PAMART DAAP
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JDD ONERA 2009
1
Optimisation de forme d’un avion d’affaire supersonique
en utilisant des critères acoustiques et aérodynamiques
Andrea Minelli
Doctorant 2
eme
année
Département DAAP Unité ACI
Directeur(s) de thèse
:
Jean

Antoine Désidéri
Encadrant(s) ONERA
:
Itham Salah el Din
,
Gerald Carrier
Bourse(s) :
Onera
PAMART DAAP
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Outline
•
Background
•
Shape optimization approaches for low boom configurations
–
Direct shape optimization
–
Inverse optimization approach
•
Direct shape optimization of a 3D glider
–
Acoustic optimization
–
Multidisciplinary aero

acoustics optimization
•
Inverse shape optimization
•
Hybrid approach. Wing optimization on a shaped nose fuselage
•
Conclusions and perspectives
MINELLI DAAP/ACI
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JDD ONERA 2012
THEORY/METHODS
APPLICATIONS
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•
A supersonic aircraft creates pressure
disturbances
which propagates to the ground
through the atmosphere and tend to coalesce into a typical
N

shaped wave
due to
nonlinear effects.
annoyance for people and vibration for ground structures.
Background
MINELLI DAAP/ACI
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JDD ONERA 2010
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Key points
of aeroacoustic shape optimization:
Multiscale physics
: from mm (near aircraft)
to km (domain altitude);
CFD near field
fidelity
, mesh adaptation,
matching between CFD and acoustic
model;
Modelisation of acoustic
propagation
through the atmosphere from the aircraft to
the ground;
Multidisciplinary
optimization of a non
smooth function.
•
The problem
consists in minimizing the sonic boom annoyance in order to have
unrestricted
overland supersonic flight
without
any decrease in the aerodynamic
performance.
PAMART DAAP
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•
Background
•
Shape optimization approaches for low boom configurations
–
Direct shape optimization
–
Inverse optimization approach
•
Direct shape optimization of a 3D glider
–
Acoustic optimization
–
Multidisciplinary aero

acoustics optimization
•
Inverse shape optimization
•
Hybrid approach. Wing optimization on a shaped nose
fuselage
•
Conclusions
MINELLI DAAP/ACI
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JDD ONERA 2012
THEORY/METHODS
Outline
PAMART DAAP
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JDD ONERA 2009
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Convergence
reached
Direct shape optimization
EVALUATOR
Geometry
parameterization
Mesh generation
CFD computation
Post processing
OPTIMIZER
Update design variables
Optimization
algorithm
Cl, Cd,
Delta P
Optimal
configuration(s)
MINELLI DAAP/ACI
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JDD ONERA 2012
IN HOUSE
IN HOUSE
IN HOUSE +TRAPS
ELSA
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IDEA 1:
From an ideal target ground signature reproduce the corresponding geometry
•
In the fifties
Whitham
was the first to define a method to evaluate the perturbations
generated by an
axi

symmetric supersonic projectile
using an F

function representing the
disturbance due to the volume of the body.
•
Walkden
extended the formulation to lifting bodies lift
.
→
The lifting body from an acoustic point of view is described by an
equivalent area
distribution
:
A
e
=A
V
+A
L
The Whitham F

function is defined as:
And it is proportional to the pressure by:
The limitation
is the link of the Equivalent area and the geometry: non
uniqueness of solution and non trivial determination
Inverse approach for sonic boom minimisation. (1/3)
MINELLI DAAP/ACI
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Inverse approach for sonic boom minimisation. (2/3)
MINELLI DAAP/ACI
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JDD ONERA 2012
The F

function could be described by piece

wise linear functions, and the
Equivalent area evaluated
analytically
(using the Abel transform)
A specific module,
AIDA (Acoustics Inverse Design Approach)
using as input flight
conditions, weight, geometry properties (total length, nose length,..) and ground signal
properties (typically the pattern : ramp like, flat top,..) has been developed and
validated for this purpose.
Parameterised F

function
IDEA 2
: obtain low boom configuration is to define a
parameterised F

function
that
produces specified ground signature.
Multiple unknown system (H,B
i
,C
i
,D
i
)
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Inverse approach for sonic boom minimisation. (3/3)
AIDA
only known European method
today for inverse design approach.
Has been validated using as reference the work of Darden
C.M.
1979. Sonic

