Aerodynamic Shape Optimization of Laminar Wings A. Hanifi 1,2, O. Amoignon 1 & J. Pralits 1 1...
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Transcript of Aerodynamic Shape Optimization of Laminar Wings A. Hanifi 1,2, O. Amoignon 1 & J. Pralits 1 1...
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
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
Drag breakdown
G. Schrauf, AIAA 2008
Friction drag reduction
Possible area for Laminar Flow Control:
Laminar wings, tail, fin and nacelles -> 15% lower fuel consumption
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
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
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
Parameters
Geometry parameters :
Mean flow:
Disturbance energy:
Gradient to find:
iy
Q
iy
E
Q
E
NLF: HLFC:
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
• 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
Minimize the objective function:
J = uE + dCD + L(CL-CL0)2 + m(CM-CM
0)2
can be replaced by constraints
Problem formulation
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
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%
Low Mach No., 2D airfoil
Optimisation history
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
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)
Low Mach No., 2D airfoil (wing root)
Optimization of upper and lower surface for laminar flow
Amoignon, Hanifi, Pralits & Chevalier (CESAR)
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
Minimize a new object function
where Hsp is a large value.
dxHdxHJTE
sp
sp x
x
sp
x
0
12
Minimizing H12
Not so good!
Minimizing H12 + CD
D
x
x
sp
x
CdxHdxHJTE
sp
sp
0
12
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
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
2D constant-chord wing
Structured grid(medium)
Unstructured grid(medium)
Unstructured grid(fine)
2D constant-chord wing
Structured grid(medium)
Unstructured grid(medium)
Unstructured grid(fine)