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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
2/24
Introduction - Similarity and Optimization
Reference aircraft
Scaled model
2/24
Introduction - Similarity and Optimization
Reference aircraft
Scaled model
2/24
Introduction - Similarity and Optimization
Reference aircraft
Scaled model
2/24
Introduction - Similarity and Optimization
Reference aircraft
Scaled model
2/24
Introduction - Similarity and Optimization
Reference aircraft
Scaled model
2/24
Introduction - Dynamic Aeroelastic Similarity
Reference aircraft mode shape⇤Optimized scale demonstrator
mode shape⇤
⇤[Richards et al., AIAA/ATIO Conference, 2010]
3/24
Outline
1 Tools
2 Dynamic Aeroelastic Scaling
3 CRM wing modal optimization
4 Aerodynamic Flutter Optimization
5 Conclusion
6 Perspectives
4/24
1 Tools
2 Dynamic Aeroelastic Scaling
3 CRM wing modal optimization
4 Aerodynamic Flutter Optimization
5 Conclusion
6 Perspectives
5/24
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
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
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
7/24
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]
8/24
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]
8/24
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]
8/24
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]
8/24
Dynamic Aeroelastic Scaling
Adimensionalize with reference quantities:
hmi {??⌘}+⌦m!2
↵{⌘} =
V
2
b
2!21| {z }
1/21
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]{??⌘}
◆
9/24
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)]{⌘}
10/24
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)] {⌘}
10/24
1 Tools
2 Dynamic Aeroelastic Scaling
3 CRM wing modal optimization
4 Aerodynamic Flutter Optimization
5 Conclusion
6 Perspectives
11/24
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]
12/24
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
13/24
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
14/24
CRM Modal Optimization: ResultsBest Found Point vs IterationCriterion: Point with best objective function AND sum of constraints
15/24
1 Tools
2 Dynamic Aeroelastic Scaling
3 CRM wing modal optimization
4 Aerodynamic Flutter Optimization
5 Conclusion
6 Perspectives
16/24
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)]{⌘}
17/24
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)] {⌘}
17/24
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)] {⌘}
17/24
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
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
18/24
Aerodynamic Optimization: Goland Wing Test Case
19/24
Aerodynamic Optimization: Goland Wing Test Case
19/24
1 Tools
2 Dynamic Aeroelastic Scaling
3 CRM wing modal optimization
4 Aerodynamic Flutter Optimization
5 Conclusion
6 Perspectives
20/24
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
21/24
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
21/24
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
21/24
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
21/24
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
21/24
1 Tools
2 Dynamic Aeroelastic Scaling
3 CRM wing modal optimization
4 Aerodynamic Flutter Optimization
5 Conclusion
6 Perspectives
22/24
Perspectives
Perform flutter-based wing planform optimization withthe CRM model
From the optimized planform, optimize wing twistdistribution and structure properties to match staticdeflection
23/24
Perspectives
Perform flutter-based wing planform optimization withthe CRM model
From the optimized planform, optimize wing twistdistribution and structure properties to match staticdeflection
23/24
Thanks for your attention!
Questions?
24/24