Abstract
The three-dimensional transition to turbulence in the wake of a tapered circular cylinder with the taper ratio 75:1 has been analyzed by performing direct numerical simulation. The Reynolds number based on the uniform inflow velocity and the diameters at the wide and narrow ends were 300 and 102, respectively. The same Reynolds number range was previously studied by Parnaudeau et al. (J. Turbulence, 2007) but with a different taper ratio 40:1. The effect of taper ratio on the transition to turbulence was investigated in the present study. It was found that the Strouhal number versus Reynolds number curves nearly collapse, thereby indicating that a change in the taper ratio by a factor of two has only a modest effect on the Strouhal number. However, there still exists a significant contrast in the cellular shedding pattern. Flow-visualization of instantaneous λ2-structures and the enstrophy ǀ ω ǀ revealed that the mode A instability appeared around Re ≈ 200 and mode B around Re ≈ 250.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Papangelou, A., Vortex shedding from slender cones at low Reynolds numbers. J. FluidMech. 242 (1992), 299–321.
Piccirillo, P. S. and Van Atta, C. W., An experimental study of vortex shedding behind linearly tapered cylinders at low Reynolds number. J. Fluid Mech. 246 (1993), 163–195.
Vallès, B., Andersson, H. I. and Jenssen, C. B., Oblique vortex shedding behind tapered cylinders. J. Fluids Struct. 16 (2002), 453–463.
Narasimhamurthy, V. D., Schwertfirm, F., Andersson, H. I. and Pettersen, B., Simulation of unsteady flow past tapered circular cylinders using an immersed boundary method. In: Proc. ECCOMAS Computational Fluid Dynamics 06, Eds. P. Wesseling, E. Oñate, J. Périaux, TU Delft, The Netherlands, Egmond aan Zee (2006).
Parnaudeau, P., Heitz, D., Lamballais, E. and Silvestrini, J. H., Direct numerical simulations of vortex shedding behind cylinders with spanwise linear nonuniformity. J. Turbulence 8 (2007), No. 13.
Visscher, J., Pettersen, B. and Andersson, H. I., PIV study on the turbulent wake behind tapered cylinders. In: Advances in Turbulence XI, Eds. J. M. L. M. Palma, A. Silva Lopes, Springer, Portugal, Porto (2007), 254–256.
Williamson, C. H. K., The natural and forced formation of spot-like vortex dislocations in the transition of a wake. J. Fluid Mech. 243 (1992), 393–441.
Williamson, C. H. K., Vortex dynamics in the cylinder wake. Annu. Rev. Fluid. Mech. 28 (1996), 477–539.
Peller, N., Le Duc, A., Tremblay, F. and Manhart M., High-order stable interpolations for immersed boundary methods. Int. J. Num. Meth. Fluids. 52 (2006), 1175–1193.
Manhart M., A zonal grid algorithm for DNS of turbulent boundary layers. Comp. & Fluids, 33 (2004), 435–461.
Zdravkovich, M. M., Flow Around Circular Cylinders: Volume 1, Oxford University. Press (1997).
Jeong, J. and Hussain, F., On the identification of a vortex. J. Fluid Mech. 285 (1995), 69–94.
Barkley, D. and Henderson, R. D., Three-dimensional Floquet stability analysis of the wake of a circular cylinder. J. Fluid Mech. 322 (1996), 215–241.
Acknowledgments
This work has received support from The Research Council of Norway (Programme for Supercomputing) through a grant of computing time. The first author was the recipient of a research fellowship offered by The Research Council of Norway.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer Science+Business Media B.V.
About this paper
Cite this paper
Narasimhamurthy, V.D., Andersson, H.I., Pettersen, B. (2009). Direct Numerical Simulation of Vortex Shedding Behind a Linearly Tapered Circular Cylinder. In: Braza, M., Hourigan, K. (eds) IUTAM Symposium on Unsteady Separated Flows and their Control. IUTAM Bookseries, vol 14. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-9898-7_17
Download citation
DOI: https://doi.org/10.1007/978-1-4020-9898-7_17
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-9897-0
Online ISBN: 978-1-4020-9898-7
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)