Dynamic Aeroelastic Scaling of the CRMWing via Multidisciplinary Optimization

Joan Mas Colomer2nd year PhD Student at ONERA and ISAE

Nathalie Bartoli, Thierry Lefebvre,Sylvain Dubreuil (ONERA). Joseph Morlier (ISAE)

With the collaboration of: T. Achard,C. Blondeau (ONERA). J. R. R. A. Martins (UMich)

WCSMO12

Braunschweig, GermanyJune 5, 2017

Introduction - Similarity and Optimization

Reference aircraft

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Introduction - Similarity and Optimization

Reference aircraft

Scaled model

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Introduction - Similarity and Optimization

Reference aircraft

Scaled model

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Introduction - Similarity and Optimization

Reference aircraft

Scaled model

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Introduction - Similarity and Optimization

Reference aircraft

Scaled model

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Introduction - Similarity and Optimization

Reference aircraft

Scaled model

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Introduction - Dynamic Aeroelastic Similarity

Reference aircraft mode shape⇤Optimized scale demonstrator

mode shape⇤

⇤[Richards et al., AIAA/ATIO Conference, 2010]

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Outline

1 Tools

2 Dynamic Aeroelastic Scaling

3 CRM wing modal optimization

4 Aerodynamic Flutter Optimization

5 Conclusion

6 Perspectives

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1 Tools

2 Dynamic Aeroelastic Scaling

3 CRM wing modal optimization

4 Aerodynamic Flutter Optimization

5 Conclusion

6 Perspectives

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Tools

Nastran 95⇤: Normal Modes and Flutter Analysis

Panair/a502†: Static aerodynamics

OpenMDAO‡ Framework

Optimizer: SLSQP (Gradient-based, from Scipy library)

⇤[github.com/nasa/NASTRAN-95]

†[pdas.com/panair.html]

‡[Gray et al., AIAA/ISSMO, 2014]

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Tools

Nastran 95⇤: Normal Modes and Flutter Analysis

Panair/a502†: Static aerodynamics

OpenMDAO‡ Framework

Optimizer: SLSQP (Gradient-based, from Scipy library)

⇤[github.com/nasa/NASTRAN-95]

†[pdas.com/panair.html]

‡[Gray et al., AIAA/ISSMO, 2014]

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Tools

Nastran 95⇤: Normal Modes and Flutter Analysis

Panair/a502†: Static aerodynamics

OpenMDAO‡ Framework

Optimizer: SLSQP (Gradient-based, from Scipy library)

⇤[github.com/nasa/NASTRAN-95]

†[pdas.com/panair.html]

‡[Gray et al., AIAA/ISSMO, 2014]

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Tools

Nastran 95⇤: Normal Modes and Flutter Analysis

Panair/a502†: Static aerodynamics

OpenMDAO‡ Framework

Optimizer: SLSQP (Gradient-based, from Scipy library)

⇤[github.com/nasa/NASTRAN-95]

†[pdas.com/panair.html]

‡[Gray et al., AIAA/ISSMO, 2014]

6/24

Tools

Nastran 95⇤: Normal Modes and Flutter Analysis

Panair/a502†: Static aerodynamics

OpenMDAO‡ Framework

Optimizer: SLSQP (Gradient-based, from Scipy library)

⇤[github.com/nasa/NASTRAN-95]

†[pdas.com/panair.html]

‡[Gray et al., AIAA/ISSMO, 2014]

6/24

1 Tools

2 Dynamic Aeroelastic Scaling

3 CRM wing modal optimization

4 Aerodynamic Flutter Optimization

5 Conclusion

6 Perspectives

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Dynamic Aeroelastic Scaling

Aeroelastic equations of motion:

[M]{x}+ [K]{x} = [Ak]{x}+ [Ac]{x}+ [Am]{x}+ [M]{ag}

In modal coordinates ({x}=[�]{⌘}):

[�]T [M][�]{⌘}+ [�]T [K][�]{⌘} = [�]T [Ak][�]{⌘}+

[�]T [Ac][�]{⌘}+ [�]T [Am][�]{⌘}+ 1

b

[�]T [M]{ag}

[Ricciardi et al., Journal of Aircraft, 2014]

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Dynamic Aeroelastic Scaling

Aeroelastic equations of motion:

[M]{x}+ [K]{x} = [Ak]{x}+ [Ac]{x}+ [Am]{x}+ [M]{ag}

In modal coordinates ({x}=[�]{⌘}):

[�]T [M][�]{⌘}+ [�]T [K][�]{⌘} = [�]T [Ak][�]{⌘}+

[�]T [Ac][�]{⌘}+ [�]T [Am][�]{⌘}+ 1

b

[�]T [M]{ag}

[Ricciardi et al., Journal of Aircraft, 2014]

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Dynamic Aeroelastic Scaling

Aeroelastic equations of motion:

