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Compressibility effects on the secondary instabilities of the circular cylinder wake

Published online by Cambridge University Press:  05 July 2023

Laura Victoria Rolandi Open the ORCID record for Laura Victoria Rolandi [Opens in a new window] ,
Jérôme Fontane Open the ORCID record for Jérôme Fontane [Opens in a new window] ,
Thierry Jardin Open the ORCID record for Thierry Jardin [Opens in a new window] ,
Jérémie Gressier Open the ORCID record for Jérémie Gressier [Opens in a new window]  and
Laurent Joly Open the ORCID record for Laurent Joly [Opens in a new window]
Laura Victoria Rolandi*
Affiliation:
ISAE-SUPAERO, Université de Toulouse, 31400 Toulouse, France
Jérôme Fontane
Affiliation:
ISAE-SUPAERO, Université de Toulouse, 31400 Toulouse, France
Thierry Jardin
Affiliation:
ISAE-SUPAERO, Université de Toulouse, 31400 Toulouse, France
Jérémie Gressier
Affiliation:
ISAE-SUPAERO, Université de Toulouse, 31400 Toulouse, France
Laurent Joly
Affiliation:
ISAE-SUPAERO, Université de Toulouse, 31400 Toulouse, France
*
†Email address for correspondence: laura-victoria.rolandi@isae-supaero.fr
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Abstract

With a growing interest in low Reynolds number compressible flows, compressibility effects on the secondary instabilities developing on the circular cylinder periodic wake are investigated. The unsteady and time-averaged two-dimensional flows are characterised for Reynolds numbers ${{Re}} \in [200;350]$ and Mach numbers up to ${{M}}_{\infty }=0.5$, revealing different flow structures which influence the characteristics of the secondary unstable modes. The two-dimensional time-periodic solution is used as the base state for a global linear stability analysis performed by means of Floquet theory coupled with a time-stepping finite-difference approach of the nonlinear operator. The influence of compressibility on mode A and mode B secondary instabilities which are responsible for the three-dimensionalisation of the two-dimensional periodic wake is analysed. A stabilising or a destabilising effect of compressibility is observed on mode A, depending on the Reynolds number and the spanwise wavelength of the mode, while mode B is stabilised by the increase of the Mach number. Compressibility is indeed found to decrease the mode kinetic energy production due to base flow shear conversion, which drives the growth of mode B. This results in a delay of the three-dimensionalisation process of the wake due to compressibility.

JFM classification

Compressible Flows: Compressible Flows Instability: Instability Low-Reynolds-number flows: Low-Reynolds-number flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 966 , 10 July 2023 , A36
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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References

