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A comparison of manufacturing constraints in 3D topologically optimized heat sinks for forced air cooling

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Abstract

In this paper, the manufacturability of 3D topologically optimized (TO) heat sinks for forced-air cooling is studied for both additive manufacturing and subtractive numerical control machining. To mitigate the manufacturing difficulties which are frequently encountered when fabricating TO designs, we adopt two approaches. First, a constraint on the projected undercut perimeter is added to the standard optimization formulation to limit the number and severity of costly non-self supporting features in additive manufacturing. Second, a multi-axis machining (MAM) constraint is adopted to serve as the basis for enforcing manufacturability in a TO design for an alternative, highly-popular manufacturing modality. Locally refined nonuniform unstructured meshing and unit-cell assembly techniques for increasing the mesh and design resolution were pursued during optimization. Post-analyses were conducted in OpenFOAM for all TO and corresponding parallel-fin designs. Simulation results showed that topologically optimized heat sinks offer a 35–40% advantage in temperature performance over conventional parallel fins. A limited or non-existent compromising of thermal-hydraulic performance was necessary to enforce manufacturability. Finally, to prove the practical efficacy of the overhang angle control constraint, the AM-constrained heat sinks designs were fabricated through direct metal laser sintering in both aluminum and stainless steel.

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References

  1. Alonso JJ, LeGresley P, Pereyra V (2009) Aircraft design optimization. Math Comput Simul 79(6):1948–1958

    MathSciNet  MATH  Google Scholar 

  2. Behrou R, Kirsch K, Ranjan R, Guest JK (2022) Topology optimization of additively manufactured fluidic components free of internal support structures. Comput Methods Appl Mech Eng 389:114270

    MathSciNet  MATH  Google Scholar 

  3. Bendsøe MP, Sigmund O (2003) Topology optimization: theory, methods, and applications. Springer, Berlin

    MATH  Google Scholar 

  4. Bourdin B (2001) Filters in topology optimization. Int J Numer Methods Eng 50(9):2143–2158

    MathSciNet  MATH  Google Scholar 

  5. Dede EM, Joshi SN, Zhou F (2015) Topology optimization, additive layer manufacturing, and experimental testing of an air-cooled heat sink. J Mech Des 137(11)

  6. Donea J, Huerta A (2003) Finite element methods for flow problems. Wiley, New York

    Google Scholar 

  7. Elman H, Howle VE, Shadid J, Shuttleworth R, Tuminaro R (2008) A taxonomy and comparison of parallel block multi-level preconditioners for the incompressible Navier-Stokes equations. J Comput Phys 227(3):1790–1808

    MathSciNet  MATH  Google Scholar 

  8. Ford S, Despeisse M (2016) Additive manufacturing and sustainability: an exploratory study of the advantages and challenges. J Clean Prod 137:1573–1587

    Google Scholar 

  9. Gasick J, Qian X (2021) Simultaneous topology and machine orientation optimization for multiaxis machining. Int J Numer Methods Eng 6839

  10. Gaynor AT, Guest JK (2016) Topology optimization considering overhang constraints: Eliminating sacrificial support material in additive manufacturing through design. Struct Multidiscip Optim 54(5):1157–1172

    MathSciNet  Google Scholar 

  11. Gaynor AT, Meisel NA, Williams CB, Guest JK (2014) Topology optimization for additive manufacturing: considering maximum overhang constraint. In: 15th AIAA/ISSMO multidisciplinary analysis and optimization conference, p 2036

  12. Gersborg AR, Andreasen CS (2011) An explicit parameterization for casting constraints in gradient driven topology optimization. Struct Multidiscip Optim 44(6):875–881

    Google Scholar 

  13. Guest JK, Zhu M (2012) Casting and milling restrictions in topology optimization via projection-based algorithms. In: Volume 3: 38th design automation conference, parts A and B. Chicago, Illinois, USA: American Society of Mechanical Engineers, pp 913–920

  14. Haertel JHK, Engelbrecht K, Lazarov BS, Sigmund O (2018) Topology optimization of a pseudo 3D thermofluid heat sink model. Int J Heat Mass Transf 121:1073–1088

