Description of an efficient optimization method for flow-exposed geometries by mapping adjoint shape sensitivities to the CAD model parameters. The method is demonstrated on a case study for a sports car's rear wing. Presentation from the German NAFEMS conference, May 2014.

Published on: **Mar 3, 2016**

- 1. DNV GL © 2014 SAFER, SMARTER, GREENERDNV GL © 2014 Efficient Optimization of Flow-Exposed Geometries 1 by mapping adjoint shape sensitivities to CAD model parameters Mattia Brenner, Andre Zimmer, Sebastian Weickgenannt
- 2. DNV GL © 2014 Optimization Task Rear wing of a hyper sports car should be optimized with respect to the objectives drag and downforce iconCFD is used for adjoint CFD computations CAESES is used for parametric modeling, mapping of the adjoint sensitivities to the CAD model parameters and subsequent geometry modification 2 With kind permission of: Koenigsegg Automotive AB www.koenigsegg.com
- 3. DNV GL © 2014 CAESES Specifically geared for automated CFD-driven design Focus on complex free-form surfaces and shapes, difficult to parameterize Models defined and varied according to “smart parametric” descriptions Reduced degrees-of-freedom; constraints can be built in to the description Complex models and their variants maintain high-fidelity and fairness 3 Profile defined using specialized curve types and controlled by user- defined parameters Initial profile is transformed along a specified path, and its parameters are varied based on functional distributions Proprietary meta-surface technology creates complex surfaces with intelligent parameterization and high quality
- 4. DNV GL © 2014 Parametric Model 4
- 5. DNV GL © 2014 Parametric Model 5
- 6. DNV GL © 2014 Parametric Model 19 design variables control the shape with the help of spanwise distributions of profile parameters Geometry constraints regarding span and chord length are automatically met 6
- 7. DNV GL © 2014 Optimization with a Parametric Model Usually, a high number of parameters defines a parametric model (in this case 19, often 30-50 for a typical CAESES model) Way too much effort to involve all of them in a conventional optimization process… How to select the most suitable parameters for the optimization task at hand? Normally, the designer selects or specifically creates a small number of parameters based on experience and engineering judgment – This reduces the design space for the optimization – The designer might not have enough experience to make a good selection – Especially difficult if the model was created by someone else Solution: adjoint analysis 7
- 8. DNV GL © 2014 What is Adjoint Analysis? Comparison to direct gradient-based method: 8 Adjoint method Question: what changes to the design parameters are necessary to get an optimal product performance? 1 primal + 1 adjoint simulation run for each objective necessary Direct method Question: how do changes of the design parameters influence the product‘s performance? n+1 simulation runs necessary nn J J J J 33 22 11 optn J ,,,, 321 J: objective function, α: parameter
- 9. DNV GL © 2014 Adjoint Analysis Results In shape optimization: shape sensitivity (change of objective function J due to normal displacement of cells on the design boundary) A positive shape sensitivity means that the boundary should be moved in positive normal direction A negative shape sensitivity calls for boundary movement in negative normal direction 9 kn J With kind permission of: Koenigsegg Automotive AB www.koenigsegg.com Push inwards Pull outwards
- 10. DNV GL © 2014 How to Use the Adjoint Sensitivities Adjoint shape sensitivity values can be used to displace the surface cells directly and to morph the shape, e.g. in a CAD independent approach Downside is that the shape changes cannot easily be fed back into the design workflow, geometry constraints may be violated Solution: map shape sensitivities to CAD model parameters 10 .avg k k n k kn A An n JJ Adjoint shape sensitivity Normal displacement of model boundary due to CAD parameter change: „design velocity“ Relative local cell size Parametric sensitivity
- 11. DNV GL © 2014 Design Velocities Normal displacement of the boundary due to changes of CAD parameter values Determined by perturbing the parameters and measuring the normal displacement of given positions on the model boundary (surface tessellation nodes) CAESES Sensitivity Computation Input: model boundary as surface geometry Automatically determines all design variables that are suppliers to the boundary User can deselect design variables and set individual deltas Result: design velocity maps for all selected parameters 11
