Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Multi-scale topology optimization of porous heat sinks with voided lattice structure using a two-layer Darcy-Forchheimer model

Tatsuki Saito, Yuto Kikuchi, Kuniharu Ushijima, Kentaro Yaji

TL;DR

The paper tackles high pressure-drop issues in porous heat sinks by introducing a multi-material topology optimization that explicitly blends voids with graded lattice regions. It employs a two-layer Darcy-Forchheimer formulation to provide a reduced-order yet accurate representation of thermo-fluid coupling across porous-void media, with relative density and transport properties interpolated from RVE data. The authors demonstrate that optimized voided lattices yield 20-30% higher maximum Nusselt numbers than plate-fin or uniform-lattice references under the same pressure drop, while maintaining lower pressure losses, and they validate the approach via full-scale FE analyses and cross-checks. The work offers a practical pathway to manufacturable, open-cell heat sinks with enhanced thermal performance, and it highlights the potential of lattice miniaturization to further boost efficiency, subject to manufacturing constraints and future experimental validation.

Abstract

This study presents a topology optimization framework for the design of water cooled heat sinks that incorporate voided lattice structures, formulated using a two-layer Darcy-Forchheimer model. Conventional porous heat sinks often suffer from excessive pressure drops due to their intricate geometries, which limit their practical applicability. To overcome this issue, the proposed method introduces an explicit representation of both void and porous regions, together with graded lattice density, within a multi-material optimization framework. The two-layer Darcy-Forchheimer model enables efficient reduced-order simulations, allowing direct consideration of the heterogeneous porous-void distribution during the optimization process. The optimized designs are reconstructed into full-scale lattice geometries and validated through coupled thermo-fluid finite element analyses under fixed pressure-drop conditions. The results demonstrate that the voided lattice configurations significantly outperform conventional plate-fin and uniform lattice heat sinks, achieving approximately 20-30 percent higher maximum Nusselt numbers while maintaining lower pressure losses.

Multi-scale topology optimization of porous heat sinks with voided lattice structure using a two-layer Darcy-Forchheimer model

TL;DR

The paper tackles high pressure-drop issues in porous heat sinks by introducing a multi-material topology optimization that explicitly blends voids with graded lattice regions. It employs a two-layer Darcy-Forchheimer formulation to provide a reduced-order yet accurate representation of thermo-fluid coupling across porous-void media, with relative density and transport properties interpolated from RVE data. The authors demonstrate that optimized voided lattices yield 20-30% higher maximum Nusselt numbers than plate-fin or uniform-lattice references under the same pressure drop, while maintaining lower pressure losses, and they validate the approach via full-scale FE analyses and cross-checks. The work offers a practical pathway to manufacturable, open-cell heat sinks with enhanced thermal performance, and it highlights the potential of lattice miniaturization to further boost efficiency, subject to manufacturing constraints and future experimental validation.

Abstract

This study presents a topology optimization framework for the design of water cooled heat sinks that incorporate voided lattice structures, formulated using a two-layer Darcy-Forchheimer model. Conventional porous heat sinks often suffer from excessive pressure drops due to their intricate geometries, which limit their practical applicability. To overcome this issue, the proposed method introduces an explicit representation of both void and porous regions, together with graded lattice density, within a multi-material optimization framework. The two-layer Darcy-Forchheimer model enables efficient reduced-order simulations, allowing direct consideration of the heterogeneous porous-void distribution during the optimization process. The optimized designs are reconstructed into full-scale lattice geometries and validated through coupled thermo-fluid finite element analyses under fixed pressure-drop conditions. The results demonstrate that the voided lattice configurations significantly outperform conventional plate-fin and uniform lattice heat sinks, achieving approximately 20-30 percent higher maximum Nusselt numbers while maintaining lower pressure losses.
Paper Structure (23 sections, 66 equations, 21 figures, 3 tables)

This paper contains 23 sections, 66 equations, 21 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Formulation
  3. Methodology outline
  4. Two-layer Darcy-Forchheimer model
  5. Interpolation of equivalent physical properties
  6. Optimization problem setting
  7. Numerical implementation
  8. Results and discussion
  9. Problem setting
  10. The property of lattice unit cell
  11. The analysis setting
  12. Validation of the two-layer DF model using random distributions
  13. Optimization result
  14. Evaluation of optimized designs via full-scale analysis
  15. Introducing reference fins
  16. ...and 8 more sections

Figures (21)

  • Figure 1: Schematic of the multi-scale topology optimization applied in present study.
  • Figure 2: Overview of two-layer theory and porous approximation used in two-layer DF model.
  • Figure 3: Boundary condition of RVE domain for (a) heat conductivity, (b) fluid resistance.
  • Figure 4: Interpolation function of pressure gradient with respect to Darcy velocity of the lattice.
  • Figure 5: Schematic of density mapping algorithm through updating process.
  • ...and 16 more figures