Variable-Lattice-Density Optimization of Pin-Fin Heat Sinks under High-Reynolds-Number Flow Conditions

Abstract

This study extends variable-lattice-density optimization to high-Reynolds-number flows for the design of periodically arranged pin-fin heat sinks. Effective permeability and drag coefficient are identified from unit-cell Reynolds-averaged Navier--Stokes analyses of cylindrical pin-fin arrays and incorporated into a reduced model based on the Darcy--Forchheimer law for macroscopic design exploration. To enable stable optimization under high-Reynolds-number conditions, a dual-mesh framework is introduced, in which the flow field and sensitivities are evaluated on a fine mesh, whereas the design variables are updated on a coarse mesh corresponding to the unit-cell arrangement. For the base condition, the $L_2$ norm of the temperature deviation from the area-averaged temperature is decreased from 4.38 K to 1.00 K in the reduced model, and geometry-resolved analysis of the reconstructed design confirms a reduction from 5.98 K to 1.17 K. Additional calculations with higher inlet velocities and modified outlet locations show that the proposed method captures the dominant flow-redistribution trends under different operating and geometric conditions, although the thermal objective became less accurate when local solid-temperature variations became pronounced. These results indicate that the proposed approach is useful as practical design-exploration for identifying candidate pin-fin heat sink configurations under high-Reynolds-number conditions.