Homogenization-based optimization of wall thickness distribution for TPMS two-fluid heat exchangers

TL;DR

This work addresses improving TPMS-based two-fluid heat exchangers by optimizing wall thickness distributions using a homogenization-based topology optimization framework. A two-tier modeling approach is developed: an effective porous-media model that captures wall–fluid heat exchange via an effective coefficient $h^*$ and a Brinkman–Forchheimer flow description, and a high-fidelity Navier–Stokes/energy solver used to compute properties and validate the homogenized predictions. Wall thickness is controlled through a level-set parameter $c$ (and its spatial field $ ilde{oldsymbol{ ho}}$ via filtering), with effective properties $oldsymbol{ ext{alpha}}$, $oldsymbol{ extbeta}$, $oldsymbol{h}^*$, and conductivities interpolated as functions of $ ilde{oldsymbol{ ho}}$ for optimization. The optimization minimizes $J=-Q_{ ext{ave}}+w~ ext{Δ}p_{ ext{ave}}$ using MMA across multiple $w$ values, followed by dehomogenization and full-scale simulations that show up to a 12.2% improvement in the PEC and a 4.16% increase in volumetric heat density, validating the approach and highlighting enhanced utilization of the HX core. The framework significantly reduces computational cost and is extendable to other TPMS types and flow configurations, with future work focusing on improved predictive accuracy and experimental validation.

Abstract

Triply Periodic Minimal Surface (TPMS) structures are attracting growing attention as promising geometries for next-generation high-performance heat exchangers (HXs), due to their continuous flow paths and high surface-area-to-volume ratio that enhance heat transfer performance. Among these, graded TPMS structures with spatially varying thickness have emerged as a potential means to further improve performance. This study proposes an optimization method of wall thickness distribution for TPMS HXs based on an effective porous media model, which allows accurate performance prediction while significantly reducing computational cost. The proposed method is applied to a gyroid two-fluid HX aiming to improve the thermal-hydraulic performance. Furthermore, full-scale numerical simulations of the optimized-thickness design show a 12.2% improvement in the performance evaluation criterion (PEC) compared to the uniform-thickness design. The improvement is primarily attributed to the optimized non-uniform wall thickness, which directs more flow toward the core ends and enhances velocity uniformity. As a result, heat transfer is enhanced at the core ends, leading to more effective use of the entire HX core and improved overall thermal performance.

Figures (36)

• Figure 1: Gyroid unit cell with constant parameter $c$
• Figure 2: Gyroid structure with spatially varying $c$
• Figure 4: Schematic of heat exchange between fluid $i$ and the wall within a representative volume element (RVE)
• Figure 5: Boundary conditions applied to the RVE used for computing effective properties $\alpha$, $\beta$, and $h^*_i$
• Figure 6: Computational domain and boundary conditions employed for numerical model validation