The final phd dissertation of Dr. Corrado Groth. The synergy between advanced mesh morphing and adjoint sensitivity for reshaping shapes according to multi physics performances. Aeronautical and automotive examples, experimentally verified, provide a quantitative evaluation of benefits.

1. Supervisor
Coordinator
Course
Cycle
Academic year
Ph.D. thesis
: Prof. Marco Evangelos Biancolini
: Prof. Roberto Montanari
: Doctorate in industrial engineering
: XXIX
: 2015/16
Adjoint-based shape optimization
workflows using RBF
Corrado Groth

2. Introduction
• Implemented in RBF4AERO
'Innovative benchmark technology for aircraft engineering
design and efficient design phase optimisation' partially
funded by the EUs 7th Framework Programme (FP7-AAT,
2007-2013) under Grant Agreement no. 605396.
• Adjoint preview and adjoint sculpting
two optimization workflows using adjoint-based sensitivity data are proposed
• Preview: a number of shape parameters are evaluated using sensitivities. The most
effective ones are chosen and applied in a sensitivity driven workflow.
• Sculpting: The adjoint solver directly suggests shape evolution by imposing each
boundary node movement
• RBF at the core of the method
used to link the numerical analysis and optimization, exploited also for advanced tasks
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3. Motivation
• Human interaction as a bottleneck
The technological evolution allows now to solve complex problems in short time, making
human interaction more relevant and sometime a bottleneck. Automatic workflows are
attractive
• Optimization is often carried manually
• Optimal shape parameterization is difficult
Analizable systems are always more complex, making physical phenomena difficult to be
predicted. An optimal shape parameterization is hard to be chosen especially in a multiphysics
scenario
• Advanced manufacturing processes
Evolution of manufacturing processes (i.e AM) requires advanced free-form
optimization workflows. Current practice is focused on standard production
technology
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4. Motivation
• Human interaction as a bottleneck
The technological evolution allows now to solve complex problems in short time, making
human interaction more relevant and sometime a bottleneck. Automatic workflows are
attractive
• Optimization is often carried manually
• Optimal shape parameterization is difficult
Analizable systems are always more complex, making physical phenomena difficult to be
predicted. An optimal shape parameterization is hard to be chosen especially in a multiphysics
scenario
• Advanced manufacturing processes
Evolution of manufacturing processes (i.e AM) requires advanced free-form
optimization workflows. Current practice is focused on standard production
technology
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5. Sensitivity analysis
• System behavior depends on BC
The result of the calculation changes depending on how sensitive is the system to BC
variations.
• Several methods to achieve sensitivities
Finite differencing, complex-step differentiation, automatic differentiation, adjoint method
• CFD and in-house FEM adjoint solver
ANSYS® Fluent®, NTUA OpenFOAM® implementation, Adjoint variable continuum-discrete in-
house solver
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6. Shape parameterization
• Multiple techniques taken into account
Boundary Displacement Method, Free-Form Deformations, RBF
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7. Shape parameterization
• Multiple techniques taken into account
Boundary Displacement Method, Free-Form Deformations, RBF
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8. Shape parameterization
• Multiple techniques taken into account
Boundary Displacement Method, Free-Form Deformations, RBF
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9. Shape parameterization
• Multiple techniques taken into account
Boundary Displacement Method, Free-Form Deformations, RBF
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10. Shape parameterization
• Multiple techniques taken into account
Boundary Displacement Method, Free-Form Deformations, RBF
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11. Adjoint sculpting
• How to provide meaningful shape variations?
Sensitivity data naturally sculpts surfaces
• Gradient-based algorithm
Direction search and step given by adjoint solution
• Noisy sensitivity data
Especially for CFD applications, noisy sensitivity maps can result in ill-posed problems
• Design constraints
Packaging and functional constraints can be maintained using RBF
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12. Adjoint sculpting: noise filtering
• Noise filtering: spline smoothing
The parameter tunes between fidelity to data and smoothness
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13. Adjoint sculpting: noise filtering
• Noise filtering: implicit smoothing
Original data is not lost, but implicitly smoothed by convolution using a smoothing kernel
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14. Adjoint sculpting: noise filtering
• Noise filtering: least squares smoothing
Data is sub-sampled, error between full and reduced problems is minimized
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15. Adjoint sculpting: RBF set-up
• Evolutive reshape: new set-up at each iteration
Fixed set-up to force constraints, moving set-up to apply evolutive shape variations
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16. Adjoint sculpting workflow
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17. Adjoint preview
• Shape variations provided by the user
An expressive modeling paradigm is required
• Sensitivities used to calculate shape variation
influence
For each shape variation sensitivities are used to calculate its influence on the objective
function. The most important shapes can be employed for zero order optimization
• Gradient-based optimization
Shape variations can be linearly amplified around current shape, carrying a gradient-based
adjoint preview optimization
• Design constraints
Packaging and functional constraints are implictly maintained being already defined in the
shape variation by the user
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18. Adjoint preview: shape modifiers
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19. Adjoint preview workflow
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20. Bracket
• Displacement minimization
Young's modulus = 200 Gpa, Poisson's ratio = 0.3, F = 5000 N along the x axis, fixed hole
Step length is varied at each cycle to assure a maximum displacement of 1 mm
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21. Bracket
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• Displacement reduction
22% after 9 cycles with regard to original displacement
• Optimal shape variation
6% increase in mass compared to 9% increase achieved
employing zero order methods with constant thickness
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22. T-beam
• Displacement free end minimization
Young's modulus = 200 Gpa, Poisson's ratio = 0.3, F = 10000 N load
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23. T-beam
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• Achieved results
25% reduction after 21 cycles with regard to
original displacement
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24. Airbox
• Three runners automotive airbox
Optimization goal is pressure drop and unbalance reduction between runners
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• Achieved result
Unbalance cancelled in 32 cycles,
pressure drop reduced of 15.3%
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25. Airbox
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26. Glider
• Taurus glider by Pipistrel
Efficiency affected by flow separation on wing junction region, demonstrated experimentally
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27. Glider
• Baseline calculation
Flow detachment is clearly visible on
the wing, fuselage and their junction
area as expected.