    Google Scholar 

  15. Høghøj LC, Träff EA (2022) An advection-diffusion based filter for machinable designs in topology optimization. Comput Methods Appl Mech Eng 391:114488

    MathSciNet  MATH  Google Scholar 

  16. Kawamoto A, Matsumori T, Yamasaki S, Nomura T, Kondoh T, Nishiwaki S (2011) Heaviside projection based topology optimization by a PDE-filtered scalar function. Struct Multidiscip Optim 44(1):19–24

    MATH  Google Scholar 

  17. 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 64:759–772

    Google Scholar 

  18. Kranz J, Herzog D, Emmelmann C (2015) Design guidelines for laser additive manufacturing of lightweight structures in TiAl6V4. J Laser Appl 27(S1):S14001

  19. Langelaar M (2019) Topology optimization for multi-axis machining. Comput Methods Appl Mech Eng 351:226–252

    MathSciNet  MATH  Google Scholar 

  20. Langelaar M (2016) Topology optimization of 3D self-supporting structures for additive manufacturing. Addit Manuf 12:60–70

    Google Scholar 

  21. Lazarov BS, Sigmund O (2011) Filters in topology optimization based on Helmholtztype differential equations. Int J Numer Methods Eng 86(6):765–781

    MATH  Google Scholar 

  22. Lee G, Lee I, Kim SJ (2021) Topology optimization of a heat sink with an axially uniform cross-section cooled by forced convection. Int J Heat Mass Transf 168:120732

    Google Scholar 

  23. Liu J, Duke K, Ma Y (2016) Multi-material plastic part design via the level set shape and topology optimization method. Eng Optim 48(11):1910–1931

    MathSciNet  Google Scholar 

  24. Liu J, Ma Y (2016) A survey of manufacturing oriented topology optimization methods. Adv Eng Softw 100:161–175

    Google Scholar 

  25. Liu J, Ma YS (2015) 3D level-set topology optimization: a machining feature-based approach. Struct Multidiscip Optim 52(3):563–582

    MathSciNet  Google Scholar 

  26. Logg A, Mardal K-A, Wells G (2012) Automated solution of differential equations by the finite element method: the FEniCS book, vol 84. Springer, Berlin

    MATH  Google Scholar 

  27. Logg A, Mardal KA, Wells G (eds) (2012) Automated solution of differential equations by the finite element method: the fenics book. In: Lecture notes in computational science and engineering, vol 84. Springer, Heidelberg

  28. Mezzadri F, Bouriakov V, Qian X (2018) Topology optimization of self-supporting support structures for additive manufacturing. Addit Manuf 21:666–682

    Google Scholar 

  29. Mezzadri F, Qian X (2020) A second-order measure of boundary oscillations for overhang control in topology optimization. J Comput Phys 410:109365

    MathSciNet  MATH  Google Scholar 

  30. Mirzendehdel AM, Behandish M, Nelaturi S (2020) Topology optimization with accessibility constraint for multi-axis machining. Comput Aided Des 122:102825

    MathSciNet  Google Scholar 

  31. Mirzendehdel AM, Suresh K (2016) Support structure constrained topology optimization for additive manufacturing. Comput Aided Des 81:1–13

    Google Scholar 

  32. Qian X (2017) Undercut and overhang angle control in topology optimization: a density gradient based integral approach. Int J Numer Methods Eng 111(3):247–272

    MathSciNet  Google Scholar 

  33. Qian X, Dede EM (2016) Topology optimization of a coupled thermal-fluid system under a tangential thermal gradient constraint. Struct Multidiscip Optim 54(3):531–551

    MathSciNet  Google Scholar 

  34. Qian X, Sigmund O (2013) Topological design of electromechanical actuators with robustness toward over- and under-etching. Comput Methods Appl Mech Eng 253:237–251

