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. 2021 Feb 10;11:3517. doi: 10.1038/s41598-021-83035-0

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© The Author(s) 2021

Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

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Predicted bulk drag coefficient as a function of the streamwise spacing $s_{x}$ and spanwise spacing $s_{y}$ between cylinders compared to the cylinder diameter, d. The diagram shows lines of constant volumetric porosity n. Three examples of regularly spaced configurations with constant porosity of $n = 0.8$ but varying streamwise/spanwise spacing are given. Flow direction relative to the arrays is indicated by a blue arrow (from left to right). The diagram shows that given a constant porosity, higher drag values can be obtained for smaller spanwise spacings $s_{y}$ and longer streamwise spacings $s_{x}$ .