Aref, H., Brøns, M. & Stremler, M.A. 2007 Bifurcation and instability problems in vortex wakes. J. Phys.: Conf. Ser. 64, 012015.Google Scholar
Arnoldi, W.E. 1951 The principle of minimized iterations in the solution of the matrix eigenvalue problem. Q. Appl. Maths 9 (1), 17–29.CrossRefGoogle Scholar
Arratia, C., Caulfield, C.P. & Chomaz, J.-M. 2013 Transient perturbation growth in time-dependent mixing layers. J. Fluid Mech. 717, 90–133.CrossRefGoogle Scholar
Barkley, D. & Henderson, R.D. 1996 Three-dimensional Floquet stability analysis of the wake of a circular cylinder. J. Fluid Mech. 322, 215–241.CrossRefGoogle Scholar
Bauchau, O.A. & Nikishkov, Y.G. 2001 An implicit Floquet analysis for rotorcraft stability evaluation. J. Am. Helicopter Soc. 46 (3), 200–209.CrossRefGoogle Scholar
Bermejo-Moreno, I., Campo, L., Larsson, J., Bodart, J., Helmer, D. & Eaton, J.K. 2014 Confinement effects in shock wave/turbulent boundary layer interactions through wall-modelled large-eddy simulations. J. Fluid Mech. 758, 5–62.CrossRefGoogle Scholar
Blackburn, H.M., Marques, F. & Lopez, J.M. 2005 Symmetry breaking of two-dimensional time-periodic wakes. J. Fluid Mech. 522, 395–411.CrossRefGoogle Scholar
Canuto, D. & Taira, K. 2015 Two-dimensional compressible viscous flow around a circular cylinder. J. Fluid Mech. 785, 349–371.CrossRefGoogle Scholar
Chiba, S. 1998 Global stability analysis of incompressible viscous flow. J. Jpn. Soc. Comput. Fluid Dyn. 7, 20–48.Google Scholar
Chiba, S. 2001 Three-dimensional global stability analysis for the time-periodic cylinder wake. Theor. Appl. Mech. 50, 321–326.Google Scholar
Chomaz, J.M., Huerre, P. & Redekopp, L.G. 1988 Bifurcations to local and global modes in spatially developing flows. Phys. Rev. Lett. 60 (1), 25.CrossRefGoogle ScholarPubMed
Gabbai, R.D. & Benaroya, H. 2005 An overview of modeling and experiments of vortex-induced vibration of circular cylinders. J. Sound Vib. 282 (3–5), 575–616.CrossRefGoogle Scholar
Gerrard, J.H. 1966 The mechanics of the formation region of vortices behind bluff bodies. J. Fluid Mech. 25 (2), 401–413.CrossRefGoogle Scholar
Gómez Carrasco, F.J. 2013 Matrix-free time-stepping methods for the solution of triglobal instability problems. PhD thesis, School of Aeronautics, Universidad Politécnica de Madrid.Google Scholar
Gowen, F.E. & Perkins, E.W. 1953 Drag of circular cylinders for a wide range of Reynolds numbers and Mach numbers. Tech. Rep. NACA-TN-2960. Ames Aeronautical Laboratory.Google Scholar
Grébert, A., Bodart, J., Jamme, S. & Joly, L. 2018 Simulations of shock wave/turbulent boundary layer interaction with upstream micro vortex generators. Intl J. Heat Fluid Flow 72, 73–85.CrossRefGoogle Scholar
Henderson, R.D. 1995 Details of the drag curve near the onset of vortex shedding. Phys. Fluids 7 (9), 2102–2104.CrossRefGoogle Scholar
Hernández, V., Román, J.E., Tomás, A. & Vidal, V. 2007 Krylov–Schur methods in SLEPc. Tech. Rep. STR-7, Universitat Politecnica de Valencia.Google Scholar
Hochstadt, H. 2014 Differential Equations. Courier Corporation.Google Scholar
Huerre, P. & Monkewitz, P.A. 1990 Local and global instabilities in spatially developing flows. Annu. Rev. Fluid Mech. 22 (1), 473–537.CrossRefGoogle Scholar
Jiang, H. 2021 Three-dimensional wake transition of a diamond-shaped cylinder. J. Fluid Mech. 918, A35.CrossRefGoogle Scholar
Kitchens, C.W. & Bush, C.C. 1972 Low Reynolds number flow past a transverse cylinder at Mach two. AIAA J. 10 (10), 1381–1382.CrossRefGoogle Scholar
Kuchment, P.A. 1993 Floquet Theory for Partial Differential Equations. Springer.CrossRefGoogle Scholar
Leontini, J.S., Lo Jacono, D. & Thompson, M.C. 2015 Stability analysis of the elliptic cylinder wake. J. Fluid Mech. 763, 302–321.CrossRefGoogle Scholar
