0 .1
X /C
Spanwise conical camber
Half geometry-mesh
Top view
Accueil école
9 control sections
4*9=36 design variables
36+1=37 optimization variables
Accueil école
 Impact in term of time in the CFD design process (3
months
2-3 days)
 Impact in term of quality for the aerodynamic solution
(18%)
page : 22
Conclusion for wing optimization
Engine integration optimization











Objective function: Pressure drag minimization (inviscid flow, Euler
CFD)
Main design point:
free stream Mach number = 1.6
altitude = 15545m (close to 51000 ft)
angle of attack = 0 degree
Mach number = 0.7 in the compressor inlet plane
A/A*, total pressure, total temperature in the turbine outlet plane
L fixed (=40 m)
wing: geometry + position frozen
nacelle + pylon: geometry + position frozen
cabin constraint: fuselage geometry frozen between x=0.5 m and x=7.7
m (xnose=-11 m)
Geometry Parameterization
(Dassault Aviation)
 Number of design variables: 66
 (thickness, scale, camber)
 Cabin constraint taken into account in the geometric
modeler
 Untrimmed surfaces enabling to deal with
fuselage/wing intersection and fuselage/pylon
intersection
• Automatic optimization for the complete
configuration has been performed for both design
point case at M=1.6 and multi point case including
conditions at M=1.5
• Optimizer: Interior Point Algorithm (line search :
Wolfe)
• Discrete adjoint, linear solver: GMRES
• Mesh deformation (domain decomposition, parallel,
MPI)
• Euler solver (domain decomposition, parallel, MPI)
• Unstructured mesh (538064 vertices, 3024834
tetrahedral elements)
• 5 h on 64 processors IBM pwr5
Cp distribution (rear)
Z
X
Y
Z
KP-G001
0.5
0.458824
0.417647
0.376471
0.335294
0.294118
0.252941
0.211765
0.170588
0.129412
0.0882353
0.0470588
0.00588235
-0.0352941
-0.0764706
-0.117647
-0.158824
-0.2
X
Y
Implementation strategy
Formulation for derivatives 1 et 2
Notations:
E
W
X
x
Non linear system for fluid (Euler or Navier-Stokes)
L
State, solution of
Linear system for mesh deformation
J
E


Volume coordinates
Surface coordinates


T
Fluid Adjoint, solution of 
T
Mesh Adjoint, solution of
Second derivative operator
2
G1 ,G2
D
Observation
Aerodynamic parameters
Geometric parameters
E
J

W W
L
J
E

 T
X X
X
2
2M
2M
T
T  M
M .[V1 ,V2 ]  V
V1  2V1
V2  V2
V2
2
2
G1
G1G2
G2
T
1
Implementation strategy
Formulation for derivatives 1 et 2
dJ J
E

 T
d 

d 2J
W
W
2
T
2
 DW , J .[
,1]  DW , E.[
,1]
2
d


Implicit CFD
Explicit
dJ
T L x
 
d
x 
2
d 2J

W

X

W

X

L

x
2
T
2
T

D
J
.[
,
]


D
E
.[
,
]


W ,X
W ,X
d 2
 
 
x  2
Explicit
Implicit CFD
Implicit deformation
Generic fuselage
zoom
3D Euler
Mach 1.6
451287 vertices
10 mn on 16 procs
IBM pwr5
Pressure drag
CDp
Side slip angle
Thèse Ludovic Martin
Angle of attack
Utilisation des dérivées secondes




Méthode des moments (propagation d'incertitudes)
Méthode de Newton (optimisation)
Surfaces de réponses avec dérivées
…
Optimisation avec contrainteCz > 0.01
aile ONERA m6, Mach = 0,84 et incidence = 3,06°
BFGS: cout = 20 (19 NF + 10 Ng)
Newton: cout = 16 (15 NF + 8 Ng + 8 Nh )
BFGS
Newton
BFGS
Newton
Drag Breakdown of Polar
CL
induced
Wave
Trim
Operational
Domain
33
Miscella Friction
neous
+ Shape
C
D
Dream … and Real Life
Aeroelasticity
Atmospheric conditions
34
Dream … and Real Life
Antennas
Bleed
Steps and gaps
35
Prise en compte des incertitudes
Utilisation des dérivées secondes




