Auxetics 2006 4 - 6 September 2006, University of ExeterExeter, UK 1
Alessandro Spadoni, Massimo RuzzeneSchool of Aerospace EngineeringGeorgia Institute of Technology
Atlanta GA - USA
Chrystel Remillat, Fabrizio Scarpa, Kevin PotterDepartment of Aerospace Engineering
University of BristolBristol, UK
MORPHING CHARACTERISTICS OF CHIRAL CORE AIRFOILS
Auxetics 2006 4 - 6 September 2006, University of ExeterExeter, UK 2
Objective:Application of chiral geometry for the design of an airfoil with morphing characteristics;
Motivation:
- Morphing is an effective way to enhance performance of wings and rotor blades:
• improve flow conditions, • minimize drag,• eliminate the need for flap mechanisms,• improve handling and control of aircraft.
- A chiral structure provides compliance and allows continuous deformation of airfoil.
Objectives & Motivation
Auxetics 2006 4 - 6 September 2006, University of ExeterExeter, UK 3
• Negative Poisson’s ratio:
Estimated νxy ~-0.9;
• High in-plane shear modulus:
As a result of νxy being close to -1;
• Unique deformation mechanism:
Allows large deflections, while material remains in elastic range;
• Design flexibility:
Property of the assembly strongly depends on characteristic parameters of chiral geometry (r,R,L,θ);
)1(2 xyx
xy
EGυ+
=
r
θ
R
Lt
Chiral Geometry
Auxetics 2006 4 - 6 September 2006, University of ExeterExeter, UK 4
Objective:Passive changes of mean camber line of the wing in response to changing incident airflow speeds
Reduction of the TAB ANGLE in response to increase in car speed;Corresponding elastic deformations are recovered when the speed decreases, so that the wing tip moves back upward;
Increase in MAXIMUM SPEED and better HANDLING
Previous Work:Racecar wing with passive adaptive capabilities(*)
EPPLER 420 Airfoil with 300 mm chord
5 mm
(*) Bornengo, D., Scarpa, F., Remillat, C. "Morphing airfoil concept with chiral core structure,“IMechE J. Aer. Eng., 2005.
Homogeneous material with homogenized chiral properties
Auxetics 2006 4 - 6 September 2006, University of ExeterExeter, UK 5
Rationale
x
y
z
Τ = GJdxdθ
M = EIxx 22
dxwd
• Given a Poisson’s ratio of ≈ -1, G ≈ ∞ Wing does not require close section to carry torsional loads;
• Large decambering deformations can be sustained within the elastic range of the constitutive material;
• The core allows for continuous deformations which are important to maintain aerodynamic efficiency;
• The airfoil core can be tuned to achieve different functionalities by changing core geometric parameters;
Auxetics 2006 4 - 6 September 2006, University of ExeterExeter, UK 6
Outline
U. Of BRISTOLGATECH
• Present two designs resulting from parallel developments; • Discuss results and provide recommendations for future research;• Show related research on chiral structures.
Auxetics 2006 4 - 6 September 2006, University of ExeterExeter, UK 7
Development of GATech’s chiral airfoil
Auxetics 2006 4 - 6 September 2006, University of ExeterExeter, UK 8
Eppler 420 series
• Eppler 420’s camber provides significant lift at low speed;
• Assembly is intended to conform as dictated by flow conditions camber decreases as velocity and lift increase
• Lift-induced drag decreases with velocity;
• Configuration can be modified for active morphing applications (active camber control).
Overview• The airfoil hosts a MACROSCOPIC chiral structure;• Evaluation of compliance characteristics:
– Numerical analysis with steady aerodynamic loads;– Experimental investigation using static loads.
Auxetics 2006 4 - 6 September 2006, University of ExeterExeter, UK 9
Design• Chiral core is MAPPED into airfoil;• Influence of number of cells and L/R ratio is investigated;• All other parameters are kept constant.
