Skip to main content
×
Home
    • Aa
    • Aa

Cellular vortex shedding in the wake of a tapered plate

  • VAGESH D. NARASIMHAMURTHY (a1), HELGE I. ANDERSSON (a1) and BJØRNAR PETTERSEN (a2)
Abstract

Direct numerical simulation (DNS) of vortex shedding behind a tapered plate with the taper ratio 20 placed normal to the inflow has been performed. The Reynolds numbers based on the uniform inflow velocity and the width of the plate at the wide and narrow ends were 1000 and 250, respectively. For the first time ever cellular vortex shedding was observed behind a tapered plate in a numerical experiment (DNS). Multiple cells of constant shedding frequency were found along the span of the plate. This is in contrast to apparent lack of cellular vortex shedding found in the high-Reynolds-number experiments by Gaster & Ponsford (Aero. J., vol. 88, 1984, p. 206). However, the present DNS data is in good qualitative agreement with similar high-Reynolds-number experimental data produced by Castro & Watson (Exp. Fluids, vol. 37, 2004, p. 159). It was observed that a tapered plate creates longer formation length coupled with higher base pressure as compared to non-tapered (i.e. uniform) plates. The three-dimensional recirculation bubble was nearly conical in shape. A significant base pressure reduction towards the narrow end of the plate, which results in a corresponding increase in Strouhal number, was noticed. This observation is consistent with the experimental data of Castro & Rogers (Exp. Fluids, vol. 33, 2002, p. 66). Pressure-driven spanwise secondary motion was observed, both in the front stagnation zone and also in the wake, thereby reflecting the three-dimensionality induced by the tapering.

