Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-27T02:25:05.010Z Has data issue: false hasContentIssue false
  • English
  • Français

Secondary vortex, laminar separation bubble and vortex shedding in flow past a low aspect ratio circular cylinder

Published online by Cambridge University Press:  08 November 2021

Gaurav Chopra Open the ORCID record for Gaurav Chopra [Opens in a new window]  and
Sanjay Mittal Open the ORCID record for Sanjay Mittal [Opens in a new window]
Gaurav Chopra
Affiliation:
Department of Aerospace Engineering, Indian Institute of Technology Kanpur, 208016 Kanpur, India
Sanjay Mittal*
Affiliation:
Department of Aerospace Engineering, Indian Institute of Technology Kanpur, 208016 Kanpur, India
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Large eddy simulation of flow past a circular cylinder of low aspect ratio ($AR=1$ and $3$), spanning subcritical, critical and supercritical regimes, is carried out for $2\times 10^3 \le Re \le 4\times 10^5$. The end walls restrict three-dimensionality of the flow. The critical $Re$ for the onset of the critical regime is significantly lower for small aspect ratio cylinders. The evolution of secondary vortex (SV), laminar separation bubble (LSB) and the related transition of boundary layer with $Re$ is investigated. The plateau in the surface pressure due to LSB is modified by the presence of SV. Proper orthogonal decomposition of surface pressure reveals that although the vortex shedding mode is most dominant throughout the $Re$ regime studied, significant energy of the flow lies in a symmetric mode that corresponds to expansion–contraction of the vortex formation region and is responsible for bursts of weak vortex shedding. A triple decomposition of the time signals comprising of contributions from shear layer vortices, von Kármán vortex shedding and low frequency modulation due to the symmetric mode of flow is proposed. A moving average, with appropriate size of window, is utilized to estimate the component due to vortex shedding. It is used to assess the variation, with $Re$, of strength of vortex shedding as well as its coherence along the span. Weakening of vortex shedding in the high subcritical and critical regime is followed by its rejuvenation in the supercritical regime. Its spanwise correlation is high in the subcritical regime, decreases in the critical regime and improves again in the supercritical regime.

