Hostname: page-component-8448b6f56d-jr42d Total loading time: 0 Render date: 2024-04-17T14:50:36.244Z Has data issue: false hasContentIssue false
  • English
  • Français

An almost subharmonic instability in the flow past rectangular cylinders

Published online by Cambridge University Press:  21 October 2022

Alessandro Chiarini Open the ORCID record for Alessandro Chiarini [Opens in a new window] ,
Maurizio Quadrio Open the ORCID record for Maurizio Quadrio [Opens in a new window]  and
Franco Auteri Open the ORCID record for Franco Auteri [Opens in a new window]
Alessandro Chiarini
Affiliation:
Dipartimento di Scienze e Tecnologie Aerospaziali, Politecnico di Milano, via La Masa 34, 20156 Milano, Italy
Maurizio Quadrio
Affiliation:
Dipartimento di Scienze e Tecnologie Aerospaziali, Politecnico di Milano, via La Masa 34, 20156 Milano, Italy
Franco Auteri*
Affiliation:
Dipartimento di Scienze e Tecnologie Aerospaziali, Politecnico di Milano, via La Masa 34, 20156 Milano, Italy
*
†Email address for correspondence: franco.auteri@polimi.it
Get access Rights & Permissions [Opens in a new window]

Abstract

The three-dimensional instability of the flow past a 5 : 1 rectangular cylinder is investigated via Floquet analysis and direct numerical simulations. A quasi-subharmonic (QS) unstable mode is detected, marking an important difference with the flow past bodies with lower aspect ratio and/or with smooth leading edge. The QS mode becomes unstable at Reynolds number (based on the cylinder thickness and free-stream velocity) $Re \approx 480$; its spanwise wavelength is approximately three times the cylinder thickness. The structural sensitivity locates the wavemaker region over the longitudinal sides of the cylinder, indicating that the instability is triggered by the mutual inviscid interaction of vortices generated by the leading edge shear layer.

JFM classification

Wakes/Jets: Wakes Vortex Flows: Vortex shedding Instability: Absolute/convective instability
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 950 , 10 November 2022 , A20
Check for updates
Copyright
© The Author(s), 2022. 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

