| Summary: | Fin arrays are widely utilized in many engineering applications, such as heat exchangers and micro-post reactors, for higher level of fluid–solid contacts. However, high fluid pressure loss is reportedly the major drawback of fin arrays and a challenge for pumping supply, particularly at micro-scales. Previous studies also indicate that fin shapes, spacing and alignment play an important role on the overall pressure losses. Therefore, we present a numerical tool to minimize pressure losses, considering the geometrical aspects related to fin arrays. In this regard, a density-based topology optimization approach is developed based on the pseudo-spectral scheme and Brinkman penalization in 2D periodic domains. Discrete sensitives are derived analytically and computed at relatively low cost using a factorization technique. We study different test cases to demonstrate the flexibility, robustness and accuracy of the present tool. In-line and staggered arrays are considered at various Reynolds numbers and fluid–solid volume fractions. The optimal topologies interestingly indicate a pressure loss reduction of nearly <inline-formula> <math display="inline"> <semantics> <mrow> <mn>53.6</mn> <mo>%</mo> </mrow> </semantics> </math> </inline-formula> compared to circular fins. In passive optimization test examples, the added solid parts reduced pressure loss of a circular fin (<inline-formula> <math display="inline"> <semantics> <mrow> <mn>9</mn> <mo>%</mo> </mrow> </semantics> </math> </inline-formula>) by eliminating the flow separation and filling the wake region.
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