Predefined layout
Mapped to conformTo airfoil profile
Note:• Core mapping facilitates meshing;• Core periodicity is lost
Auxetics 2006 4 - 6 September 2006, University of ExeterExeter, UK 10
STRUCTURAL MODEL
Numerical AnalysisCFD-FEA Coupled models
• Steady-state aerodynamic loads are defined by specified flow conditions;
• Airfoil performance is investigated through weakly-coupled structural and computational fluid dynamics (CFD) models;
• Air-loads and corresponding displacements are iteratively passed to the structural and fluid codes respectively until convergence is achieved
x,u2u1
y,v2
φ2
v1
-φ1zz
Timoshenko beam element
u1v1
u2
u3
v3
φ3
Isoparametric planar element
E = 71 GPadensity = 2700 Kg/m3ν = 0.33 wall t = 0.76 mmOut-of-plane t = 2.54 cm
E = 710 MPadensity = 2700 Kg/m3ν = 0.33 wall t = 0.76 mmOut-of-plane t = 2.54 cm
Soft skin
Fixed
Auxetics 2006 4 - 6 September 2006, University of ExeterExeter, UK 11
Unstructured triangular mesh, using finite-volume Galerkin NSC2KE(*)
Inflow points
Outflow pointsCharacteristic technique(*)
Wall boundary, 0=⋅nu rr Tangency condition
• Minimum element size 0.001 chord, at leading and trailing edges
• Wake elements near trailing edge have a size of 0.001 chord
• Airfoil element size is linearly relaxed away from LE and TE by 5
• Wake element size linearly relaxed up to outflow boundary
• Inflow and Outflow boundaries are at least 6 chords away from airfoil
• Total of approximately 11,500 fluid elements.•Mohammadi, B., "Fluid Dynamics Computation with NSC2KE," INRIA Report 0164, 1994.
Steady-state Fluid Model
http://www.inria.fr/rrrt/rt-0164.html
http://www.inria.fr/rrrt/rt-0164.html
Auxetics 2006 4 - 6 September 2006, University of ExeterExeter, UK 12
0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000
1.3
1.4
1.5
1.6
1.7
1.8
1.9
Cl
Number of Iterations 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000
10-5
10-4
10-3
10-2
10-1
100
log 1
0(N
orm
aliz
ed L
2 N
orm
)Number of Iterations
Analysis of convergence of fluid model
8000 iterations are used, as reasonable residual reduction target is 4 orders of
magnitude
• Sea level conditions• Mach 0.45• angle of attack 2°
• No gravity • Euler time stepping (steady-state solution)
Lift Coefficient Residual norm
Steady-state Fluid Model
Auxetics 2006 4 - 6 September 2006, University of ExeterExeter, UK 13
Structural mesh of airfoil and chiral core
are obtained
ANSYS
Beginning of convergence iterations MATLAB
Flow field region is discretized with an
unstructured triangular-element mesh
Flow field is solved forpressure, density and
velocityNSC2KE
Equilibrium is solvedimposing aerodynamicloads on chiral-core
airfoil
MATLAB
Deformed airfoil is splinedand new profile is
computed MATLAB
Initial Iteration
Beginning of next Iteration
Solution
YesNo
L/RNumber of core cellsMaterial propertiesFree-stream conditionsAngle of attack
New Iteration converges with previous one?
uuL T ⋅=
31 101
−− ×
Auxetics 2006 4 - 6 September 2006, University of ExeterExeter, UK 14
TE displacement 1.3 cm
L/R = 0.6 L/R = 0.9
0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 10.006
0.007
0.008
0.009
0.01
0.011
0.012
0.013
0.014
L/R
Trai
ling-
Edg
e D
ispl
acem
ent [
m]
Results: 3 cellsInfluence of L/R ratio
Auxetics 2006 4 - 6 September 2006, University of ExeterExeter, UK 15
Results: 2 cells Influence of L/R ratio
L/R = 0.6 L/R = 0.95
0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 10
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08Tr
ailin
g-E
dge
Dis
plac
emen
t, [m
]
L/R, [m]
3 cells
Auxetics 2006 4 - 6 September 2006, University of ExeterExeter, UK 16
L/R = 0.70 L/R = 0.90
Large node radius facilitates bending deformation of the ligaments,which is a main contributor of overall deformation
Results:Influence of L/R ratio
Auxetics 2006 4 - 6 September 2006, University of ExeterExeter, UK 17
Lift vs. Mach number
0.15 0.2 0.25 0.3 0.35 0.4 0.451
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2
M
Cl
Lift coefficient
L/R = 0.60
L/R = 0.90
0.15 0.2 0.25 0.3 0.35 0.4 0.450
0.5
1
1.5
2
2.5x 104
L/R = 0.60
L/R = 0.90
M
Lift
Ll
2nd CHIRAL-CORE AIRFOIL CONFIGURATION
Auxetics 2006 4 - 6 September 2006, University of ExeterExeter, UK 18
Experimental ValidationStatic compliance tests
L/R = 0.602-y cells
L/R = 0.603-y cells
L/R = 0.943-y cells
Water-jet manufacturing
Auxetics 2006 4 - 6 September 2006, University of ExeterExeter, UK 19
Out-of-plane thickness = 2.00 cm
0.7 m
2.54 cm
0.36 m
0.7 m
2.54 cm
0.36 m
0.7 m
2.54 cm
0.36 m
r
t
r
t
t
r
r = 0.67 cm t = 0.65 mm
r = 1.07 cm t = 0.65 mm
r = 0.3 cm t = 0.65 mm
E = 71 GPadensity = 2700 Kg/m3ν = 0.33
Material: Aluminum 6061 T651
Out-of-plane thickness and chord dimensions were chosen given manufacturing restrictions
Experimental ValidationStatic compliance tests
Auxetics 2006 4 - 6 September 2006, University of ExeterExeter, UK 20
Strain gages
Clamped b.c.