• Boundary conditions
Mach = 0.08, Re = 106 (c = 0.8 m), altitude = 6561.68 ft (2000 m), AoA =10 degrees
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28. Glider
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29. • Adjoint preview approach
Sensitivities employed to evaluate the 4 most
important shape variations.
• Zero order optimization
4 shape variations used in an EA, 36 DP
calculated
Glider
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30. • Adjoint preview approach
Sensitivities employed to evaluate the 4 most
important shape variations.
• Zero order optimization
4 shape variations used in an EA, 36 DP
calculated
Glider
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31. • Adjoint sculpting approach
4 sculpting cycles maintaining unaltered the wing geometry
Glider
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32. • DrivAer geometry
Test Case developed by Technical University of Munich, Optimization carried with the
National Technical University of Athens. Audi A4 + BMW 3 series
• Optimization goal
Reduce drag force by employing 6 shape parameters and Adjoint preview method using
gradient-based optimization logic
DrivAer
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33. DrivAer
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34. DrivAer
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• Optimization result
After 15 optimization cycles DrivAer mean drag was reduced of 7%
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35. DrivAer
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36. • LPT blade by TEI
Study to determine the feasibility of a
transonic operational condition for a
highly loaded LPT blade
• Optimization goal
Two optimization goals:
drag minimization for high performances
lift maximization for higher loading
LPT blade
28/04/2017 | University of Rome Tor Vergata | Adjoint-based shape optimization workflows using RBF
• Achieved result
drag coefficient reduced
approximately of 4.5%, lift
coefficient for the final geometry
increased approximately of
3.52%
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37. • WT validation by VKI
Experimental characterization was carried in VKI S1
facility
• WT characteristics
Continuous facility, linear cascade, Reynolds number
representative of high-altitude cruising conditions
LPT blade
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38. • WT conditions
Ambient temperature (295 K), Pressure 7,000-10,000 Pa
for numerical validation 85000 Re, WT at Reynolds
numbers 70000 and 100000 wrt chord
LPT blade
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39. LPT blade
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0,0
0,2
0,4
0,6
0,8
1,0
1,2
1,4
0,0 0,2 0,4 0,6 0,8 1,0
Mis[-]
x/cax [-]
LoRe - Baseline LoRe - Optimized HiRe - Baseline HiRe - Optimized
1,00
1,05
1,10
1,15
1,20
1,25
1,30
0,70 0,75 0,80 0,85 0,90 0,95 1,00
Mis[-]
x/cax [-]
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40. 0,0
0,2
0,4
0,6
0,8
1,0
1,2
1,4
0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0
Mis[-]
x/cax [-]
TEI
VK Low ReI
VKI High Re
• Isentropic Mach number distribution
Experiment shows an high velocity peak, important deceleration and possible second peak:
possible flow separation along suction side. Very good match!
LPT blade
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41. • Turbine Internal Channel Cooling
U-turn reshape for a turbine internal channel cooling, ribs to enhance heat transfer
• Optimization goal
Reduce pressure losses, reduce mean temperature on surfaces
TIC U-turn
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42. • Optimization result
14.4% reduction of pressure losses
Recirculation zone shortens for the
optimized case (left original, right
optimized)
TIC U-turn
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43. • Optimization result
14.4% reduction of pressure losses
Recirculation zone shortens for the
optimized case (left original, right
optimized)
TIC U-turn
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44. • Optimization result
14.4% reduction of pressure losses
Recirculation zone shortens for the
optimized case (left original, right
optimized)
TIC U-turn
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45. TIC U-turn
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46. Conclusions
• Two adjoint-based automatic workflows
The two shape optimization workflows were shown for FEM and CFD applications but can be
applied also for other physics. The two workflows are called Adjoint sculpting and adjoint
preview.
• RBF for shape parameterization
Automatic reshape in adjoint sulpting, as a modelling tool for adjoint preview. Packaging and
functional constraints are maintained.
• RBF for advanced tasks
RBF are used to filter noisy data, can be used to define implicit surfaces for offset or
projection modifiers.
• FEM and CFD applications
Tools and workflows implemented in RBF4AERO were tested in FEM and CFD applications
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47. THANKS FOR YOUR ATTENTION