Abdalla, I.E. & Yang, Z. 2004 Numerical study of the instability mechanism in transitional separating–reattaching flow. Intl J. Heat Fluid Flow 25 (4), 593–605.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
Bernal, L.P., Breidenthal, R.E., Brown, G.L., Konrad, J.H. & Roshko, A. 1979 On the development of three dimensional small scales in turbulent mixing layers. In 2nd Symposium on Turbulent Shear Flows (ed. L.J.S. Bradbury), pp. 8.1–8.6. Springer-Verlag.Google Scholar
Blackburn, H.M. & Lopez, J.M. 2003 On three-dimensional quasiperiodic Floquet instabilities of two-dimensional bluff body wakes. Phys. Fluids 15 (8), L57–L60.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
Blackburn, H.M. & Sheard, G.J. 2010 On quasiperiodic and subharmonic Floquet wake instabilities. Phys. Fluids 22 (3), 031701.CrossRefGoogle Scholar
Boghosian, M.E. & Cassel, K.W. 2016 On the origins of vortex shedding in two-dimensional incompressible flows. Theor. Comput. Fluid Dyn. 30 (6), 511–527.CrossRefGoogle ScholarPubMed
Brezzi, F. 1974 On the existence, uniqueness and approximation of saddle-point problems arising from Lagrangian multipliers. ESAIM. Math. Model Numer. Anal. 8 (R2), 129–151.Google Scholar
Browand, F.K. & Troutt, T.R. 1980 A note on spanwise structure in the two-dimensional mixing layer. J. Fluid Mech. 97 (4), 771–781.CrossRefGoogle Scholar
Chandrsuda, C., Mehta, R.D., Weir, A.D. & Bradshaw, P. 1978 Effect of free-stream turbulence on large structure in turbulent mixing layers. J. Fluid Mech. 85 (4), 693–704.CrossRefGoogle Scholar
Chaurasia, H.K. & Thompson, M.C. 2011 Three-dimensional instabilities in the boundary-layer flow over a long rectangular plate. J. Fluid Mech. 681, 411–433.CrossRefGoogle Scholar
Chiarini, A., Gatti, D., Cimarelli, A. & Quadrio, M. 2022 a Structure of turbulence in the flow around a rectangular cylinder. J. Fluid Mech. 946, A35.CrossRefGoogle Scholar
Chiarini, A. & Quadrio, M. 2021 The turbulent flow over the BARC rectangular cylinder: a DNS study. Flow Turbul. Combust. 107, 875–899.CrossRefGoogle Scholar
Chiarini, A., Quadrio, M. & Auteri, F. 2021 Linear stability of the steady flow past rectangular cylinders. J. Fluid Mech. 929, A36.CrossRefGoogle Scholar
Chiarini, A., Quadrio, M. & Auteri, F. 2022 b On the frequency selection mechanism of the low-$Re$ flow around rectangular cylinders. J. Fluid Mech. 933, A44.CrossRefGoogle Scholar
Choi, C.-B. & Yang, K.-S. 2014 Three-dimensional instability in flow past a rectangular cylinder ranging from a normal flat plate to a square cylinder. Phys. Fluids 26 (6), 061702.CrossRefGoogle Scholar
Cimarelli, A., Leonforte, A. & Angeli, D. 2018 On the structure of the self-sustaining cycle in separating and reattaching flows. J. Fluid Mech. 857, 907–936.CrossRefGoogle Scholar
Citro, V., Luchini, P., Giannetti, F. & Auteri, F. 2017 Efficient stabilization and acceleration of numerical simulation of fluid flows by residual recombination. J. Comput. Phys. 344, 234–246.CrossRefGoogle Scholar
Giannetti, F., Camarri, S. & Luchini, P. 2010 Structural sensitivity of the secondary instability in the wake of a circular cylinder. J. Fluid Mech. 651, 319–337.CrossRefGoogle Scholar
Giannetti, F. & Luchini, P. 2007 Structural sensitivity of the first instability of the cylinder wake. J. Fluid Mech. 581, 167–197.CrossRefGoogle Scholar
Hecht, F. 2012 New development in FreeFem++. J. Numer. Maths 20 (3–4), 251–266.Google Scholar
Hourigan, K., Thompson, M.C. & Tan, B.T. 2001 Self-sustained oscillations in flows around long blunt plates. J. Fluids Struct. 15 (3), 387–398.CrossRefGoogle Scholar
Huang, Y., Zhou, B., Tang, Z. & Zhang, F. 2017 Transition scenario and transition control of the flow over a semi-infinite square leading-edge plate. Phys. Fluids 29 (7), 074105.CrossRefGoogle Scholar
Jallas, D., Marquet, O. & Fabre, D. 2017 Linear and nonlinear perturbation analysis of the symmetry breaking in time-periodic propulsive wakes. Phys. Rev. E 95 (6-1), 063111.CrossRefGoogle ScholarPubMed
Jeong, J., Hussain, F., Schoppa, W. & Kim, J. 1997 Coherent structures near the wall in a turbulent channel flow. J. Fluid Mech. 332, 185–214.CrossRefGoogle Scholar
Jiang, H. & Cheng, L. 2018 Hydrodynamic characteristics of flow past a square cylinder at moderate Reynolds numbers. Phys. Fluids 30 (10), 104107.CrossRefGoogle Scholar
Jiang, H., Cheng, L. & An, H. 2018 Three-dimensional wake transition of a square cylinder. J. Fluid Mech. 842, 102–127.CrossRefGoogle Scholar
Kerswell, R.R. 2002 Elliptical instability. Annu. Rev. Fluid Mech. 34 (1), 83–113.CrossRefGoogle Scholar
Luchini, P. 2013 Linearized no-slip boundary conditions at a rough surface. J. Fluid Mech. 737, 349–367.CrossRefGoogle Scholar