Boom
Minimisation with Nose

Bluntness Relaxation.
NASA TP

1348
,
with a flat

top test case.
The coefficients of the F

function are evaluated using an internal BFGS optimization
method, and in addition it is able to define an equivalent axysimmetric body that
corresponds to the obtained equivalent area.
The need of the corresponding real geometry remains. Further improvements in this
direction are planned.
MINELLI DAAP/ACI
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JDD ONERA 2012
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DIRECT
INVERSE
Direct optimization and inverse design method with
F

function. Summary
MINELLI DAAP/ACI
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JDD ONERA 2012
Flight condition
Target Ground signal
characteristics
Parameterisation of
Whitham function
Equivalent Area
Geometrical area law
Pressure near field
F

function
Signature at ground
Ray tracing
algorithm
Geometrical area law
Flight condition
PAMART DAAP
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JDD ONERA 2009
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Direct Optimization vs Inverse Design
MINELLI DAAP/ACI
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JDD ONERA 2012
DIRECT OPTIMIZATION
INVERSE APPROACH
•
It acts directly on the
geometry
modifying the design variables;
•
Each evaluation is computationally
expensive
;
•
An appropriate selection of the objective function is required;
•
The algorithm search space is
limited
by the design variables
selected.
PROS
PROS
CONS
CONS
CONS
•
It is possible to obtain a
specific ground signature
without
direct optimization;
•
It permits to validate and/or define specific
parameterisation
of
the geometry
•
The evalution of the geometry area law is a non trivial problem
without unique
solution. In addition to analytical relationship
between the equivalent and the geometry area law
CONS
PROS
PROS
PROS
PAMART DAAP
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JDD ONERA 2009
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Outline
•
Background
•
Shape optimization approaches for low boom configurations
–
Direct shape optimization
–
Inverse optimization approach
•
Direct shape optimization of a 3D glider
–
Acoustic optimization
–
Multidisciplinary aero

acoustics optimization
•
Inverse shape optimization
•
Hybrid approach. Wing optimization on a shaped nose fuselage
•
Conclusions
MINELLI DAAP/ACI
–
JDD ONERA 2012
APPLICATIONS
PAMART DAAP
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JDD ONERA 2009
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DIRECT
INVERSE
Direct optimization and inverse design method with
F

function. Summary
MINELLI DAAP/ACI
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JDD ONERA 2012
Flight condition
Target Ground signal
characteristics
Parameterisation of
Whitham function
Equivalent Area
Geometrical area law
Pressure near field
F

function
Signature at ground
Ray tracing
algorithm
Geometrical area law
Flight condition
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Direct shape optimization. Test case presentation (1/2)
MINELLI DAAP/ACI
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JDD ONERA 2012
INPUT
DESIGN VARIABLES
OPTIMIZATION
PARAMETERS
DVs
19 (7 fuse (y

coord Bezier spline), 11 wing , AoA)
Algorithm
CMA

ES (Covariance Matrix
Adaptation Evolutionary strategy)
1
Objective
Sum of shock amplitude
Contraints
Lift coeff.
i
i
p
PROBLEM
: Wing body configuration, MonoDisciplinary (acoustic), MonoObjective,
Constrained.
Altitude
18000m
Mach
1.6
Length
30m
1
Hansen and Ostermeier. Completely Derandomized Self

Adaptation in Evolution Strategies. Evolutionary Computation 9 (2) 2001.
S
ref
, C
L0
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Direct shape optimization. Results (2/2)
MINELLI DAAP/ACI
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GEOMETRY
OBJECTIVE FUNCTION
NEAR FIELD CFD
GROUND SIGNATURE
NOSE NON AXI