JFM classification

Boundary Layers: Boundary layer separation Turbulent Flows: Turbulent boundary layers Wakes/Jets: Vortex streets
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 930 , 10 January 2022 , A12
Check for updates
Copyright
© The Author(s), 2021. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Achenbach, E. 1968 Distribution of local pressure and skin friction around a circular cylinder in cross-flow up to $Re= 5\times 10^6$. J. Fluid Mech. 34 (4), 625–639.CrossRefGoogle Scholar
Achenbach, E. & Heinecke, E. 1981 On vortex shedding from smooth and rough cylinders in the range of Reynolds numbers 6$\times 10^3$ to 5$\times 10^6$. J. Fluid Mech. 109, 239–251.CrossRefGoogle Scholar
Bearman, P.W. 1969 On vortex shedding from a circular cylinder in the critical Reynolds number regime. J. Fluid Mech. 37 (3), 577–585.CrossRefGoogle Scholar
Behara, S. & Mittal, S. 2009 Parallel finite element computation of incompressible flows. Parallel Comput. 35 (4), 195–212.CrossRefGoogle Scholar
Behara, S. & Mittal, S. 2010 Wake transition in flow past a circular cylinder. Phys. Fluids 22 (11), 114104.CrossRefGoogle Scholar
Behara, S. & Mittal, S. 2011 Transition of the boundary layer on a circular cylinder in the presence of a trip. J. Fluids Struct. 27 (5–6), 702–715.CrossRefGoogle Scholar
Berkooz, G., Holmes, P. & Lumley, J.L. 1993 The proper orthogonal decomposition in the analysis of turbulent flows. Annu. Rev. Fluid Mech. 25 (1), 539–575.CrossRefGoogle Scholar
Bloor, M.S. 1964 The transition to turbulence in the wake of a circular cylinder. J. Fluid Mech. 19 (2), 290–304.CrossRefGoogle Scholar
Cadot, O., Desai, A., Mittal, S., Saxena, S. & Chandra, B. 2015 Statistics and dynamics of the boundary layer reattachments during the drag crisis transitions of a circular cylinder. Phys. Fluids 27 (1), 014101.CrossRefGoogle Scholar
Cao, Y. & Tamura, T. 2015 Numerical investigations into effects of three-dimensional wake patterns on unsteady aerodynamic characteristics of a circular cylinder at $Re= 1.3\times 10^5$. J. Fluids Struct. 59, 351–369.CrossRefGoogle Scholar
Chatterjee, A. 2000 An introduction to the proper orthogonal decomposition. Curr. Sci. 808–817.Google Scholar
Cheng, W., Pullin, D.I., Samtaney, R., Zhang, W. & Gao, W. 2017 Large-eddy simulation of flow over a cylinder with $Re_D$ from $3.9\times 10^3$ to $8.5\times 10^5$: a skin-friction perspective. J. Fluid Mech. 820, 121–158.CrossRefGoogle Scholar
Chopra, G. & Mittal, S. 2017 The intermittent nature of the laminar separation bubble on a cylinder in uniform flow. Comput. Fluids 142, 118–127.CrossRefGoogle Scholar
Chopra, G. & Mittal, S. 2019 Drag coefficient and formation length at the onset of vortex shedding. Phys. Fluids 31 (1), 013601.CrossRefGoogle Scholar
Desai, A., Mittal, S. & Mittal, S. 2020 Experimental investigation of vortex shedding past circular cylinder in the high subcritical regime. Phys. Fluids 32 (1), 014105.CrossRefGoogle Scholar
Deshpande, R., Kanti, V., Desai, A. & Mittal, S. 2017 Intermittency of laminar separation bubble on a sphere during drag crisis. J. Fluid Mech. 812, 815–840.CrossRefGoogle Scholar
Eljack, E., Soria, J., Elawad, Y. & Ohtake, T. 2021 Simulation and characterization of the laminar separation bubble over a NACA-0012 airfoil as a function of angle of attack. Phys. Rev. Fluids 6 (3), 034701.CrossRefGoogle Scholar
Fung, Y.C. 1960 Fluctuating lift and drag acting on a cylinder in a flow at supercritical Reynolds numbers. J. Aerosp. Sci. 27 (11), 801–814.CrossRefGoogle Scholar
Gerrard, J.H. 1978 The wakes of cylindrical bluff bodies at low Reynolds number. Phil. Trans. R. Soc. Lond. A 288 (1354), 351–382.Google Scholar
Johari, H. & Stein, K. 2002 Near wake of an impulsively started disk. Phys. Fluids 14 (10), 3459–3474.CrossRefGoogle Scholar
Keefe, R.T. 1962 Investigation of the fluctuating forces acting on a stationary circular cylinder in a subsonic stream and of the associated sound field. J. Acoust. Soc. Am. 34 (11), 1711–1714.CrossRefGoogle Scholar
Kravchenko, A.G. & Moin, P. 2000 Numerical studies of flow over a circular cylinder at $RE_D= 3900$. Phys. Fluids 12 (2), 403–417.CrossRefGoogle Scholar
Kumar, B., Kottaram, J.J., Singh, A.K. & Mittal, S. 2009 Global stability of flow past a cylinder with centreline symmetry. J. Fluid Mech. 632, 273–300.CrossRefGoogle Scholar
Kumar, B. & Mittal, S. 2006 Prediction of the critical Reynolds number for flow past a circular cylinder. Comput. Meth. Appl. Mech. Engng 195 (44–47), 6046–6058.CrossRefGoogle Scholar
Landau, L.D. & Lifshitz, E.M. 1982 Fluid Mechanics. Pergamon.Google Scholar
Lehmkuhl, O., Rodríguez, I., Borrell, R., Chiva, J. & Oliva, A. 2014 Unsteady forces on a circular cylinder at critical Reynolds numbers. Phys. Fluids 26 (12), 125110.CrossRefGoogle Scholar
