Abstract—
Flow structures around a wavy square cylinder with a perturbation wavelength of 5.6D are investigated using large eddy simulation at the Reynolds number of 23 500. The detailed force characteristics and wake flow structures of the wavy square cylinder are captured and compared with a square cylinder. Under the effect of wavy leading edge up to 27% and 98% reduction in the mean drag and the lift fluctuations are achieved, respectively. The 3D mean flow field implies a high shear flow between node and saddle positions, which is associated with the generation of additional streamwise and vertical vortex pairs. These vortex structures are responsible for the three-dimensionality of the wake flow behind the wavy square cylinder. The instantaneous flow patterns suggest that the staggered pattern of von Kármán vortex shedding is suppressed and replaced by symmetric vortex shedding into the near wake region of the wavy square cylinder. This symmetric vortex structure in the near wake plays a role in preventing the upper and lower shear layers from interacting with each other. The time–frequency analysis exhibits a reduction in the dominating vortex shedding frequency for the case of wavy square cylinder, indicating a relatively steady wake flow. This can be attributed to the vortex dislocation behind the wavy square cylinder. In the range of high frequencies, small streaks associated with small-scale fluctuations are enhanced by the wavy leading edge. The present study suggests that the perturbation wavelength obtained from the wavelength of Mode A instability at laminar flow regime can be served as a basis for flow control in turbulent flow regime.
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REFERENCES
Chen, Y.J. and Shao, C.P., Suppression of vortex shedding from a rectangular cylinder at low Reynolds numbers, J. Fluids Struct., 2013, vol. 43, no. 7, pp. 15–27.
Chauhan, M.K., Dutta, S., and Gandhi, B.K., Wake flow modification behind a square cylinder using control rods, J. Wind Eng. Ind. Aerodyn., 2019, vol. 184, pp. 342–361.
Kim, J. and Choi, H., Distributed forcing of flow over a circular cylinder, Phys. Fluids, 2005, vol. 17, no. 3, pp. 35–35.
Rathakrishnan, E., Effect of splitter plate on bluff body drag, AIAA J., 1999, vol. 37, no. 9, pp. 1125–1126.
Lam, K. and Lin, Y.F., Effect of wavelength and amplitude of a wavy cylinder in cross flow at low Reynolds numbers, J. Fluid Mech., 2009, vol. 620, pp. 195–220.
Williamson, C.H.K., Vortex dynamics in cylinder wake, Annu. Rev. Fluid Mech., 1996, vol. 28, pp. 477–539.
Robichaux, J., Balachandar, S., and Vanka, S.P., Three-dimensional Floquet instability of the wake of square cylinder, Phys. Fluids, 1999, vol. 11, no. 3, pp. 560–578.
Naghib-Lahouti, A., Lavoie, P., and Hangan, H., Wake instabilities of a blunt trailing edge profiled body at intermediate Reynolds numbers, Exp. Fluids, 2014, vol. 55, no. 7, p. 1779.
Luo, S.C., Tong, X.H., and Khoo, B.C., Transition phenomena in the wake of a square cylinder, J. Fluids Struct., 2007, vol. 23, pp. 227–248.
Ryan, K., Thompson, M.C., and Hourigan, K., Three-dimensional transition in the wake of elongated bluff bodies, J. Fluid Mech., 2005, vol. 538, pp. 1–29.
El-Gammal, M. and Hangan, H., Three-dimensional wake dynamics of a blunt and divergent trailing edge airfoil, Exp. Fluids, 2008, vol. 44, no. 5, pp. 705–717.
Lam, K., Lin, Y.F., Zou, L., and Liu, Y., Investigation of turbulent flow past a yawed wavy cylinder, J. Fluids Struct., 2010, vol. 26, nos. 7–8, pp. 1078–1097.
Zhang, W., Daichin, and Sang, J.L., PIV measurements of the near-wake behind a sinusoidal cylinder, Exp. Fluids, 2005, vol. 38, no. 6, pp. 824–832.
New, T.H., Shi, S., and Liu, Y., On the flow behaviour of confined finite-length wavy cylinders, J. Fluids Struct., 2015, vol. 54, pp. 281–296.
Naghib-Lahouti, A., Doddipatla, L.S., and Hangan, H., Secondary wake instabilities of a blunt trailing edge profiled body as a basis for flow control, Exp. Fluids, 2012, vol. 52, no. 6, pp. 1547–1566.
