Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-12-05T02:38:13.777Z Has data issue: false hasContentIssue false
  • English
  • Français

First instability and structural sensitivity of the flow past two side-by-side cylinders

Published online by Cambridge University Press:  19 May 2014

M. Carini ,
F. Giannetti  and
F. Auteri
M. Carini
Affiliation:
Dipartimento di Scienze e Tecnologie Aerospaziali, Politecnico di Milano, via La Masa 34, 20156 Milano, Italy
F. Giannetti
Affiliation:
Dipartimento di Ingegneria Industriale, Università degli studi di Salerno, via Ponte don Melillo, 84084 Fisciano (SA), Italy
F. Auteri*
Affiliation:
Dipartimento di Scienze e Tecnologie Aerospaziali, Politecnico di Milano, via La Masa 34, 20156 Milano, Italy
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The onset of two-dimensional instabilities in the flow past two side-by-side circular cylinders is numerically investigated in the ranges $0.1\leq g\leq 3$ and $\mathit{Re}<100$, with $g$ being the non-dimensional gap spacing between the surfaces of the two cylinders and $\mathit{Re}$ the Reynolds number. A comprehensive, global stability analysis of the symmetric base flow is carried out, indicating that three harmonic modes and one steady antisymmetric mode become unstable at different values of $g$ and $\mathit{Re}$. These modes are known to promote distinct flow regimes at increasing values of $g$: single bluff-body, asymmetric, in-phase and antiphase synchronized vortex shedding. For each mode, the inherent structural sensitivity is examined in order to identify the core region of the related instability mechanism. In addition, by exploiting the structural sensitivity analysis to base flow modifications, a passive control strategy is proposed for the simultaneous suppression of the two synchronized shedding modes using two small secondary cylinders. Its effectiveness is then validated a posteriori by means of direct numerical simulations.

JFM classification

Flow Control: Instability control Wakes/Jets: Separated flows Wakes/Jets: Wakes/Jets
Type
Papers
Information
Journal of Fluid Mechanics , Volume 749 , 25 June 2014 , pp. 627 - 648
Copyright
© 2014 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