    MathSciNet  MATH  Google Scholar 

  35. Saad Y (1993) A flexible inner-outer preconditioned GMRES algorithm. SIAM J Sci Comput 14(2):461–469

    MathSciNet  MATH  Google Scholar 

  36. Sato Y, Yamada T, Izui K, Nishiwaki S (2017) Manufacturability evaluation for molded parts using fictitious physical models, and its application in topology optimization. Int J Adv Manuf Technol 92(1–4):1391–1409

    Google Scholar 

  37. Sigmund O, Maute K (2013) Topology optimization approaches: a comparative review. Struct Multidiscip Optim 48(6):1031–1055

    MathSciNet  Google Scholar 

  38. Simons M (2018) Additive manufacturing—a revolution in progress? Insights from a multiple case study. Int J Adv Manuf Technol 96(1–4):735–749

    Google Scholar 

  39. Strano G, Hao L, Everson RM, Evans KE (2013) A new approach to the design and optimisation of support structures in additive manufacturing. Int J Adv Manuf Technol 66(9–12):1247–1254

    Google Scholar 

  40. Sun S, Liebersbach P, Qian X (2020) 3D topology optimization of heat sinks for liquid cooling. Appl Therm Eng 178:115540

    Google Scholar 

  41. Svanberg K (1987) The method of moving asymptotes—a new method for structural optimization. Int J Numer Methods Eng 24(2):359–373

    MathSciNet  MATH  Google Scholar 

  42. Thomas DS, Gilbert SW (2014) Costs and cost effectiveness of additive manufacturing. Technical report NIST SP 1176. National Institute of Standards and Technology, NIST SP 1176

  43. Vatanabe SL, Lippi TN, Lima CR, Paulino GH, Silva ECN (2016) Topology optimization with manufacturing constraints: a unified projection-based approach. Adv Eng Softw 100:97–112

    Google Scholar 

  44. Wang C, Qian X (2020) Simultaneous optimization of build orientation and topology for additive manufacturing. Addit Manuf 34:101246

    Google Scholar 

  45. Wang C, Qian X, Gerstler WD, Shubrooks J (2018) Boundary slope control in topology optimization for additive manufacturing. In: Volume 2: materials; joint MSEC-NAMRC-manufacturing USA. College Station, Texas, USA: American Society of Mechanical Engineers, V002T07A002

  46. Weller HG, Tabor G, Jasak H, Fureby C (1998) A tensorial approach to computational continuum mechanics using object-oriented techniques. Comput Phys 12(6):620

    Google Scholar 

  47. Yaji K, Ogino M, Chen C, Fujita K (2018) Large-scale topology optimization incorporating local-in-time adjoint-based method for unsteady thermal-fluid problem. Struct Multidiscip Optim 58(2):817–822

    MathSciNet  Google Scholar 

  48. Yoon GH (2010) Topological design of heat dissipating structure with forced convective heat transfer. J Mech Sci Technol 24(6):1225–1233

    Google Scholar 

  49. Zeng S, Kanargi B, Lee PS (2018) Experimental and numerical investigation of a mini channel forced air heat sink designed by topology optimization. Int J Heat Mass Transf 121:663–679

    Google Scholar 

  50. Zhu J, Zhou H, Wang C, Zhou L, Yuan S, Zhang W (2021) A review of topology optimization for additive manufacturing: status and challenges. Chin J Aeron 34(1):91–110

    Google Scholar 

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Acknowledgements

The authors want to acknowledge the support from the ONR grant N00014-18-1-2685 managed by Dr. Mark Spector and Sony Faculty Innovation award. This work used the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation grant number ACI-1548562. This work used XSEDE TACC Dell/Intel Knights Landing, SkylakeSystem (Stampede2) at the service-provider through allocation TG-DDM190003. J. Gasick wants to acknowledge the support of the National Science Foundation Graduate Research Fellowship Program under Grant No. DGE-1747503.

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Correspondence to Xiaoping Qian.

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Wang, T., Gasick, J., Sun, S. et al. A comparison of manufacturing constraints in 3D topologically optimized heat sinks for forced air cooling. Engineering with Computers 39, 1711–1733 (2023). https://doi.org/10.1007/s00366-023-01786-y

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