Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-13T16:04:12.517Z Has data issue: false hasContentIssue false

Turbulent wake behind a curved circular cylinder

Published online by Cambridge University Press:  21 February 2014

José P. Gallardo*
Affiliation:
Department of Marine Technology, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway
Helge I. Andersson
Affiliation:
Department of Energy and Process Engineering, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway
Bjørnar Pettersen
Affiliation:
Department of Marine Technology, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway
*
Email address for correspondence: jose.p.gallardo@ntnu.no

Abstract

This paper reports results from a direct numerical simulation of the flow past a circular cylinder with axial curvature. The main objective is to explore the effects of spanwise curvature on the stability of the shear layers and the turbulent wake at the subcritical Reynolds number of 3900. The bluff-body geometry is adapted from a previous study conducted at lower Reynolds numbers, in which a quarter segment of a ring represented the deformed cylinder. A convex configuration in which the free-stream direction is towards the outer face of the ring is adopted here. The present results show a striking distinction between the upper and lower wake regions. Despite the turbulent character of the wake, the upper wake region is more coherent due to the periodic vortex shedding of primary vortical structures, which are in close alignment with the axial curvature. A mild axial flow develops upwards along the lee face of the curved cylinder, displacing the vortex formation region further downstream from the location expected for a straight cylinder at the same Reynolds number. In the lower wake region the vortex shedding strength is drastically reduced due to larger local inclination, resulting in higher three-dimensionality and loss of coherence. A strong downdraft with a swirling pattern is the dominating feature in the lower base region. This is associated with a substantial decrease of the base suction, and the suppression of the characteristic recirculating backflow.