LVDT
Strain gage conditioner and amplifierVishay Measurement Group 2100 System
Iotech 2000 series acquisition board
Experimental set-up
Strain-gage locations are chosenbased on a preliminary FE analysis
Experimental ValidationStatic compliance tests
Auxetics 2006 4 - 6 September 2006, University of ExeterExeter, UK 21
Static compliance testsL/R = 0.60, 3 unit cells across airfoil thickness
1
2
34
56
0 5 10 150
10
20
30
40
50
60
T.E. disp, [mm]
App
lied
load
, [N
]
P
Four cuts have been used to core and skin compliance
0 5 10 150
100
200
stra
in g
auge
1 μ ε
T.E. disp, [mm]0 5 10 15
0
1000
2000
3000
stra
in g
auge
2 μ ε
T.E. disp, [mm]
0 5 10 150
200
400
600
stra
in g
auge
3 μ ε
T.E. disp, [mm]0 5 10 15
0
50
100
stra
in g
auge
4 μ ε
T.E. disp, [mm]
0 5 10 150
1000
2000
stra
in g
auge
5 μ ε
T.E. disp, [mm]0 5 10 15
-50
0
50
100
stra
in g
auge
6 μ ε
T.E. disp, [mm]
Auxetics 2006 4 - 6 September 2006, University of ExeterExeter, UK 22
1 2 35
4
0 2 4 6 8 10 12 14 16 18 200
5
10
15
20
25
T.E. disp, [mm]
App
lied
load
, [N
]
0 5 10 15 200
500
1000
stra
in g
auge
1 μ ε
T.E. disp, [mm]0 5 10 15 20
0
500
1000
1500
stra
in g
auge
2 μ ε
T.E. disp, [mm]
0 5 10 15 200
500
1000
1500
stra
in g
auge
3 μ ε
T.E. disp, [mm]0 5 10 15 20
0
500
1000
stra
in g
auge
4 μ ε
T.E. disp, [mm]
0 5 10 15 200
2000
4000
stra
in g
auge
5 μ ε
T.E. disp, [mm]
P
Static compliance testsL/R = 0.60, 2 unit cells across airfoil thickness
Auxetics 2006 4 - 6 September 2006, University of ExeterExeter, UK 23
Non-linear FE models suggest more compliance within elastic range
0 10 20 30 40 50 60 70 80 90 1000
10
20
30
40
50
60
70
80
90
T.E. disp, [mm]
App
lied
load
, [N
]Experimental results
Numerical results
Static compliance testsL/R = 0.60, 2 unit cells across airfoil thickness
Auxetics 2006 4 - 6 September 2006, University of ExeterExeter, UK 24
4
1
32
5
0 2 4 6 8 10 120
10
20
30
40
50
60
70
80
90
100
T.E. disp, [mm]
App
lied
load
, [N
]
0 5 10 150
1000
2000
stra
in g
auge
1 μ ε
T.E. disp, [mm]0 5 10 15
0
500
1000
stra
in g
auge
2 μ ε
T.E. disp, [mm]
0 5 10 150
1000
2000
stra
in g
auge
3 μ ε
T.E. disp, [mm]0 5 10 15
0
500
1000
stra
in g
auge
4 μ ε
T.E. disp, [mm]
0 5 10 150
1000
2000
stra
in g
auge
5 μ ε
T.E. disp, [mm]
Static compliance testsL/R = 0.94, 3 unit cells across airfoil thickness
Auxetics 2006 4 - 6 September 2006, University of ExeterExeter, UK 25
0 2 4 6 8 100
2
4
6
8
10
12
14
16
18
20
Applied Load, [N]
Trai
ling-
Edg
e di
spla
cem
ent,
[mm
]
3y cells, L/R = 0.942y cells, L/R = 0.603y cells, L/R = 0.60
• The core can be designed to achieve different compliance through a change in a limited
number of geometric (L/R);
• Significant decambering deformations can be sustained within the elastic range of the
constitutive material;
Static compliance testsSummary
Auxetics 2006 4 - 6 September 2006, University of ExeterExeter, UK 26
Development of U. of Bristol’s chiral airfoil
Auxetics 2006 4 - 6 September 2006, University of ExeterExeter, UK 27
Design Constraints
• Selective Laser Sintering for core manufacturing– Maximum core length is 0.2 m, chord 0.3 m;– Minimum thickness is 1mm for any part of the structure:
• Ligaments thickness is 1 mm;• Opted for solid nodes (nodes are stiff compared to the ligaments)• Only a two cell deep core would fit into the aerofoil whilst
maintaining a reasonable ligament aspect ratio.
