Multiobjective shape optimization of TPMS-based compact heat exchangers through RBF-FD meshless simulations

Triply periodic minimal surfaces (TPMS) are increasingly recognized in various engineering fields for their advantageous properties. In thermal applications, TPMS-based heat exchangers can achieve superior performance when designed correctly. Therefore, precise characterization of these structures is crucial to fully exploit their potential benefits. In this paper we describe a general procedure for the 3D geometric parameterization and shape optimization of TPMS where the objectives are the maximization of the heat transfer rate and the minimization of the pressure drop. The eigenmodes of the surface Laplacian are employed to parameterize the complex shape of the TPMS, while the evaluation of heat transfer and fluid flow performance is carried out by means of the Radial Basis Function-generated Finite Difference (RBF-FD) meshless method. The flexibility of this numerical method adapts seamlessly with the intricate geometry of TPMS structures, allowing for accurate and automated simulations. Moreover, the robustness of this approach is a key requirement for shape optimization problems where a large number of simulations are required for different combinations of the design variables. Since TPMS-based heat exchangers are characterized by a periodic repetition in space of a basic cell structure, periodic and fully developed conditions for both fluid flow and heat transfer can be employed to model the bulk of the exchanger, whereas boundary effects are limited to few modules from the inlet. The computational domain is therefore reduced to a single periodic module, with great advantages in terms of accuracy and computational effort. The optimization results are presented in the form of Pareto fronts for different flow parameters and different choices of the design space, highlighting the set of optimal, i.e., non-dominated, designs in terms of Nusselt number and friction factor.