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Structural and Multidisciplinary Optimization

, Volume 57, Issue 5, pp 1905–1918 | Cite as

Density based topology optimization of turbulent flow heat transfer systems

  • Sumer B. Dilgen
  • Cetin B. Dilgen
  • David R. Fuhrman
  • Ole Sigmund
  • Boyan S. Lazarov
Research Paper

Abstract

The focus of this article is on topology optimization of heat sinks with turbulent forced convection. The goal is to demonstrate the extendibility, and the scalability of a previously developed fluid solver to coupled multi-physics and large 3D problems. The gradients of the objective and the constraints are obtained with the help of automatic differentiation applied on the discrete system without any simplifying assumptions. Thus, as demonstrated in earlier works of the authors, the sensitivities are exact to machine precision. The framework is applied to the optimization of 2D and 3D problems. Comparison between the simplified 2D setup and the full 3D optimized results is provided. A comparative study is also provided between designs optimized for laminar and turbulent flows. The comparisons highlight the importance and the benefits of full 3D optimization and including turbulence modeling in the optimization process, while also demonstrating extension of the methodology to include coupling of heat transfer with turbulent flows.

Keywords

Topology optimization Automatic differentiation Turbulent flow Thermal-fluid Heat sink 

Notes

Acknowledgements

The authors acknowledge the financial support received from the TopTen project sponsored by the Danish Council for Independent Research (DFF-4005-00320). During the final part, the work of the last author was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.

