from packaging space to cad geometry: optimal ducted …€¦ · requirements of the...
TRANSCRIPT
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]
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]
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
Pressure drop 100% vs. 53%
Manual CAD build-up guided by topo result
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