Flow-priority optimization of additively manufactured variable-TPMS lattice heat exchanger based on macroscopic analysis

Heat exchangers incorporating triply periodic minimal surface (TPMS) lattice structures have attracted considerable research interest because they promote uniform flow distribution, disrupt boundary layers, and improve convective heat-transfer performance. However, from the perspective of forming a macroscopic flow pattern optimized for heat-exchange efficiency, a uniform lattice is not necessarily the optimal configuration. This study initially presents a macroscopic modeling approach for a two-fluid heat exchanger equipped with a TPMS Primitive lattice. The macroscopic flow analysis is conducted based on the Darcy–Forchheimer theory. Under the assumption that heat is transferred solely at the interface between the fluid and the TPMS walls, a macroscopic heat-transfer model is developed using a volumetric heat-transfer coefficient, which serves as an artificial property characterizing the unit-volume heat-transfer capability. To regulate the relative dominance of the hot and cold flows-effectively, the channel widths-within the heat exchanger, we adopt the isosurface threshold of the Primitive lattice as the design variable and construct an optimization scheme for the lattice distribution using the previously described macroscopic model. The optimization is subsequently carried out for a planar heat exchanger where the hot and cold fluids each follow U-shaped flow trajectories. The optimal solution was verified, and its validity was examined through detailed geometric analysis and experiments conducted using metal LPBF. The optimal solution derived from the macroscopic model also demonstrated a clear performance advantage over the uniform lattice in the experimental results. The optimal solution obtained from the macroscopic model also demonstrated a clear performance improvement over the uniform lattice, with an average enhancement of 28.7% in the experimental results.

💡 Research Summary

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This paper presents a comprehensive framework for optimizing the flow‑priority distribution in a two‑fluid heat exchanger that incorporates a triply periodic minimal surface (TPMS) lattice, specifically the Primitive surface, using a macroscopic analysis approach. The authors first develop a macroscopic model that treats the TPMS lattice as a porous medium. Fluid flow is described by the Darcy–Forchheimer law, and the Brinkman–Forchheimer equation is employed to capture both viscous and inertial effects within the porous matrix. Heat transfer is modeled by introducing a volumetric heat‑transfer coefficient h, which represents the rate of thermal exchange per unit volume between the solid lattice walls and each fluid, thereby avoiding explicit resolution of the fluid–solid interface.

Effective material properties—permeability κ, drag coefficient β, effective thermal conductivities λ for the hot fluid, cold fluid, and solid, and the volumetric heat‑transfer coefficients h—are obtained through representative volume element (RVE) homogenization. In each RVE, a single period of the Primitive TPMS is simulated under prescribed pressure gradients (to compute κ and β) and temperature gradients (to compute λ). The volumetric heat‑transfer coefficient is derived by imposing a temperature difference between fluid inlet and solid wall and evaluating the resulting heat flux, linking it directly to the average inlet velocity.

The design variable is the isosurface threshold C of the Primitive TPMS function cos(2πlx)+cos(2πly)+cos(2πlz)=C. Varying C shifts the solid–fluid partition, thereby adjusting the thickness of the hot‑fluid and cold‑fluid channels. C = 0 corresponds to equal flow resistance for both streams; C > 0 enlarges the hot‑fluid channel (giving it flow priority), while C < 0 enlarges the cold‑fluid channel. The optimization problem seeks the value of C that maximizes overall heat‑exchange effectiveness, defined as the temperature difference between inlet and outlet streams. A gradient‑based optimizer iteratively evaluates the macroscopic model for different C values, updating C until the objective converges.

The methodology is applied to a planar heat exchanger in which both fluids follow U‑shaped counter‑flow paths—a configuration that introduces significant design challenges because the two streams intersect and reverse direction. The optimal solution features a non‑uniform distribution of the TPMS lattice: the hot‑fluid side possesses a wider passage, while the cold‑fluid side is more constricted, effectively balancing pressure drop and heat‑transfer area. This configuration was fabricated using metal laser powder‑bed fusion (LPBF) and experimentally tested. Pressure drop measurements and temperature profiling demonstrated an average 28.7 % improvement in heat‑exchange performance compared with a baseline design employing a uniform TPMS lattice.

Further validation was performed using detailed CFD simulations and structural analyses, confirming that the macroscopic model accurately predicts the flow fields, temperature distributions, and mechanical integrity of the optimized lattice. The study thus validates the macroscopic approach as a low‑cost, high‑fidelity tool for guiding the design of additively manufactured TPMS heat exchangers.

Key contributions include: (1) a parametric representation of TPMS geometry via the isosurface threshold C, enabling straightforward control of flow priority; (2) integration of Darcy–Forchheimer flow modeling with a volumetric heat‑transfer coefficient to capture coupled fluid‑solid heat exchange without resolving microscale geometry; (3) demonstration that macroscopic homogenization can provide reliable effective properties for optimization; and (4) experimental verification that the optimized, variable‑density TPMS lattice yields a substantial performance gain over uniform lattices.

Future work is suggested in extending the framework to multi‑objective optimization (e.g., simultaneously minimizing pressure loss, maximizing heat transfer, and ensuring structural strength), incorporating turbulent flow regimes, exploring other TPMS families such as Gyroid or Schwarz‑D, and applying the method to more complex three‑dimensional heat‑exchanger topologies.