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Experimental investigation of flow behind a cube for moderate Reynolds numbers

  • L. Klotz (a1) (a2), S. Goujon-Durand (a1), J. Rokicki (a2) and J. E. Wesfreid (a1)


The wake behind a cube with a face normal to the flow was investigated experimentally in a water tunnel using laser induced fluorescence (LIF) visualisation and particle image velocimetry (PIV) techniques. Measurements were carried out for moderate Reynolds numbers between 100 and 400 and in this range a sequence of two flow bifurcations was confirmed. Values for both onsets were determined in the framework of Landau’s instability model. The measured longitudinal vorticity was separated into three components corresponding to each of the identified regimes. It was shown that the vorticity associated with a basic flow regime originates from corners of the bluff body, in contrast to the two other contributions which are related to instability effects. The present experimental results are compared with numerical simulation carried out earlier by Saha (Phys. Fluids, vol. 16, 2004, pp. 1630–1646).


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Achenbach, E. 1974 Vortex shedding from spheres. J. Fluid Mech. 62, 209221.
Auguste, F., Fabre, D. & Magnaudet, J. 2010 Bifurcations in the wake of a thick circular disk. Theor. Comput. Fluid Dyn. 24, 305313.
Bagchi, P. & Balachandar, S. 2004 Response of the wake of an isolated particle to an isotropic turbulent flow. J. Fluid Mech. 518, 95123.
Bobinski, T., Goujon-Durand, S. & Wesfreid, J. E. 2014 Instabilities in the wake of a circular disk. Phys. Rev. E 89, 053021; doi: 10.1103/PhysRevE.89.053021.
Bohorquez, P. & Parras, L. 2013 Three-dimensional numerical simulation of the wake flow of an afterbody at subsonic speeds. Theor. Comput. Fluid Dyn. 27 (1–2), 201218.
Bouchet, G., Mebarek, M. & Dǔsek, J. 2006 Hydrodynamics forces acting on a rigid fixed sphere in early transitional regimes. Eur. J. Mech. (B/Fluids) 25, 321336.
Brucker, C. 2001 Spatio-temporal reconstruction of vortex dynamics in axisymmetric wakes. J. Fluids Struct. 15 (3–4), 543554.
El Khoury, G. K., Andersson, H. I. & Pettersen, B. 2012 Wakes behind a prolate spheroid in crossflow. J. Fluid Mech. 701, 98136.
Fabre, D., Auguste, F. & Magnaudet, J. 2008 Bifurcations and symmetry breaking in the wake of axisymmetric bodies. Phys. Fluids 20, 051702.
Goujon-Durand, S., Jenffer, P. & Wesfreid, J. E. 1994 Downstream evolution of the Bénard-von Kármán instability. Phys. Rev. E 50 (1), 308313.
Gumowski, K., Miedzik, J., Goujon-Durand, S., Jenffer, P. & Wesfreid, J. E. 2008 Transition to a time-dependent state of fluid flow in the wake of a sphere. Phys. Rev. E 77, 055308(R).
Jeong, J. & Hussain, F. 1995 On the identification of a vortex. J. Fluid Mech. 285, 6994.
Johnson, T. A. & Patel, V. C. 1999 Flow past a sphere up to a Reynolds number of 300. J. Fluid Mech. 378, 1970.
Marais, C.2011 Dynamique tourbillonnaire dans le sillage d’un aileron oscillant: propulsion par ailes battantes biomimtiques. PhD thesis, ESPCI ParisTech.
Mathis, C., Provansal, M. & Boyer, L. 1984 The Bénard–von Kármán instability: an experimental study near the threshold. J. Phys. Lett. Paris 45, 483491.
