Optimization of Higher-Order Harmonic Surface Tessellations for Additively Manufactured Air-to-Air Heat Exchangers

Air-to-air heat exchangers are vital for energy recovery and thermal management but often suffer from reduced effectiveness, high pressure losses, and increased pumping power in conventional designs. Advances in additive manufacturing have enabled nature-inspired geometries, such as lattice and triply periodic minimal surface (TPMS) structures, which enhance heat transfer through complex first-order surfaces but frequently cause excessive pressure drops. This study proposes an optimized higher-order harmonic heat-transfer surface tessellation developed through an optimization framework integrating analytical and numerical methods. The goal is to improve the overall thermal-hydraulic performance of the heat exchanger over a range of operating conditions. Results of sensitivity analysis show that secondary surface modification of this type can yield significant increase in the effectiveness reaching up to 70% although with associated increase in the pressure drop. The secondary surface wave frequency was found to be a more important control parameter than the amplitude in achieving high thermal-hydraulic performance. Additionally, we show that the optimized second order harmonic-type structure achieved relatively higher effectiveness and lower pressure-drop than the gyroid structure in the turbulent flow regime for . Although the gyroid TPMS structure had relatively higher effectiveness in the laminar and weakly turbulent flow regime, the associated pressure drop was found to be significantly higher than that of the harmonic-type structure. While the gyroid structure had significantly higher heat transfer efficiency with an average Nusselt number about 5.2 times that the harmonic-type structure, the corresponding flow resistance was likewise observed to be significantly higher on average, about 8.4 times higher in the laminar flow regime and about 1.87 times higher in the turbulent flow regime. The London area goodness factor (AGF) was used to assess the overall thermal-hydraulic performance of both architectures which showed that the harmonic-type structure performed better in the laminar flow regime ( ) which had an average AGF of about 1.72 times the AGF of the gyroid structure and reaching up 2.18 times the gyroid’s AGF when . However, the gyroid structure outperformed the harmonic-type structure in the turbulent flow regime. The findings from this study demonstrate a balanced pathway for additively manufacturable, high-performance air-to-air heat exchangers, offering compact, energy-efficient solutions for applications in building ventilation, aerospace, and electronics cooling.