3D shape optimization in supersonic flows

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3D shape optimization in supersonic flows
Carl-Gustav Unckel Advisors Ardeshir Hanifi and
Dan Henningson
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• Part of EU-project SUPERTRAC Aim of the project
  is to increase laminar region on aircraft wings
  at supersonic speeds.
• Have previously studied effect of micron-sized
  roughness and suction optimization in 2.5D.
• Currently working on shape optimization
• Existing 3D wing geometry
• Mach 1.6
• Flight conditions at 44000 feet

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Previous work

• Work on shape optimization using a parameterised
  wing surface and adjoint euler equations by
  Olivier Amoignon (FOI).
• Adjoint PSE and Boundary layer equations by Jan
  Pralits (FOI)

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Optimization

• Optimizing of airfoil shape
• Objective function
• Control variable Pressure distribution (shape of
  airfoil)
• Constraints
• Lift coefficient
• Pitching moment
• Airfoil thickness
• Leading edge radius
• Trailing edge angle

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Adjoint formulation

• Need to find derivative of objective function
  w.r.t pressure distribution.
• Finite differences
• Require 2N ( Nnumber of points on airfoil)
  calculations
• Adjoint equations
• Adjoint equations

Perturb pi
BLE
PSE
J
BLE
PSE
APSE
ABLE
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General idea
BLE
PSE
EULER
Update of geometry
APSE
AEULER
ABLE

• Loop for one airfoil

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In 3D

• Euler and adjoint Euler are in 3D
• BLE,PSE,APSE and ABLE are in 2.5D
• Solution
• Euler calc. in 3D
• Cut 3D geometry into multiple 2D airfoils
• Inner loop on each cut
• Transfer gradient to 3D geometry
• Adjoint Euler in 3D

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Final loop
Cut geometry
Interpolation2
Structured 3D mesh
Global eigenmode solver
Interpolation
Interpolation2
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Difficulties

• Overall complexity with increasing number of cuts
• Automatisation between different parts of the
  loop
• Resolution requirements, Euler PSE
• Occurrence of for example shocks or separation
• Interpolation difficulties
• Cases run so far very strong growth close to
  leading edge has proved difficult.