Afgan, I., Kahil, Y., Benhamadouche, S. & Sagaut, P. 2011 Large eddy simulation of the flow around single and two side-by-side cylinders at subcritical Reynolds numbers. Phys. Fluids 23, 075101.CrossRefGoogle Scholar
Akinaga, T. & Mizushima, J. 2005 Linear stability of flows past two circular cylinders in a side-by-side arrangement. J. Phys. Soc. Japan 74 (5), 1366–1369.CrossRefGoogle Scholar
Alam, M. M., Moriya, M. & Sakamoto, H. 2003 Aerodynamic characteristics of two side-by-side circular cylinders and application of wavelet analysis on the switching phenomenon. J. Fluids Struct. 23, 325–346.CrossRefGoogle Scholar
Alam, M. M. & Zhou, Y. 2007 Flow around two side-by-side closely spaced circular cylinders. J. Fluids Struct. 18, 799–805.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
Bearman, P. W. & Wadcock, A. J. 1973 The interaction between a pair of circular cylinders normal to a stream. J. Fluid Mech. 61, 499–511.CrossRefGoogle Scholar
Carini, M., Giannetti, F. & Auteri, F. 2014 On the origin of the flip-flop instability of two side-by-side cylinder wakes. J. Fluid Mech. 742, 552–576.CrossRefGoogle Scholar
Carini, M., Auteri, F. & Giannetti, F.2014 Centre-manifold reduction of bifurcating flows. J. Fluid Mech. (submitted).CrossRefGoogle Scholar
Chen, L., Tu, J. Y. & Yeoh, G. H. 2003 Numerical simulation of turbulent wake flows behind two side-by-side cylinders. J. Fluids Struct. 18, 387–403.CrossRefGoogle Scholar
Davis, T. A. 2004 Algorithm 832: UMFPACK, an unsymmetric-pattern multifrontal method. ACM Trans. Math. Softw. 30 (2), 196–199.CrossRefGoogle Scholar
Fani, A., Camarri, S. & Salvetti, M. V. 2012 Stability analysis and control of the flow in a symmetric channel with a sudden expansion. Phys. Fluids 24, 084102.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
Huerre, P. & Rossi, M. 1998 Hydrodynamic instabilities in open flows. In Hydrodynamics and Nonlinear Instabilities (ed. Godrèche, C. & Manneville, P.), pp. 81–294. Cambridge University Press.CrossRefGoogle Scholar
Ishigai, S., Nishikawa, E., Nishmura, K. & Cho, K. 1972 Experimental study on structure of gas flow in tube banks with tube axes normal to flow: Part 1, Kármán vortex flow around two tubes at various spacings. Bull. JSME 15, 949–956.CrossRefGoogle Scholar
Jester, W. & Kallinderis, Y. 2003 Numerical study of the incompressible flow about a fixed cylinder pairs. J. Fluids Struct. 17, 561–577.CrossRefGoogle Scholar
Kang, S. 2003 Characteristics of flow over two circular cylinders in a side-by-side arrangement at low Reynolds numbers. Phys. Fluids 15, 2486–2498.CrossRefGoogle Scholar
Lashgari, I., Pralits, J. O., Giannetti, F. & Brandt, L. 2012 First instability of the flow of shear-thinning and shear-thickening fluids past a circular cylinder. J. Fluid Mech. 701, 201–227.CrossRefGoogle Scholar
Lehoucq, R. B., Sorensen, D. C. & Yang, C. 1998 ARPACK Users Guide. SIAM.CrossRefGoogle Scholar
Liu, K., Ma, D. -J., Sun, D. -J. & Yin, X. -J. 2007 Wake patterns of flow past a pair of circular cylinders in side-by-side arrangements at low Reynolds numbers. J. Hydrodyn. B 19 (6), 690–697.CrossRefGoogle Scholar
Luchini, P. & Bottaro, A. 2014 Adjoint equations in stability analysis. Annu. Rev. Fluid Mech. 46, 493–517.CrossRefGoogle Scholar
Luchini, P., Giannetti, F. & Pralits, J. O. 2008 Structural sensitivity of linear and nonlinear global modes. In Proceedings of the 5th AIAA Theoretical Fluid Mechanics Conference, 23–26 June, Seattle, WA, pp. 1–19. Curran Associates Inc.Google Scholar
Luchini, P., Pralits, J. O. & Giannetti, F. 2007 Structural sensitivity of the finite-amplitude vortex shedding behind a circular cylinder. In Proceedings of the 2nd IUTAM Symposium on Unsteady Separated Flows and Their Control, 18–22 June 2007, Corfu, Greece (ed. Braza, M. & Houringan, K.), pp. 151–160. Springer.Google Scholar
Magri, L. & Juniper, M. P. 2013 Sensitivity analysis of a time-delayed thermo-acoustic system via an adjoint-based approach. J. Fluid Mech. 719, 183–202.CrossRefGoogle Scholar
Marquet, O., Sipp, D. & Jacquin, L. 2008 Sensitivity analysis and passive control of cylinder flow. J. Fluid Mech. 615, 221–252.CrossRefGoogle Scholar
Meliga, P. & Chomaz, J. -M. 2011 An asymptotic expansion for the vortex-induced vibrations of a circular cylinder. J. Fluid Mech. 671, 137–167.CrossRefGoogle Scholar
Meliga, P., Gallaire, F. & Chomaz, J. -M. 2012 A weakly nonlinear mechanism for mode selection in swirling jets. J. Fluid Mech. 699, 216–262.CrossRefGoogle Scholar
Meneghini, J. R., Saltara, F., Siqueira, C. L. R. & Ferrari, J. A. 2001 Numerical simulation of flow interference between two circular cylinders in tandem and side-by-side arrangements. J. Fluids Struct. 15, 327–350.CrossRefGoogle Scholar
Mizushima, J. & Ino, Y. 2008 Stability of flows past a pair of circular cylinders in a side-by-side arrangement. J. Fluid Mech. 595, 491–507.CrossRefGoogle Scholar
Peschard, I. & Le Gal, P. 1996 Coupled wakes of cylinders. Phys. Rev. Lett. 77, 3122–3125.CrossRefGoogle ScholarPubMed
Pralits, J. O., Brandt, L. & Giannetti, F. 2010 Instability and sensitivity of the flow around a rotating circular cylinder. J. Fluid Mech. 650, 1–24.CrossRefGoogle Scholar
Pralits, J. O., Giannetti, F. & Brandt, L. 2013 Three-dimensional instability of the flow around a rotating circular cylinder. J. Fluid Mech. 730, 5–18.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
Salinger, A. G., Bou-Rabee, N. M., Pawlowski, R. P., Wilkes, E. D., Burroughs, E. A., Lehoucq, E. A. & Romero, L. A.2002 LOCA 1.1 – library of continuation algorithms: theory and implementation manual Tech. Rep. SAND2002-0396. Sandia National Laboratories.CrossRefGoogle Scholar
Shao, J. & Zhang, C. 2008 Large eddy simulation of the flow past two side-by-side circular cylinders. Intl J. Comput. Fluid Dyn. 22 (6), 393–404.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
Spivack, H. M. 1946 Vortex frequency and flow pattern in the wake of two parallel cylinders at varied spacings normal to an airstream. J. Aero. Sci. 13, 289–297.CrossRefGoogle Scholar
Sumner, D. 2010 Two circular cylinders in cross-flows: a review. J. Fluids Struct. 26, 849–899.CrossRefGoogle Scholar
Sumner, D., Wong, S. S. T., Price, S. J. & Païdoussis, M. P. 1999 Fluid behavior of side-by-side circular cylinders in steady cross-flow. J. Fluids Struct. 13, 309–338.CrossRefGoogle Scholar
Theofilis, V. 2011 Global linear instability. Annu. Rev. Fluid Mech. 43, 319–352.CrossRefGoogle Scholar
Williamson, C. H. K. 1985 Evolution of a single wake behind a pair of bluff bodies. J. Fluid Mech. 159, 1–18.CrossRefGoogle Scholar
Xu, S. J., Zhou, Y. & So, R. M. C. 2003 Reynolds number effects on the flow structure behind two side-by-side cylinders. Phys. Fluids 15, 1214–1219.CrossRefGoogle Scholar
Zdravkovich, M. M. & Pridden, D. L. 1977 Interference between two circular cylinders; series of unexpected discontinuities. J. Wind Engng Ind. Aerodyn. 2, 255–270.CrossRefGoogle Scholar
Zhou, Y., Zhang, H. J. & Yiu, M. W. 2002 The turbulent wake of two side-by-side circular cylinders. J. Fluid Mech. 458, 303–332.CrossRefGoogle Scholar