direct optimization inverse approach - Onera

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PAMART DAAP


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


JDD ONERA 2009

2

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


JDD ONERA 2012

THEORY/METHODS

APPLICATIONS

PAMART DAAP


JDD ONERA 2009

3


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


JDD ONERA 2010



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


JDD ONERA 2009

4


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

THEORY/METHODS

Outline

PAMART DAAP


JDD ONERA 2009

5

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


JDD ONERA 2012

IN HOUSE

IN HOUSE

IN HOUSE +TRAPS

ELSA

PAMART DAAP


JDD ONERA 2009

6


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


JDD ONERA 2012

PAMART DAAP


JDD ONERA 2009

7

Inverse approach for sonic boom minimisation. (2/3)

MINELLI DAAP/ACI


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
)

PAMART DAAP


JDD ONERA 2009

8

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


JDD ONERA 2012

PAMART DAAP


JDD ONERA 2009

9

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

PAMART DAAP


JDD ONERA 2009

10

Direct Optimization vs Inverse Design

MINELLI DAAP/ACI


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


JDD ONERA 2009

11

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


JDD ONERA 2009

12

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

PAMART DAAP


JDD ONERA 2009

13

Direct shape optimization. Test case presentation (1/2)

MINELLI DAAP/ACI


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

PAMART DAAP


JDD ONERA 2009

14

Direct shape optimization. Results (2/2)

MINELLI DAAP/ACI


JDD ONERA 2012

GEOMETRY

OBJECTIVE FUNCTION

NEAR FIELD CFD

GROUND SIGNATURE

NOSE NON AXI
-
SYMMETRY

> DIEDRAL
ANGLE

REDUCED EXPANSION

REDUCED WING SHOCK

PAMART DAAP


JDD ONERA 2009

15

Multidisciplinary optimization.

Test case presentation(1/2)

MINELLI DAAP/ACI


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

PAMART DAAP


JDD ONERA 2009

16

Multidisciplinary optimization. Results (2/2)

MINELLI DAAP/ACI


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


JDD ONERA 2009

17

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

PAMART DAAP


JDD ONERA 2009

18

Inverse design approach. Test case presentation (1/2)

MINELLI DAAP/ACI


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.

PAMART DAAP


JDD ONERA 2009

19

MINELLI DAAP/ACI


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


JDD ONERA 2009

20

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


JDD ONERA 2012

PAMART DAAP


JDD ONERA 2009

21

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


JDD ONERA 2012

The solution

proposed is a direct optimization of the wing on a fixed
shaped nose fuselage.


INVERSE APPROACH

(FIXED)

DIRECT OPTIMIZATION

PAMART DAAP


JDD ONERA 2009

22

Hybridization. Test case presentation(2/3)

MINELLI DAAP/ACI


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

PAMART DAAP


JDD ONERA 2009

23

MINELLI DAAP/ACI


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

PAMART DAAP


JDD ONERA 2009

24

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


JDD ONERA 2012

PAMART DAAP


JDD ONERA 2009

25

Conclusions

MINELLI DAAP/ACI


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.



PAMART DAAP


JDD ONERA 2009

26

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


JDD ONERA 2012

PAMART DAAP


JDD ONERA 2009

27

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


JDD ONERA 2012

PAMART DAAP


JDD ONERA 2009

28

Thanks for your attention

MINELLI DAAP/ACI


JDD ONERA 2012

Questions ?

PAMART DAAP


JDD ONERA 2009

29

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