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Turbulent wake behind side-by-side flat plates: computational study of interference effects

  • Fatemeh H. Dadmarzi (a1), Vagesh D. Narasimhamurthy (a2), Helge I. Andersson (a3) and Bjørnar Pettersen (a1)


The complex wake behind two side-by-side flat plates placed normal to the inflow direction has been explored in a direct numerical simulation study. Two gaps, $g=0.5d$ and $1.0d$ , were considered, both at a Reynolds number of 1000 based on the plate width $d$ and the inflow velocity. For gap ratio $g/d=0.5$ , the biased gap flow resulted in an asymmetric flow configuration consisting of a narrow wake with strong vortex shedding and a wide wake with no periodic near-wake shedding. Shear-layer transition vortices were observed in the wide wake, with characteristic frequency 0.6. For $g/d=1.0$ , two simulations were performed, started from a symmetric and an asymmetric initial flow field. A symmetric configuration of Kármán vortices resulted from the first simulation. Surprisingly, however, two different three-dimensional instability features were observed simultaneously along the span of the upper and lower plates. The spanwise wavelengths of these secondary streamwise vortices, formed in the braid regions of the primary Kármán vortices, were approximately $1d$ and $2d$ , respectively. The wake bursts into turbulence some $5d$ $10d$ downstream. The second simulation resulted in an asymmetric wake configuration similar to the asymmetric wake found for the narrow gap $0.5d$ , with the appearance of shear-layer instabilities in the wide wake. The analogy between a plane mixing layer and the separated shear layer in the wide wake was examined. The shear-layer frequencies obtained were in close agreement with the frequency of the most amplified wave based on linear stability analysis of a plane mixing layer.


