Model Reduction for Linear and Nonlinear Gust Loads Analysi - PowerPoint Presentation

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Model Reduction for Linear and Nonlinear Gust Loads AnalysisA. Da Ronch, N.D. Tantaroudas, S.Timme and K.J. BadcockUniversity of Liverpool, U.K.

AIAA Paper 2013-

1942

Boston, MA, 08 April 2013

email:

K.J.Badcock@liverpool.ac.ukSlide2

Shape OptimisationFlutter CalculationsGust LoadsMini Process Chain Based on CFD+ iterationsCFD GridsFE ModelseigenvectorsSlide3

Stability studied from an eigenvalue problem:Schur Complement formulation:Flutter CalculationsBadcock et al., Progress in Aerospace Sciences; 47(5): 392-423, 2011Slide4
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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.Slide6

Shape OptimisationFlutter CalculationsGust LoadsMini Process Chain Based on CFD+ iterationsCFD GridsFE ModelseigenvectorsThis TalkSlide7

Model ReductionSlide8

Model ReductionBadcock et al., “Transonic Aeroelastic Simulation for Envelope Searches and Uncertainty Analysis”, Progress in Aerospace Sciences; 47(5): 392-423, 2011Project against left eigenvectors Ψ to obtain differential equations for zSlide9

Model Reduction2nd/3rd Jacobian operators for NROMDa Ronch et al., “Nonlinear Model Reduction for Flexible Aircraft Control Design”, AIAA paper 2012-4404; AIAA Atmospheric Flight Mechanics, 2012Slide10

Model Reductioncontrol surfaces,gust encounter, speed/altitudeDa Ronch et al., “Model Reduction for Linear and Nonlinear Gust Loads Analysis”, AIAA paper 2013-1942; AIAA Structural Dynamics and Materials, 2013Slide11

CFD Solver OverviewEuler (Inviscid) results shown in this paperSolvers include RANS alsoImplicit Formulation2 Spatial Schemes2d results  meshless formulation3d results  block structured gridsOsher/MUSCL + exact Jacobians Time domain: Pseudo Time SteppingLinearised Frequency Domain SolverSlide12

Overview of Meshless SolverKennett, D. J., Timme, S., Angulo, J., and Badcock, K. J., “An Implicit Meshless Method for Application in Computational Fluid Dynamics,” International Journal for Numerical Methods in Fluids, Vol. 71, No. 8, 2013, pp. 1007–1028.Slide13

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 atmosphereSlide14

PrecomputedEvaluated in ROMSlide15

NACA 0012 Aerofoil point cloudCoarse 7974 pointsMedium 22380 pointsFine 88792 pointsBadcock, K. J. and Woodgate, M. A, AIAA Journal, Vol. 48, No. 6, 2010, pp. 1037–1046Slide16

Steady state: Mach 0.85; α=1 degSlide17

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 DoFSlide18

1-cosine gust: Intensity 1% Gust length 25 semi-chordsSlide19

Peak-Peak very similarDiscrepancies in magnitude  enrich basis1-cosine gust: Intensity 1% Gust length 25 semi-chordsSlide20

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)Slide21
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Response to Von Karman gust, frequencies to 2.5 HzSlide23

Finite Differences for Gust Influence  reduce to virtually zero by analytical evaluationSlide24

GOLAND WINGMach 0.92400k points1.72 Hz11.10 Hz9.18 Hz3.05 HzSlide25

Mach 0.85; α=1degROM calculated at 405 ft/sec EASModes corresponding to normal modes retained  4 modes; 8 DoF Slide26

1-cosine gust: Intensity 0.1% Gust length 480 ftSlide27

Worst Gust Search at M=0.8; 1-cos familyGust Lengths between 5 and 150 chordsKriging Method, Worst Case Sampling: 20 ROM evaluations Worst Case: 65 chords (excites first bending mode)Slide28

ConclusionsModel Reduction method formulatedTests on pitch-plunge, flexible wing caseFutureRANSRigid Body DoFsAlleviation