variable-fidelity aerodynamic analysis for ... -...

VARIABLE-FIDELITY

AERODYNAMIC ANALYSIS

FOR MULTIDISCIPLINARY

WING DESIGN

STAR Global Conference 2012

19-21 March 2012, Amsterdam, NL

Ing. Laura MAININI Ph.D. Candidate – Research Assistant

Ing. Marco TOSETTI Research Assistant

Prof. Paolo MAGGIORE Associate Professor

Department Of Mechanical

and Aerospace Engineering

(DIMEAS)

Outline

Introduction

The design problem

The design environment

Multidisciplinarity & Interdisciplinarity

Time and cost containment

Approximated model for aerodynamic coefficients

Methodology

Conclusions

2

STAR Global Conference - Amsterdam, March 19-21, 2012

Introduction

Aerospace engineering project is

characterized by:

need to manage complexity

need to maintain competitiveness

design quality

reduction of time to market

development & production costs

containment

Necessity to develop an

Optimal Design since

preliminary stages i.o.t.

reduce changes in further

design phases

Multidisciplinary Analysis and

Optimization (MAO) Concurrent Engineering (CE) &

Addressing:

Complexity management

Competitiveness requirements

Need to integrate

design phases

3


The design problem

Design of wing eventually able to assume optimized shape for

different mission legs

Multidisciplinary Integrated Design Environment

Able to address the three main key issues:

Multidisciplinarity

Interdisciplinarity

Cost & time containment

4


Multidisciplinarity & Interdisciplinarity

The design environment 5



Wing design framework that

integrates different

disciplines

Multilevel distributed

analyses architecture that

manages variables and

models distributing the

process across three levels

Multidisciplinarity Interdisciplinarity

6



Multilevel Analysis architecture

The most external loop deals with geometric configuration and mission variables

A first inner loop manages performance and structural layout variables

The most internal loop performs structural sizing

7



Geometry management

Geometry layout

Flight conditions & mission leg

management

Aerodynamic analysis pressure field

Structural layout

management

Flight conditions

Aerodynamic analysis CL & CD

Approximation

Performance analysis

Flight mechanics

Structural layout

Structural sizing management

Structural sizing

Material model

Structural static

& dynamic analysis

Manufacturing costs analysis

Level 1

Level 2

Level 3

8


Cost & time containment

The design environment 9



Geometry management

Geometry layout

Flight conditions & mission leg

management

Aerodynamic analysis pressure field

Structural layout

management

Flight conditions

Aerodynamic analysis CL & CD

Approximation

Performance analysis

Flight mechanics

Structural layout

Structural sizing management

Structural sizing

Material model

Structural static

& dynamic analysis

Manufacturing costs analysis

Level 1

Level 2

Level 3

10



Focusing attention on the most expansive HF analysis involved in the design

process

Aerodynamic analysis of the wing i.o.t. evaluate lift and drag coefficients

The use of a finite volume CFD model to solve the Navier-Stokes equations at

each cycle is definitely too much expensive.

However a good accuracy in the results is necessary and what comes from

other cheaper models is not enough

Variable fidelity strategies and surrogate modeling techniques to obtain a

fast and agile model for aerodynamic analysis

Ad hoc methodology

11


The methodology

Aerodynamic Coefficients Approx

1 • Complete design space exploration

2 • Screening and reduction of space dimensionality

3 • Reduced design space exploration

4 • Surrogate models construction and comparison

5 • Correction for low fidelity model

12


1. Complete design space exploration

All design variables are considered, 23 variables:

20 geometry variables

3 flight condition variables

Exploration technique: 2-level fractional factorial

It allows broad but intensive investigation of design space

It provides useful information about the edges of the space

64 sample points are evaluated using high fidelity

aerodynamic analysis model:

Finite volume CFD commercial code STAR-CCM+ is used

13


High fidelity model

Fully parametric models

Finite Volume model

implemented using

STAR-CCM+ by CD-adapco.

Java macros have been

recorded and

parameterized.

14


High fidelity model

The model for this CFD analysis is based onto the solution of

Navier-Stokes governing equations for three dimensional,

turbulent flow.

It represents the high fidelity (HF) aerodynamic analysis option.

15


2. Screening and reduction of space dimensionality

Determination of which variables predominantly contribute to the output

A variance based technique was chosen

It is very fast

It exploits

the 2-level DOE

Variables whose

total effects

contribute up to

85% of the results

are considered

16


Variables Complete

Activation

Reduced

Activation Range Initial value

Dihedral Angle [deg]

Root chord [m]

Semi Wing Span [m]

Sweep Angle [deg]

Taper Ratio

Twist Angle [deg]

Airfoil Camber a

Airfoil Camber Position a

Airfoil Thickness % a

X

X

X

X

X

X

[X X X X]

[X X X X]

[X X X X]

X

-

-

X

-

-

[ - - - - ]

[ - - - - ]

[ - X - -]

2 : 6

6 : 9

15 : 20

10 : 40

0.15 : 0.5

0 : 5

0 : 4

0 : 4

10 : 40

5

7

16

30

0.3

5

0

0

12

Aifoil Position (spanwide) % b

Airspeed [m/s]

Altitude [m]

Angle of attack [deg]

[ - X X - ]

X

X

X

[ - - - - ]

X

-

X

25 : 50 – 60 : 75

100 : 200

6000 : 12000

-2 : 12

0 - 30 - 60 - 100

180

10000

5

aEach value of the vector refers to a different naca4digit generative airfoil spanwise; the first one is the root airfoil, the last one is the tip airfoil so that their position is fixed bBecause the root and tip airfoil are fixed, the only two airfoils which position can change are the mid-ones

2. Screening and reduction of space dimensionality

17


3. Reduced design space exploration

Only 5 screened variables are considered, 18 are blocked to initial values

Exploration technique: 5-level Central Composite Design (CCD) space inscribed

It allows a denser exploration that enable the construction of more reliable approximated models

Inscribed because mid-points are more interesting than outer points

27 sample points are evaluated using different fidelity aerodynamic analysis models:

High fidelity model HF – finite volume CFD

Low fidelity model LF – Vortex Lattice Method

18


Low fidelity model

Fully parametric panel model

Vortex Lattice Method code: AVL –

Athena Vortex Lattice 3.27

Computational Fluid Dynamic (CFD)

numerical method based on the theory of

ideal and potential flow.