Type
Papers
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

Barkley, D., Tuckerman, L. S. & Golubitsky, M. 2000 Bifurcation theory for three-dimensional flow in the wake of a circular cylinder. Phys. Rev. E 61, 52475252.Google ScholarPubMed
Bearman, P. W. 1965 Investigation of the flow behind a two-dimensional model with a blunt trailing edge and fitted with splitter plates. J. Fluid Mech. 21, 241255.CrossRefGoogle Scholar
Bearman, P. W. & Takamoto, M. 1988 Vortex shedding behind rings and discs. Fluid Dyn. Res. 3, 214218.CrossRefGoogle Scholar
Bloor, M. S. 1964 The transition to turbulence in the wake of a circular cylinder. J. Fluid Mech. 19, 290304.CrossRefGoogle Scholar
De Vecchi, A., Sherwin, S. J. & Graham, J. M. R. 2008 Wake dynamics of external flow past a curved circular cylinder with the free-stream aligned to the plane of curvature. J. Fluids Struct. 24, 12621270.CrossRefGoogle Scholar
Dong, S., Karniadakis, G. E., Ekmekci, A. & Rockwell, D. 2006 A combined direct numerical simulation-particle image velocimetry study of the turbulent near wake. J. Fluid Mech. 569, 185207.CrossRefGoogle Scholar
Eisenlohr, H. & Eckelmann, H. 1989 Vortex splitting and its consequences in the vortex street wake of cylinders at low Reynolds number. Phys. Fluids A 1, 189192.CrossRefGoogle Scholar
Gallardo, J. P., Pettersen, B. & Andersson, H. I. 2011 Dynamics in the turbulent wake of a curved circular cylinder. J. Phys.: Conf. Ser. 318, 06288.Google Scholar
Gallardo, J. P., Pettersen, B. & Andersson, H. I. 2013 Effects of free-slip boundary conditions on the flow around a curved circular cylinder. Comput. Fluids 86, 389394.CrossRefGoogle Scholar
Gaster, M. 1971 Vortex shedding from circular cylinders at low Reynolds numbers. J. Fluid Mech. 46, 749756.CrossRefGoogle Scholar
Jeong, J. & Hussain, F. 1995 On the identification of a vortex. J. Fluid Mech. 285, 6994.CrossRefGoogle Scholar
Kravchenko, A. G. & Moin, P. 2000 Numerical studies of flow over a circular cylinder at $Re=3900$ . Phys. Fluids 12, 403417.CrossRefGoogle Scholar
Leweke, T. & Provansal, M. 1995 The flow behind rings: bluff body wakes without end effects. J. Fluid Mech. 288, 265310.CrossRefGoogle Scholar
Lucor, D. & Karniadakis, G. E. M. 2003 Effects of oblique inflow in vortex-induced vibrations. Flow Turbul. Combust. 71, 375389.CrossRefGoogle Scholar
Ma, X., Karamanos, G.-S. & Karniadakis, G. E. 2000 Dynamics and low-dimensionality of a turbulent near wake. J. Fluid Mech. 410, 2965.CrossRefGoogle Scholar
Manhart, M. 2004 A zonal grid algorithm for DNS of turbulent boundary layers. Comput. Fluids 33, 435461.CrossRefGoogle Scholar
Manhart, M., Tremblay, F. & Friedrich, R. 2001 MGLET: a parallel code for efficient DNS and LES of complex geometries. In Parallel Computational Fluid Dynamics – Trends and Applications (ed. Jenssen, C. B., Andersson, H. I., Ecer, A., Satofuka, N., Kvamsdal, T., Pettersen, B., Periaux, J. & Fox, P.), pp. 449456. Elsevier.Google Scholar
Mansy, H., Yang, P.-M. & Williams, D. R. 1994 Quantitative measurements of three-dimensional structures in the wake of a circular cylinder. J. Fluid Mech. 270, 277296.CrossRefGoogle Scholar
Matsumoto, M., Shiraishi, N., Kitazawa, M., Knisely, C., Shirato, H., Kim, Y. & Tsujii, M. 1990 Aerodynamic behaviour of inclined circular cylinders – cable aerodynamics. J. Wind Engng. Ind. Aerodyn. 33, 6372.CrossRefGoogle Scholar
Miliou, A., De Vecchi, A., Sherwin, S. J. & Graham, J. M. R. 2007 Wake dynamics of external flow past a curved circular cylinder with the free stream aligned with the plane of curvature. J. Fluid Mech. 592, 89115.CrossRefGoogle Scholar
Miliou, A., Sherwin, S. J. & Graham, J. M. R. 2003 Fluid dynamic loading on curved riser pipes. Trans. ASME: J. Offshore Mech. Arctic Engng 125, 176182.Google Scholar
Narasimhamurthy, V. D., Andersson, H. I. & Pettersen, B. 2008 Cellular vortex shedding in the wake of a tapered plate. J. Fluid Mech. 617, 355379.CrossRefGoogle Scholar
Narasimhamurthy, V. D., Andersson, H. I. & Pettersen, B. 2009 Cellular vortex shedding behind a tapered circular cylinder. Phys. Fluids 21, 044106.CrossRefGoogle Scholar