SYMMETRY
> DIEDRAL
ANGLE
REDUCED EXPANSION
REDUCED WING SHOCK
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Multidisciplinary optimization.
Test case presentation(1/2)
MINELLI DAAP/ACI
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JDD ONERA 2012
INPUT
DESIGN VARIABLES
OPTIMIZATION
PARAMETERS
DVs
19 (7 fuse (y

coord Bezier spline), 11 wing , AoA)
Algorithm
MOGA (MultiObjective Genetic
Algorithm)
Objectives
Sum shock amplitude, Drag coeff.
Contraints
Lift coeff.
Altitude
18000m
Mach
1.6
Length
30m
PROBLEM
: Wing body configuration, MultiDisciplinary (aero

acoustic),
MultiObjective, Constrained.
S
ref
, C
L0
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Multidisciplinary optimization. Results (2/2)
MINELLI DAAP/ACI
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JDD ONERA 2012
INI
INI
INI
OPT
OPT
OPT
B
A
C
•
The wave drag increases due to the creation of
a new nose shock that coalensce with the wing
shock at ground(B, C)
•
The nose amplitude is slightly reduced (A,B,C)
C
d
Delta p
PAMART DAAP
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DIRECT
INVERSE
Direct optimization and inverse design method with
F

function. Summary
MINELLI DAAP/ACI
–
JDD ONERA 2012
Flight condition
Target Ground signal
characteristics
Parameterisation of
Whitham function
Equivalent Area
Geometrical area law
Pressure near field
F

function
Signature at ground
Ray tracing
algorithm
Geometrical area law
Flight condition
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Inverse design approach. Test case presentation (1/2)
MINELLI DAAP/ACI
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JDD ONERA 2012
Altitude:
18000 m
Mach:
1.6
Aircraft length
30 m
F

function target
Some Parameters (the others
evaluated using AIDA)
INPUT
DESIGN VARIABLES
DVs
9 (9 fuse)
Objective
Flat top ground signature
REQUIREMENTS
PROBLEM
: Axysimmetric fuselage configuration, MonoDisciplinary (acoustic),
No Objective, non Constrained.
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MINELLI DAAP/ACI
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JDD ONERA 2012
Inverse design approach. Results (2/2)
•
The inverse approach is efficicient to provide good
axisymetrical geometry shapes
, for example in aircraft
main body pre

design step.
•
It does
not require
computationally expensive
calculations and the CFD phases can be avoided for
the sonic boom evaluations
The shaped nose is combined with the initial conventional fuselage after an appropriate scaling
of the shaped equivalent area law.
GEOMETRY
EQUIVALENT AREA
GROUND SIGNATURE
AMPLITUDE REDUCED
BY AN HALF
INCREASED NOSE LENGTH
PAMART DAAP
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Outline
•
Background
•
Shape optimization approaches
for low boom configurations
–
Direct shape optimization
–
Inverse optimization approach
•
Direct shape optimization of a 3D glider
–
Acoustic optimization
–
Multiobjective aero

acoustics optimization
•
Inverse shape optimization
•
Hybrid approach. Wing optimization on a shaped nose
fuselage
•
Conclusions
MINELLI DAAP/ACI
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JDD ONERA 2012
PAMART DAAP
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Problem:
The introduction of the wing introduces another shock that in
some cases may
coalesce
with the nose shock, producing a N

wave
signature without flat

top.
SCHEMA
Hybridization. Test case presentation(1/3)
MINELLI DAAP/ACI
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JDD ONERA 2012
The solution
proposed is a direct optimization of the wing on a fixed
shaped nose fuselage.
INVERSE APPROACH
(FIXED)
DIRECT OPTIMIZATION
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Hybridization. Test case presentation(2/3)
MINELLI DAAP/ACI
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JDD ONERA 2012
INPUT
DESIGN VARIABLES
OPTIMIZATION
PARAMETERS
DVs
12 ( 11 wing , AoA)
Algorithm
CMA

