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Onset of vortex shedding around a short cylinder

Published online by Cambridge University Press:  20 December 2021

Yongliang Yang Open the ORCID record for Yongliang Yang [Opens in a new window] ,
Zhe Feng  and
Mengqi Zhang Open the ORCID record for Mengqi Zhang [Opens in a new window]
Yongliang Yang
Affiliation:
School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing 210094, PR China Department of Mechanical Engineering, National University of Singapore, 9 Engineering Drive 1, 117575 Republic of Singapore
Zhe Feng
Affiliation:
Department of Mechanical Engineering, National University of Singapore, 9 Engineering Drive 1, 117575 Republic of Singapore
Mengqi Zhang*
Affiliation:
Department of Mechanical Engineering, National University of Singapore, 9 Engineering Drive 1, 117575 Republic of Singapore
*
†Email address for correspondence: [email protected]
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Abstract

This paper presents results of three-dimensional direct numerical simulations (DNS) and global linear stability analyses of a viscous incompressible flow past a finite-length cylinder with two free flat ends. The cylindrical axis is normal to the streamwise direction. The work focuses on the effects of aspect ratios (in the range of $0.5\leq {\small \text{AR}} \leq 2$, cylinder length over diameter) and Reynolds numbers ($Re\leq 1000$ based on cylinder diameter and uniform incoming velocity) on the onset of vortex shedding in this flow. All important flow patterns have been identified and studied, especially as ${\small \text{AR}}$ changes. The appearance of a steady wake pattern when ${\small \text{AR}} \leq 1.75$ has not been discussed earlier in the literature for this flow. Linear stability analyses based on the time-mean flow has been applied to understand the Hopf bifurcation past which vortex shedding happens. The nonlinear DNS results indicate that there are two vortex shedding patterns at different $Re$, one is transient and the other is nonlinearly saturated. The vortex-shedding frequencies of these two flow patterns correspond to the eigenfrequencies of the two global modes in the stability analysis of the time-mean flow. Wherever possible, we compare the results of our analyses to those of the flows past other short-${\small \text{AR}}$ bluff bodies in order that our discussions bear more general meanings.

JFM classification

Vortex Flows: Vortex shedding Wakes/Jets: Wakes
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 933 , 25 February 2022 , A7
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

