This paper uses a multi-objective topology optimization method for thermal-fluid problems applied to the design of fins for primary use in plate-fin heat exchangers. The presented method was derived to obtain optimal fin topology for a wide range of design parameters and constraints, with the primary focus on aerospace applications. The performance of obtained fin topologies is evaluated based on the heat transfer and flow energy-loss objective functions. A level-set-based optimization is used, in which the sensitivity to the change in topology toward an optimal solution is obtained by the adjoint method. To reduce computational costs and allow for higher complexity designs, the design domain is reduced to a small two-dimensional (2-D) section of the overall fin structure. A three-dimensional (3-D) model is generated using 2-D topology optimization results, and the effects of model differences are analyzed. The results for various combinations of objective functions show similarity between the 2-D and 3-D models. Topologies consisting of multiple fins converge to a result that exhibits a novel cyclic motion of the topology, by which individual fins or segments of multiple fins cycle in a specific order. This behavior maintains the converged value of objective functions between cycles, indicating similarity among obtained topologies.

本文针对热流体问题采用了一种多目标拓扑优化方法，该方法适用于板翅式换热器中主要使用的翅片设计。推导提出的方法以针对各种设计参数和约束条件获得最佳的鳍形拓扑，主要侧重于航空航天应用。基于传热和流动能量损失目标函数评估获得的鳍形拓扑的性能。使用基于级别集的优化，其中通过伴随方法获得对拓扑向最佳解决方案的更改的敏感性。为了减少计算成本并允许进行更高复杂度的设计，将设计域缩小为整个鳍结构的较小的二维（2-D）部分。使用2-D拓扑优化结果生成三维（3-D）模型，并分析模型差异的影响。目标函数的各种组合的结果显示了2-D模型和3-D模型之间的相似性。由多个鳍片组成的拓扑收敛到一个结果，该结果显示出该拓扑结构的一种新颖的循环运动，通过该运动，单个鳍片或多个鳍片的片段以特定顺序循环。这种行为保持了循环之间目标函数的收敛值，表明所获得拓扑之间的相似性。单个鳍或多个鳍的段以特定顺序循环。这种行为保持了循环之间目标函数的收敛值，表明所获得拓扑之间的相似性。单个鳍或多个鳍的段以特定顺序循环。这种行为保持了循环之间目标函数的收敛值，表明所获得拓扑之间的相似性。