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