Lehmkuhl, O., Rodríguez, I., Borrell, R. & Oliva, A. 2013 Low-frequency unsteadiness in the vortex formation region of a circular cylinder. Phys. Fluids 25 (8), 085109.CrossRefGoogle Scholar
Mathis, C., Provansal, M. & Boyer, L. 1984 The Bénard–von Kármán instability: an experimental study near the threshold. J. Phys. Lett. 45 (10), 483–491.CrossRefGoogle Scholar
Nicoud, F., Toda, H.B., Cabrit, O., Bose, S. & Lee, J. 2011 Using singular values to build a subgrid-scale model for large eddy simulations. Phys. Fluids 23 (8), 085106.CrossRefGoogle Scholar
Norberg, C. 1994 An experimental investigation of the flow around a circular cylinder: influence of aspect ratio. J. Fluid Mech. 258, 287–316.CrossRefGoogle Scholar
Norberg, C. 2001 Flow around a circular cylinder: aspects of fluctuating lift. J. Fluids Struct. 15 (3–4), 459–469.CrossRefGoogle Scholar
Ono, Y. & Tamura, T. 2008 LES of flows around a circular cylinder in the critical Reynolds number region. In Proceedings of BBAA VI International Colloquium on Bluff Bodies Aerodynamics and Applications.Google Scholar
Pandi, J.S.S. & Mittal, S. 2019 Wake transitions and laminar separation bubble in the flow past an Eppler 61 airfoil. Phys. Fluids 31 (11), 114102.CrossRefGoogle Scholar
Parnaudeau, P., Carlier, J., Heitz, D. & Lamballais, E. 2008 Experimental and numerical studies of the flow over a circular cylinder at Reynolds number 3900. Phys. Fluids 20 (8), 085101.CrossRefGoogle Scholar
Perrin, R., Braza, M., Cid, E., Cazin, S., Chassaing, P., Mockett, C., Reimann, T. & Thiele, F. 2008 Coherent and turbulent process analysis in the flow past a circular cylinder at high Reynolds number. J. Fluids Struct. 24 (8), 1313–1325.CrossRefGoogle Scholar
Prasad, A. & Williamson, C.H.K. 1997 The instability of the shear layer separating from a bluff body. J. Fluid Mech. 333, 375–402.CrossRefGoogle Scholar
Rodríguez, I., Lehmkuhl, O., Chiva, J., Borrell, R. & Oliva, A. 2015 On the flow past a circular cylinder from critical to super-critical Reynolds numbers: wake topology and vortex shedding. Intl J. Heat Fluid Flow 55, 91–103.CrossRefGoogle Scholar
Roshko, A. 1961 Experiments on the flow past a circular cylinder at very high Reynolds number. J. Fluid Mech. 10 (3), 345–356.CrossRefGoogle Scholar
Saad, Y. & Schultz, M.H. 1986 GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Stat. Comput. 7 (3), 856–869.CrossRefGoogle Scholar
Schewe, G. 1983 On the force fluctuations acting on a circular cylinder in crossflow from subcritical up to transcritical Reynolds numbers. J. Fluid Mech. 133, 265–285.CrossRefGoogle Scholar
Singh, S.P. & Mittal, S. 2005 Flow past a cylinder: shear layer instability and drag crisis. Intl J. Numer. Meth. Fluids 47 (1), 75–98.CrossRefGoogle Scholar
Son, J.S. & Hanratty, T.J. 1969 Velocity gradients at the wall for flow around a cylinder at Reynolds numbers from $5\times 10^3$ to $10^5$. J. Fluid Mech. 35 (2), 353–368.CrossRefGoogle Scholar
Sreenivasan, K.R., Strykowski, P.J. & Olinger, D.J. 1987 Hopf bifurcation, Landau equation, and vortex shedding behind circular cylinders. In Forum on Unsteady Flow Separation (ed. K.N. Ghia), vol. 1, pp. 1–13. American Society for Mechanical Engineers.Google Scholar
Szepessy, S. 1993 On the control of circular cylinder flow by end plates. Eur. J. Mech. B/Fluids 12 (2), 217–244.Google Scholar
Szepessy, S. 1994 On the spanwise correlation of vortex shedding from a circular cylinder at high subcritical Reynolds number. Phys. Fluids 6 (7), 2406–2416.CrossRefGoogle Scholar
Szepessy, S. & Bearman, P.W. 1992 Aspect ratio and end plate effects on vortex shedding from a circular cylinder. J. Fluid Mech. 234, 191–217.CrossRefGoogle Scholar
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 J. 4013–4041.CrossRefGoogle Scholar
Tani, I. 1964 Low-speed flows involving bubble separations. Prog. Aerosp. Sci. 5, 70–103.CrossRefGoogle Scholar
Tezduyar, T.E., Mittal, S., Ray, S.E. & Shih, R. 1992 Incompressible flow computations with stabilized bilinear and linear equal-order-interpolation velocity-pressure elements. Comput. Meth. Appl. Mech. Engng 95 (2), 221–242.CrossRefGoogle Scholar
Unal, M.F. & Rockwell, D. 1988 On vortex formation from a cylinder. Part 1. The initial instability. J. Fluid Mech. 190, 491–512.CrossRefGoogle Scholar
Williamson, C.H.K. 1992 The natural and forced formation of spot-like ‘vortex dislocations’ in the transition of a wake. J. Fluid Mech. 243, 393–441.CrossRefGoogle Scholar
Williamson, C.H.K. 1996 a Three-dimensional wake transition. J. Fluid Mech. 328, 345–407.CrossRefGoogle Scholar
Williamson, C.H.K. 1996 b Vortex dynamics in the cylinder wake. Annu. Rev. Fluid Mech. 28 (1), 477–539.CrossRefGoogle Scholar