Hydrodynamic characterization of Gyroid, Diamond and Split-P Triply Periodic Minimal Surfaces as porous medium

Triply Periodic Minimal Surfaces are gaining significant attention as engineered porous media for applications in fluid transport and thermal management systems due to their unique geometric properties. However, accurate prediction of pressure drop across TPMS structures remains a challenge, particularly in transitioning flow regimes. This study addresses this gap by investigating the hydrodynamic behavior of Gyroid, Diamond, and Split-P geometries using computational fluid dynamics simulations across a range of Reynolds numbers, from viscous to weakly inertial regimes. Two modeling frameworks were utilized: the Ergun equation, commonly used for packed beds, and the Darcy-Forchheimer equation, enhanced with newly developed correlations for permeability and inertial drag factor. An adapted Kozeny-Carman equation was also applied for permeability prediction. The developed correlations, expressed as power-law functions of porosity and tortuosity, demonstrated high accuracy, with relative errors below 10 % for most configurations and a maximum error of 21 % for the more complex Split-P1 geometry. Validation in larger-scale geometries, such as pipes filled with TPMS, confirmed the scalability and robustness of the proposed models, even when accounting for variations in the hydraulic diameter due to wall effects. The results demonstrate the superior suitability of the Darcy-Forchheimer equation with the developed permeability and inertial drag factor models, particularly for complex geometries like Split-P. In contrast, the Ergun equation fails to accurately predict pressure drop across the investigated TPMS, underscoring its limitations for these geometries. Furthermore, while the inclusion of tortuosity in the correlations provides additional detail, it does not offer significant advantages over the simpler permeability-porosity relation for any of the investigated TPMS, making the latter a more practical choice for design and optimization applications in systems such as heat sinks and porous flow devices