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Improvment and application of topology optimization algorithms
for ducted flows
Thorsten Grahs
move-csc UG, Braunschweig
Nikolaus Peller
AUDI AG, Development Fluid Dynamics Simulation, Ingolstadt
OSSCFD 2010, Munich, Germany
Agenda
• Topology Optimization
• Application to a simple test case(forward facing step)
• Application to a real world example(fantasy channel)
• Conclusions & Outlook
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
Topology optimization process
Topo Shape
Sequence of topological optimization:
1. Topological optimization on a rough design domain description
2. Transfer of the results into a smooth surface
3. Resulting shape or further fine-tuning via shape-optimization
• Dissipated power, uniformity index, mass flux ratio, flow swirl
• Implementation into OpenFOAM® [Othmer, de Villiers and Weller, 2007]
Different cost-functions are possible
Example: Optimization of an air duct segment
Example by Dr. Carsten Othmer, Volkswagen Cooperate Research, VW AG
Example: Optimization of an air duct segment
Pressure Drop Improvement: 50%
Benefits and draw backs of Topology optimization
+ optimization of ducted flows with installation space constraints
+ variety of cost functions
+ very efficient: cost corresponds to only two CFD computations
• Discovered in our basic algorithm:
Problems with stepped geometries, due to vanishing velocity in stagnation points e.g. In forward facing steps
Problematic area:
Forward Facing step geometry
vanishing Velocityleads to problematicscaling of sensitivity/porosity
Application of the basic algorithm
Lack of induced porous cells due toproblematic scaling/vanishing viscosityin the vicinity of the step
Remedy
Solution:
turn the whole idea upside downturn the whole idea upside down
Not introducing “bad” cells and delete them out of the flow field
Let the flow dig his own flow field in a porous design space, like a river in a sandy bed.
Remedy
Advantage:Areas where the flow (e.g. scaling/sensitivity) to weak stay porous.
original improved
Pressure loss [Pa] 143.4 134.8
Improvement around 8% on porous solution, On an redesign geometry we expect up to 25%
Real World Test Case
Application of the improved algorithm to thefantasy channel (validation duct)
Original vs optimized channel
Original channel
Optimized channel
Original channel
optimized channel (basic algorithm)
Stream lines
Porous cells
Optimized contours (basic algorithm)
Optimized flow – basic vs. improved algorithm
Streamlines for both optimization runs
basic
improved
basic
Vector plot for both optimization runs
basic
improved
Optimized flow – basic vs. improved algorithm
Optimized flow – basic vs. improved algorithm
Removed and kept sets of cellsfor both optimization runs
improved
basic
Gain in pressure drop ~ 4% on porous channele.g. around 10-15% on designed chanel geometry
Improved optimization run – resulting geometry
Improved Optimization run – stream lines
Conclusions & Outlook
Conclusions
• Requirements of topology optimization in industry: stability and simplicity
• Presentation of different approaches for local criteria
• „Forward facing step“ problem and „upside down“ solution
• Successfull application of improved algorithm to different duct flows
Outlook
• Analysis of additional criteria and their combination
• Integration of an Immersed boundary method
• Tests and validation on different test cases