Dynamic Aeroelastic Scaling of the CRM Wing via Multidisciplinary Optimization

Transcription

1 This work has been supported by the EU project NextGen Airliners funded by Marie Skłodowska-Curie actions (MSCA). Dynamic Aeroelastic Scaling of the CRM Wing via Multidisciplinary Optimization Joan Mas Colomer 2nd 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, Germany June 5, 2017

2 Introduction - Similarity and Optimization Reference aircraft 2/24

3 Introduction - Similarity and Optimization Reference aircraft Scaled model 2/24

4 Introduction - Similarity and Optimization Reference aircraft Scaled model 2/24

5 Introduction - Similarity and Optimization Reference aircraft Scaled model 2/24

6 Introduction - Similarity and Optimization Reference aircraft Scaled model 2/24

7 Introduction - Similarity and Optimization Reference aircraft Scaled model 2/24

8 Introduction - Dynamic Aeroelastic Similarity Reference aircraft mode shape Optimized scale demonstrator mode shape [Richards et al., AIAA/ATIO Conference, 2010] 3/24

9 Outline 1 Tools 2 Dynamic Aeroelastic Scaling 3 CRM wing modal optimization 4 Aerodynamic Flutter Optimization 5 Conclusion 6 Perspectives 4/24

10 1 Tools 2 Dynamic Aeroelastic Scaling 3 CRM wing modal optimization 4 Aerodynamic Flutter Optimization 5 Conclusion 6 Perspectives 5/24

11 Tools Nastran 95 : Normal Modes and Flutter Analysis 6/24

12 Tools Nastran 95 : Normal Modes and Flutter Analysis Panair/a502 :Staticaerodynamics 6/24

13 Tools Nastran 95 : Normal Modes and Flutter Analysis Panair/a502 :Staticaerodynamics OpenMDAO Framework 6/24

14 Tools Nastran 95 : Normal Modes and Flutter Analysis Panair/a502 :Staticaerodynamics OpenMDAO Framework Optimizer: SLSQP (Gradient-based, from Scipy library) 6/24

15 Tools Nastran 95 : Normal Modes and Flutter Analysis Panair/a502 :Staticaerodynamics 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

16 1 Tools 2 Dynamic Aeroelastic Scaling 3 CRM wing modal optimization 4 Aerodynamic Flutter Optimization 5 Conclusion 6 Perspectives 7/24

17 Dynamic Aeroelastic Scaling Aeroelastic equations of motion: [M]{ẍ} +[K]{x} =[A k ]{x} +[A c ]{ẋ} +[A m ]{ẍ} +[M]{a g } 8/24

18 Dynamic Aeroelastic Scaling Aeroelastic equations of motion: [M]{ẍ} +[K]{x} =[A k ]{x} +[A c ]{ẋ} +[A m ]{ẍ} +[M]{a g } In modal coordinates ({x}=[ ]{ }): 8/24

19 Dynamic Aeroelastic Scaling Aeroelastic equations of motion: [M]{ẍ} +[K]{x} =[A k ]{x} +[A c ]{ẋ} +[A m ]{ẍ} +[M]{a g } In modal coordinates ({x}=[ ]{ }): [ ] T [M][ ]{ } +[ ] T [K][ ]{ } =[ ] T [A k ][ ]{ }+ [ ] T [A c ][ ]{ } +[ ] T [A m ][ ]{ } + 1 b [ ]T [M]{a g } 8/24

20 Dynamic Aeroelastic Scaling Aeroelastic equations of motion: [M]{ẍ} +[K]{x} =[A k ]{x} +[A c ]{ẋ} +[A m ]{ẍ} +[M]{a g } In modal coordinates ({x}=[ ]{ }): [ ] T [M][ ]{ } +[ ] T [K][ ]{ } =[ ] T [A k ][ ]{ }+ [ ] T [A c ][ ]{ } +[ ] T [A m ][ ]{ } + 1 b [ ]T [M]{a g } [Ricciardi et al., Journal of Aircraft, 2014] 8/24

21 Dynamic Aeroelastic Scaling Adimensionalize with reference quantities: h m i{?? } + m! 2 { } = V 2 b 2! Sb m 1 {z} µ 1 V 2! 1 2b2 {z } 1/apple 2 1 {z } 1/apple 2 1 [ā k ]{ } +! 1b {z} V gb h m i [ ] {z} V 2 1/Fr 2 1 {ā g }? [ā c ]{ } +!2 1b 2 [ā V 2 m ]{?? {z } apple 1 apple 2 1 } 9/24

22 Traditional Dynamic Aeroelastic Scaling Nondimensional aeroelastic equations of motion (harmonic solution): Reference aircraft: r Scaled model: m h m r i{?? } + m r! 2 r 1 µ 1r { } = [ā 2 apple 2 hr (X ar,apple,m r )]{ } 1r h m m i{?? } + m m! 2 m { } = 1 2 µ 1m [ā apple 2 hm (X am,apple,m m )]{ } 1m 10/24

23 Traditional Dynamic Aeroelastic Scaling Nondimensional aeroelastic equations of motion (harmonic solution): Reference aircraft: r Scaled model: m h m r i{?? } + m r! r 2 {z } { } = 1 2 µ 1r apple 2 1r [ā hr (X ar,apple,m r )] {z } { } Match [ ], h!i, h m i (from the problem K! 2 [M]{ } =0) through optimization z } { h m m i{?? } + m m! m 2 { } = 1 2 µ 1m apple 2 1m Equal if same aerodynamic shape and flow similarity z } { [ā hm (X am,apple,m m )] { } 10/24