REFERENCES

Åkervik, E., Brandt, L., Henningson, D.S., Hœpffner, J., Marxen, O. & Schlatter, P. 2006 Steady solutions of the Navier–Stokes equations by selective frequency damping. Phys. Fluids 18 (6), 068102.CrossRefGoogle Scholar
Barkley, D. 2006 Linear analysis of the cylinder wake mean flow. Europhys. Lett. 75 (5), 750–756.CrossRefGoogle Scholar
Beneddine, S., Sipp, D., Arnault, A., Dandois, J. & Lesshafft, L. 2016 Conditions for validity of mean flow stability analysis. J. Fluid Mech. 798, 485–504.CrossRefGoogle Scholar
Beneddine, S., Yegavian, R., Sipp, D. & Leclaire, B. 2017 Unsteady flow dynamics reconstruction from mean flow and point sensors: an experimental study. J. Fluid Mech. 824, 174–201.CrossRefGoogle Scholar
Bengana, Y., Loiseau, J.-C., Robinet, J.-C. & Tuckerman, L.S. 2019 Bifurcation analysis and frequency prediction in shear-driven cavity flow. J. Fluid Mech. 875, 725–757.CrossRefGoogle Scholar
Cadieux, F., Sun, G. & Domaradzki, J.A. 2017 Effects of numerical dissipation on the interpretation of simulation results in computational fluid dynamics. Comput. Fluids 154, 256–272, iCCFD8.CrossRefGoogle Scholar
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, 395–431.CrossRefGoogle Scholar
Citro, V., Tchoufag, J., Fabre, D., Giannetti, F. & Luchini, P. 2016 Linear stability and weakly nonlinear analysis of the flow past rotating spheres. J. Fluid Mech. 807, 62–86.CrossRefGoogle Scholar
Doedel, E. & Tuckerman, L.S. 2012 Numerical Methods for Bifurcation Problems and Large-Scale Dynamical Systems, vol. 119. Springer Science & Business Media.Google Scholar
El Khoury, G.K., Andersson, H.I. & Pettersen, B. 2012 Wakes behind a prolate spheroid in crossflow. J. Fluid Mech. 701, 98–136.CrossRefGoogle Scholar
Feng, Z., Zhang, M., Vazquez, P.A. & Shu, C. 2021 Deterministic and stochastic bifurcations in two-dimensional electroconvective flows. J. Fluid Mech. 922, A20.CrossRefGoogle Scholar
Fischer, P., Kerkemeier, S. & Peplinski, A. 2020 Nek5000 home page. Website, https://nek5000.mcs.anl.gov/.Google Scholar
Fornberg, B. 1988 Steady viscous flow past a sphere at high Reynolds numbers. J. Fluid Mech. 190, 471–489.CrossRefGoogle Scholar
Gao, W., Nelias, D., Liu, Z. & Lyu, Y. 2018 Numerical investigation of flow around one finite circular cylinder with two free ends. Ocean Engng 156, 373–380.CrossRefGoogle Scholar
Gao, Z., Sergent, A., Podvin, B., Xin, S., Le Quéré, P. & Tuckerman, L.S. 2013 Transition to chaos of natural convection between two infinite differentially heated vertical plates. Phys. Rev. E 88, 023010.CrossRefGoogle ScholarPubMed
Giannetti, F. & Luchini, P. 2007 Structural sensitivity of the first instability of the cylinder wake. J. Fluid Mech. 581, 167–197.CrossRefGoogle Scholar
Guckenheimer, J. & Holmes, P. 1983 Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences, vol. 42. Springer.CrossRefGoogle Scholar
Hammond, D.A. & Redekopp, L.G. 1997 Global dynamics of symmetric and asymmetric wakes. J. Fluid Mech. 331, 231–260.CrossRefGoogle Scholar
Henderson, R.D. & Barkley, D. 1996 Secondary instability in the wake of a circular cylinder. Phys. Fluids 8 (6), 1683–1685.CrossRefGoogle Scholar
Inoue, O. & Sakuragi, A. 2008 Vortex shedding from a circular cylinder of finite length at low Reynolds numbers. Phys. Fluids 20 (3), 033601.CrossRefGoogle Scholar
Jackson, C.P. 1987 A finite-element study of the onset of vortex shedding in flow past variously shaped bodies. J. Fluid Mech. 182, 23–45.CrossRefGoogle Scholar
Johnson, T.A. & Patel, V.C. 1999 Flow past a sphere up to a Reynolds number of 300. J. Fluid Mech. 378, 19–70.CrossRefGoogle Scholar
Kim, I. & Pearlstein, A.J. 1990 Stability of the flow past a sphere. J. Fluid Mech. 211, 73–93.CrossRefGoogle Scholar
Lehoucq, R.B., Sorensen, D.C. & Yang, C. 1998 ARPACK Users’ Guide: Solution of Large-Scale Eigenvalue Problems With Implicitly Restarted Arnoldi Methods. SIAM.CrossRefGoogle Scholar
Leontini, J.S., Thompson, M.C. & Hourigan, K. 2010 A numerical study of global frequency selection in the time-mean wake of a circular cylinder. J. Fluid Mech. 645, 435–446.CrossRefGoogle Scholar
Magarvey, R.H. & MacLatchy, C.S. 1965 Vortices in sphere wakes. Can. J. Phys. 43 (9), 1649–1656.CrossRefGoogle Scholar
Natarajan, R. & Acrivos, A. 1993 The instability of the steady flow past spheres and disks. J. Fluid Mech. 254, 323–344.CrossRefGoogle Scholar
Noack, B.R. & Eckelmann, H. 1994 A global stability analysis of the steady and periodic cylinder wake. J. Fluid Mech. 270, 297–330.CrossRefGoogle Scholar