- 12. DNV GL © 2014 Parametric Sensitivities Also computed by Sensitivity Computation in CAESES Adjoint shape sensitivities are mapped to the positions on the boundary used to determine the normal displacement (tessellation nodes) by probing the result data set of the adjoint computation For each parameter adjoint sensitivities are locally multiplied with the design velocities and summed up, weighted with the relative area of the local element Result: one scalar parametric sensitivity for each parameter 12
- 13. DNV GL © 2014 Parametric Sensitivities From the list of parametric sensitivities select the parameters with the biggest influence on the objective function manually change values or follow up with conventional optimization or Multiply the vector of the parametric sensitivities with a step size factor and add to the parameter values determine the right step size with 1-dimensional search using primal CFD computations or …? 13
- 14. DNV GL © 2014 CFD Setup Mesh size: 18 Mill. cells Spalart-Allmaras turbulence model Primal run: 6000 iterations, ~7h on 64 CPUs Adjoint run: 6000 iterations, ~5h on 64 CPUs Adjoints computed for drag and downforce Inlet velocity: 40m/s turbulence intensity: 0.005 turbulence length scale: 0.01 Wheels with rotating wall Incompressible, rho=1.204, nu= 1.436877e-05 Three radiators modeled as porous media Frozen adjoint turbulence 14 With kind permission of: Koenigsegg Automotive AB www.koenigsegg.com
- 15. DNV GL © 2014 Design Velocity Results Thickness_pressCenter – Rank 1 for drag – Rank 2 for downforce 15 Adjoint Sensitivities (drag) Adjoint Sensitivities (downforce) Design Velocity
- 16. DNV GL © 2014 Design Velocity Results StepPos_yShift – Rank 2 for drag – Rank 1 for downforce 16 Adjoint Sensitivities (drag) Adjoint Sensitivities (downforce) Design Velocity
- 17. DNV GL © 2014 Design Velocity Results Camber_pressCenter – Rank 5 for drag – Rank 4 for downforce 17 Adjoint Sensitivities (drag) Adjoint Sensitivities (downforce) Design Velocity
- 18. DNV GL © 2014 Design Velocity Results Thickness_pressTip – Rank 3 for downforce 18 Adjoint Sensitivities (drag) Adjoint Sensitivities (downforce) Design Velocity
- 19. DNV GL © 2014 Design Velocity Results Thickness_sucCenter – Rank 3 for drag – Rank 5 for downforce 19 Adjoint Sensitivities (drag) Adjoint Sensitivities (downforce) Design Velocity
- 20. DNV GL © 2014 Design Velocity Results Thickness_sucInner – Rank 4 for drag 20 Adjoint Sensitivities (drag) Adjoint Sensitivities (downforce) Design Velocity
- 21. DNV GL © 2014 Parametric Sensitivity Results Top 5 of most influential parameters for drag and downforce Most of these parameters point in opposite direction for the two objectives Three modified geometries were generated 1. Based on the top 5 parametric sensitivities for drag 2. Based on the top 5 parametric sensitivities for downforce 3. Changing all parameters that primarily affect one objective while having little influence on the other, in an effort to improve both objectives 21
- 22. DNV GL © 2014 Optimization Results Baseline geometry 22 With kind permission of: Koenigsegg Automotive AB www.koenigsegg.com
- 23. DNV GL © 2014 Optimization Results Drag optimized geometry -0.96% drag -3.75% downforce 23 With kind permission of: Koenigsegg Automotive AB www.koenigsegg.com
- 24. DNV GL © 2014 Optimization Results Downforce optimized geometry -0.03% drag +3.86% downforce 24 With kind permission of: Koenigsegg Automotive AB www.koenigsegg.com
- 25. DNV GL © 2014 Optimization Results Combined optimized geometry -10.58% drag +2.94% downforce 25 With kind permission of: Koenigsegg Automotive AB www.koenigsegg.com
- 26. DNV GL © 2014 Discussion Adjoint sensitivities can be mapped to the CAD geometry parameters to allow for feasible shape modifications Largest possible design space can be considered All parameters in the model can be involved in the optimization, without the need for the user to understand the effect of each parameter The effort does not scale with the number of parameters Parametric sensitivities for all parameters in the model can be computer more quickly than for a small set using the direct approach Separate adjoint solutions may be used to perform a multi-objective optimization But: Predictions based on sensitivities are only valid for small changes in shape In practice iterative process: new sensitivities should be computed for modified shape 26
- 27. DNV GL © 2014 SAFER, SMARTER, GREENER www.dnvgl.com CAESES , Your Upfront CAE System for Shape Optimization 27 Dipl.-Ing. Mattia Brenner brenner@friendship-systems.com +49 331 96 766 0 Design Solve Optimize