DualMS: Implicit Dual-Channel Minimal Surface Optimization for Heat Exchanger Design

TL;DR

DualMS directly optimizes the separating surface between two fluids in freeform heat exchangers by eschewing TPMS tilings. It uses a two-stage pipeline: first, a dual-flow skeleton optimization via a constrained connected maximum cut to maximize interface area, then a minimal-surface refinement realized as a neural implicit space classifier with a total-variation regularization grounded in geometric measure theory. The method yields flexible surface topologies and improved flow dynamics, achieving lower pressure drops while preserving heat-transfer performance relative to TPMS baselines under equivalent material cost. CFD and classical-minimal-surface comparisons, along with ablations and fabrication demonstrations, validate the practical potential of DualMS for efficient, freeform heat exchanger design.

Abstract

Heat exchangers are critical components in a wide range of engineering applications, from energy systems to chemical processing, where efficient thermal management is essential. The design objectives for heat exchangers include maximizing the heat exchange rate while minimizing the pressure drop, requiring both a large interface area and a smooth internal structure. State-of-the-art designs, such as triply periodic minimal surfaces (TPMS), have proven effective in optimizing heat exchange efficiency. However, TPMS designs are constrained by predefined mathematical equations, limiting their adaptability to freeform boundary shapes. Additionally, TPMS structures do not inherently control flow directions, which can lead to flow stagnation and undesirable pressure drops. This paper presents DualMS, a novel computational framework for optimizing dual-channel minimal surfaces specifically for heat exchanger designs in freeform shapes. To the best of our knowledge, this is the first attempt to directly optimize minimal surfaces for two-fluid heat exchangers, rather than relying on TPMS. Our approach formulates the heat exchange maximization problem as a constrained connected maximum cut problem on a graph, with flow constraints guiding the optimization process. To address undesirable pressure drops, we model the minimal surface as a classification boundary separating the two fluids, incorporating an additional regularization term for area minimization. We employ a neural network that maps spatial points to binary flow types, enabling it to classify flow skeletons and automatically determine the surface boundary. DualMS demonstrates greater flexibility in surface topology compared to TPMS and achieves superior thermal performance, with lower pressure drops while maintaining a similar heat exchange rate under the same material cost.

Figures (15)

• Figure 1: Given the design domain and boundary conditions and of the heat exchanger (a), DualMS initializes an undirected graph (b) derived from centroidal Voronoi tessellations and the given flow field. The method then optimizes the dual flow skeletons by solving a constrained connected maximum cut problem on the graph (c), and then optimizes a minimal surface (d) to effectively partition the domain into two distinct flow channels (e).
• Figure 2: An overview of our network architecture. These dual skeleton sampling points are encoded by random Fourier feature (RFF) mapping, capturing high-frequency spatial information. The processed features are passed through a multi-layer perceptron (MLP) to decode the scalar field, where the sign of the output determines the spatial classification of points.
• Figure 3: The evolution of spatial classification with increasing training iterations.
• Figure 4: Data augmentation with Gaussian noise. (a) Overfitting without noise, resulting in a decision boundary tightly clinging to the skeleton points. (b) Gaussian noise with standard deviation $\sigma=0.05$, creating a narrow “tube-like” region. (c) Gaussian noise with standard deviation $\sigma=0.08$, significantly broadening the neighborhood.
• Figure 5: Ablation study on the smoothing term loss for minimal surface generation. Result with the smoothness loss. The mean curvature of (b) is more uniform and closer to 0.