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

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 drop due to their intricate geometry, which limits their practical applicability. To address 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 voided lattice configurations significantly outperform conventional plate-fin and uniform lattice heat sinks, achieving approximately 20%–30% higher maximum Nusselt numbers while maintaining lower pressure losses.