References

  1. Aage N, Lazarov B (2013) Parallel framework for topology optimization using the method of moving asymptotes. Struct Multidiscip Optim 47(4):493–505MathSciNetCrossRefMATHGoogle Scholar
  2. Aage N, Poulsen TH, Gersborg-Hansen A, Sigmund O (2008) Topology optimization of large scale stokes flow problems. Struct Multidiscip Optim 35(2):175–180.  https://doi.org/10.1007/s00158-007-0128-0 MathSciNetCrossRefMATHGoogle Scholar
  3. Aage N, Andreassen E, Lazarov B (2015) Topology optimization using petsc: An easy-to-use, fully parallel, open source topology optimization framework. Struct Multidiscip Optim 51(3):565–572MathSciNetCrossRefGoogle Scholar
  4. Alexandersen J, Sigmund O, Aage N (2016) Large scale three-dimensional topology optimisation of heat sinks cooled by natural convection. Int J Heat Mass Transf 100:876–891.  https://doi.org/10.1016/j.ijheatmasstransfer.2016.05.013. http://www.sciencedirect.com/science/article/pii/S0017931015307365 CrossRefGoogle Scholar
  5. Amstutz S (2005) The topological asymptotic for the navier-stokes equations. Esaim-control Optim Calc Var 11(3):401–425.  https://doi.org/10.1051/cocv:2005012 MathSciNetCrossRefMATHGoogle Scholar
  6. Arquis E, Caltagirone JP (1984) Sur les conditions hydrodynamiques au voisinage d’une interface milieu fluide-milieux poreux: application à la convection naturelle. In: C.R. Acad. Sci., Paris II, vol 299, pp 1–4Google Scholar
  7. Balay S, Gropp WD, McInnes LC, Smith BF (1997) Efficient management of parallelism in object oriented numerical software libraries. In: Arge E, Bruaset AM, Langtangen HP (eds) Modern Software Tools in Scientific Computing. Birkhȧuser Press, pp 163–202Google Scholar
  8. Balay S, Abhyankar S, Adams MF, Brown J, Brune P, Buschelman K, Dalcin L, Eijkhout V, Gropp WD, Kaushik D, Knepley MG, May DA, McInnes LC, Rupp K, Sanan P, Smith BF, Zampini S, Zhang H, Zhang H (2017a) PETSc users manual. Technical Report ANL-95/11 - Revision 3.8, Argonne National Laboratory. http://www.mcs.anl.gov/petsc
  9. Balay S, Abhyankar S, Adams MF, Brown J, Brune P, Buschelman K, Dalcin L, Eijkhout V, Gropp WD, Kaushik D, Knepley MG, May DA, McInnes LC, Rupp K, Smith BF, Zampini S, Zhang H, Zhang H (2017b) PETSc Web page. http://www.mcs.anl.gov/petsc
  10. Bendsøe MP, Sigmund O (2003) Topology Optimization - Theory, Methods and Applications. Springer Verlag, Berlin HeidelbergMATHGoogle Scholar
  11. Borrvall T, Petersson J (2003) Topology optimization of fluids in stokes flow. Int J Numer Methods Fluids 41(1):77–107MathSciNetCrossRefMATHGoogle Scholar
  12. Bourdin B (2001) Filters in topology optimization. Int J Numer Methods Eng 50:2143–2158MathSciNetCrossRefMATHGoogle Scholar
  13. CoDiPack (2016) code differentiation package. http://www.scicomp.uni-kl.de/software/codi/. Accessed: 2016-10-18
  14. Dede E (2009) Multiphysics topology optimization of heat transfer and fluid flow systems. In: Proceedings of the COMSOL users conferenceGoogle Scholar
  15. Dilgen CB, Dilgen SB, Fuhrman DR, Sigmund O, Lazarov B (2018) Topology optimization of turbulent flows. Comput Methods Appl Mech Eng 331:363 – 393.  https://doi.org/10.1016/j.cma.2017.11.029. https://www.sciencedirect.com/science/article/pii/S0045782517307478 MathSciNetCrossRefGoogle Scholar
  16. Ferziger JH, Peric M (2001) Computational Methods for Fluid Dynamics. Springer, Berlin HeidelbergMATHGoogle Scholar
  17. Gersborg-Hansen A, Sigmund O, Haber R (2005) Topology optimization of channel flow problems. Struct Multidiscip Optim 30(3): 181–192MathSciNetCrossRefMATHGoogle Scholar
  18. Griewank A, Walther A (2008) Evaluating derivatives : principles and techniques of algorithmic differentiation. SIAM, BangkokCrossRefMATHGoogle Scholar
  19. Guillaume P, Idris K (2004) Topological sensitivity and shape optimization for the stokes equations. Siam J Control Optim 43(1):1–31.  https://doi.org/10.1137/S0363012902411210 MathSciNetCrossRefMATHGoogle Scholar
  20. Hogan RJ (2014) Fast reverse-mode automatic differentiation using expression templates in C++. ACM Trans Math Softw 40(4):26MathSciNetCrossRefMATHGoogle Scholar
  21. Koga AA, Lopes ECC, Nova HFV, de Lima CR, Silva ECN (2013) Development of heat sink device by using topology optimization. Int J Heat Mass Transf 64(0):759–772CrossRefGoogle Scholar
  22. Kontoleontos EA, Papoutsis-Kiachagias EM, Zymaris AS, Papadimitriou DI, Giannakoglou KC (2013) Adjoint-based constrained topology optimization for viscous flows, including heat transfer. Eng Optim 45(8):941–961MathSciNetCrossRefGoogle Scholar
  23. Matsumori T, Kondoh T, Kawamoto A, Nomura T (2013) Topology optimization for fluid-thermal interaction problems under constant input power. Struct Multidiscip Optim 47(4):571–581.  https://doi.org/10.1007/s00158-013-0887-8 CrossRefMATHGoogle Scholar
  24. Menter FR (1994) Two-equation eddy-viscosity turbulence models for engineering applications. Aiaa J 32:1598–1605.  https://doi.org/10.2514/3.12149 CrossRefGoogle Scholar
  25. Nørgaard SA, Sagebaum M, Gauger NR, Lazarov B (2017) Applications of automatic differentiation in topology optimization. Struct Multidiscip Optim:1–12Google Scholar
  26. Olesen L, Okkels F, Bruus H (2006) A high-level programming-language implementation of topology optimization applied to steady-state navier-stokes flow. Int J Numer Methods Eng 65(7):975–1001MathSciNetCrossRefMATHGoogle Scholar
  27. Othmer C (2008) A continuous adjoint formulation for the computation of topological and surface sensitivities of ducted flows. Int J Numer Methods Fluids 58(8):861–877MathSciNetCrossRefMATHGoogle Scholar
  28. Patankar S (1980) Numerical heat transfer and fluid flow. HemisphereGoogle Scholar
  29. Pietropaoli M, Ahlfeld R, Montomoli F, Ciani A, D’Ercole M (2017) Design for additive manufacturing: Internal channel optimization. J Eng Gas Turbines Power 139(10):102,101–102:101–8CrossRefGoogle Scholar
  30. Pingen G, Evgrafov A, Maute K (2007) Topology optimization of flow domains using the lattice boltzmann method. Struct Multidiscip Optim 34(6):507–524MathSciNetCrossRefMATHGoogle Scholar
  31. Spalart P, Allmaras S (1994) A one-equation turbulence model for aerodynamic flows. Recherche Aerospatiale (1):5–21Google Scholar
  32. Svanberg K (1987) The method of moving asymptotes - a new method for structural optimization. Int J Numer Methods Eng 24:359–373MathSciNetCrossRefMATHGoogle Scholar
  33. Versteeg H, Malalasekera W (2007) An Introduction to Computational Fluid Dynamics: The Finite Volume Method. Prentice Hall, Upper Saddle RiverGoogle Scholar
  34. Wang F, Lazarov B, Sigmund O (2011) On projection methods, convergence and robust formulations in topology optimization. Struct Multidiscip Optim 43(6):767–784CrossRefMATHGoogle Scholar
  35. Wilcox D (2006) Turbulence Modeling for CFD. DCW Industries, IncorporatedGoogle Scholar
  36. Wilcox D (2008) Formaulation of the k-ω Turbulence Model Revisited. AIAA J 46:2823–2838.  https://doi.org/10.2514/1.36541 CrossRefGoogle Scholar
  37. Yaji K, Yamada T, Kubo S, Izui K, Nishiwaki S (2015) A topology optimization method for a coupled thermal-fluid problem using level set boundary expressions. Int J Heat Mass Transf 81: 878–888CrossRefGoogle Scholar
  38. Yaji K, Yamada T, Yoshino M, Matsumoto T, Izui K, Nishiwaki S (2016) Topology optimization in thermal-fluid flow using the lattice boltzmann method. J Comput Phys 307:355–377MathSciNetCrossRefMATHGoogle Scholar
  39. Zymaris AS, Papadimitriou DI, Giannakoglou KC, Othmer C (2009) Continuous adjoint approach to the Spalart-Allmaras turbulence model for incompressible flows. Comput Fluids 38(8):1528–1538CrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Electrical EngineeringTechnical University of DenmarkLyngbyDenmark
  2. 2.Department of Mechanical EngineeringTechnical University of DenmarkLyngbyDenmark
  3. 3.Lawrence Livermore National LaboratoryLivermoreUSA
  4. 4.School of Mechanical, Aerospace and Civil EngineeringThe University of ManchesterManchesterUK

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