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Effects of annulation on low Reynolds number flows over an orthocone

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Abstract

This study numerically examines the influences of transverse annulation around a cone surface on the characteristics of a flow over an orthocone. This work is inspired by Spyroceras, a fossilized genus of nautiloid cephalopods from the Paleozoic era, whose method of locomotion is understudied. As a baseline case, a flow over a smooth orthoconic model with a blunt cone end is investigated numerically at Reynolds numbers from 500 to 1500. As Reynolds increases, two different shedding mechanisms—hairpin-vortex wake and spiral-vortex wake—are captured. We notice that an introduction of annulation over the cone surface changes the critical Reynolds number for the transition of the shedding mechanism. The dominant shedding frequency increases with the Reynolds number for the smooth and annulated cone flows. Moreover, the annulation reduces the dominant frequency for the same Reynolds number and increases the time-averaged drag coefficient. Modal decompositions—Proper Orthogonal Decomposition (POD) and Spectral Proper Orthogonal Decomposition (SPOD)—are used to capture the coherent structures and their oscillating frequencies. We have captured modes corresponding to the hairpin-vortex wake and spiral-vortex wake shedding mechanisms. Comparing the leading POD modes for the smooth and the annulated cone flows, we find that the annulation can reduce the twisting effects of the coherent structures in the wake. Additionally, we find that the SPOD analysis can identify modes presenting both hairpin-vortex wake and spiral-vortex wake in one flow condition as leading modes, while the POD leading modes only reveal one shedding mechanism in each flow.

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Acknowledgements

This work is supported by Syracuse University in the form of a Collaboration for Unprecedented Success and Excellence grant to Sun, Green, and Ivany, and by Syracuse Office of Undergraduate Research and Creative Engagement grants to Fernandez and Seh. We acknowledge the Research Computing Center at Syracuse University providing computational resources. We also thank Lisa Amati at the New York State Museum for a loan of specimens from the Invertebrate Paleontology collection.

Funding

The Collaboration for Unprecedented Success and Excellence Grant at Syracuse University; and the Syracuse Office of Undergraduate Research and Creative Engagement.

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Authors and Affiliations

  1. Department of Mechanical and Aerospace Engineering, Syracuse University, Syracuse, 13244, NY, USA

    Mitesh Thakor, Kee Horng Seh, Sareta R. Gladson & Yiyang Sun

  2. Department of Earth and Environmental Sciences, Syracuse University, Syracuse, 13244, NY, USA

    Martin L. Fernandez & Linda C. Ivany

  3. Department of Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, 55455, MN, USA

    Melissa Green

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  1. Mitesh Thakor
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Correspondence to Mitesh Thakor.

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Authors’ contributions

Conceptualization, YS, MG, and LI; methodology, YS, SG, MG, and MT; software, YS; validation, KS, MT, and YS; formal analysis, MT, KS, and SG; investigation, YS, MG, and LI; resources, YS and LI; data curation, MT, MLF, and KS; writing original draft preparation, MT, KS, and YS; writing review and editing, Y.S. and M.T.; visualization, MT, YS, and KS; supervision, YS; project administration, YS; funding acquisition, YS, MG, and LI.

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Data are publicly available through the publication.

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Communicated by Ashok Gopalarathnam.

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Thakor, M., Seh, K.H., Gladson, S.R. et al. Effects of annulation on low Reynolds number flows over an orthocone. Theor. Comput. Fluid Dyn. 37, 357–374 (2023). https://doi.org/10.1007/s00162-023-00649-y

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