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Flow states and transitions in flows past arrays of tandem cylinders

Published online by Cambridge University Press:  15 January 2021

Negar Hosseini Open the ORCID record for Negar Hosseini [Opens in a new window] ,
Martin D. Griffith Open the ORCID record for Martin D. Griffith [Opens in a new window]  and
Justin S. Leontini Open the ORCID record for Justin S. Leontini [Opens in a new window]
Negar Hosseini*
Affiliation:
Department of Mechanical and Product Design Engineering, Swinburne University of Technology, John Street, Hawthorn, VIC3122, Australia
Martin D. Griffith
Affiliation:
Department of Mechanical and Product Design Engineering, Swinburne University of Technology, John Street, Hawthorn, VIC3122, Australia
Justin S. Leontini
Affiliation:
Department of Mechanical and Product Design Engineering, Swinburne University of Technology, John Street, Hawthorn, VIC3122, Australia
*
†Email address for correspondence: [email protected]
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Abstract

Direct numerical simulations at $Re=200$ have been conducted of the flow past rows of tandem cylinders. It is shown that when the pitch between the two upstream cylinders is large, the wake downstream is characterised by a two-row vortex structure. Placing a third body on the wake centreline in the majority of this two-row structure has basically no impact both upstream and downstream – the third body is cloaked. However, a region is identified where the placement of a body suppresses vortex shedding from the first cylinder and the two-row structure is destroyed, globally broadcasting the presence of the third body. The effect is shown to occur for different third-body shapes. To understand the existence of this broadcasting region, local instability analysis is conducted which shows the majority of the two-row structure to be convectively unstable, with only a small region adjacent to the rear of the second cylinder that is absolutely unstable. This suggests only bodies placed close to the second body will trigger the global change, and this is supported by a global sensitivity analysis and observation from the simulations. However, neither the local analysis nor the global sensitivity analysis explains the presence of a lower limit for the third-body position that will trigger a global change. However the simulation results clearly show that a third body placed very close to the second body does not trigger this change.

JFM classification

Instability: Absolute/convective instability Vortex Flows: Vortex shedding Wakes/Jets: Wakes
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 910 , 10 March 2021 , A34
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