The flow field is considered inviscid,

incompressible and irrotational

(compressible flow can be considered by

the use of the Prandtl-Glauert

transformation)

The thickness of the modeled surfaces is

neglected

The small angle of approximation is

applied.

19

4. Surrogate models construction and comparison

27 sample points

21 for models construction

6 for models validation

HF data-fit surrogates

Response surfaces

Kriging models

27 sample points

21 for models construction

6 for models validation

LF data-fit surrogates

Response surface

Kriging models

High fidelity Low fidelity

20



The response surface with interaction terms (RSi) seems to be

the best approximation for both CL and CD coefficients such as

for both low and high fidelity evaluations

It is the basic model to which the implemented corrections are

applied and tested

0

1

( )p p

i i ij i j

i i j

RSi x a a x a x x

21


Test Points 1 2 3 4 5 6 Variables values

Dihedral Angle [deg]

Sweep Angle [deg]

Airfoil Thickness %(2)

Airspeed

Angle of Attack

4

25

40

150

5

6

25

10

100

5

4

40

25

200

5

4

25

25

150

-2

4

25

25

150

12

4

25

25

150

5

CD

HF

RSi-HF

LF

RSi-LF

0.011567

0.019149

0.013670

0.019846

0.009817

0.010905

0.013670

0.018676

0.012381

0.019703

0.013670

0.018676

0.013279

-0.004207

0.002170

-0.019511

0.051549

0.034816

0.080930

0.056863

0.010403

0.015304

0.013670

0.018676

CL

HF

RSi-HF

LF

RSi-LF

0.228673

0.199417

0.788860

0.783809

0.255110

0.252604

0.788850

0.784479

0.294012

0.237006

0.788850

0.784479

-0.350229

-0.318142

-0.313840

-0.320575

0.702166

0.807753

1.922960

1.889534

0.270949

0.244805

0.788850

0.784479


22


5. Correction for low fidelity model

Objective: cheap and lean model able to provide reliable values for

aerodynamic coefficients as close and consistent as possible with those

provided by a CFD high fidelity analysis

Correction of the surrogate model built on low fidelity evaluations with

high fidelity points collected in an available database

Two types:

Global: for correction on the entire design space

Local: for correction on a small portion of design space

23



Global:

determination of b1 and b2 in order to obtain

LF is: Direct evaluation of low fidelity model in the external loop

The RSi of the low fidelity model in the internal loop

1 1 11

2 2

1 1 1

1n n n

i i

i i i

n n n

i i i i

i i i

LF HF

LF LF HF LF

b

b

1 2M LFb b

24



25



26



Local:

Necessary where global correction is not enough

In order to fix global correction

Proposals:

second order Taylor expansion based local correction

Neural Networks based local correction

SOM based clustering of the errors, identification of similar subspaces and subspace

based calibration of the correction model.

27


Conclusions

Variable fidelity techniques are used to build and evaluate

approximated models for the estimation of aerodynamic

coefficients in a multidisciplinary integrated wing design

framework

The high fidelity model is a Finite Volume model implemented

using STAR-CCM+ by CD-adapco.

The low fidelity model is Vortex Lattice Method based code, AVL

– Athena Vortex Lattice 3.27 by M. Drela (MIT)

28


Conclusions

A methodology for surrogate model construction is proposed

involving:

Variables screening

Data-fit surrogates assessment

Effective global correction

Lean, cheap and robust

surrogate model

Time ratio Fidelity

HF/LF Hours/minutes HF >> LF

HF / RSi Hours/ 10 -1 s HF >> RSi

HF / RSi _corrected Hours/ 10 -1 s HF ~ RSi_corrected

29


References

Mainini L., Maggiore P. (2012) Multidisciplinary Integrated Framework for the Optimal Design of a

Jet Aircraft Wing. International Journal of Aerospace Engineering. (In press)

Mainini L., Tosetti M., Maggiore P. (2011) Approximated models for aerodynamic coefficients

estimation in a multidisciplinary design environment. In: 4th European Conference for Aerospace

Sciences (EUCASS) 2011, Saint Petersburg (RUSSIA), 4-8 July 2011.

Mainini L., Mattone M., Di Sciuva M., Maggiore P. (2010) Multidisciplinary integrated design

environment for aircraft wing sizing. In: MAO 2010, 13th AIAA/ISSMO Multidisciplinary Analysis

Optimization Conference, Fort Worth, TX (USA), 13-16 September 2010.

Mainini L. (2009) Structural Wing Sizing Using Multidisciplinary Integrated Design Environment. In:

5th PEGASUS-AIAA Student Conference, Toulouse, France, March 2009.

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Acknowledgments

The authors gratefully acknowledge the assistance of Professor Karen

Willcox of Massachusetts Institute of Technology and Ing. Antonio Caimano

for sharing their expertise.

The authors would also like to thank CD-adapco for the kind collaboration

with STAR-CCM+.

Part of this research benefits of the funding coming from the framework of

CRESCENDO European Research Project.

31


Thank you for your kind attention

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