Two Dimensional Vortex Shedding from a Rotating Cluster of Cylinders

Document Type : Regular Article

Authors

1 CSIR, Department of Defence, and Security, Pretoria, Gauteng, 0001, South Africa

2 Department of Mechanical, Industrial, and Aeronautical Engineering, University of the Witwatersrand, Johannesburg, 2000, South Africa

10.47176/jafm.16.11.1773

Abstract

The dynamics of two-dimensional vortex shedding from a rotating cluster of three cylinders was investigated using Computational Fluid Dynamics (CFD) and Dynamic Mode Decomposition (DMD). The cluster was formed from three circles with equal diameters in mutual contact and allowed to rotate about an axis passing through the cluster centroid. While immersed in an incompressible fluid with Reynolds number of 100, the cluster was allowed to rotate at non-dimensionalised rotation rates (Ω) between 0 and 1. The rotation rates were non-dimensionalised using the free-stream velocity and the cluster characteristic diameter, the latter being equal to the diameter of the circle circumscribing the cluster. CFD simulations were performed using StarCCM+. Dynamic Mode Decomposition based on the two-dimensional vorticity field was used to decompose the field into its fundamental mode-shapes. It was then possible to relate the mode-shapes to lift and drag. Transverse and longitudinal mode-shapes corresponded to lift and drag, respectively. Lift–drag polars showed a more complex pattern dependent on Ω in which the flow fields could be classified into three regimes: Ω less than 0.3, greater than 0.5, and between 0.3 and 0.5. In general, the polars formed open curves in contrast to those of static cylinders, which were closed. However, some cases, such as Ω = 0.01, 0.22, and 0.28, formed closed curves. Whether a lift-drag polar was closed or open was deduced to be determined by the ratio of Strouhal numbers calculated using lift and drag time series, with closed curves forming when the ratio is an integer.