REFERENCES

Barkley, D. 2006 Linear analysis of the cylinder wake mean flow. Europhys. Lett. 75 (5), 750.Google Scholar
Barkley, D., Blackburn, H. M. & Sherwin, S. J. 2008 Direct optimal growth analysis for timesteppers. Intl J. Numer. Meth. Fluids 57, 1435–1458.CrossRefGoogle Scholar
Browand, F. K. 1966 An experimental investigation of the instability of an incompressible separated shear layer. J. Fluid Mech. 26, 281–307.CrossRefGoogle Scholar
Brown, G. L. & Roshko, A. 1974 On density effects and large structure in turbulent mixing layers. J. Fluid Mech. 64, 775–816.Google Scholar
Carmo, B., 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
Chomaz, J. M. 2005 Global instabilities in spatially developing flows: non-normality and nonlinearity. Annu. Rev. Fluid Mech. 37, 357–392.CrossRefGoogle Scholar
Drazin, P. G. & Reid, W. H. 2004 Hydrodynamic Stability. Cambridge University Press.CrossRefGoogle Scholar
Dušek, J., Le Gal, P. & Fraunié, P. 1994 A numerical and theoretical study of the first Hopf bifurcation in a cylinder wake. J. Fluid Mech. 264, 59–80.CrossRefGoogle Scholar
Ghoniem, A. F. & Ng, K. K. 1987 Numerical study of the dynamics of a forced shear layer. Phys. Fluids 30, 706–721.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
Griffith, M. D. & Leontini, J. S. 2017 Sharp interface immersed boundary methods and their application to vortex-induced vibration of a cylinder. J. Fluids Struct. 72, 38–58.CrossRefGoogle Scholar
Griffith, M. D., Lo Jacono, D., Sheridan, J. & Leontini, J. S. 2017 Flow-induced vibration of two cylinders in tandem and staggered arrangements. J. Fluid Mech. 833, 98–130.CrossRefGoogle Scholar
Hammond, D. A. & Redekopp, L. G. 1997 Global dynamics of symmetric and asymmetric wakes. J. Fluid Mech. 331, 231–260.CrossRefGoogle Scholar
Hanke, W., Witte, M., Miersch, L., Brede, M. & Oeffner, J. 2010 Harbor seal vibrissa morphology suppresses vortex-induced vibrations. J. Expl Biol. 213 (15), 2665–2672.CrossRefGoogle ScholarPubMed
Ho, C. M. & Huerre, P. 1984 Perturbed free shear layers. Annu. Rev. Fluid Mech. 16, 365–424.CrossRefGoogle Scholar
Hu, J. C. & Zhou, Y. 2008 Flow structure behind two staggered circular cylinders. Part 1. Downstream evolution and classification. J. Fluid Mech. 607, 51–80.Google Scholar
Huerre, P. & Monkewitz, P. A. 1985 Absolute and convective instabilities in free shear layers. J. Fluid Mech. 159, 151–168.CrossRefGoogle Scholar
Huerre, P. & Rossi, M. 1998 Hydrodynamic instabilities in open flows. In Hydrodynamics and Nonlinear Instabilities (ed. C. Godréche & P. Manneville), pp. 81–294. Cambridge University Press.CrossRefGoogle Scholar
Khor, M., Sheridan, J., Thompson, M. C. & Hourigan, K. 2008 Global frequency selection in the observed time-mean wakes of circular cylinders. J. Fluid Mech. 601, 425–441.CrossRefGoogle Scholar
Kupfer, K., Bers, A. & Ram, A. K. 1987 The cusp map in the complex-frequency plane for absolute instabilities. Phys. Fluids 30 (10), 3075–3082.CrossRefGoogle Scholar
Lee, C. M. & Choi, Y. D. 2007 Comparison of thermo-hydraulic performances of large scale vortex flow (LSVF) and small scale vortex flow (SSVF) mixing vanes in $17 \times 17$ nuclear rod bundle. Nucl. Engng Des. 237, 2322–2331.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
Luchini, P. & Bottaro, A. 2014 Adjoint equations in stability analysis. Annu. Rev. Fluid Mech. 46, 493–517.CrossRefGoogle Scholar
Mantič-Lugo, V., Arratia, C. & Gallaire, F. 2014 Self-consistent mean flow description of the nonlinear saturation of the vortex shedding in the cylinder wake. Phys. Rev. Lett. 113, 084501.CrossRefGoogle ScholarPubMed
Marquet, O., Lombardi, M., Chomaz, J.-M., Sipp, D. & Jacquin, L. 2009 Direct and adjoint global modes of a recirculation bubble: lift-up and convective non-normalities. J. Fluid Mech. 622, 1–21.Google 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., Boujo, E., Pujals, G. & Gallaire, F. 2014 Sensitivity of aerodynamic forces in laminar and turbulent flow past a square cylinder. Phys. Fluids 26 (10), 104101.Google Scholar
Mittal, R., Dong, H., Bozkurttas, M., Najjar, F. M., Vargas, A. & von Loebbecke, A. 2008 A versatile sharp interface immersed boundary method for incompressible flows with complex boundaries. J. Comput. Phys. 227, 4825–4852.CrossRefGoogle ScholarPubMed
Monkewitz, P. A. & Huerre, P. 1982 Influence of the velocity ratio on the spatial instability of mixing layers. Phys. Fluids 25, 1137–1143.CrossRefGoogle Scholar
Nepf, H. M. 2012 Flow and transport in regions with aquatic vegetation. Annu. Rev. Fluid Mech. 44, 123–142.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
Seo, J. H. & Mittal, R. 2011 A sharp-interface immersed boundary method with improved mass conservation and reduced spurious pressure oscillations. J. Comput. Phys. 230, 7347–7363.CrossRefGoogle ScholarPubMed
Sumner, D. 2010 Two circular cylinders in cross-flow: a review. J. Fluids Struct. 26 (6), 849–899.CrossRefGoogle Scholar
Sumner, D., Price, S. & Paidoussis, M. 2000 Flow-pattern identification for two staggered circular cylinders in cross-flow. J. Fluid Mech. 411, 263–303.CrossRefGoogle Scholar
Thiria, B. & Weisfreid, J. E. 2007 Stability properties of forced wakes. J. Fluid Mech. 579, 137–161.CrossRefGoogle Scholar
Tsui, Y. T. 1986 On wake-induced vibration of a conductor in the wake of another via a 3-D finite element method. J. Sound Vib. 107 (1), 39–58.CrossRefGoogle Scholar
Wang, S. Y., Tian, F. B., Jia, L. B., Lu, X. Y. & Yin, X. Z. 2010 Secondary vortex street in the wake of two tandem circular cylinders at low Reynolds numbers. Phys. Rev. E 81, 036305.CrossRefGoogle Scholar
Zdravkovich, M. M. 1987 The effects of interference between circular cylinders in cross flow. J. Fluids Struct. 1 (2), 239–261.CrossRefGoogle Scholar
Zhou, Y. & Alam, M. M. 2016 Wake of two interacting circular cylinders: a review. Intl J. Heat Fluid Flow 62, 510–537.CrossRefGoogle Scholar