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

TL;DR

This paper introduces a multi-scale topology optimization method for porous heat sinks with voided lattice structures, using a two-layer Darcy-Forchheimer model to improve thermal performance and reduce pressure drops.

Contribution

It develops a novel multi-material optimization framework incorporating a two-layer Darcy-Forchheimer model for efficient design of heterogeneous porous-void heat sinks.

Findings

Void lattice structures outperform traditional designs in heat transfer.

Optimized designs achieve 20-30% higher Nusselt numbers.

Pressure losses are maintained at lower levels.

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.