Patera, A.T. 1984 A spectral element method for fluid dynamics: laminar flow in a channel expansion. J. Comput. Phys. 54 (3), 468–488.CrossRefGoogle Scholar
Pier, B. 2002 On the frequency selection of finite-amplitude vortex shedding in the cylinder wake. J. Fluid Mech. 458, 407–417.CrossRefGoogle Scholar
Pierson, J.-L., Auguste, F., Hammouti, A. & Wachs, A. 2019 Inertial flow past a finite-length axisymmetric cylinder of aspect ratio 3: effect of the yaw angle. Phys. Rev. Fluids 4, 044802.CrossRefGoogle Scholar
Prosser, D.T. & Smith, M.J. 2016 Numerical characterization of three-dimensional bluff body shear layer behaviour. J. Fluid Mech. 799, 1–26.CrossRefGoogle Scholar
Radke, R.J. 1996 A matlab implementation of the implicitly restarted arnoldi method for solving large-scale eigenvalue problems. PhD thesis, Rice University.Google Scholar
Saha, A.K. 2004 Three-dimensional numerical simulations of the transition of flow past a cube. Phys. Fluids 16 (5), 1630–1646.CrossRefGoogle Scholar
Sakamoto, H. & Haniu, H. 1995 The formation mechanism and shedding frequency of vortices from a sphere in uniform shear flow. J. Fluid Mech. 287, 151–171.CrossRefGoogle Scholar
Sansica, A., Robinet, J.-C., Alizard, F. & Goncalves, E. 2018 Three-dimensional instability of a flow past a sphere: Mach evolution of the regular and hopf bifurcations. J. Fluid Mech. 855, 1088–1115.CrossRefGoogle Scholar
Schmid, P.J. 2010 Dynamic mode decomposition of numerical and experimental data. J. Fluid Mech. 656, 5–28.CrossRefGoogle Scholar
Schouveiler, L. & Provansal, M. 2001 Periodic wakes of low aspect ratio cylinders with free hemispherical ends. J. Fluids Struct. 15 (3), 565–573.CrossRefGoogle Scholar
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, 45–78.CrossRefGoogle Scholar
Sheard, G.J., Thompson, M.C. & Hourigan, K. 2005 Computing the flow past a cylinder with hemispherical ends. ANZIAM J. 46, 1296–1310.CrossRefGoogle Scholar
Sheard, G.J., Thompson, M.C. & Hourigan, K. 2008 Flow normal to a short cylinder with hemispherical ends. Phys. Fluids 20 (4), 041701.CrossRefGoogle Scholar
Sipp, D. & Lebedev, A. 2007 Global stability of base and mean flows: a general approach and its applications to cylinder and open cavity flows. J. Fluid Mech. 593, 333–358.CrossRefGoogle Scholar
Taneda, S. 1956 Experimental investigation of the wake behind a sphere at low Reynolds numbers. J. Phys. Soc. Japan 11 (10), 1104–1108.CrossRefGoogle Scholar
Tezuka, A. & Suzuki, K. 2006 Three-dimensional global linear stability analysis of flow around a spheroid. AIAA J. 44 (8), 1697–1708.CrossRefGoogle Scholar
Theofilis, V. 2011 Global linear instability. Annu. Rev. Fluid Mech. 43 (1), 319–352.CrossRefGoogle Scholar
Thompson, M.C., Leweke, T. & Provansal, M. 2001 Kinematics and dynamics of sphere wake transition. J. Fluids Struct. 15 (3–4), 575–585.CrossRefGoogle Scholar
Tomboulides, A.G. & Orszag, S.A. 2000 Numerical investigation of transitional and weak turbulent flow past a sphere. J. Fluid Mech. 416, 45–73.CrossRefGoogle Scholar
Toupoint, C., Ern, P. & Roig, V. 2019 Kinematics and wake of freely falling cylinders at moderate Reynolds numbers. J. Fluid Mech. 866, 82–111.CrossRefGoogle Scholar
Turton, S.E., Tuckerman, L.S. & Barkley, D. 2015 Prediction of frequencies in thermosolutal convection from mean flows. Phys. Rev. E 91 (4), 043009.CrossRefGoogle ScholarPubMed
Williamson, C.H.K. 1988 Defining a universal and continuous Strouhal–Reynolds number relationship for the laminar vortex shedding of a circular cylinder. Phys. Fluids 31 (10), 2742–2744.CrossRefGoogle Scholar
Williamson, C.H.K. 1989 Oblique and parallel modes of vortex shedding in the wake of a circular cylinder at low Reynolds numbers. J. Fluid Mech. 206, 579–627.CrossRefGoogle Scholar
Wu, J.S. & Faeth, G.M. 1993 Sphere wakes in still surroundings at intermediate Reynolds numbers. AIAA J. 31 (8), 1448–1455.CrossRefGoogle Scholar
Yang, Y., Guo, R., Liu, R., Chen, L., Xing, B. & Zhao, B. 2021 Quasi-steady aerodynamic characteristics of terminal sensitive bullets with short cylindrical portion. Def. Technol. 17 (2), 633–649.CrossRefGoogle Scholar
Zdravkovich, M.M., Brand, V.P., Mathew, G. & Weston, A. 1989 Flow past short circular cylinders with two free ends. J. Fluid Mech. 203, 557–575.CrossRefGoogle Scholar
Zebib, A. 1987 Stability of viscous flow past a circular cylinder. J. Engng Maths 21 (2), 155–165.CrossRefGoogle Scholar