From packaging space to CAD geometry:Optimal ducted flows with sequenced topological

and shape optimisation

Thorsten Grahs

move-csc UG, Braunschweig

Carsten Othmer

Volkswagen AG, Corporate Research, Wolfsburg

Trevor T Robinson and Cecil G Armstrong

School of Mechanical and Aerospace Enginieerung, Queen‘s University Belfast

Agenda

1 Automotive CFD optimization to date

2 An optimization process chain based on the adjoint method

– Topology optimization

– Shape optimization: Linking sensitivity maps to CAD parameters

3 Application of the developed process chain

• Basis: parametric geometry (CATIA-V5, Pro/E, Morphing)

• Automatic process chain:

CAD – meshing – solving – evaluation – optimization algorithm

Automotive CFD optimization to date

• Basis: parametric CAD geometry (CATIA-V5)

• 9 geometry parameters

• Computation of about 500 variants: 35% reduction of pressure drop

Automotive CFD optimization to date: Example

Deficiencies and a possible solution

Deficiencies of today‘s automotive CFD optimization :

• huge CPU requirements: hard upper limit for the number of parameters to be optimized

� some optimization tasks are not feasible

� available optimization potential cannot be exploited

Possible solution:

• Optimization based on “Sensitivity Maps“

Sensitivity maps: Examples

Shape Optimization

Drag

Dissipated Power

Topology Optimization

Pressure Drop

Power

Uniformity

Computation of sensitivity maps

Sensitivity = Gradient dJ/d α = (∂J/∂α1 , … , ∂J/∂αn)

… via finite differences:

∂J/∂αi ~ (J(αi+dαi)-J(αi))/dαi for each i

� n+1 solver calls, i.e. n+1 CFD computations

… via the adjoint method:

one call to the CFD solver + one call to the adjoint solver

� 2 solver calls – independent of n !

Proposed optimization process chain

Topo Shape

Sequence of topological and shape optimization based on sensitivity maps:

1. Topological optimization on a rough design domain description

2. Transfer of the results into a smooth surface

3. Shape optimization for fine-tuning

Proposed optimization process chain

Topo Shape

Sequence of topological and shape optimization based on sensitivity maps:

1. Topological optimization on a rough design domain description ���� ok

2. Transfer of the results into a smooth surface ���� to do

3. Shape optimization for fine-tuning ���� to do

Fluid dynamic topology optimization

• Discretization of the entire installation space

– CFD solution

– identification of “counter-productive“ cells via a local criterion

– removal/punishment of “counter-productive“ cells

• Result: Optimal topology

IN OUT

• Dissipated power, uniformity index, mass flux ratio, flow swirl

Proof-of-principle for relevant cost functions done

• Implementation into OpenFOAM® [Othmer, de Villiers and Weller, 2007]

Example: Optimization of an air duct segment

Example: Optimization of an air duct segment

Example: Optimization of an air duct segment

Pressure Drop Improvement: 50%

1st half of process chain: Done

+ optimization of ducted flows with installation space constraints

+ variety of cost functions

+ very efficient: cost corresponds to only two CFD computations

- stepped geometry � inaccurate CFD solution

� Combination with a method for geometrical “fine-tuning“ would be ideal!

Topo Shape

Adjoint method for shape optimization

• Adjoint-based topology optimization:

– Sensitivity = ∂(cost function)/∂(porosity) for each volume cell[see Othmer and Grahs, 2007; Othmer, de Villiers and Weller, 2007]

• Adjoint-based shape optimization:

– Design variable = displacement of surface nodes in normal – Design variable = displacement of surface nodes in normal direction

– Sensitivity = ∂(cost function)/∂(surface displacement in normal direction) for each surface node[see Othmer, 2008]

Shape sensitivity maps: Examples

Pressure dropDrag

Uniformity

Possibilities for Reshape:

1. Movement of individual nodes, smoothing (see previous talk)

• Smooth shape vs. Conservation of sensitivity information

2. Mapping to Morphing Control Points

Translating the sensitivities into a new shape: “Reshape“

• Ongoing collaboration with BETA Systems, Greece

3. Mapping to CAD parameters

Mapping of sensitivities to CAD parameters: Why?

+ Final geometry has to be delivered in CAD anyway

+ consideration of design constraints (feature lines, curvature radii, other manufacturing constraints) is done in the CAD system

+ We are talking about fine-tuning after topo optimization, i.e. small geometric changes: relaxes the otherwise tough stability requirements of the parametrization a lotrequirements of the parametrization a lot

Mapping of sensitivities to CAD parameters

“Which parameter values do I need to modify, and by what amount, to optimize

the performance of my CAD model?“the performance of my CAD model?“

Mapping of sensitivities to CAD parameters

• CAD parameters are either given or defined according to sensitivity distribution

• Computation of CAD sensitivities via chain rule

Sensitivities

Parametrized areas

Mapping of sensitivities to CAD parameters

• Node sensitivities � CAD parameter sensitivities

• Move along steepest descent under consideration of constraints

• Realization in CATIA V5 with Queen‘s Univ. Belfast[see Armstrong et al., 2007; Robinson et al., 2009]

Sample application: Air duct segment

Inlet

Pressure drop 100%

Packaging space

Outlet

Sample application: Air duct segment

Pressure drop 100% vs. 53%

Manual CAD build-up guided by topo result

Sample application: Air duct segment

Pressure drop 53%

Topo-optimal duct

Sample application: Air duct segment

Pressure drop 40%

Shape optimization within packaging space

Sample application: Air duct segment

Pressure drop 40%

Shape-optimal duct

Sample application: Air duct segment

Pressure drop 53% vs. 40%

Topo-optimal vs. shape-optimal duct

Sensitivity

2nd half of process chain: Done

1. Topology optimization delivers optimal design from scratch (~ 2 runs)

2. Manual build-up of CAD geometry guided by topo result

3. Single step CAD-based optimization (~ 2 runs + parameter mapping)

� Inherent consideration of geometric constraints (packaging space)

� Nearly full potential of available design domain recovered

� From packaging space to the optimum in CAD with less than 5 solver runs

Topo Shape

Outlook

• The present formulation of parametric sensitivities allows to rate the effectiveness of the model parametrization

� Determines when and where more flexibility is required in the model

� Basis for automatic adaptation of the model parametrization [see Armstrong et al., 2009]