Electrical Tortuosities of Porous Structures Based on Triply Periodic Minimal Surfaces and Honeycombs for Power-to-Heat Systems

Power-to-heat (P2H) systems offer an efficient solution for decarbonization by facilitating the integration of renewable energy into the industrial, heating, and transport sectors. Its key requirements include high thermal efficiency and an appropriate electrical resistivity to meet application-specific electrical needs. When designing P2H systems, materials and electrical boundary conditions are often limited by application-specific requirements, whereas geometric structures offer high degrees of freedom. While thermal design calculations are often straightforward due to a variety of available Nusselt and pressure loss correlations, simplified design pathways, particularly for porous structures, are lacking in electrical design. Given the wide range of geometric degrees of freedom for porous structures and the fact that detailed modeling involves substantial computational effort, this work employed electrical tortuosity to capture and correlate the geometry-dependent impacts on the effective electrical resistance in a compact way. Honeycomb and triply periodic minimal surface (TPMS)-based structures were selected for this purpose, as they are characterized by high specific surfaces, allowing for high total heat transfer coefficients. The results show that the effective electrical resistance of both TPMS and honeycomb structures can be adjusted by the geometric structure. It was found that the electrical tortuosities of the investigated TPMS structures are nearly identical, while honeycomb structures show slightly higher values. Furthermore, the electrical tortuosity is mainly a function of the void fraction and does not change with the specific surface when the void fraction is kept constant. Finally, correlations for electrical tortuosity depending on geometric parameters with a mean error below 5% are derived for the first time, thereby providing a basis for simplified and computationally efficient electrical design calculations for P2H systems.