[M]{x}+ [K]{x} = [Ak]{x}+ [Ac]{x}+ [Am]{x}+ [M]{ag}

In modal coordinates ({x}=[�]{⌘}):

[�]T [M][�]{⌘}+ [�]T [K][�]{⌘} = [�]T [Ak][�]{⌘}+

[�]T [Ac][�]{⌘}+ [�]T [Am][�]{⌘}+ 1

b

[�]T [M]{ag}

[Ricciardi et al., Journal of Aircraft, 2014]

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Dynamic Aeroelastic Scaling

Aeroelastic equations of motion:

[M]{x}+ [K]{x} = [Ak]{x}+ [Ac]{x}+ [Am]{x}+ [M]{ag}

In modal coordinates ({x}=[�]{⌘}):

[�]T [M][�]{⌘}+ [�]T [K][�]{⌘} = [�]T [Ak][�]{⌘}+

[�]T [Ac][�]{⌘}+ [�]T [Am][�]{⌘}+ 1

b

[�]T [M]{ag}

[Ricciardi et al., Journal of Aircraft, 2014]

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Dynamic Aeroelastic Scaling

Adimensionalize with reference quantities:

hmi {??⌘}+⌦m!2

↵{⌘} =

V

2

b

2!21| {z }

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gb

V

2|{z}1/Fr2

hmi [�]�1{ag}

+1

2

⇢Sb

m1|{z}µ1

V

2

!21b

2

| {z }1/2

1

✓[ak]{⌘}+

!1b

V|{z}1

[ac]{?⌘}+ !2

1b2

V

2| {z }21

[am]{??⌘}

◆

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Traditional Dynamic Aeroelastic Scaling

Nondimensional aeroelastic equations of motion (harmonicsolution):

Reference aircraft: r

Scaled model: m

hmri {??⌘}+

⌦mr!

2r

↵{⌘} =

1

2

µ1r

21r

[ahr(Xar,,Mr)]{⌘}

hmmi {??⌘}+

⌦mm!

2m

↵{⌘} =

1

2

µ1m

21m

[ahm(Xam,,Mm)]{⌘}

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Traditional Dynamic Aeroelastic Scaling

Nondimensional aeroelastic equations of motion (harmonicsolution):Reference aircraft: rScaled model: m

hmri {??⌘}+

⌦mr!

2r

↵| {z }

{⌘} =1

2

µ1r

21r

[ahr(Xar,,Mr)]| {z } {⌘}

Match [�], h!i , hmi(from the problemK � !2[M]{�} = 0)through optimizationz }| {

hmmi {??⌘}+

⌦mm!

2m

↵{⌘} =

1

2

µ1m

21m

Equal if same aerodynamicshape and flow similarityz }| {[ahm(Xam,,Mm)] {⌘}

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1 Tools

2 Dynamic Aeroelastic Scaling

3 CRM wing modal optimization

4 Aerodynamic Flutter Optimization

5 Conclusion

6 Perspectives

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CRM Model

Reference Design⇤ (jig shape): For all elements tr = 8.89mm

Model provided by T. Achard and C. Blondeau⇤

⇤[Achard et al., AIAA/ISSMO, 2016]

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CRM modal optimization: Problem definitionHypothesis: Flow similarity assumed

Objective Function Dimension BoundsMode shape di↵erence minimization min(N � trace(MAC([�r ], [�m]))) RDesign VariablesSkin thicknesses vector [t] R10 [0.0889, 26.67] mmConstraintsReduced frequency matching k!r � !mk = 0 RMass matching Mr �Mm = 0 RGeneralized masses matching kmr �mmk = 0 R

! Upper skin panels

Lower skin panels

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Traditional Modal OptimizationHypothesis: Flow similarity assumed

[t]0 [�ref ] [!ref ] M

0 [mref ]

[t]⇤0, 3!1:

Optimization1 : [t]

[�]⇤, [!]⇤,M⇤

1:NastranModalAnalysis

2 : [�] 2 : [!] 2 : M 2 : [m]

3 : f2:

ObjectiveFunction

3 : c12:

Frequency

3 : c22:

Mass

3 : c3

2:Generalized

ModalMasses

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CRM Modal Optimization: ResultsBest Found Point vs IterationCriterion: Point with best objective function AND sum of constraints

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1 Tools

2 Dynamic Aeroelastic Scaling

3 CRM wing modal optimization

4 Aerodynamic Flutter Optimization

5 Conclusion

6 Perspectives

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What if the flow is not similar?

Reference aircraft: r

Scaled model: m

hmri {??⌘}+

⌦mr!

2r

↵{⌘} =

1

2

µ1r

21r

[ahr(Xar,,Mr)]{⌘}

hmmi {??⌘}+

⌦mm!

