Multi-scale topology optimization of hybrid porous heat sinks using multiple lattice configurations

This study develops a multi-scale topology optimization method with multiple lattice configurations used for the design of hybrid porous heat sink structures in high-power electronic devices. To enhance the design flexibility, two types of design variables are introduced for the microstructure design: the discrete type variables that characterize lattice configuration types, and the continuous density variables that determine the geometric characteristic dimensions of microstructures under specific lattice configurations. By integrating the Darcy-Forchheimer law with the averaging theorem, a governing equation system is formulated to describe the multi-scale thermal-flow phenomena in porous media. It is worth noting that this study develops a multi-configuration interpolation model to determine the effective physical properties of the hybrid structure with multiple lattice configurations by integrating the discrete type variables and the data-driven interpolation models. On this basis, a multi-material optimization approach is employed to achieve the multi-scale topology optimization design of hybrid porous heat sink structures with multiple lattice configurations. Numerical results confirm the effectiveness and unique advantages of the developed method, which can harness the differential advantages offered by various lattice configurations with differing types and densities, thereby enabling the optimized heat sink structures to achieve superior flow and heat transfer performance. Compared with the single-configuration optimal design, the developed dual-configuration optimal design achieves approximately 50% improvement in relative average temperature. Furthermore, the resulting multi-configuration heat sink significantly outperforms conventional uniform lattice designs.