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NOFUN 2014

24th September 2014

Braunschweig, Germany

Georgios Karpouzas, Engys Ltd. – NTUA

Eugene De Villiers, Engys Ltd.

Thomas Schumacher, Engys UG

“Adjoint Optimization with HELYX”

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Contents

• Introduction

• Topology Optimization

• Shape Optimization

• Adjoint Coupled Solver

• Summary

© 2014 Engys Ltd.

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Introduction | Continuous Adjoint

© 2014 Engys Ltd.

• Gradient based optimization method

• Used to calculate sensitivities w.r.t. user defined objective functions

• Cost doesn’t increase with the number of parameters

• The calculation of the sensitivity derivatives is approximately equivalent with the solution of one primal problem

• Avoid calculating the computationally expensive terms (δU/δb, δp/δb) by making their multipliers (adjoint equations+BCs) zero

C.Othmer. Adjoint methods for car aerodynamics. Journal of Mathematics in Industry 2014 4:6.

G.K. Karpouzas, E. De Villiers, “Level-set based topology optimization using the Continuous Adjoint Method". OPTi2014 - International Conference on Engineering and Applied Sciences Optimization, June 4-6 2014, Kos, Greece.

I.S Kavvadias, G.K. Karpouzas, E.M. Papoutsis-Kiachagias, D.I. Papadimitriou, K.C. Giannakoglou: “Optimal Flow Control and Topology Optimization Using the Continuous Adjoint Method in Unsteady Flows”, EUROGEN 2013

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Introduction | HELYX Adjoint Features

© 2014 Engys Ltd.

• “One-shot” primal/adjoint/topology update

• Incompressible & compressible flows

• Adjoint MRF and porous media support

• Level-set immersed boundary for interface tracking

• 2nd order accuracy

• Multi-objective:

forces & moments, uniformity, pressure loss, massflow split,

swirl, wall shear stress, etc.

• No expert operator knowledge required

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Contents

• Introduction

• Topology Optimization

Simple Duct

HVAC duct

Gear pump

• Shape Optimization

• Adjoint Coupled Solver

• Summary

© 2014 Engys Ltd.

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Topology Optimization | Overview

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• Specify design space and inlet/outlet interfaces

• Define optimization objectives

• Run single simulation till geometry converges

Iteration: Primal Adjoint Geometry update

• Output optimized shape

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Contents

• Introduction

• Topology Optimization

Simple Duct

HVAC duct

Gear pump

• Shape Optimization

• Adjoint Coupled Solver

• Summary

© 2014 Engys Ltd.

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Topology Optimization | Simple Duct

© 2014 Engys Ltd.

• Topology Optimization

• Pressure loss minimization

• Design space with obstacles

9 © 2014 Engys Ltd.

Topology Optimization | Simple Duct

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Topology Optimization | Simple Duct

© 2014 Engys Ltd.

• 50% Pressure Loss improvement

• Optimized shape:

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Contents

• Introduction

• Topology Optimization

Simple Duct

HVAC duct

Gear pump

• Shape Optimization

• Adjoint Coupled Solver

• Summary

© 2014 Engys Ltd.

12 © 2014 Engys Ltd.

• Multiple objective functions employed

Minimize pressure loss in domain

Maximize flow uniformity through porous media

Target flow split through outlets 3x33%

Topology Optimization | HVAC Duct

13 © 2014 Engys Ltd.

Topology Optimization | HVAC Duct

14 © 2014 Engys Ltd.

• Final shape

• 30% reduction in pressure loss achieved

• Other objectives unchanged

Topology Optimization | HVAC Duct

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Contents

• Introduction

• Topology Optimization

Simple Duct

HVAC duct

Gear pump

• Shape Optimization

• Adjoint Coupled Solver

• Summary

© 2014 Engys Ltd.

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Topology Optimization | Gear pump

© 2014 Engys Ltd.

Inlet Port Outlet Port

Gear

• Geometry provided by Aisin AW

• Case separated into two parts: Inlet port (low pressure)

Outlet port (high pressure)

• Objective: minimization of power losses

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Topology Optimization | Gear pump

© 2014 Engys Ltd.

Power Losses Inport Outport Gear Pump

Baseline 2.208 W 31.017 W 33.325 W

Optimized 1.635 W 25.379 W 27.013 W

Percentage 29.17 % 18.18 % 18.94 %

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Contents

• Introduction

• Topology Optimization

• Shape Optimization

• Adjoint Coupled Solver

• Summary

© 2014 Engys Ltd.

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Shape Optimization | DRIVAER

© 2014 Engys Ltd.

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Shape Optimization | DRIVAER

© 2014 Engys Ltd.

• Comparison of 2nd order accuracy (top) with former 1st order (bottom) results

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Contents

• Introduction

• Topology Optimization

• Shape Optimization

• Adjoint Coupled Solver

• Summary

© 2014 Engys Ltd.

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Adjoint Coupled Solver

© 2014 Engys Ltd.

• Block coupled adjoint solver

• Fully implicit ATC term

• Speedup ~x4

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Adjoint Coupled Solver

© 2014 Engys Ltd.

• Top: segregated volumetric sensitivities

• Bottom: block volumetric sensitivities

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Contents

• Introduction

• Topology Optimization

• Shape Optimization

• Adjoint Coupled Solver

• Summary

© 2014 Engys Ltd.

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Summary

© 2014 Engys Ltd.

• Proven methodology Robust implementation

2nd order accurate adjoint

Many successful industrial applications

• Unique Level-Set immersed boundary technology Better control of the optimization

More manufacturable final shape

Improved primal accuracy due to IB

• Coupled solver > ~x4 speed up

Implicit ATC more robust

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Looking Ahead

© 2014 Engys Ltd.

• GUI support to enable routine use

• Integrated shape morphing

CARAT++ from FEMopt

Harmonic coordinates (IODA ITN 7)

• Algorithmic improvements

Enhanced immersed boundaries

Composite objectives (e.g. Lift/Drag, Pump efficiency)

Multipoint optimization (pseudo-transient & transient)

Adjoint thermal and species

Integration with Coupled Primal Solver

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Acknowledgements

© 2014 Engys Ltd.

• Aboutflow ITN

• Adjoint-Based optimization of industrial and unsteady flows

• http://aboutflow.sems.qmul.ac.uk

“This project has received funding from the European

Union’s Seventh Framework Programme for research,

technological development and demonstration under

grant agreement no [317006]”.

• Volkswagen Research: C. Othmer, M.M. Gregersen

• Volkswagen Methods Development: D. Schreader

• Volkswagen Engine Developement: W. Py

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Questions

© 2014 Engys Ltd.