Meliga, P., Chomaz, J.-M. & Sipp, D. 2009 Global mode interaction and pattern selection in the wake of disk: a weakly nonlinear expansion. J. Fluid Mech. 633, 159189.
Mittal, R. 2000 Response of the sphere wake to free stream fluctuations. Theor. Comput. Fluid Dyn. 13, 397419.
Monkewitz, P. A. & Huerre, P. 1982 Influence of the velocity ratio on the spatial instability of mixing layers. Phys. Fluids 25 (7), 11371143.
Ormiéres, D. & Provansal, M. 1999 Transition to turbulence in the wake of a sphere. Phys. Rev. Lett. 83 (1), 8083.
Provansal, M. 2006 Wake instabilities behind bluff bodies. In Dynamics of Spatio-Temporal Cellular Structures: Henri Benard Centenary Review (ed. Mutabazi, I., Wesfreid, J. E. & Guyon, E.), Springer Tracts in Modern Physics, vol. 207, pp. 179202. Springer.
Przadka, A., Miedzik, J., Gumowski, K., Goujon-Durand, S. & Wesfreid, J. E. 2008 The wake behind the sphere; analysis of vortices during transition from steadiness to unsteadiness. Arch. Mech. 60, 465472.
Raul, R., Bernard, P. S. & Buckley Jr, F. T. 1990 An application of the vorticity-vector potential method to laminar cube flow. Intl J. Numer. Meth. Fluids 10, 875888.
Saha, A. K. 2004 Three-dimensional numerical simulations of the transition of flow past a cube. Phys. Fluids 16 (5), 16301646.
Saha, A. K. 2006 Three-dimensional numerical study of flow and heat transfer from a cube placed in a uniform flow. Intl J. Heat Fluid Flow 26, 8094.
Schouveiler, L. & Provansal, M. 2002 Self-sustained oscillations in the wake of a sphere. Phys. Fluids 14 (11), 38463854.
Shenoy, A. R. & Kleinstreuer, C. 2008 Flow over a thin circular disk at low to moderate Reynolds numbers. J. Fluid Mech. 605, 253262.
Szaltys, P., Chrust, M., Przadka, A., Goujon-Durand, S., Tuckerman, L. S. & Wesfreid, J. E. 2011 Nonlinear evolution of instabilities behind spheres and disks. J. Fluids Struct. 28, 483487.
Thiria, B., Goujon-Durand, S. & Wesfreid, J. E. 2006 The wake of a cylinder performing rotary oscillations. J. Fluid Mech. 560, 123147.
Thompson, M. C., Leweke, T. & Provansal, M. 2001 Kinematics and dynamics of sphere wake transition. J. Fluids Struct. 15, 575585.
Tomboulides, A. G. & Orszag, S. A. 2000 Numerical investigation of transitional and weak turbulent flow past a sphere. J. Fluid Mech. 416, 4573.
Wesfreid, J. E. 2006 Scientific biography of Henri Bénard (1874–1939). In Dynamics of Spatio-Temporal Cellular Structures: Henri Benard Centenary Review (ed. Mutabazi, I., Wesfreid, J. E. & Guyon, E.), Springer Tracts in Modern Physics, vol. 207, pp. 937. Springer.
Wesfreid, J. E., Goujon-Durand, S. & Zielinska, B. J. A. 1996 Global mode behavior of the streamwise velocity in wakes. J. Phys. II (Paris) 6, 13431357.
Wu, J.-S. & Faeth, G. M. 1994 Sphere wakes at moderate Reynolds numbers in a turbulent environment. AIAA J. 32, 535541.
Zhou, J., Adrian, R. J., Balachandar, S. & Kendall, T. M. 1999 Mechanisms for generating coherent packets of hairpin vortices in channel flow. J. Fluid Mech. 387, 353396.
Zielinska, B. J. A., Goujon-Durand, S., Dǔsek, J. & Wesfreid, J. E. 1997 Strongly nonlinear effect in unstable wakes. Phys. Rev. Lett. 79 (20), 38933896.
Zielinska, B. J. A. & Wesfreid, J. E. 1995 On the spatial structure of global modes in the wake flow. Phys. Fluids 7 (6), 14181428.
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