The final dissertation of Dr. Ubaldo Cella. High fidelity CAE with FSI and verification against experimental wind tunnel test.

1. Setup and Validation of High Fidelity
Aeroelastic Analysis Methods Based
on RBF Mesh Morphing
Ubaldo Cella
Rome 27 March 2017
Supervisor : Prof. Marco Evangelos Biancolini
Coordinator : Prof. Roberto Montanari

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Research framework

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High fidelity FSI analyses
CFD
FEM

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Overview of the work
• Setup of FSI analysis methods
• 2-way (CFD-CSM) coupling
• Modal approach for aeroelastic analyses
• Validation against experiments
• Piaggio P1XX aircraft (transonic)
• RIBES wing (subsonic)

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2 ways FSI procedure
CFD
computation
Loads
mapping
FEM
computation
CFD Mesh
updating
Deformed
shape
Shape
changed?
Undeformed
geometry
END
Yes No

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Mesh morphing

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RBF Morph tool
• Setup
• Select fixed and
moving walls by source
points
• Prescribe the
displacements (or a
combination of)
• Fitting
• Solving the RBF system
and storing the solution
• Smoothing
• Application of the
morphing action on
surfaces and volume

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Modal approach for FSI
Structural modal analysis
Morphed CFD mesh database (one per mode)
Parametric mesh update
Modal coordinates
Convergence?
Undeformed geometry
END
No
Yes
CFD iterations
CFD
flexible
model
= +
modal coordinate
nodal modes
displacement
number of
natural modes
Parametric mesh formulation

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Advantages and limits
• Main advantages
• simpler numerical environments respect 2-way
• Higher robustness
• Mesh adaptation during computation (faster
solution)
• Limits
• Linear problems only (small displacements)
• Uncertainness on the modal base dimension

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Piaggio P1XX

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Computational domains
CFD mesh
structured 14 mill. Cells
FEM mesh
28.000 hexa elementsfully steel-made

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RBF problem setup
2 steps mesh morphing procedure

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2-ways convergence hist.
Undef. 1 2 3
Iteration
CL
CL = 0.005
Undef. 1 2 3
Iteration
CD
CD = 2 dc
~1% of the wing
exposed semispan
(figure amplified)

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Modal shapes
Modal base composed with up to 6 modes

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CL
α
α = 0.1 deg
Solutions comparison
CL
CD
Exp.
Undef.
2-ways
1 mode
2 modes
3 modes
4 modes
5 modes
6 modes
CL = 0.01
CD = 2 dc
Mach 0.8

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Aero-structure coupling
Flow direction
Elastic axis

17. Surface pressure

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Pressure comparison

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RIBES wing

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Critical points of design
• Challenging structural similitude with a real
full scale wing
• Impracticable manufacturing
• Conflicting high deformation requirement
• Relatively higher thickness and lower loads
• Difficult to load the spars and unload the skin
• Panels stability was the main design driver
• Manufacturing requirements defined on
progress
• Several iteration with the model manufacturer

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Final test article details
Span = 1.6 m
Material = AL2024T3 (Yeld Stress = 270 Mpa, Ultimate stress = 440 Mpa)

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Pressure taps installation
80 pressure taps

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Strain gauges installation
3 rosettes (three channels)
16 unidirectional

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Model under construction

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Measured geometry
model measured
by HEXAGON
metrology
electronic harm
measured

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Effects on aerodynamics
-2
-1.5
-1
-0.5
0
0.5
1
1.5
0 0.2 0.4 0.6 0.8 1
Cp Alfa 5 deg
Measured
Nominal

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CAD reconstruction

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Free flight CFD domain
C-H structured 3.2 mill. Hexa, farfield at 50 MAC

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Structural model
97000 shell elements

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Modal shapes

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RBF problem domain
31000 source points, (fitting in 62 sec.,
smoothing in 40 sec.)

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Aerodynamic solutions
CFD with rigid
model (no elasticity
accounted)
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
-5 0 5 10 15
CL
α
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
0 0.02 0.04 0.06 0.08
CL
CD
CFD
Experiments

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Deformation measurement
High-precision
inclinometer

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Deformation solutions
0
1
2
3
4
5
6
7
8
9
0 400 800 1200 1600
Δz,mm
y, mm
Measurements
Δz 2-way
Δz 8modes
-0.002
0
0.002
0.004
0.006
0.008
1 2 3 4 5 6 7 8
Mode
Modal coordinate

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Elements junction

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FEM verification
Exp. σy = -15.6 MPa
FEM σy = ∼ -38 MPa
Exp. σy = -143.2 MPa
FEM σy = ∼ -21 MPa

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Spar reinforcements

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Conclusions
• RBF morphing provide a very efficient and
robust coupling of CFD and FEM solutions
• 2-way and modal FSI analyses provided
almost the same solutions
• the modal approach is a valid candidate to setup
efficient and accurate FSI analyses of wings
• A very poorly populated modal base us sufficient
for lifting surfaces
• Failure in modeling the load shared between
skin and spar.
• A more accurate FEM model is probably necessary
for complex topologies including root junctions

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Future work
• Unsteady dynamic FSI implementation to
study complex phenomena as flutter or
buffet.
• Validation against dynamic test cases
• HiReNASD ?
• AGARD 445.6 ?
• Extension of RIBES model tests?
• Sails ?