Antiohos, A.A. and Thorpe, G.R., Effect of aspect ratio of a spanwise sinusoidal profile on the control of turbulent flows around bluff bodies, J. Wind Eng. Ind. Aerodyn., 2015, vol. 145, pp. 237–251.
Lam, K., Lin, Y.F., Zou, L., and Liu, Y., Numerical study of flow patterns and force characteristics for square and rectangular cylinders with wavy surfaces, J. Fluids Struct., 2012, vol. 28, pp. 359–377.
Choi, H., Jeon, W.P., and Kim, J., Control of flow over a bluff body, Annu. Rev. Fluid Mech., 2008, vol. 40, pp. 113–139.
Darekar, R.M. and Sherwin, S.J., “Flow past a square-section cylinder with wavy stagnation face, J. Fluid Mech., 2001, vol. 426, pp. 263–295.
Sheard, G.J., Fitzgerald, M.J., and Ryan, K., Cylinders with square cross-section: wake instabilities with incidence angle variation, J. Fluid Mech., 2009, vol. 630, pp. 43–69.
Tong, X.H., Luo, S.C., and Khoo, B.C., Transition phenomena in the wake of an inclined square cylinder, J. Fluids Struct., 2008, vol. 24, pp. 994–1005.
Dobre, A., Hangan, H., and Vickery, B.J., Wake control based on spanwise sinusoidal perturbation, AIAA J., 2006, vol. 44, no. 3, pp. 485–492.
Dobre, A. and Hangan, H., Investigation of the three-dimensional intermediate wake topology for a square cylinder at high Reynolds number, Exp. Fluids, 2004, vol. 37, no. 4, pp. 518–530.
Bearman, P.W. and Owen, J.C., Reduction of bluff body drag and suppression of vortex shedding by the introduction of wavy separation lines, J. Fluids Struct., 1998, vol. 12, pp. 123–130.
Oka, S. and Ishihara, T., Numerical study of aerodynamic characteristics of a square prism in a uniform flow, J. Wind Eng. Ind. Aerodyn., 2009, vol. 97, pp. 548–559.
Mankbadi, M.R. and Georgiadis, N.J., Examination of parameters affecting large-eddy simulations of flow past a square cylinder, AIAA J., 2015, vol. 53, no. 6, pp. 1706–1712.
Lyn, D.A., Einav, S., Rodi, W., and Park, J.H., A laser-Doppler velocimetry study of ensemble-averaged characteristics of the turbulent near wake of a square cylinder, J. Fluid Mech., 1995, vol. 304, pp. 285–319.
Murakami, S. and Mochida, A., On turbulent vortex shedding flow past 2d square cylinder predicted by CFD, J. Wind Eng. Ind. Aerodyn., 1995, vol. 54–55, pp. 192–211.
Lin, Y.F., Bai, H.L., Alam, M.M., Zhang, W.G., and Lam, K., Effects of large spanwise wavelength on the wake of a sinusoidal wavy cylinder, J. Fluids Struct., 2016, vol. 61, p. 392.
Zheng, Y., Rinoshika, H., Zhang, D., and Rinoshika, A., Analyses on flow structures behind a wavy square cylinder based on continuous wavelet transform and dynamic mode decomposition, Ocean Eng., 2020, vol. 206, p. 108117.
Lin, Y.F., Bai, H.L., and Alam, M.M., The turbulent wake of a square prism with wavy faces, Wind. Struct. An Int. J., 2016, vol. 23, no. 2, pp. 127–142.
Norberg, C., Flow around rectangular cylinders: Pressure forces and wake frequencies, J. Wind Eng. Ind. Aerodyn., 1993, vol. 49, nos. 1–3, pp. 187–196.
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The author ZY wishes to acknowledge the financial support by National Natural Science Foundation of China (grant no. 11802108), Major Basic Research Project of the Natural Science Foundation of the Jiangsu Higher Education Institutions, China (grant no. 19KJA510002), Science and Technology Project of Changzhou (grant no. CE20205036), and Research Fund of Key Laboratory of Unsteady Aerodynamics and Flow Control, MIIT, Nanjing University of Aeronautics and Astronautics (grant no. KLUAFC-E-202102).
The author AR wishes to acknowledge the financial support by National Natural Science Foundation of China (grants nos. 11721202 and 11772035).
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Zhang, D., Rinoshika, A., Zheng, Y. et al. Turbulent Flow Structures around a Wavy Square Cylinder Based on Large Eddy Simulation. Fluid Dyn 57, 96–110 (2022). https://doi.org/10.1134/S0015462822010116
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DOI: https://doi.org/10.1134/S0015462822010116