aerodynamic shape optimization of laminar wings a. hanifi 1,2, o. amoignon 1 & j. pralits 1 1...
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Aerodynamic Shape Optimization of Laminar Wings
A. Hanifi1,2, O. Amoignon1 & J. Pralits1
1Swedish Defence Research Agency, FOI2Linné Flow Centre, Mechanics, KTH
Co-workers: M. Chevalier, M. Berggren, D. Henningson
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Why laminar flow? Environmental issues!
A Vision for European Aeronautics in 2020:
”A 50% cut in CO2 emissions per passenger kilometre (which means a 50% cut in fuel consumption in the new aircraft of 2020) and an 80% cut in nitrogen oxide emissions.”
”A reduction in perceived noise to one half of current average levels.”
Advisory Council for Aeronautics Research in Europe
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Drag breakdown
G. Schrauf, AIAA 2008
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Friction drag reduction
Possible area for Laminar Flow Control:
Laminar wings, tail, fin and nacelles -> 15% lower fuel consumption
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Transition control
Transition is caused by
breakdown of growing
disturbances inside the
boundary layer.
Prevent/delay transition by
suppressing the growth
of small perturbations.
instability waves
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Control parameters
Growth of perturbations can be controlled through e.g.:
• Wall suction/blowing
• Wall heating/cooling
• Roughness elements
• Pressure gradient (geometry)
} active control
} passive control
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Theory
We use a gradient-based optimization algorithm to minimize a given objective function J for a set of control parameters .
J can be disturbance growth, drag, …
can be wall suction, geometry, …
Problem to solve:?
J
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Parameters
Geometry parameters :
Mean flow:
Disturbance energy:
Gradient to find:
iy
Q
iy
E
Q
E
NLF: HLFC:
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Gradients
Gradients can be obtained by :
• Finite differences : one set of
calculations for each control
parameter (expensive when no.
control parameters is large),
• Adjoint methods : gradient for all
control parameters can be found by
only one set of calculations including
the adjoint equations (efficient for
large no. control parameters).
i
e
ei y
P
P
Q
Q
E
y
E
Adjoint Stability
equations
Adjoint Boundary-layer
equations
Adjoint Euler
equations
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• Solve Euler, BL and stability equations for a given geometry,
• Solve the adjoint equations,
• Evaluate the gradients,
• Use an optimization scheme to update geometry
• Repeat the loop until convergence
Solution procedure
*ShapeOpt is a KTH-FOI software (NOLOT/PSE was developed by FOI and DLR)
PSEEuler BL
Adj.BL
Adj. PSE
Adj.Euler
Optimization
EE
AESOP ShapeOpt
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Minimize the objective function:
J = uE + dCD + L(CL-CL0)2 + m(CM-CM
0)2
can be replaced by constraints
Problem formulation
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Comparison between gradient obtained from solution of adjoint equations and finite differences. (Here, control parameters are the surface nodes)
Accuracy of gradient
dydxwvuEJ 222
Fixed nose radius
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Low Mach No., 2D airfoil (wing tip)
Subsonic 2D airfoil:
• M∞ = 0.39
• Re∞ = 13 Mil
Constraints:
• Thickness ≥ 0.12
• CL ≥ CL0
• CM ≥ CM0
J= uE + dCD
Amoignon, Hanifi, Pralits & Chevalier (CESAR)
Transition (N=10) moved from x/C=22% to x/C=55%
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Low Mach No., 2D airfoil
Optimisation history
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Low Mach No., 2D airfoil (wing root)
Subsonic 2D airfoil:
• NASA TP 1786
• M∞ = 0.374
• Re∞ = 12.1 Mil
Constraints:
• Thickness ≥ t0
• CL ≥ CL0
• CM ≥ CM0
J= uE + dCD
Amoignon, Hanifi, Pralits & Chevalier (CESAR)
Transition (N=10) moved from x/C=15% to x/C=50% (caused by separation)
InitialIntermediateFinal
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Low Mach No., 2D airfoil (wing root)
RANS computations with transition prescribed at:
N=10 or Separation
Need to account for separation.
Separation at high AoA
Amoignon, Hanifi, Pralits & Chevalier (CESAR)
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Low Mach No., 2D airfoil (wing root)
Optimization of upper and lower surface for laminar flow
Amoignon, Hanifi, Pralits & Chevalier (CESAR)
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The boundary-layer computations stop at point of separation:
No stability analyses possible behind that point.
Force point of separation to move downstream:
Minimize integral of shape factor H12
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Minimize a new object function
where Hsp is a large value.
dxHdxHJTE
sp
sp x
x
sp
x
0
12
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Minimizing H12
Not so good!
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Minimizing H12 + CD
D
x
x
sp
x
CdxHdxHJTE
sp
sp
0
12
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Include a measure of wall friction directly into the object function:
cf is evaluated based on BL computations.
Turbulent computations downstream of separation point if no turbulent separation occurs.
Gradient of J is easily computed if transition point is fixed.
Difficulty: to compute transition point wrt to control parameters.
TEx
f dxcJ0
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3D geometry
Extension to 3D geometry:
Simultaneous optimization of several cross-sections
Important issues:
• quality of surface mesh (preferably structured)
• extrapolation of gradient values
• paramerization of the geometry
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2D constant-chord wing
Structured grid(medium)
Unstructured grid(medium)
Unstructured grid(fine)
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2D constant-chord wing
Structured grid(medium)
Unstructured grid(medium)
Unstructured grid(fine)