Copyright
Corresponding author
Email address for correspondence: vagesh@ntnu.no
References
Hide All
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.
Bearman P. W. 1967 The effect of base bleed on the flow behind a two-dimensional model with a blunt trailing edge. Aero. Q. 18, 207.
Bloor M. S. 1964 The transition to turbulence in the wake of a circular cylinder. J. Fluid Mech. 19, 290304.
Bradshaw P. & Perot J. B. 1993 A note on turbulent energy dissipation in the viscous wall region. Phys. Fluids A 5, 33053306.
Castro I. P. & Rogers P. 2002 Vortex shedding from tapered plates. Exp. Fluids 33, 6674.
Castro I. P. & Watson L. 2004 Vortex shedding from tapered, triangular plates: taper and aspect ratio effects. Exp. Fluids 37, 159167.
Dennis S. C. R., Wang Q., Coutanceau M. & Launay J. L. 1993 Viscous flow normal to a flat plate at moderate Reynolds numbers. J. Fluid Mech. 248, 605635.
Fage A. & Johansen F. C. 1927 On the flow of air behind an inclined flat plate of infinite span. Br. Aero. Res. Coun. Rep. Memo. 1104, 81106.
Ferziger J. H. & Peric M. 1996 Computational Methods for Fluid Dynamics. Springer.
Gaster M. 1969 Vortex shedding from slender cones at low Reynolds numbers. J. Fluid Mech. 38, 565576.
Gaster M. & Ponsford P. J. 1984 The flows over tapered flat plates normal to the stream. Aero. J. 88, 206212.
Hudson J. D. & Dennis S. C. R. 1985 The flow of a viscous incompressible fluid past a normal flat plate at low and intermediate Reynolds numbers: the wake. J. Fluid Mech. 160, 369383.
Iaccarino G. & Verzicco R. 2003 Immersed boundary technique for turbulent flow simulations. Appl. Mech. Rev. 56, 331347.
In K. M., Choi D. H. & Kim M.-U. 1995 Two-dimensional viscous flow past a flat plate. Fluid Dyn. Res. 15, 1324.
Ingham D. B., Tang T. & Morton B. R. 1991 Steady two-dimensional flow past a normal flat plate. J. Appl. Math. Phys. (ZAMP) 42, 584604.
Jeong J. & Hussain F. 1995 On the identification of a vortex. J. Fluid Mech. 285, 6994.
Julien S., Lasheras J. & Chomaz J.-M. 2003 Three-dimensional instability and vorticity patterns in the wake of a flat plate. J. Fluid Mech. 479, 155189.
Julien S., Ortiz S. & Chomaz J.-M. 2004 Secondary instability mechanisms in the wake of a flat plate. Eur. J. Mech. B/Fluids 23 (1), 157165.
Koumoutsakos P. & Shiels D. 1996 Simulations of the viscous flow normal to an impulsively started and uniformly accelerated flat plate. J. Fluid Mech. 328, 177227.
Manhart M. 2004 A zonal grid algorithm for DNS of turbulent boundary layers. Comput. Fluids 33, 435461.
Maull D. J. & Young R. A. 1973 Vortex shedding from bluff bodies in a shear flow. J. Fluid Mech. 60, 401409.
Mittal R. & Iaccarino G. 2005 Immersed boundary methods. Annu. Rev. Fluid Mech. 37, 239261.
Moser R. D., Rogers M. M. & Ewing D. W. 1998 Self-similarity of time-evolving plane wakes. J. Fluid Mech. 367, 255289.
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. & Pettersen B. (in press) Direct numerical simulation of vortex shedding behind a linearly tapered circular cylinder. In Proc. IUTAM Symposium on Unsteady Separated Flows and Their Control. Springer, Heidelberg.
Narasimhamurthy V. D., Schwertfirm F., Andersson H. I. & Pettersen B. 2006 Simulation of unsteady flow past tapered circular cylinders using an immersed boundary method. In Proc. ECCOMAS Computational Fluid Dynamics (ed. Périaux J., Wesseling P. & Oñate E.). TU Delft.
Parnaudeau P., Heitz D., Lamballais E. & Silvestrini J. H. 2007 Direct numerical simulations of vortex shedding behind cylinders with spanwise linear nonuniformity. J. Turbul. 8 (13), 113.
Peller N., Le Duc A., Tremblay F. & Manhart M. 2006 High-order stable interpolations for immersed boundary methods. Intl J. Num. Meth. Fluids 52, 11751193.
Piccirillo P. S. & Van Atta C. W. 1993 An experimental study of vortex shedding behind linearly tapered cylinders at low Reynolds number. J. Fluid Mech. 246, 163195.
Roshko A. 1954 On the development of turbulent wakes from vortex streets. Tech. Rep. 1191. NACA.
Smith F. T. 1985 On large-scale eddy closure. J. Math. Phys. Sci. 19, 1.
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.
Thompson M. C., Leweke T. & Williamson C. H. K. 2001 The physical mechanism of transition in bluff body wakes. J. Fluids Struct. 15, 607616.
Tremblay F., Manhart M. & Friedrich R. 2001 DNS and LES of flow around a circular cylinder at a subcritical Reynolds number with cartesian grids. In LES of Complex Transitional and Turbulent Flows, pp. 133150. Kluwer Academic Publishers.
Vallès B., Andersson H. I. & Jenssen C. B. 2002 a Direct-mode interactions in the wake behind a stepped cylinder. Phys. Fluids 14, 15481551.
Vallès B., Andersson H. I. & Jenssen C. B. 2002 b Oblique vortex shedding behind tapered cylinders. J. Fluids Struct. 16, 453463.
Williamson C. H. K. 1992 The natural and forced formation of spot-like dislocations in the transition of a wake. J. Fluid Mech. 243, 393441.
Williamson C. H. K. 1996 Vortex dynamics in the cylinder wake. Annu. Rev. Fluid Mech. 28, 477539.
Wu S. J., Miau J. J., Hu C. C. & Chou J. H. 2005 On low-frequency modulations and three-dimensionality in vortex shedding behind a normal plate. J. Fluid Mech. 526, 117146.
Yao Y. F., Thomas T. G., Sandham N. D. & Williams J. J. R. 2001 Direct numerical simulation of turbulent flow over a rectangular trailing edge. Theor. Comput. Fluid Dyn. 14, 337358.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 45 *
Loading metrics...

Abstract views

Total abstract views: 126 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 23rd October 2017. This data will be updated every 24 hours.