Leweke, T. & Williamson, C.H.K. 1998 Three-dimensional instabilities in wake transition. Eur. J. Mech. (B/Fluids) 17 (4), 571–586.CrossRefGoogle Scholar
Lindsey, W.F. 1938 Drag of cylinders of simple shapes. NACA Tech. Rep. 619, 169–176.Google Scholar
Lo Jacono, D., Leontini, J.S., Thompson, M.C. & Sheridan, J. 2010 Modification of three-dimensional transition in the wake of a rotationally oscillating cylinder. J. Fluid Mech. 643, 349–362.CrossRefGoogle Scholar
Loiseau, J.-C., Bucci, M.A., Cherubini, S. & Robinet, J.-C. 2019 Time-stepping and Krylov methods for large-scale instability problems. In Computational Modelling of Bifurcations and Instabilities in Fluid Dynamics (ed. A. Gelfgat), pp. 33–73. Springer.CrossRefGoogle Scholar
McCarthy, J.F. Jr. & Kubota, T. 1964 A study of wakes behind a circular cylinder at $M=5.7$. AIAA J. 2 (4), 629–636.CrossRefGoogle Scholar
Meliga, P., Sipp, D. & Chomaz, J.-M. 2010 Effect of compressibility on the global stability of axisymmetric wake flows. J. Fluid Mech. 660, 499–526.CrossRefGoogle Scholar
Murthy, V & Rose, W 1977 Form drag, skin friction, and vortex shedding frequencies for subsonic and transonic crossflows on circular cylinder. AIAA Paper 77-687.CrossRefGoogle Scholar
Nagata, T., Noguchi, A., Kusama, K., Nonomura, T., Komuro, A., Ando, A. & Asai, K. 2020 Experimental investigation on compressible flow over a circular cylinder at Reynolds number of between 1000 and 5000. J. Fluid Mech. 893, A13.CrossRefGoogle Scholar
Nastro, G., Fontane, J. & Joly, L. 2020 Optimal perturbations in viscous round jets subject to Kelvin–Helmholtz instability. J. Fluid Mech. 900, A13.CrossRefGoogle Scholar
Rodriguez, O 1984 The circular cylinder in subsonic and transonic flow. AIAA J. 22 (12), 1713–1718.CrossRefGoogle Scholar
Rolandi, L.V. 2021 Stability of low Reynolds number compressible flows. PhD thesis, ISAE-SUPAERO, Université de Toulouse.Google Scholar
Rolandi, L.V., Jardin, T., Fontane, J., Gressier, J. & Joly, L. 2021 Stability of the low Reynolds number compressible flow past a NACA0012 airfoil. AIAA J. 60 (2), 1052–1066.CrossRefGoogle Scholar
Saez-Mischlich, G. 2021 High order numerical methods for unstructured grids and sliding mesh. PhD thesis, ISAE-SUPAERO, Université de Toulouse.Google 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. 2007 Nonmodal stability theory. Annu. Rev. Fluid Mech. 39 (1), 129–162.CrossRefGoogle Scholar
Stewart, G.W. 2002 A Krylov–Schur algorithm for large eigenproblems. SIAM J. Matrix Anal. Applics. 23 (3), 601–614.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
Thompson, M.C., Leweke, T. & Williamson, C.H.K. 2001 The physical mechanism of transition in bluff body wakes. J. Fluids Struct. 15 (3–4), 607–616.CrossRefGoogle Scholar
Williamson, C.H.K. 1988 The existence of two stages in the transition to three-dimensionality of a cylinder wake. Phys. Fluids 31 (11), 3165–3168.CrossRefGoogle Scholar
Williamson, C.H.K. 1996 a Three-dimensional vortex dynamics in bluff body wakes. Exp. Therm. Fluid Sci. 12 (2), 150–168.CrossRefGoogle Scholar
Williamson, C.H.K. 1996 b Three-dimensional wake transition. J. Fluid Mech. 328, 345–407.CrossRefGoogle Scholar
Williamson, C.H.K. 1996 c Vortex dynamics in the cylinder wake. Annu. Rev. Fluid Mech. 28 (1), 477–539.CrossRefGoogle Scholar
Xia, Z., Xiao, Z., Shi, Y. & Chen, S. 2016 Mach number effect of compressible flow around a circular cylinder. AIAA J. 54 (6), 2004–2009.CrossRefGoogle Scholar
Xu, C.-Y., Chen, L.-W. & Lu, X.-Y. 2009 Numerical simulation of shock wave and turbulence interaction over a circular cylinder. Mod. Phys. Lett. B 23 (03), 233–236.CrossRefGoogle Scholar