• It was chosen not to have ligaments attached to the aerofoil skin, to avoid high point loads.
• A custom chiral core was created, joining only nodes onto the skin and following the curvature of the aerofoil.
Auxetics 2006 4 - 6 September 2006, University of ExeterExeter, UK 28
Configuration
Nose:Stiff, made of pine wood
Skin:• 0.5mm glass fibre composite • Flexible but stiff enough to maintain the aerofoil shape and prevent surface
buckling.• Non-symmetric lay-up [0º,90º,+45º,-45º] facilitates conforming to airfoil shape
Chiral Honeycomb Core:• Material Polyamide Duraform. • Design attempts to keep L/r and R/r ratios uniform (uniform E)• Node radii (r) are decreased along the chord as the ligament length (L) was constrained by the taper of the aerofoil.
- Some of the internal cell angles, θ, differ from 30°- Initial chiral geometry has been used as a guideline.
Rubber Strip:Added to induce the chiral rotation(*)
(*) Bornengo, D., Scarpa, F., Remillat, C. "Morphing airfoil concept with chiral core structure,“ IMechE J. Aer. Eng., 2005.
Auxetics 2006 4 - 6 September 2006, University of ExeterExeter, UK 29
Numerical analysis
Static Analysis:– Structural model is coupled with two flow solvers– An iterative process was required to achieve
convergence of the solution.– Ansys FE is used for the structure part;– Structural FE model is validated experimentally– Flow solvers:
• Inviscid– vortex lattice panel method coded in Matlab, assumes two-
dimensional (2-D) inviscid flow, and does not consider flow separation.
• Viscous (XFoil)– combines a vortex panel method with a boundary layer model to
provide a viscous analysis. It includes boundary layer growth, producing a more realistic pressure distribution, especially at higher angles.
Auxetics 2006 4 - 6 September 2006, University of ExeterExeter, UK 30
Example of Results
• Viscous analysis predicts a much lower deflection:– pressure forces acting close to the trailing edge are reduced
due to the predicted boundary layer at high angles.
Graph of Tip Vertical Deflection Against Velocity at an Angle of 15º
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0 10 20 30 40 50 60 70
V elo cit y ( m/ s)
Tip
Vert
ical
Def
lect
ion
(mm
)
ViscousInviscid
Airfoil tip deflection for increasing velocity, at 15ºInviscid and viscous predictions
Auxetics 2006 4 - 6 September 2006, University of ExeterExeter, UK 31
Analysis of modified Airfoil
• Effects of:– Higher number of cells;– Reduction of ligament thickness (0.2 mm) and length (6 mm);
• Changes produce a 200% increase in tip deflection at 80 m/s.
Effect of chiral cell density on tip displacement
0
2
4
6
8
10
0 20 40 60 80 100
Airspeed (m/s)
Tip
Dis
plac
emen
t (m
m)
5 Cell Deep
2 Cell Deep
Auxetics 2006 4 - 6 September 2006, University of ExeterExeter, UK 32
Aerodynamic testing:• Wind tunnel:
– Maximum speed ~70m/s. – Equipped for lift, drag and pitching moment measurements
• Visual Measurement Technique:– The motion of the aerofoil is tracked by a digital camera system, connected to a
laptop for real-time processing. – The position of a number of “targets” can be tracked at a rate of 7.50Hz.– Two targets could be used at once to monitor the strains.
Wing Prototype
Prototype mounted in low turbulence wind tunnel
Auxetics 2006 4 - 6 September 2006, University of ExeterExeter, UK 33
Examples of Results
Numerical (FEA) Experimental
Lift Force against Displacement at Varying Incidence for the Experimental Analysis
0
50
100
150
200
250
300
350
0.0 0.5 1.0 1.5 2.0 2.5
Vertical Deflection (mm)
Lift
(N)
15º
10º
5º
0º
Deflection vs Speed at varying angles of incidence
0
0.5
1
1.5
2
2.5
0 10 20 30 40 50 60 70 80
Speed (m/s)
Def
lect
ion
(mm
)
15º EXP
10º EXP
5º EXP
15º FEA
Auxetics 2006 4 - 6 September 2006, University of ExeterExeter, UK 34
Comments
• Deflections increase as velocity increases. • The relationship is non linear with respect to the lift force on the aerofoil:
– At low velocities, the rate of increase of deflection is lower than at higher velocities.