24 1 Tools 2 Dynamic Aeroelastic Scaling 3 CRM wing modal optimization 4 Aerodynamic Flutter Optimization 5 Conclusion 6 Perspectives 11/24

25 CRM Model Reference Design (jig shape): For all elements t r =8.89mm Model provided by T. Achard and C. Blondeau [Achard et al., AIAA/ISSMO, 2016] 12/24

26 CRM modal optimization: Problem definition Hypothesis: Flow similarity assumed Objective Function Dimension Bounds Mode shape di erence minimization min(n trace(mac([ r], [ m]))) R Design Variables Skin thicknesses vector [t] R 10 [0.0889, 26.67] mm Constraints Reduced frequency matching k!r!mk =0 R Mass matching Mr Mm =0 R Generalized masses matching kmr mmk = 0 R! Upper skin panels Lower skin panels 13/24

27 Traditional Modal Optimization Hypothesis: Flow similarity assumed [t] 0 [ ref ] [! ref ] M 0 [m ref ] [t] 0, 3!1: Optimization 1:[t] [ ], [!], M 1: Nastran Modal Analysis 3:f 2 : [ ] 2:[!] 2:M 2:[m] 2: Objective Function 3:c 1 2: Frequency 3:c 2 2: Mass 14/24 3:c 3 2: Generalized Modal Masses

28 CRM Modal Optimization: Results Best Found Point vs Iteration Criterion: Point with best objective function AND sum of constraints 15/24

29 1 Tools 2 Dynamic Aeroelastic Scaling 3 CRM wing modal optimization 4 Aerodynamic Flutter Optimization 5 Conclusion 6 Perspectives 16/24

30 What if the flow is not similar? Reference aircraft: r Scaled model: m h m r i{?? } + m r! 2 r 1 µ 1r { } = [ā 2 apple 2 hr (X ar,apple,m r )]{ } 1r h m m i{?? } + m m! 2 m { } = 1 2 µ 1m [ā apple 2 hm (X am,apple,m m )]{ } 1m 17/24

31 What if the flow is not similar? Reference aircraft: r Scaled model: m h m r i{?? } + m r! r 2 {z } { } = 1 2 µ 1r apple 2 1r [ā hr (X ar,apple,m r )] {z } { } matched through modal optimization z } { h m m i{?? } + m m! m 2 { } = 1? µ 1m z } { [ā 2 apple 2 hm (X am,apple,m m )] { } 1m 17/24

32 What if the flow is not similar? Reference aircraft: r Scaled model: m h m r i{?? } + m r! r 2 {z } { } = 1 2 µ 1r apple 2 1r [ā hr (X ar,apple,m r )] {z } { } matched through modal optimization z } { h m m i{?? } + m m! m 2 { } = 1 optimize w.r.t. X am µ 1m z } { [ā 2 apple 2 hm (X am,apple,m m )] { } 1m 17/24

33 What if the flow is not similar? Aerodynamic Optimization Reference aircraft: r Scale model: m 18/24

34 What if the flow is not similar? Aerodynamic Optimization Reference aircraft: r Reduced frequency: apple Scale model: m Mach number: M 18/24

35 What if the flow is not similar? Aerodynamic Optimization Reference aircraft: r Reduced frequency: apple Scale model: m Mach number: M Objective function: 18/24

36 What if the flow is not similar? Aerodynamic Optimization Reference aircraft: r Reduced frequency: apple Scale model: m Mach number: M Objective function: f = X i (k[ā hr (X ar,apple i, M r )] [ā hm (X am,apple i, M m )]k) 18/24

37 What if the flow is not similar? Aerodynamic Optimization Reference aircraft: r Reduced frequency: apple Scale model: m Mach number: M Objective function: f = X i (k[ā hr (X ar,apple i, M r )] [ā hm (X am,apple i, M m )]k) Design variables: 18/24

38 What if the flow is not similar? Aerodynamic Optimization Reference aircraft: r Reduced frequency: apple Scale model: m Mach number: M Objective function: f = X i (k[ā hr (X ar,apple i, M r )] [ā hm (X am,apple i, M m )]k) Design variables: X am :Parametersdefiningthewingplanform 18/24

39 Aerodynamic Optimization: Goland Wing Test Case 19/24

40 Aerodynamic Optimization: Goland Wing Test Case 19/24

41 1 Tools 2 Dynamic Aeroelastic Scaling 3 CRM wing modal optimization 4 Aerodynamic Flutter Optimization 5 Conclusion 6 Perspectives 20/24

42 Conclusion Review of the traditional dynamic aeroelastic scaling approach 21/24

43 Conclusion Review of the traditional dynamic aeroelastic scaling approach Modal optimization for similarity 21/24

44 Conclusion Review of the traditional dynamic aeroelastic scaling approach Modal optimization for similarity Application to the CRM test case 21/24

45 Conclusion Review of the traditional dynamic aeroelastic scaling approach Modal optimization for similarity Application to the CRM test case Importance of no flow similarity 21/24

46 Conclusion Review of the traditional dynamic aeroelastic scaling approach Modal optimization for similarity Application to the CRM test case Importance of no flow similarity Wing planform optimization for flutter similarity 21/24

47 1 Tools 2 Dynamic Aeroelastic Scaling 3 CRM wing modal optimization 4 Aerodynamic Flutter Optimization 5 Conclusion 6 Perspectives 22/24

48 Perspectives Perform flutter-based wing planform optimization with the CRM model 23/24

49 Perspectives Perform flutter-based wing planform optimization with the CRM model From the optimized planform, optimize wing twist distribution and structure properties to match static deflection 23/24

50 Thanks for your attention! Questions? 24/24