2m

↵{⌘} =

1

2

µ1m

21m

[ahm(Xam,,Mm)]{⌘}

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What if the flow is not similar?

Reference aircraft: r

Scaled model: m

hmri {??⌘}+

⌦mr!

2r

↵| {z }

{⌘} =1

2

µ1r

21r

[ahr(Xar,,Mr)]| {z } {⌘}

matched through modal optimizationz }| {hmmi {

??⌘}+

⌦mm!

2m

↵{⌘} =

1

2

µ1m

21m

?z }| {[ahm(Xam,,Mm)] {⌘}

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What if the flow is not similar?

Reference aircraft: r

Scaled model: m

hmri {??⌘}+

⌦mr!

2r

↵| {z }

{⌘} =1

2

µ1r

21r

[ahr(Xar,,Mr)]| {z } {⌘}

matched through modal optimizationz }| {hmmi {

??⌘}+

⌦mm!

2m

↵{⌘} =

1

2

µ1m

21m

optimize w.r.t. Xamz }| {[ahm(Xam,,Mm)] {⌘}

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What if the flow is not similar? AerodynamicOptimization

Reference aircraft: r

Scale model: m

Reduced frequency:

Mach number: M

Objective function:

f =X

i

(k[ahr(Xar,i,Mr)]� [ahm(Xam,i,Mm)]k)

Design variables:

Xam: Parameters defining the wing planform

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What if the flow is not similar? AerodynamicOptimization

Reference aircraft: r

Scale model: m

Reduced frequency:

Mach number: M

Objective function:

f =X

i

(k[ahr(Xar,i,Mr)]� [ahm(Xam,i,Mm)]k)

Design variables:

Xam: Parameters defining the wing planform

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What if the flow is not similar? AerodynamicOptimization

Reference aircraft: r

Scale model: m

Reduced frequency:

Mach number: M

Objective function:

f =X

i

(k[ahr(Xar,i,Mr)]� [ahm(Xam,i,Mm)]k)

Design variables:

Xam: Parameters defining the wing planform

18/24

What if the flow is not similar? AerodynamicOptimization

Reference aircraft: r

Scale model: m

Reduced frequency:

Mach number: M

Objective function:

f =X

i

(k[ahr(Xar,i,Mr)]� [ahm(Xam,i,Mm)]k)

Design variables:

Xam: Parameters defining the wing planform

18/24

What if the flow is not similar? AerodynamicOptimization

Reference aircraft: r

Scale model: m

Reduced frequency:

Mach number: M

Objective function:

f =X

i

(k[ahr(Xar,i,Mr)]� [ahm(Xam,i,Mm)]k)

Design variables:

Xam: Parameters defining the wing planform

18/24

What if the flow is not similar? AerodynamicOptimization

Reference aircraft: r

Scale model: m

Reduced frequency:

Mach number: M

Objective function:

f =X

i

(k[ahr(Xar,i,Mr)]� [ahm(Xam,i,Mm)]k)

Design variables:

Xam: Parameters defining the wing planform

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Aerodynamic Optimization: Goland Wing Test Case

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Aerodynamic Optimization: Goland Wing Test Case

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1 Tools

2 Dynamic Aeroelastic Scaling

3 CRM wing modal optimization

4 Aerodynamic Flutter Optimization

5 Conclusion

6 Perspectives

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Conclusion

Review of the traditional dynamic aeroelastic scalingapproach

Modal optimization for similarity

Application to the CRM test case

Importance of no flow similarity

Wing planform optimization for flutter similarity

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Conclusion

Review of the traditional dynamic aeroelastic scalingapproach

Modal optimization for similarity

Application to the CRM test case

Importance of no flow similarity

Wing planform optimization for flutter similarity

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Conclusion

Review of the traditional dynamic aeroelastic scalingapproach

Modal optimization for similarity

Application to the CRM test case

Importance of no flow similarity

Wing planform optimization for flutter similarity

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Conclusion

Review of the traditional dynamic aeroelastic scalingapproach

Modal optimization for similarity

Application to the CRM test case

Importance of no flow similarity

Wing planform optimization for flutter similarity

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Conclusion

Review of the traditional dynamic aeroelastic scalingapproach

Modal optimization for similarity

Application to the CRM test case

Importance of no flow similarity

Wing planform optimization for flutter similarity

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1 Tools

2 Dynamic Aeroelastic Scaling

3 CRM wing modal optimization

4 Aerodynamic Flutter Optimization

5 Conclusion

6 Perspectives

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Perspectives

Perform flutter-based wing planform optimization withthe CRM model

From the optimized planform, optimize wing twistdistribution and structure properties to match staticdeflection

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Perspectives

Perform flutter-based wing planform optimization withthe CRM model

From the optimized planform, optimize wing twistdistribution and structure properties to match staticdeflection

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Thanks for your attention!

Questions?

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