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Three-dimensional wake transition of a square cylinder

  • Hongyi Jiang (a1), Liang Cheng (a1) (a2) and Hongwei An (a1)

Abstract

Three-dimensional (3-D) wake transition for flow past a square cylinder aligned with sides perpendicular and parallel to the approaching flow is investigated using direct numerical simulation. The secondary wake instability, namely a Mode A instability, occurs at a Reynolds number ( $Re$ ) of 165.7. A gradual wake transition from Mode A* (i.e. Mode A with vortex dislocations) to Mode B is observed over a range of $Re$ from 185 to 210, within which the probability of occurrence of vortex dislocations decreases monotonically with increasing $Re$ . The characteristics of the Strouhal–Reynolds number relationship are analysed. At the onset of Mode A*, a sudden drop of the 3-D Strouhal number from its two-dimensional counterpart is observed, which is due to the subcritical nature of the Mode A* instability. A continuous 3-D Strouhal–Reynolds number curve is observed over the mode swapping regime, since Mode A* and Mode B have extremely close vortex shedding frequencies and therefore only a single merged peak is observed in the frequency spectrum. The existence of hysteresis for the Mode A and Mode B wake instabilities is examined. The unconfined Mode A and Mode B wake instabilities are hysteretic and non-hysteretic, respectively. However, a spanwise confined Mode A could be non-hysteretic. It is proposed that the existence of hysteresis at a wake instability can be identified by examining the sudden/gradual variation of the 3-D flow properties at the onset of the wake instability, with sudden and gradual variations corresponding to hysteretic (subcritical) and non-hysteretic (supercritical) flows, respectively.

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Corresponding author

Email address for correspondence: liang.cheng@uwa.edu.au

References

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Akbar, T., Bouchet, G. & Dušek, J. 2011 Numerical investigation of the subcritical effects at the onset of three-dimensionality in the circular cylinder wake. Phys. Fluids 23, 094103.
Barkley, D. & Henderson, R. D. 1996 Three-dimensional Floquet stability analysis of the wake of a circular cylinder. J. Fluid Mech. 322, 215241.
Blackburn, H. M. & Lopez, J. M. 2003 On three-dimensional quasiperiodic Floquet instabilities of two-dimensional bluff body wakes. Phys. Fluids 15, L57L60.
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. J. Fluid Mech. 597, 129.
Carmo, B. S., Meneghini, J. R. & Sherwin, S. J. 2010 Secondary instabilities in the flow around two circular cylinders in tandem. J. Fluid Mech. 644, 395431.
Choi, C., Jang, Y. & Yang, K. 2012 Secondary instability in the near-wake past two tandem square cylinders. Phys. Fluids 24, 024102.
Dušek, J., Le Gal, P. & Fraunié, P. 1994 A numerical and theoretical study of the first Hopf bifurcation in a cylinder wake. J. Fluid Mech. 264, 5980.
Henderson, R. D. 1997 Nonlinear dynamics and pattern formation in turbulent wake transition. J. Fluid Mech. 352, 65112.
Henderson, R. D. & Barkley, D. 1996 Secondary instability in the wake of a circular cylinder. Phys. Fluids 8, 16831685.
Issa, R. I. 1986 Solution of implicitly discretized fluid flow equations by operator-splitting. J. Comput. Phys. 62, 4065.
Jiang, H. & Cheng, L. 2017 Strouhal–Reynolds number relationship for flow past a circular cylinder. J. Fluid Mech. 832, 170188.
Jiang, H., Cheng, L., Draper, S., An, H. & Tong, F. 2016 Three-dimensional direct numerical simulation of wake transitions of a circular cylinder. J. Fluid Mech. 801, 353391.
Jiang, H., Cheng, L. & An, H. 2017a On numerical aspects of simulating flow past a circular cylinder. Intl J. Numer. Meth. Fluids 85, 113132.
Jiang, H., Cheng, L., Draper, S. & An, H. 2017b Prediction of the secondary wake instability of a circular cylinder with direct numerical simulation. Comput. Fluids 149, 172180.
Jiang, H., Cheng, L., Draper, S. & An, H. 2017c Two- and three-dimensional instabilities in the wake of a circular cylinder near a moving wall. J. Fluid Mech. 812, 435462.
Jiang, H., Cheng, L., Draper, S. & An, H. 2017d Three-dimensional wake transition for a circular cylinder near a moving wall. J. Fluid Mech. 818, 260287.
Landau, L. D. & Lifshitz, E. M. 1976 Mechanics, 3rd edn. Pergamon.
Leweke, T. & Williamson, C. H. K. 1998 Three-dimensional instabilities in wake transition. Eur. J. Mech. (B/Fluids) 17, 571586.
Luo, S. C., Chew, Y. T. & Ng, Y. T. 2003 Characteristics of square cylinder wake transition flows. Phys. Fluids 15, 25492559.
Luo, S. C., Tong, X. H. & Khoo, B. C. 2007 Transition phenomena in the wake of a square cylinder. J. Fluids Struct. 23, 227248.
Park, D. & Yang, K. 2016 Flow instabilities in the wake of a rounded square cylinder. J. Fluid Mech. 793, 915932.
Robichaux, J., Balachandar, S. & Vanka, S. P. 1999 Three-dimensional Floquet instability of the wake of square cylinder. Phys. Fluids 11, 560578.
Saha, A. K., Muralidhar, K. & Biswas, G. 2000 Transition and chaos in two-dimensional flow past a square cylinder. J. Engng Mech. ASCE 126, 523532.
Saha, A. K., Biswas, G. & Muralidhar, K. 2003 Three-dimensional study of flow past a square cylinder at low Reynolds numbers. Intl J. Heat Fluid Flow 24, 5466.
Saha, A. K. 2009 Effect of transitions on flow past a square cylinder at low Reynolds number. J. Engng Mech. ASCE 135, 839851.
Sheard, G. J., Fitzgerald, M. J. & Ryan, K. 2009 Cylinders with square cross-section: wake instabilities with incidence angle variation. J. Fluid Mech. 630, 4369.
Sheard, G. J., Thompson, M. C. & Hourigan, K. 2004 From spheres to circular cylinders: non-axisymmetric transitions in the flow past rings. J. Fluid Mech. 506, 4578.
Sohankar, A., Norberg, C. & Davidson, L. 1999 Simulation of three-dimensional flow around a square cylinder at moderate Reynolds numbers. Phys. Fluids 11, 288306.
Thompson, M. C., Leweke, T. & Williamson, C. H. K. 2001a The physical mechanism of transition in bluff body wakes. J. Fluids Struct. 15, 607616.
Thompson, M. C., Leweke, T. & Provansal, M. 2001b Kinematics and dynamics of sphere wake transition. J. Fluids Struct. 15, 575585.
Williamson, C. H. K. 1996 Three-dimensional wake transition. J. Fluid Mech. 328, 345407.
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Three-dimensional wake transition of a square cylinder

  • Hongyi Jiang (a1), Liang Cheng (a1) (a2) and Hongwei An (a1)

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