Méthode des moments (propagation d'incertitudes)
Méthode de Newton (optimisation)
Surfaces de réponses avec dérivées
…
0.84
cdf
0.0150
P[ CD > 0.0150 ] = 16%
Thèse Ludovic Martin, 2010,
Prix CANUM
FOSM, SOSM
Mean value, variance, skewness, kurtosis
order 1
order 2
order 1
order 2
order 1
Taylor
order 2
1  E ( X )
2  E[( X  1 )2 ]
  2
3  E[( X  1 )3 ]
C 3 
3
3
2 2
4  E[( X  1 )4 ]
C4 
4
 22
Chaos 5 points
Method of Moments
order 1
Method of Moments
order 2
ONERA M6 wing, Euler, uncertain aoa
Accueil école
Chaos 4 points
page : 38
Chaos ? Points; Moments order ?
Uncertain twist angle distribution
Full Falcon jet configuration
transonic cruise (given Cl)
tip
control
section
crank control
section
Given pdf for the 2
uncertain twist
angle parameters
39
Strategy for uncertainty propagation
Approx Monte-Carlo
Polynomial Chaos
Perturbation Method
Uncertain parameter, given pdf
Pearson
system
Four
first
Moments
Kurtosis
Not allowed area
Four Four Pearson
first
first validation
PM vs Chaos
Moment
Moment
Reference=Approx
MonteNot possible area
s Carlo s
Normal law
Square of skewness
40
Uncertainty propagation on industrial context
Influence of uncertainty of geometrical parameters (twist angles) on
global criteria (range) . Probability of failure.
displacement ...
Ps, Flexion mt ...
General scheme with the propagation of numerical information:
Aerodynamical
field
Global
Geometrical
criteria
parameters
W W
V C
R
l
gcs CD,eq
ln 

s
Ws
f



Structural
field
Remarks: CD including trim drag (RANS3D, fixed Cl). Ms is the
result of an optimization (post buckling, flutter, extreme loads, …)
How to propagate uncertainty through this
bidisciplinary system ?
1. full Monte Carlo approach, Polynomial Chaos, Perturbation
Method, …
2. RSM for the range respect to the 2 twist angles + MC …
3. RSM for the drag and for the structural mass respect to the 2 twist
angles +MC … + stochastic interpolation …
Approach 1, direct propagation of uncertainties
• full Monte Carlo approach: more than 10000 evaluations + we are
looking for the tail of probability
• Polynomial Chaos, Perturbation Method: too intrusive.
Alternative: non intrusive PC or Collocation Method
Approach 2, RSM for the global criteria
Deterministic calculations (3 aoa / design pt)
3^N
values
for the
Global
criterium
N Geometrical
parameters
* 3 values per
parameter
Given pdf for the 2
uncertain twist angle
parameters
Surrogate model
(Kriging, RBF, …)
Uncertainty
propagation
pdf, cdf, Pearson:
uncertainty law
(type + parameters)
for the global
criterium
Approach 3, RSM for each disciplinary
Deterministic calculations (3 aoa / design pt)
3^N values
for the
disciplinary
observation
N Geometrical
parameters
* 3 values per
parameter
Given pdf for the 2
uncertain twist angle
parameters
Surrogate model
(Kriging, RBF, …)
Uncertainty
propagation
pdf, cdf, Pearson:
uncertainty law
(type + parameters)
for the disciplinary
observation
Approach 3, continued
Aerodyn. Dpt
Stochastic RSM for the CD
MC
Stochastic RSM for the rang
Structural Mech. Dpt
Stochastic RSM for the Ms
Stochastic Responses Surface Model
Probability law of range vs geometrical nominal values (two twist angles)
Kurtosis
Not allowed area
Normal law
Not possible area
Square of skewness
Gamma, Bêta and Fisher probability laws. Connex domains
Change of geometrical nominal values: prediction of probability
law possible
47
The key message
Each team needs to provide a disciplinary date base
including, at least, bounds but complete stochastic
information is the ultimate goal (useful for MDO
optimization)
Alternative approaches: FORM, SORM, …
48
Robust Design (1)
Cl < 0.3
Minimal
drag
Cl > 0.3
Final
Population
Minimal
probability
lift
ONERA M6 wing, 2 design parameters: twist and camber angles
Euler, RSM RBF like but with 1rst and 2nd derivatives (original approach, Duchon
extension)
MOGA, Robust design. Objectives: to control Drag and P(CL<0.3)
49
Robust Design (2)
P(Cl<0.3)
Minimal
drag
Initial population
Final population
Minimal
probability
lift
E(CD)
50
Robust Design (3)
P(Cl<0.3)
Decision: we accept a probability lift of p = x% with
minimal drag
Determination of drag mean CD
(Pareto
front) of nominal values of
Determination
geomerical parameters a1 and a2 (camber and
twist angles)
Minimal
drag
p
Cd
Minimal
drag
Minimal
probability
lift
E(CD)
a1
a2
Minimal
probability
lift
51
What to keep in mind ?
• Generalization of the basic Mean-Standard Deviation
approaches (not limited to Normal Law …)
• RSM:
• How to control the quality ?
• Bottleneck: large number of parameters (Sparse Grid
?)
• Convergence to the true Pareto Front …
52
Prise en compte des incertitudes (15/17)





