Scilab Optimization process control with mesh morphing - Airfoil Shape Optimization

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Scilab Optimization
process control
with mesh morphing
G/EO/17,014
Yann Debray & Hugues-Arthur Garioud – Scilab – ESI Group
2017/10/17

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Agenda
Introduction
1. Design of Experiment
2. Model Reduction
3. Optimization
Results & Conclusion
2

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Introduction
OpenFOAM + Scilab = CFD automation
Mesh Perturbations
- Hicks-Henne Sine Bumps -
Mesh Generation
- Mesh Morphing -
DOE Generation Surrogate Modeling
DOE Simulations
- simpleFoam -
Model reduction
- POD -
Optimization
Optimization
- Gradient/GA -
Validation
- simpleFoam -

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Shape parametrization
Scilab – Hicks & Henne sine bumps
Based on initial airfoil
I
𝑦 = 𝑦 𝑏𝑎𝑠𝑖𝑠 +
𝑖=1
𝑁
α𝑖 𝑓𝑖(𝑥)
𝑓𝑖 𝑥 = sin π𝑥
log 0.5
log 𝑡1𝑖
𝑡2𝑖
One perturbation = One parameter αi
NACA0012 perturbated with 3 sine bumps.
Width t2 = 4 and position t1i = [0.33 0.66 upper 0.66 lower]

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Mesh Morphing
OpenFOAM – Mesh Morphing
POD need mesh with same topology
- LaplacianDisplacement -
1] Set template for
PointDisplacement and
DynamicMesh files
2] Copy of the Scilab computed
perturbations
3] Manually adjust with frozen points,
hence avoiding non orthogonal cells
I
Perturbated NACA0012 mesh and pointDisplacement File

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Design Of Experiment
OpenFOAM – DOE simulations
DOE set up
1] From template case,
create new cases
2] Change the
constant/polymesh/points
file
I
2-level full factorial + center point DOE for 3 parameters varying pressure

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Model reduction with POD method
Scilab – Proper Orthogonal Decomposition
II
First 4 dominant POD modes for pressure DOE case pressure field projection on 4 modes
POD basis
4 modes
99.96% of the
global energy
Modesenergy

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• Minimize cost function: 𝑓 𝑥 =
𝐶 𝐷
𝐶𝐿
• Considering 3 shape parameters:
(Sine bumps amplitude)
𝑥 = (α1, α2, α3)
• Under the constraints:
−0.05 ≤ α1 ≤ 0.05
−0.02 ≤ α2 ≤ 0.02
−0.02 ≤ α3 ≤ 0.02
And CL > 0
Airfoil Case
• NACA0012
• Re = 3e6
• M = 0.15
• α = 0
Optimization process
Scilab - Optimization problem expression
III

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Optimization process
Scilab – Optimization cycle
III
Initialization
Starting parameter x0
Cost function evaluation
POD field prediction
New parameter value
CD, CL computation
Cost function evaluation
Minimization following the
gradient
Minimization using
selection, mutation and
cross-over
Random population of
starting parameters
Cost function gradient
evaluation
New population of
parameters
CYCLE / GENERATION
Gradient Method
Genetic Algorithm
Shared Process

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Optimization process
Scilab – Pressure field prediction
III
Projection coefficients (ai) interpolation
with RBF
𝑢 ≃
𝑖=1
𝑁 𝑃𝑂𝐷
𝑎𝑖φ𝑖
Assumption :
Field can be decomposed on the POD basis
Field error around airfoil for different prediction methods,
within and out of DOE

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Results: Global Optimum
Within DOE - Linear behavior of the pressure
IV
[0.05 0.02 0.02] - Logical !

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Results: Reduced model limits
Out of DOE - Low error in lift prediction
IV
v
[0.07 0.04 0.05] - Model not trained for flow reattachment and recirculation zone

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Results: Reduced model limits
Out of DOE - High error in pressure drag prediction
IV
[0.07 0.04 0.05] – Iso-pressure on suction side are left-oriented for predicted case (left)

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Optimization
• 3D/Unsteady/Multiphysic
• Transonic/Hypersonic
(control of pressure drop)
• Real time optimization for
morphing wing
Leveraging other
Scilab capabilities
• Image & signal processing
• Control system
• Statistics
• GUI & automation
Conclusion
Go further
Modeling
• Model based design
OpenFOAM  Scilab-Xcos
• Reduced order model
Scilab  OpenFOAM

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Thank you
yann.debray@esi-group.com