Luchini, P. 2016 Immersed-boundary simulation of turbulent flow past a sinusoidally undulated river bottom. Eur. J. Mech. (B/Fluids) 55, 340–347.CrossRefGoogle Scholar
Marques, F., Lopez, J.M. & Blackburn, H.M. 2004 Bifurcations in systems with Z2 spatio-temporal and O(2) spatial symmetry. Phys. D: Nonlinear Phenom. 189 (3), 247–276.CrossRefGoogle Scholar
Mills, R., Sheridan, J. & Hourigan, K. 2002 Response of base suction and vortex shedding from rectangular prisms to transverse forcing. J. Fluid Mech. 461, 25–49.CrossRefGoogle Scholar
Mills, R., Sheridan, J., Hourigan, K. & Welsh, M.C. 1995 The mechanism controlling vortex shedding from rectangular bluff bodies. In Proceeding Twelfth Australas. Fluid Mech. Conf., pp. 227–230.Google Scholar
Monkewitz, P.A., Huerre, P. & Chomaz, J.-M. 1993 Global linear stability analysis of weakly non-parallel shear flows. J. Fluid Mech. 251, 1–20.CrossRefGoogle Scholar
Moore, D.M., Letchford, C.W. & Amitay, M. 2019 Energetic scales in a bluff body shear layer. J. Fluid Mech. 875, 543–575.CrossRefGoogle Scholar
Nakamura, Y., Ohya, Y. & Tsuruta, H. 1991 Experiments on vortex shedding from flat plates with square leading and trailing edges. J. Fluid Mech. 222, 437–447.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
Okajima, A. 1982 Strouhal numbers of rectangular cylinders. J. Fluid Mech. 123, 379–398.CrossRefGoogle Scholar
Ozono, S., Ohya, Y., Nakamura, Y. & Nakayama, R. 1992 Stepwise increase in the Strouhal number for flows around flat plates. Intl J. Numer. Meth. Fluids 15 (9), 1025–1036.CrossRefGoogle Scholar
Park, D. & Yang, K.-S. 2016 Flow instabilities in the wake of a rounded square cylinder. J. Fluid Mech. 793, 915–932.CrossRefGoogle Scholar
Pierrehumbert, R.T. & Widnall, S.E. 1982 The two- and three-dimensional instabilities of a spatially periodic shear layer. J. Fluid Mech. 114, 59–82.CrossRefGoogle Scholar
Rai, M.M. & Moin, P. 1991 Direct simulations of turbulent flow using finite-difference schemes. J. Comput. Phys. 96, 15–53.Google Scholar
Robichaux, J., Balachandar, S. & Vanka, S.P. 1999 Three-dimensional Floquet instability of the wake of square cylinder. Phys. Fluids 11 (3), 560–578.CrossRefGoogle Scholar
Robinson, A.C. & Saffman, P.G. 1982 Three-dimensional stability of vortex arrays. J. Fluid Mech. 125, 411–427.CrossRefGoogle Scholar
Ryan, K., Thompson, M.C. & Hourigan, K. 2005 Three-dimensional transition in the wake of bluff elongated cylinders. J. Fluid Mech. 538, 1–29.CrossRefGoogle Scholar
Saad, Y 2011 Numerical Methods for Large Eigenvalue Problems. Society for Industrial and Applied Mathematics.CrossRefGoogle Scholar
Saha, A.K., Muralidhar, K. & Biswas, G. 2000 Transition and chaos in two-dimensional flow past a square cylinder. J. Engng Mech. ASCE 126 (5), 523–532.CrossRefGoogle Scholar
Sasaki, K. & Kiya, M. 1991 Three-dimensional vortex structure in a leading-edge separation bubble at moderate Reynolds numbers. Trans. ASME J. Fluids Engng 113 (3), 405–410.CrossRefGoogle Scholar
Sheard, G.J. 2011 Wake stability features behind a square cylinder: focus on small incidence angles. J. Fluids Struct. 27 (5), 734–742.CrossRefGoogle Scholar
Sheard, G.J., Fitzgerald, M.J. & Ryan, K. 2009 Cylinders with square cross-section: wake instabilities with incidence angle variation. J. Fluid Mech. 630, 43–69.CrossRefGoogle Scholar
Sohankar, A., Norberg, C. & Davidson, L. 1999 Simulation of three-dimensional flow around a square cylinder at moderate Reynolds numbers. Phys. Fluids 11 (2), 288–306.CrossRefGoogle Scholar
Stuart, J.T. 1967 On finite amplitude oscillations in laminar mixing layers. J. Fluid Mech. 29 (3), 417–440.CrossRefGoogle Scholar
Swift, J.W. & Wiesenfeld, K. 1984 Suppression of period doubling in symmetric systems. Phys. Rev. Lett. 52 (9), 705–708.CrossRefGoogle Scholar
Tan, B.T., Thompson, M.C. & Hourigan, K. 2004 Flow past rectangular cylinders: receptivity to transverse forcing. J. Fluid Mech. 515, 33–62.CrossRefGoogle Scholar
Tenaud, C., Podvin, B., Fraigneau, Y. & Daru, V. 2016 On wall pressure fluctuations and their coupling with vortex dynamics in a separated–reattached turbulent flow over a blunt flat plate. Intl J. Heat Fluid Flow 61 (Part B), 730–748.CrossRefGoogle Scholar
Thompson, M.C., Hourigan, K., Ryan, K. & Sheard, G.J. 2006 Wake transition of two-dimensional cylinders and axisymmetric bluff bodies. J. Fluids Struct. 22 (6), 793–806.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), 607–616.CrossRefGoogle Scholar
Waleffe, F. 1990 On the three-dimensional instability of strained vortices. Phys. Fluids A: Fluid Dyn. 2 (1), 76–80.CrossRefGoogle Scholar
Williamson, C.H.K. & Govardhan, R. 2008 A brief review of recent results in vortex-induced vibrations. J. Wind Engng Ind. Aerodyn. 96 (6), 713–735.CrossRefGoogle Scholar