RBF-FD meshless simulation of 3D fully developed flow and heat transfer in triply periodic minimal surfaces

Triply periodic minimal surfaces (TPMS) are gaining significant attention in many engineering applications due to their favourable properties. With reference to thermal applications, TPMS-based heat exchangers can deliver superior performance if properly designed. The accurate characterization of these structures is therefore essential to leverage such potential advantage. In this paper we investigate the heat transfer and fluid flow properties of three common TPMS, i.e., Fisher Koch S, gyroid and Schwarz D, by using a Radial Basis Function-generated Finite Difference (RBF-FD). The geometric flexibility of this numerical method fits perfectly with the geometric complexity of the TPMS structures, enabling automatic and accurate fluid flow simulations. An important novelty of this paper is the use of thermally developed formulations for the proper estimation of the heat transfer over periodic structures repeating in the three spatial directions, which is the case of TPMS-based heat exchangers. Fully developed conditions for both fluid flow and heat transfer allow the computational domain to be reduced to a single periodic module, with great advantages in terms of accuracy and computational effort. In order to provide a sufficiently thorough characterization in the laminar and steady-state regime, two types of thermal boundary conditions are employed, i.e., prescribed wall temperature and prescribed wall heat flux, and two Prandtl numbers are considered, i.e., Pr=0.71 (air) and Pr=6.97 (water). Very good agreement with literature results is found in terms of friction factor for all the considered structures, and also in terms of Nusselt number for the Fisher Koch S surface. However, some differences are obtained for the gyroid and the Schwarz D surfaces, and the reasons for these discrepancies are discussed.