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Model Reduction for Linear and Nonlinear Gust Loads Analysis
A. Da Ronch, N.D. Tantaroudas, S.Timme and K.J. BadcockUniversity of Liverpool, U.K.
AIAA Paper 2013-1942Boston, MA, 08 April 2013
email: [email protected]
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Shape Optimisation
Flutter Calculations
Gust Loads
Mini Process Chain Based on CFD
+ iterations
CFD GridsFE Models
eigenvectors
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• Stability studied from an eigenvalue problem:
•Schur Complement formulation:
Flutter Calculations
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Badcock et al., Progress in Aerospace Sciences; 47(5): 392-423, 2011
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Badcock, K.J. and Woodgate, M.A., On the Fast Prediction of Transonic Aeroelastic Stability and Limit Cycles, AIAA J 45(6), 2007.
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Shape Optimisation
Flutter Calculations
Gust Loads
Mini Process Chain Based on CFD
+ iterations
CFD GridsFE Models
eigenvectors
This Talk
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Model Reduction
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Model Reduction
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Badcock et al., “Transonic Aeroelastic Simulation for Envelope Searches and Uncertainty Analysis”, Progress in Aerospace
Sciences; 47(5): 392-423, 2011
Project against left eigenvectors Ψ to obtain differential equations for z
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Model Reduction
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Da Ronch et al., “Nonlinear Model Reduction for Flexible Aircraft Control Design”, AIAA paper 2012-4404; AIAA Atmospheric
Flight Mechanics, 2012
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Model Reduction
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control surfaces,gust encounter, speed/altitude
Da Ronch et al., “Model Reduction for Linear and Nonlinear Gust Loads Analysis”, AIAA paper 2013-1942; AIAA
Structural Dynamics and Materials, 2013
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CFD Solver Overview
• Euler (Inviscid) results shown in this paper– Solvers include RANS also
• Implicit Formulation• 2 Spatial Schemes
– 2d results meshless formulation– 3d results block structured grids
• Osher/MUSCL + exact Jacobians • Time domain: Pseudo Time Stepping• Linearised Frequency Domain Solver
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Gust Representation: Full order method (Baeder et al 1997)
Apply gust in CFD Code to grid velocities only
× No modification of gust from interaction No diffusion of gust from solverCan represent gusts defined for synthetic atmosphere
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NACA 0012 Aerofoil point cloud
Coarse 7974 pointsMedium 22380 pointsFine 88792 points
Badcock, K. J. and Woodgate, M. A, AIAA Journal, Vol. 48, No. 6, 2010, pp. 1037–1046
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Steady state: Mach 0.85; α=1 deg
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Mach 0.8; Pitch-Plunge “Heavy Case”
Flutter Speed Ubar=3.577Speed for ROM Ubar=2.0Modes corresponding to pitch/plunge retained for ROM
2 modes; 4 DoF
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1-cosine gust: Intensity 1%Gust length 25 semi-chords
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Peak-Peak very similarDiscrepancies in magnitude
enrich basis
1-cosine gust: Intensity 1%Gust length 25 semi-chords
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Worst Gust Search at M=0.8: 1-cos family
Gust Lengths between 1 and 100 chordsKriging Method and Worst Case Sampling: 31 evaluations of ROMWorst Case: 12.4 semi chords (excites pitching mode)
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Response to Von Karman gust, frequencies to 2.5 Hz
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Finite Differences for Gust Influence reduce to virtually zero by analytical evaluation
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GOLAND WING
Mach 0.92
400k points
1.72 Hz
11.10 Hz9.18 Hz
3.05 Hz
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Mach 0.85; α=1deg
ROM calculated at 405 ft/sec EASModes corresponding to normal modes retained
4 modes; 8 DoF
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1-cosine gust: Intensity 0.1%Gust length 480 ft
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Worst Gust Search at M=0.8; 1-cos family
Gust Lengths between 5 and 150 chordsKriging Method, Worst Case Sampling: 20 ROM evaluations Worst Case: 65 chords (excites first bending mode)
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Conclusions
• Model Reduction method formulated• Tests on pitch-plunge, flexible wing case
Future
RANSRigid Body DoFsAlleviation