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Akinaga, T. & Mizushima, J. 2005 Linear stability of flow past two circular cylinders in a side-by-side arrangement. J. Phys. Soc. Japan 74, 13661369.
Alam, M. M. & Zhou, Y. 2013 Intrinsic features of flow around two side-by-side square cylinders. Phys. Fluids 25, 085106.
Alam, M. M., Zhou, Y. & Wang, X. W. 2011 The wake of two side-by-side square cylinders. J. Fluid Mech. 669, 432471.
Barkley, D. & Henderson, R. D. 1996 Three-dimensional Floquet stability analysis of the wake of a circular cylinder. J. Fluid Mech. 322, 215241.
Bearman, P. W. & Wadcock, A. J. 1973 The interaction between a pair of circular cylinders normal to a stream. J. Fluid Mech. 61, 499511.
Bernal, L. P. & Roshko, A. 1986 Streamwise vortex structure in plane mixing layers. J. Fluid Mech. 170, 499525.
Bloor, M. S. 1964 The transition to turbulence in the wake of a circular cylinder. J. Fluid Mech. 19, 290304.
Brun, C., Tenchine, D. & Hopfinger, E. J. 2004 Role of the shear layer instability in the near wake behavior of two side-by-side circular cylinders. Exp. Fluids 36, 334343.
Carmo, B. S., Meneghini, J. R. & Sherwin, S. J. 2010a Secondary instabilities in the flow around two circular cylinders in tandem. J. Fluid Mech. 644, 395431.
Carmo, B. S., Meneghini, J. R. & Sherwin, S. J. 2010b Possible states in the flow around two circular cylinders in tandem with separations in the vicinity of the drag inversion spacing. Phys. Fluids 22, 054101.
Carmo, B. S., Sherwin, S. J., Bearman, P. W. & Willden, R. H. J. 2008 Wake transition in the flow around two circular cylinders in staggered arrangements. J. Fluid Mech. 597, 129.
Castro, I. 1971 Wake characteristics of two-dimensional perforated plate normal to an air-stream. J. Fluid Mech. 46, 599609.
Choi, C.-B., Jang, Y.-J. & Yang, K.-S. 2012 Secondary instability in the near-wake past two tandem square cylinders. Phys. Fluids 24, 024102.
Choi, C.-B. & Yang, K.-S. 2013 Three-dimensional instability in the flow past two side-by-side square cylinders. Phys. Fluids 25, 074107.
Cimbala, J. M., Nagib, H. M. & Roshko, A. 1988 Large structure in the far wakes of two-dimensional bluff bodies. J. Fluid Mech. 190, 265298.
Dadmarzi, F. H., Narasimhamurthy, V. D., Andersson, H. I. & Pettersen, B. 2011 The turbulent wake behind side-by-side plates. J. Phys. Conf. Ser. 318, 062010.
Gerrard, J. H. 1966 The mechanics of the formation region of vortices behind bluff bodies. J. Fluid Mech. 25, 401413.
Hayashi, M., Sakurai, A. & Ohya, Y. 1986 Wake interference of a row of normal flat plates arranged side by side in a uniform flow. J. Fluid Mech. 164, 125.
Hemmati, A., Wood, D. H. & Martinuzzi, R. J. 2016 Characteristics of distinct flow regimes in the wake of an infinite span normal thin flat plate. Intl J. Heat Fluid Flow 62 (Part B), 423436.
Higuchi, H., Lewalle, J. & Crane, P. 1994 On the structure of a two-dimensional wake behind a pair of flat plates. Phys. Fluids 6, 297305.
Ho, C.-M. & Huerre, P. 1984 Perturbed free shear layers. Annu. Rev. Fluid Mech. 16, 365422.
Huang, Z., Ferré, J. A., Kawall, J. G. & Keffer, J. F. 1995 The connection between near and far regions of the turbulent porous body wake. Exp. Therm Fluid Sci. 11 (2), 143154.
Huerre, P. & Monkewitz, P. A. 1990 Local and global instabilities in spatially developing flows. Annu. Rev. Fluid Mech. 22, 473537.
Inoue, O. 1985 A new approach to flow problems past a porous plate. AIAA J. 23, 19161921.
Kim, H. J. & Durbin, P. A. 1988 Investigation of the flow between a pair of circular cylinders in the flopping regime. J. Fluid Mech. 196, 431448.
Koch, W. 1985 Local instability characteristics and frequency determination of self-excited wake flows. J. Sound Vib. 99, 5383.
Kochin, N. E., Kibel, I. A. & Roze, N. V. 1964 Theoretical Hydrodynamics. Wiley Interscience (translated from the fifth Russian edition).
Kolar, V., Lyn, D. A. & Rodi, W. 1997 Ensemble-averaged measurements in the turbulent near wake of two side-by-side square cylinders. J. Fluid Mech. 346, 201237.
Landweber, L.1942 Flow about a pair of adjacent, parallel cylinders normal to a stream. Tech. Rep. 485. Navy Department, David W. Taylor Model Basin.
Manhart, M. 2004 A zonal grid algorithm for DNS of turbulent boundary layers. Comput. Fluids 33, 435461.
Mathis, M., Provansal, M. & Boyer, L. 1984 Bénard–von Kármán instability: an experimental study near the threshold. J. Phys. Lett. Paris 45, 483491.
Meiburg, E. & Lasheras, J. C. 1988 Experimental and numerical investigation of the three-dimensional transition in plane wakes. J. Fluid Mech. 190, 137.
Miau, J. J., Wang, G. Y. & Chou, J. H. 1992 Intermittent switching of gap flow downstream of two flat plates arranged side by side. J. Fluids Struct. 6, 563582.
Miau, J. J., Wang, H. B. & Chou, J. H. 1996 Flopping phenomenon of flow behind two plates placed side-by-side normal to the flow direction. Fluid Dyn. Res. 17, 311328.
Mizushima, J. & Hatsuda, G. 2014 Nonlinear interactions between the two wakes behind a pair of square cylinders. J. Fluid Mech. 750, 295320.
Najjar, F. M. & Balachandar, S. 1998 Low-frequency unsteadiness in the wake of a normal flat plate. J. Fluid Mech. 370, 101147.
Najjar, F. M. & Vanka, S. P. 1995 Effects of intrinsic three-dimensionality on the drag characteristics of a normal flat plate. Phys. Fluids 7, 25162518.
Narasimhamurthy, V. D. & Andersson, H. I. 2009 Numerical simulation of the turbulent wake behind a normal flat plate. Intl J. Heat Fluid Flow 30, 10371043.
Peller, N., Duc, A. L., Tremblay, F. & Manhart, M. 2006 High-order stable interpolations for immersed boundary methods. Intl J. Numer. Meth. Fluids 52, 11751193.
Prasad, A. & Williamson, C. H. 1997 The instability of the shear layer separating from a bluff body. J. Fluid Mech. 333, 375402.
Radi, A., Thompson, M. C., Rao, A., Hourigan, K. & Sheridan, J. 2013 Experimental evidence of new three-dimensional modes in the wake of a rotating cylinder. J. Fluid Mech. 734, 567594.
Robichaux, J., Balachandar, S. & Vanka, S. P. 1999 Three-dimensional Floquet instability of the wake of square cylinder. Phys. Fluids 11, 560578.
Strykowski, P. J.1986 The control of absolutely and convectively unstable shear flows. PhD thesis, Yale University, New Haven.
Sumner, D. 2010 Two circular cylinders in cross-flow: a review. J. Fluids Struct. 26, 849899.
Sumner, D., Wong, S. S. T., Price, S. J. & Paidoussis, M. P. 1999 Fluid behaviour of side-by-side circular cylinders in steady cross-flow. J. Fluids Struct. 13, 309338.
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, 793806.
Unal, M. F. & Rockwell, D. 1988a On vortex formation from a cylinder. Part 1. The initial instability. J. Fluid Mech. 190, 491512.
Wei, T. & Smith, C. R. 1986 Secondary vortices in the wake of circular cylinders. J. Fluid Mech. 169, 513533.
Williamson, C. H. K. 1985 Evolution of a single wake behind a pair of bluff bodies. J. Fluid Mech. 159, 118.
Williamson, C. H. K. 1996 Three-dimensional wake transition. J. Fluid Mech. 328, 345407.
Winant, C. D. & Browand, F. K. 1974 Vortex pairing: the mechanism of turbulent mixing-layer growth at moderate Reynolds number. J. Fluid Mech. 63, 237255.
Wood, C. J. 1964 The effect of base bleed on a periodic wake. J. R. Aero. Soc. 68, 477482.
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, 12141219.
Yen, S. C. & Liu, J. H. 2011 Wake flow behind two side-by-side square cylinders. Intl J. Heat Fluid Flow 32, 4151.
Yildirim, I., Rindt, C. C. M. & van Steenhoven, A. A. 2013 Mode C flow transition behind a circular cylinder with a near-wake wire disturbance. J. Fluid Mech. 727, 3055.
Zdravkovich, M. M. 1977 REVIEW: review of flow interference between two circular cylinders in various arrangements. Trans. ASME J. Fluids Engng 99, 618633.
Zhang, H.-Q., Fey, U., Noack, B. R., König, M. & Eckelmann, H. 1995 On the transition of the cylinder wake. Phys. Fluids 7, 779794.
Zhou, Y. 2003 Vortical structures behind three side-by-side cylinders. Exp. Fluids 34, 6876.
Zhou, Y. & Alam, M. M. 2016 Wake of two interacting circular cylinders: a review. Intl J. Heat Fluid Flow 62, 510537.
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