Method to optimize an additively-manufactured functionally-graded lattice structure for effective liquid cooling

Akihiro Takezawa*, Xiaopeng Zhang, Masaki Kato, Mitsuru Kitamura

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

39 Citations (Scopus)


The development of cooling devices is important for many industrial products, and the lattice structure fabricated by additive manufacturing is expected to be useful for effective liquid cooling. However, lattice density should be carefully designed for an effective arrangement of coolant flow. In this research, we optimize the lattice density distribution using a lattice structure approximation and the gradient method. Fluid flow is approximated by deriving effective properties from the Darcy–Forchheimer law and analyzing the flow according to the Brinkman–Forchheimer equation. Thermal conduction and convection are also approximated as a weakly coupled problem. We use a simple basic lattice shape composed of pillars, optimizing only its density distribution by setting the pillar diameter as the design variable. Steady-state pressure and temperature reductions are treated as multi-objective functions. Through 2D and 3D numerical studies, we discuss the validity and limitations of the proposed method. Although observable errors in accuracy exist between the results obtained from the optimization and full scale models, relative performance optimization was considered successful.

Original languageEnglish
Pages (from-to)285-298
Number of pages14
JournalAdditive Manufacturing
Publication statusPublished - 2019 Aug
Externally publishedYes


  • Additive manufacturing
  • Brinkman–Forchheimer equation
  • Darcy–Forchheimer law
  • Lattice density optimization
  • Thermal conduction-convection

ASJC Scopus subject areas

  • Biomedical Engineering
  • Materials Science(all)
  • Engineering (miscellaneous)
  • Industrial and Manufacturing Engineering


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