AERODYNAMIC ANALYSIS Research Assistant Prof. Paolo MAGGIORE FOR - - PowerPoint PPT Presentation

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AERODYNAMIC ANALYSIS Research Assistant Prof. Paolo MAGGIORE FOR - - PowerPoint PPT Presentation

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VARIABLE-FIDELITY Ing. Laura MAININI Ph.D. Candidate Research Assistant Ing. Marco TOSETTI AERODYNAMIC ANALYSIS Research Assistant Prof. Paolo MAGGIORE FOR MULTIDISCIPLINARY Associate Professor Department Of Mechanical WING DESIGN and

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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)

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Outline

 Introduction  The design problem  The design environment  Multidisciplinarity & Interdisciplinarity  Time and cost containment  Approximated model for aerodynamic coefficients  Methodology  Conclusions

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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

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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

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Multidisciplinarity & Interdisciplinarity

The design environment

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The design environment

Wing design framework that

integrates different disciplines

Multilevel distributed

analyses architecture that manages variables and models distributing the process across three levels

Multidisciplinarity Interdisciplinarity

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The design environment

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

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The design environment

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

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Cost & time containment

The design environment

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The design environment

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

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The design environment

 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

  • ther 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

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The methodology

Aerodynamic Coefficients Approx

1

  • Complete design space exploration

2

  • Screening and reduction of space dimensionality

3

  • Reduced design space exploration

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  • Surrogate models construction and comparison

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  • Correction for low fidelity model

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  • 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

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High fidelity model

 Fully parametric models  Finite Volume model

implemented using STAR-CCM+ by CD-adapco.

 Java macros have been

recorded and parameterized.

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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.

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  • 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

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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 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

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  • 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

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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.

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  • 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

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  • 4. Surrogate models construction and comparison

 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

1

( )

p p i i ij i j i i j

RSi x a a x a x x

 

  

 

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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

  • 4. Surrogate models construction and comparison

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  • 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

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  • 5. Correction for low fidelity model

 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 1 1 2 2 1 1 1

1

n 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 2

M LF b b  

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  • 5. Correction for low fidelity model

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  • 5. Correction for low fidelity model

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  • 5. Correction for low fidelity model

 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.

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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)

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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

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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.

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Thank you for your kind attention

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