– This could be due to a certain amount of force required to ‘activate’ the honeycomb deformation mechanism.
– These forces appear to be different for the varying angles of incidence, – This could be explained by the varying pressure distribution around the
aerofoil (with respect to angle of incidence), and – the anisotropy of the chiral structure (i.e. the main bulk of the pressure force
acts on a different area of the aerofoil at different angles, giving a different deflection response).
• This deflection at 15° incidence corresponds to:– Camber change of 0.3%, – A reduction in CL of 0.05, – A reduction of CD of ~0.02.– Whilst this change is small, it proves that the morphing concept works.
Auxetics 2006 4 - 6 September 2006, University of ExeterExeter, UK 35
Comments
• The measured strains between nodes 19 and 24, and 21 and 22 were found to be positive;– Computed values giving a Poisson’s ratio of approx. -0.9.
e1e2
Auxetics 2006 4 - 6 September 2006, University of ExeterExeter, UK 36
Future developmentsAerolastic tailoring through wings with span-wise graded properties
Spars with different L/R ratios(Different chord-wise compliance)
L/R
L/RWing with continuous variation of
L/R ratio
Auxetics 2006 4 - 6 September 2006, University of ExeterExeter, UK 37
Related researchDynamic shape control
DAQ &
Signal processing
Post-Processing
Shaker & F. Transducer
MATLAB
10-lb PCB Piezotronics
LDS V203
Polytec PSV-400 M2
Scanning head (Polytec PSV400 M2)
Auxetics 2006 4 - 6 September 2006, University of ExeterExeter, UK 38
Related research
Auxetics 2006 4 - 6 September 2006, University of ExeterExeter, UK 39
Comparison with numerical results
ω = 1744 Hz ω = 2250 Hz
Auxetics 2006 4 - 6 September 2006, University of ExeterExeter, UK 40
Dynamic Shape Control:Motivations
Control of boundary layers and flow-separation phenomena;
Vibrating airfoil skins have been found to produce similar results to synthetic jets [Munday]:
• postpone stall or airflow separation, • reduce pressure drag,• reduce wave drag.
Oscillatory camber concept by D. Munday, J. Jacob and G. Huang
Auxetics 2006 4 - 6 September 2006, University of ExeterExeter, UK 41
• Dynamic deformed shapes could be useful for reducing shock strength and thus wave drag.
Hogawa H., babinsky H., “Evaluation of wave drag reduction by flow control”, Aerospace Science and Technology, 10, pp. 1-8, 2006
Dynamic Shape Control:Motivations
Auxetics 2006 4 - 6 September 2006, University of ExeterExeter, UK 42
Wave propagationin chiral networks
O A B O0
500
1000
1500
2000
2500
k-space position
Ω
Band-gap structure
-300 -200 -100 0 100 200 300-250-200-150-100-50
050
100150200250
Cg X [m/s]
Cg
y[m
/s]
Auxetics 2006 4 - 6 September 2006, University of ExeterExeter, UK 43
Related research:Chiral Honeycombs
-30 -20 -10 0 10 20 30
500
600
700
800
900
1000
1100
1200
1300
, [deg]
( �e l) 3/�
* /�s,
[KP
a]
0.75 0.8 0.85 0.9 0.95 1
Global Buckling Chiral
Hexagonal/Auxetic Honeycombs
Co
lla
ps
es
tre
ng
thp
er
un
itw
eig
ht
�
�
L/R
-30 -20 -10 0 10 20 30
500
600
700
800
900
1000
1100
1200
1300
, [deg]
( �e l) 3/�
* /�s,
[KP
a]
( �e l) 3/�
* /�s,
[KP
a]
0.75 0.8 0.85 0.9 0.95 1
Global Buckling Chiral
Hexagonal/Auxetic Honeycombs
Co
lla
ps
es
tre
ng
thp
er
un
itw
eig
ht
�
�
L/R
Flat-wisestrength
Thermal behavior
Auxetics 2006 4 - 6 September 2006, University of ExeterExeter, UK 44
THE END
RationaleOutline DesignResults: 2 cells �Influence of L/R ratioDesign ConstraintsConfigurationNumerical analysisExample of ResultsAnalysis of modified Airfoil�Aerodynamic testing:�Examples of ResultsCommentsCommentsFuture developmentsRelated researchRelated researchComparison with numerical resultsWave propagation�in chiral networksRelated research:�Chiral Honeycombs