ES (Covariance Matrix
Adaptation ES)
Objectives
Sum shock amplitude
Contraints
Lift coeff.
Altitude
18000m
Mach
1.6
Length
30m
PROBLEM
: Wing body configuration, MonoDisciplinary (acoustic), MonoObjective,
Constrained.
Nose shaped with inverse design approach
S
ref
, C
L0
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MINELLI DAAP/ACI
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JDD ONERA 2012
Hybridization. Results(3/3)
Non optimized wing + conventional fuselage
Non optimized wing + shaped fuselage
Optimized wing + shaped fuselage
EXPANSION BEFORE WING
SHOCK
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Outline
•
Background
•
Shape optimization approaches
for low boom configurations
–
Direct shape optimization
–
Inverse optimization approach
•
Direct shape optimization of a 3D glider
–
Acoustic optimization
–
Multiobjective aero

acoustics optimization
•
Inverse shape optimization
•
Hybrid approach. Wing optimization on a shaped nose
fuselage
•
Conclusions
MINELLI DAAP/ACI
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JDD ONERA 2012
PAMART DAAP
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JDD ONERA 2009
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Conclusions
MINELLI DAAP/ACI
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JDD ONERA 2012
•
The shape optimization for a low

boom 3D configuration has been
investigated using a
direct
and an
inverse
approach;
•
A
Monocriteria
acoustic optimization using CMA

ES has been
performed obtaining a reduction of
more than 30%
of the objective
function;
•
The Inverse shape optimization approach has been implemented in an
algorithm in the
most general form
in order to consider almost all the
possible shapes in terms of aircraft geometry and ground signature,
reducing the problem of direct optimization (Typically : limited design
space and choice of objective functions);
•
An
hybrid approach
shaping the fuselage with the inverse method and
a direct optimization of the wing permits to combine the good results
obtained with the direct optimization, but with a shaped front signature.
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Perspectives
•
Some tests on multiobjective optimization has been performed on a
simple fuselage configuration with Nash Game and genetic algorithm
like NSGA

II. Future work consists in a
more deeper investigation
of
multiobjective optimization method on complex configurations (MGDA.
Multigradient Descent Algorithm, Nash Game in cooperation with
OPALE project INRIA

Sophia Antipolis);
•
Unstructured mesh
with adaptation to shock region in cooperation with
GAMMA project INRIA

Roquencourt;
•
Introduction of engine nacelle and
validation/comparison
between
experimental data (D

SEND) and Onera numerical method in
cooperation with JAXA;
•
Use of other sonic boom metrics (e.g. dB,PLDb,..) in acoustics
optimization (Already in progress).
MINELLI DAAP/ACI
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JDD ONERA 2012
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Publications and training modules
Conferences
:
AIAA

CEAS Aeroacoustics Conference, June 2012, Colorado Springs (CO)
A.Minelli I.Salah el Din G. Carrier. ‘Advanced Optimization Approach for Supersonic Low

Boom Glider
Design’
MAIN AUTHOR
ODAS Onera

DLR Aerospace Symposium , February 2011, Toulouse
I.Salah el Din, G. Carrier, R. Grenon, M.C. Le Pape, A.Minelli ‘Overview of Sonic Boom CFD Prediction
Methodology in Use at ONERA and its application to Supersonic Business Jet Configuration Design’
COAUTHOR
4th EUCASS , July 2011, St. Petersburg
I.Salah el Din, M.C Le Pape, A.Minelli, R.Grenon, G. Carrier. ‘Impact of Multipole Matching Resolution on
Supersonic Aircraft Sonic Boom Assesment’
COAUTHOR
Workshops:
Advanced optimization techniques in fluid mechanics, (P.Schmid, R.Bewley) 3

9 April
2011
Publications:
A. Minelli I.Salah el Din G. Carrier. ‘Inverse Design Optimization Method for Low

Boom Supersonic
Configurations’ submitted
MAIN AUTHOR
Academic module:
INNOVADOC 2011
Professional module:
Ansys ICEM

CFD (Hexa, Tetra). 2011
Modelisation, Numerical simulation and Optimization in Fluid Mechanics (DFH, KIT). 2010
MINELLI DAAP/ACI
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Thanks for your attention
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Questions ?
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Appendix 1. The Whitham F

function
The F

function is the result of the corrected characteristics theory proposed by Whitham in
order to take into account the local curvature of the characteristics line due to the local
Mach number.
In the Walkden formulation it has two terms that represents the volume and the lift term that
consist respectively by a combination of monopoles and dipoles.
The equivalent area (volume term) is defined by cut plane inclined as the Mach angle
(asin(1/M)). Defining the lift equivalent area distribution as:
And considering the equivalent area A
e
as the sum of A
L
and A
v
the F

function is defined as
VOLUME TERM
LIFT TERM
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