A machine-learning based approach for multi-scale optimisation of heat exchangers with lattice-like topology

In this study, we present a novel approach for the multi-scale simulation and optimisation of Micro Channel Heat Exchangers (MCHX) with lattice-like topology. By treating the Triply Periodic Minimal Surface (TPMS) lattice as an equivalent porous medium, the model enables fast and accurate simulations of full-scale 3D MCHX for industrial applications without requiring high-resolution meshing or computationally demanding high-fidelity CFD runs. Micro- and meso-scale effects are accounted for thanks to variable permeability, Forchheimer, and heat transfer coefficients, modelled as non-linear functions of local flow conditions and lattice geometry. These closure relationships are inferred using a multi-fidelity machine learning model, trained on a combination of low- and high-fidelity CFD data. This allows the model to capture the effects of fluid flow phenomena occurring at the smallest scale (such as boundary effects and head pressure losses) without the need to rely on high-fidelity simulations. The presented framework offers a favourable balance between accuracy and cost, enabling optimisation within realistic industrial timelines. As a demonstration, the proposed methodology is applied to the optimisation of a heat exchanger used by Rolls-Royce Plc for the thermal management of high-power electronics in aeronautical applications. In particular, three representative configurations are extracted from the Pareto front, respectively optimised for maximum heat transfer, minimum pressure drop, and a balanced trade-off, thus demonstrating the flexibility of the proposed method in targeting different design priorities.