Aerodynamic Shape Optimization of

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• Aerodynamic Shape Optimization of
• Laminar Wings
• A. Hanifi1,2, O. Amoignon1 J. Pralits1
• 1Swedish Defence Research Agency, FOI
• 2Linné 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 -gt 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.

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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 x.
• J can be disturbance growth, drag,
• x can be wall suction, geometry,
• Problem to solve

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Parameters

• Geometry parameters
• Mean flow
• Disturbance energy
• Gradient to find

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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).

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Solution procedure

• 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

ShapeOpt is a KTH-FOI software (NOLOT/PSE was
developed by FOI and DLR)
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Problem formulation

• Minimize the objective function
• J luE ldCD lL(CL-CL0)2 lm(CM-CM0)2
• can be replaced by
  constraints

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Accuracy of gradient
Fixed nose radius
Comparison between gradient obtained from
solution of adjoint equations and finite
differences. (Here, control parameters are the
surface nodes)
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Low Mach No., 2D airfoil (wing tip)

• Subsonic 2D airfoil
• M8 0.39
• Re8 13 Mil
• Constraints
• Thickness 0.12
• CL CL0
• CM CM0
• 
  

J luE ldCD
Transition (N10) moved from x/C22 to x/C55
Amoignon, Hanifi, Pralits Chevalier (CESAR)
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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
• M8 0.374
• Re8 12.1 Mil
• Constraints
• Thickness t0
• CL CL0
• CM CM0
• 
  

J luE ldCD
Transition (N10) moved from x/C15 to x/C50
(caused by separation)
Amoignon, Hanifi, Pralits Chevalier (CESAR)
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Low Mach No., 2D airfoil (wing root)
RANS computations with transition prescribed
at N10 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.

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Minimizing H12

• Not so good!

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Minimizing H12 CD
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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.

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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)