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Bai, X., Ji, C., Grant, P., Phillips, N., Oza, U., Avital, E. J., & Williams J. J. R. (2021). Turbulent flow simulation of a single-blade magnus rotor. Advances in Aerodynamics, 3. https://doi.org/10.1186/s42774-021-00068-9##
Carmo, B. S., Sherwin, S. J., Bearman, P. W., & Willden, R. H. J. (2008). Wake transition in the flow around two circular cylinders in staggered arrangements. Journal of Fluid Mechanics, 597, 1–29. https://doi.org/10.1017/S0022112007009639##
Chen, W., Ji, C., Alam, M. M., Williams, J., & Xu, D. (2020). Numerical simulations of flow past three circular cylinders in equilateral-triangular arrangements. Journal of Fluid Mechanics, 891, A14. https://doi.org/10.1017/jfm.2020.124##
Figueroa, A., Cuevas, S., & Ramos, E. (2017). Lissajous trajectories in electromagnetically driven vortices. Journal of Fluid Mechanics, 815, 415–434. https://doi.org/10.1017/jfm.2017.55##
Inoue, T., Rheem, C. K., Kyo, M., Sakaguchi, H., & Matsuo, M. Y. (2013). Experimental study on the characteristics of VIV and whirl motion of rotating drill pipe. ASME 2013 32nd International Conference on Ocean, Offshore and Arctic Engineering. https://doi.org/10.1115/OMAE2013-10182 ##
Kutz, J. N., Brunton, S. L., Brunton, B. W., & Proctor, J. L. (2016). Dynamic mode decomposition. Society for Industrial and Applied Mathematics. https://doi.org/10.1137/1.9781611974508##
Lienhard, J. N. (1966). Synopsis of lift, drag, and vortex frequency data for rigid circular cylinders (Vol. 300). Pullman, WA: Technical Extension Service, Washington State University. Retrieved May 11, 2023, from https://www.uh.edu/engines/vortexcylinders.pdf##
Matharu, P. S., Hazel, A. L., & Heil M. (2021). Spatio-temporal symmetry breaking in the flow past an oscillating cylinder. Journal of Fluid Mechanics, 918, A42. https://doi.org/10.1017/jfm.2021.358##
Mittal, S., & Kumar, B. (2003). Flow past a rotating cylinder. Journal of Fluid Mechanics, 476, 303–334. https://doi.org/10.1017/S0022112002002938##
Moffatt, H. (2021). Some topological aspects of fluid dynamics. Journal of Fluid Mechanics, 914, P1. https://doi.org/10.1017/jfm.2020.230##
Phillips, T. S., & Roy, C. J. (2014). Richardson extrapolation-based discretization uncertainty estimation for computational fluid dynamics. Journal of Fluids Engineering, 136.  https://doi.org/10.1115/1.4027353##
Ping, H., Zhu, H., Zhang, K., Zhou, D., Bao, Y., Xu, Y., & Han, Z. (2021). Dynamic mode decomposition based analysis of flow past a transversely oscillating cylinder. Physics of Fluids, 33, 033604. https://doi.org/10.1063/5.0042391##
Pook, L. P. (2011). Understanding pendulums: A brief introduction. Springer Netherlands. https://doi.org/10.1007/978-94-007-1415-1##
Roache, P. J. (1994). Perspective: A method for uniform reporting of grid refinement studies. Fluids Enginee,r 116, 405–413. https://doi.org/10.1115/1.2910291##
Roshko, A. (1954). On the development of turbulent wakes from vortex streets. California Institute of Technology. Retrieved May 25, 2023, from https://ntrs.nasa.gov/citations/19930092207##
Schmid, P. J. (2010, 8). Dynamic mode decomposition of numerical and experimental data. Journal of Fluid Mechanics, 656, 5–28. https://doi.org/10.1017/S0022112010001217##
Schulmeister, J. C., Dahl, J. M., Weymouth, G. D., & Triantafyllou, M. S. (2017). Flow control with rotating cylinders. Journal of Fluid Mechanics, 825, 743–763. https://doi.org/10.1017/jfm.2017.395##
Sierra, J., Fabre, D., Citro, V., & Giannetti, F. (2020). Bifurcation scenario in the two-dimensional laminar flow past a rotating cylinder. Journal of Fluid Mechanics, 905, A2. https://doi.org/10.1017/jfm.2020.692##
Sumner, D., Price, S. J., & Paidoussis, M. P. (2000). Flow-pattern identification for two staggered circular cylinders in cross-flow. Journal of Fluid Mechanics, 411, 263–303. https://doi.org/10.1017/S0022112099008137##
Taira, K., Brunton, S. L., Dawson, S. T. M., Rowley, C. W., Colonius, T., McKeon, B. J., Schmidt, O. T., Gordeyev, S., Theofilis, V., & Ukeiley, L. S. (2017). Modal analysis of fluid flows: An overview. AIAA Journal, 55, 4013– 4041. https://doi.org/10.2514/1.J056060##
Taira, K., Hemati, M. S., Brunton, S. L., Sun, Y., Duraisamy, K., Bagheri, S., Dawson, S. T. M., & Yeh, C. A. (2020). Modal analysis of fluid flows: Applications and outlook. AIAA Journal, 58, 998–1022. https://arc.aiaa.org/doi/10.2514/1.J058462##
Wang, H., Yan, Y. H., Chen, C. M., Ji, C. N., & Zhai, Q. (1996). Numerical investigation on vortex-induced rotations of a triangular cylinder using an immersed boundary method. China Ocean Engineering, 33, 723–733. https://doi.org/10.1007/s13344-019-0070-0##
Williamson, C. H. K., & Roshko A. (1988). Vortex formation in the wake of an oscillating cylinder. Journal of Fluids and Structures, 2, 355–381. https://doi.org/10.1016/S0889-9746(88)90058-8##
Zdravkovich, M. M. (1977). Review—review of flow interference between two circular cylinders in various arrangements. Journal of Fluids Engineering, 99, 618–633. https://doi.org/10.12691/ajme-5-3-3.##