Adaptation de maillage anisotrope "goal oriented"
Métrique continue
Dervieux, Alauzet, Loseille,
Renormalisation Lp
Hecht, Frey, Dobrzynski
Gradation de métrique
Adaptation iso-P2 du maillage surfacique + projection
sur la CAO
CRAS,
Ludovic Martin, 2008
Adaptation de maillage
anisotrope "goal oriented"
Sonic boom
extraction pression statique
segment à R/L=1
Bornes d'erreur en maillage par adjoint
Intervalle de confiance: AH ,h  f u   BH ,h
AH ,h  f uhH   2  hH , RuhH 
Accueil école
BH ,h  f uhH   2  hH , RuhH 
Post Doc Sophie Borel
2006, prix CANUM
En vrac




Ordre élevé
Solveurs linéaires semi-directs (FETI, …), …
Modélisation de la transition
Gestion des incertitudes (CADNA, chaos polynomial,
optimisation robuste, …)
 Bidisciplinaire (fluide-structure, fluide-thermique, fluidefurtivité, …), MDO
 …
Tera 1012
Peta 1015
Performance Development
Puissance de calcul multipliée par 100 en 10 ans
SUM
1 Eflop/s
100 Pflop/s
10 Pflop/s
10.5 PFlop/s
N=1
N=500
1 Pflop/s
100 Tflop/s
10 Tflop/s
1 Tflop/s
100 Gflop/s
10 Gflop/s
1 Gflop/s
supercalculateur
CURIE
2 PFlop/s
100 Mflop/s
Dassault Aviation: en limite du Top 500
MPI, OPENMP, acceleration GPU
Collaboration avec des
chercheurs




Universités, grandes écoles, …
INRIA, ONERA, CNRS, CEA, …
Thèses Cifre, DGA, Univ. CNRS, ERASMUS, …
Contrats de R&D: DGA, DGAC, Pôles Régionaux,
Contrats Européens (FP7, …)
Conclusion - Perspectives
 CFD Euler: TRL 5
 Chaine d'optimisation de formes aéro adaptée au pg avion
 Aéroélasticité et Aéroacoustique: Approche Euler linéarisé
fréquentielle opérationnelle. Efficacité: multi-RHS
 Laminarité. Prise en compte de la transition
 Contrôle d'écoulements. Opt d'architecture (grad topo)
 Couple (état aérodynamique, maillage), bornes d'erreur en
maillage
 Surfaces de réponses avec incertitudes (MDO)
 Optimisation robuste. Front de Pareto
 Analyse numérique: couplage d'équations, ordre élevé,
stabilité, accélération, conditions aux limites

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