Norberg, C. Reynolds number and free-stream turbulence effects on the flow and fluid forces for a circular cylinder in cross flow. PhD thesis, Chalmers University of Technology, Gothenburg, Sweden.Google Scholar
Norberg, C. 1998 LDV-measurements in the near wake of a circular cylinder. In Proceedings of the Conference on Bluff Body Wakes and Vortex-Induced Vibration (ed. Bearman, P. W. & Williamson, C. H. K.), pp. 112. Cornell University, Ithaca, NY.Google Scholar
Ong, L. & Wallace, J. 1996 The velocity field of the turbulent very near wake of a circular cylinder. Exp. Fluids 20, 441453.CrossRefGoogle Scholar
Parnaudeau, P., Carlier, J., Heitz, D. & Lamballais, E. 2008 Experimental and numerical studies of the flow over a circular cylinder at Reynolds number 3900. Phys. Fluids 20, 085101.CrossRefGoogle Scholar
Peller, N. 2010 Numerische Simulation turbulenter Strömungen mit Immersed Boundaries. Dr.-Ing. thesis, Technische Universität München.Google Scholar
Peller, N., Le Duc, A., Tremblay, F. & Manhart, M. 2006 High-order stable interpolations for immersed boundary methods. Intl J. Numer. Meth. Fluids 52, 11751193.CrossRefGoogle Scholar
Prasad, A. & Williamson, C. H. K. 1997 The instability of the shear layer separating from a bluff body. J. Fluid Mech. 333, 375402.CrossRefGoogle Scholar
Rai, M. M. 2010 A computational investigation of the instability of the detached shear layers in the wake of a circular cylinder. J. Fluid Mech. 659, 375404.CrossRefGoogle Scholar
Ramberg, S. E. 1983 The effects of yaw and finite length upon the vortex wakes of stationary and vibrating circular cylinders. J. Fluid Mech. 128, 81107.CrossRefGoogle Scholar
Razali, S. F. M., Zhou, T., Rinoshika, A. & Cheng, L. 2010 Wavelet analysis of the turbulent wake generated by an inclined circular cylinder. J. Turbul 11, 125.CrossRefGoogle Scholar
Roshko, A. 1993 Perspectives on bluff body aerodynamics. J. Wind Engng. Ind. Aerodyn. 49, 79100.CrossRefGoogle Scholar
Schlichting, H. & Gersten, K. 2000 Boundary Layer Theory. Springer.CrossRefGoogle Scholar
Stone, H. L. 1968 Iterative solution of implicit approximations of multidimensional partial differential equations. SIAM J. Numer. Anal. 5, 530558.CrossRefGoogle Scholar
Takamoto, M. & Izumi, K. 1981 Experimental observation of stable arrangement of vortex rings. Phys. Fluids 24 (8), 15821583.CrossRefGoogle Scholar
Tennekes, H. & Lumley, J. L. 1972 A First Course in Turbulence. MIT Press.CrossRefGoogle Scholar
Volino, R. J., Schultz, M. P. & Pratt, C. M. 2003 Conditional sampling in a transitional boundary layer under high free stream turbulence conditions. Trans. ASME: J. Fluids Engng. 125, 2837.Google Scholar
Wang, H. F., Mohd Razali, S. F., Zhou, T. M., Zhou, Y. & Cheng, L. 2011 Streamwise evolution of an inclined cylinder wake. Exp. Fluids 51, 553570.CrossRefGoogle Scholar
Williamson, C. H. K. 1996a Three-dimensional wake transition. J. Fluid Mech. 328, 345407.CrossRefGoogle Scholar
Williamson, C. H. K. 1996b Vortex dynamics in the cylinder wake. Annu. Rev. Fluid. Mech 28, 477539.CrossRefGoogle Scholar
Williamson, J. H. 1980 Low-storage Runge–Kutta schemes. J. Comput. Phys. 35, 4856.CrossRefGoogle Scholar
Zdravkovich, M. M. 1997 Flow Around Circular Cylinders, Vol. 1 Fundamentals. Oxford University Press.CrossRefGoogle Scholar
Zhao, M., Cheng, L. & Zhou, T. 2009 Direct numerical simulation of three-dimensional flow past a yawed circular cylinder of infinite length. J. Fluids Struct. 25, 831847.CrossRefGoogle Scholar
Zhou, T., Razali, S. F. M., Zhou, Y., Chua, L. P. & Cheng, L. 2009 Dependence of the wake on inclination of a stationary cylinder. Exp. Fluids 46, 11251138.CrossRefGoogle Scholar
Zhou, T., Wang, H., Razali, S. F. M., Zhou, Y. & Cheng, L. 2010 Three-dimensional vorticity measurements in the wake of a yawed circular cylinder. Phys. Fluids 22, 015108.CrossRefGoogle Scholar

Gallardo et al. supplementary movie

Animation shows the occurrence of instabilities in the upper and lower shear layers at z/D=8, 12, 16 and 21. Traces of the cross-stream velocity show the high amplitude velocity fluctuations arising from this instability.

Download Gallardo et al. supplementary movie(Video)
Video 7.6 MB