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Flow states and transitions in flows past arrays of tandem cylinders. (English) Zbl 1461.76307

Summary: 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.

MSC:

76F65 Direct numerical and large eddy simulation of turbulence
76D25 Wakes and jets
76E15 Absolute and convective instability and stability in hydrodynamic stability
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References:

[1] Barkley, D.2006Linear analysis of the cylinder wake mean flow. Europhys. Lett.75 (5), 750.
[2] Barkley, D., Blackburn, H. M. & Sherwin, S. J.2008Direct optimal growth analysis for timesteppers. Intl J. Numer. Meth. Fluids57, 1435-1458. · Zbl 1144.76044
[3] Browand, F. K.1966An experimental investigation of the instability of an incompressible separated shear layer. J. Fluid Mech.26, 281-307.
[4] Brown, G. L. & Roshko, A.1974On density effects and large structure in turbulent mixing layers. J. Fluid Mech.64, 775-816. · Zbl 1416.76061
[5] Carmo, B., Meneghini, J. R. & Sherwin, S. J.2010Secondary instabilities in the flow around two circular cylinders in tandem. J. Fluid Mech.644, 395-431. · Zbl 1189.76218
[6] Chomaz, J. M.2005Global instabilities in spatially developing flows: non-normality and nonlinearity. Annu. Rev. Fluid Mech.37, 357-392. · Zbl 1117.76027
[7] Drazin, P. G. & Reid, W. H.2004Hydrodynamic Stability. Cambridge University Press. · Zbl 1055.76001
[8] Dušek, J., Le Gal, P. & Fraunié, P.1994A numerical and theoretical study of the first Hopf bifurcation in a cylinder wake. J. Fluid Mech.264, 59-80. · Zbl 0813.76021
[9] Ghoniem, A. F. & Ng, K. K.1987Numerical study of the dynamics of a forced shear layer. Phys. Fluids30, 706-721.
[10] Giannetti, F. & Luchini, P.2007Structural sensitivity of the first instability of the cylinder wake. J. Fluid Mech.581, 167-197. · Zbl 1115.76028
[11] Griffith, M. D. & Leontini, J. S.2017Sharp interface immersed boundary methods and their application to vortex-induced vibration of a cylinder. J. Fluids Struct.72, 38-58.
[12] Griffith, M. D., Lo Jacono, D., Sheridan, J. & Leontini, J. S.2017Flow-induced vibration of two cylinders in tandem and staggered arrangements. J. Fluid Mech.833, 98-130. · Zbl 1419.76177
[13] Hammond, D. A. & Redekopp, L. G.1997Global dynamics of symmetric and asymmetric wakes. J. Fluid Mech.331, 231-260. · Zbl 0899.76130
[14] Hanke, W., Witte, M., Miersch, L., Brede, M. & Oeffner, J.2010Harbor seal vibrissa morphology suppresses vortex-induced vibrations. J. Expl Biol.213 (15), 2665-2672.
[15] Ho, C. M. & Huerre, P.1984Perturbed free shear layers. Annu. Rev. Fluid Mech.16, 365-424.
[16] Hu, J. C. & Zhou, Y.2008Flow structure behind two staggered circular cylinders. Part 1. Downstream evolution and classification. J. Fluid Mech.607, 51-80. · Zbl 1145.76304
[17] Huerre, P. & Monkewitz, P. A.1985Absolute and convective instabilities in free shear layers. J. Fluid Mech.159, 151-168. · Zbl 0588.76067
[18] 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. · Zbl 0904.76021
[19] Khor, M., Sheridan, J., Thompson, M. C. & Hourigan, K.2008Global frequency selection in the observed time-mean wakes of circular cylinders. J. Fluid Mech.601, 425-441. · Zbl 1151.76330
[20] Kupfer, K., Bers, A. & Ram, A. K.1987The cusp map in the complex-frequency plane for absolute instabilities. Phys. Fluids30 (10), 3075-3082.
[21] Lee, C. M. & Choi, Y. D.2007Comparison 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.
[22] Leontini, J. S., Thompson, M. C. & Hourigan, K.2010A numerical study of global frequency selection in the time-mean wake of a circular cylinder. J. Fluid Mech.645, 435-446. · Zbl 1189.76153
[23] Luchini, P. & Bottaro, A.2014Adjoint equations in stability analysis. Annu. Rev. Fluid Mech.46, 493-517. · Zbl 1297.76068
[24] Mantič-Lugo, V., Arratia, C. & Gallaire, F.2014Self-consistent mean flow description of the nonlinear saturation of the vortex shedding in the cylinder wake. Phys. Rev. Lett.113, 084501.
[25] Marquet, O., Lombardi, M., Chomaz, J.-M., Sipp, D. & Jacquin, L.2009Direct and adjoint global modes of a recirculation bubble: lift-up and convective non-normalities. J. Fluid Mech.622, 1-21. · Zbl 1165.76337
[26] Marquet, O., Sipp, D. & Jacquin, L.2008Sensitivity analysis and passive control of cylinder flow. J. Fluid Mech.615, 221-252. · Zbl 1165.76012
[27] Meliga, P., Boujo, E., Pujals, G. & Gallaire, F.2014Sensitivity of aerodynamic forces in laminar and turbulent flow past a square cylinder. Phys. Fluids26 (10), 104101.
[28] Mittal, R., Dong, H., Bozkurttas, M., Najjar, F. M., Vargas, A. & Von Loebbecke, A.2008A versatile sharp interface immersed boundary method for incompressible flows with complex boundaries. J. Comput. Phys.227, 4825-4852. · Zbl 1388.76263
[29] Monkewitz, P. A. & Huerre, P.1982Influence of the velocity ratio on the spatial instability of mixing layers. Phys. Fluids25, 1137-1143.
[30] Nepf, H. M.2012Flow and transport in regions with aquatic vegetation. Annu. Rev. Fluid Mech.44, 123-142. · Zbl 1350.76056
[31] Pier, B.2002On the frequency selection of finite-amplitude vortex shedding in the cylinder wake. J. Fluid Mech.458, 407-417. · Zbl 1060.76031
[32] Seo, J. H. & Mittal, R.2011A sharp-interface immersed boundary method with improved mass conservation and reduced spurious pressure oscillations. J. Comput. Phys.230, 7347-7363. · Zbl 1408.76162
[33] Sumner, D.2010Two circular cylinders in cross-flow: a review. J. Fluids Struct.26 (6), 849-899.
[34] Sumner, D., Price, S. & Paidoussis, M.2000Flow-pattern identification for two staggered circular cylinders in cross-flow. J. Fluid Mech.411, 263-303. · Zbl 0951.76505
[35] Thiria, B. & Weisfreid, J. E.2007Stability properties of forced wakes. J. Fluid Mech.579, 137-161. · Zbl 1113.76011
[36] Tsui, Y. T.1986On 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.
[37] Wang, S. Y., Tian, F. B., Jia, L. B., Lu, X. Y. & Yin, X. Z.2010Secondary vortex street in the wake of two tandem circular cylinders at low Reynolds numbers. Phys. Rev. E81, 036305.
[38] Zdravkovich, M. M.1987The effects of interference between circular cylinders in cross flow. J. Fluids Struct.1 (2), 239-261.
[39] Zhou, Y. & Alam, M. M.2016Wake of two interacting circular cylinders: a review. Intl J. Heat Fluid Flow62, 510-537.
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