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Statistical Flow Properties in the Turbulent Wake of a Tapered Flat Plate Placed Normal to the Free-stream

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Abstract

Reynolds-averaged statistical flow properties in the turbulent near-wake of a tapered flat plate placed normal to the free-stream were analysed by means of direct numerical simulation (DNS). A taper ratio of 20 was considered in the present study while 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. The tapering gave rise to cellular vortex shedding with randomly occurring vortex dislocations which prohibited a distinction between coherent and incoherent fluctuations. In the current DNS, it was observed that the magnitude of the Reynolds stresses and the production and dissipation rates of fluctuating kinetic energy are much lower than in the wake of a uniform normal flat plate. This reduced magnitude is perhaps due to the fact that the present tapered plate produces a highly incoherent wake, which may result in the reduction of the coherent velocity fluctuations and their overall contribution to the Reynolds-averaged data. In addition to the primary shear-stress term, a secondary shear-stress component was found to co-exist in the present case. The appearance of this secondary shear-stress term, together with the inherent spanwise inhomogeneity and the existence of a distinct secondary flow, was found to drive the fluctuations towards isotropy. In addition, the present DNS surprisingly revealed the appearance of Kelvin-Helmholtz instabilities towards the higher local Reynolds numbers, i.e. beyond 920.

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References

  1. Balachandar, S., Mittal, R., Najjar, F.M.: Properties of the mean recirculation region in the wakes of two-dimensional bluff bodies. J. Fluid Mech. 351, 167–199 (1997)

    Article  MATH  Google Scholar 

  2. Bloor, M.S.: The transition to turbulence in the wake of a circular cylinder. J. Fluid Mech. 19, 290–304 (1964)

    Article  MATH  Google Scholar 

  3. Brun, C., Aubrun, S., Goossens, T., Ravier, P.: Coherent structures and their frequency signature in the separated shear layer on the sides of a square cylinder. Flow Turbulence Combust. 81, 97–114 (2008)

    Article  MATH  Google Scholar 

  4. Brun, C., Tenchine, D., Hopfinger, E.J.: Role of the shear layer instability in the near wake behavior of two side-by-side circular cylinders. Exp. Fluids 36, 334–343 (2004)

    Article  Google Scholar 

  5. Castro, I.P., Rogers, P.: Vortex shedding from tapered plates. Exp. Fluids 33, 66–74 (2002)

    Article  Google Scholar 

  6. Castro, I.P., Watson, L.: Vortex shedding from tapered, triangular plates: taper and aspect ratio effects. Exp. Fluids 37, 159–167 (2004)

    Article  Google Scholar 

  7. Gaster, M.: Vortex shedding from slender cones at low reynolds numbers. J. Fluid Mech. 38, 565–576 (1969)

    Article  Google Scholar 

  8. Gaster, M., Ponsford, P.J.: The flows over tapered flat plates normal to the stream. Aeronaut. J. 88, 206–212 (1984)

    Google Scholar 

  9. Huang, Z., Narasimhamurthy, V.D., Andersson, H.I.: Oblique and cellular vortex shedding behind a circular cylinder in a bidirectional shear flow. Phys. Fluids 22(114105) (2010)

  10. Khaledi, H.A., Narasimhamurthy, V.D., Andersson, H.I.: Cellular vortex shedding in the wake of a tapered plate at low reynolds number. Phys. Fluids 21(013603) (2009)

  11. Kiya, M., Matsumura, M.: Incoherent turbulence structure in the near wake of a normal plate. J. Fluid Mech. 190, 343–356 (1988)

    Article  Google Scholar 

  12. Koumoutsakos, P., Shiels, D.: Simulations of the viscous flow normal to an impulsively started and uniformly accelerated flat plate. J. Fluid Mech. 328, 177–227 (1996)

    Article  MATH  Google Scholar 

  13. Kravchenko, A.G., Moin, P.: Numerical studies of flow over a circular cylinder at Re D  = 3900. Phys. Fluids 12, 403–417 (2000)

    Article  MATH  Google Scholar 

  14. Leder, A.: Dynamics of fluid mixing in separated flows. Phys. Fluids A 3, 1741–1748 (1991)

    Article  Google Scholar 

  15. Lyn, D.A., Rodi, W.: The flapping shear layer formed by flow separation from the forward corner of a square cylinder. J. Fluid Mech. 267, 353–376 (1994)

    Article  Google Scholar 

  16. Manhart, M.: A zonal grid algorithm for dns of turbulent boundary layers. Comput. Fluids 33, 435–461 (2004)

    Article  MATH  Google Scholar 

  17. Moser, R.D., Rogers, M.M., Ewing, D.W.: Self-similarity of time-evolving plane wakes. J. Fluid Mech. 367, 255–289 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  18. Najjar, F.M., Balachandar, S.: Low-frequency unsteadiness in the wake of a normal flat plate. J. Fluid Mech. 370, 101–147 (1998)

    Article  MATH  Google Scholar 

  19. Najjar, F.M., Vanka, S.P.: Effects of intrinsic three-dimensionality on the drag characteristics of a normal flat plate. Phys. Fluids 7, 2516–2518 (1995)

    Article  MATH  Google Scholar 

  20. Narasimhamurthy, V.D., Andersson, H.I.: Numerical simulation of the turbulent wake behind a normal flat plate. Int. J. Heat Fluid Flow 30, 1037–1043 (2009)

    Article  Google Scholar 

  21. Narasimhamurthy, V.D., Andersson, H.I., Pettersen, B.: Cellular vortex shedding in the wake of a tapered plate. J. Fluid Mech. 617, 355–379 (2008)

    Article  MATH  Google Scholar 

  22. Narasimhamurthy, V.D., Andersson, H.I., Pettersen, B.: Cellular vortex shedding behind a tapered circular cylinder. Phys. Fluids 21(044106) (2009)

  23. Parnaudeau, P., Heitz, D., Lamballais, E., Silvestrini, J.H.: Direct numerical simulations of vortex shedding behind cylinders with spanwise linear nonuniformity. J. Turbul. 8(13) (2007)

  24. Peller, N., Le Duc, A., Tremblay, F., Manhart, M.: High-order stable interpolations for immersed boundary methods. Int. J. Numer. Methods Fluids 52, 1175–1193 (2006)

    Article  MATH  Google Scholar 

  25. Perrin, R., Braza, M., Cid, E., Cazin, S., Moradei, F., Barthet, A., Sevrain, A., Hoarau, Y.: Near-wake turbulence properties in the high Reynolds number incompressible flow around a circular cylinder measured by two- and three-component PIV. Flow Turbulence Combust. 77, 185–204 (2006)

    Article  MATH  Google Scholar 

  26. Perrin, R., Cid, E., Cazin, S., Sevrain, A., Braza, M., Moradei, F., Harran, G.: Phase-averaged measurements of the turbulence properties in the near wake of a circular cylinder at high Reynolds number by 2C-PIV and 3C-PIV. Exp. Fluids 42, 93–109 (2007)

    Article  Google Scholar 

  27. Prasad, A., Williamson, C.H.K.: The instability of the shear layer separating from a bluff body. J. Fluid Mech. 333, 375–402 (1997)

    Article  MathSciNet  Google Scholar 

  28. Rajagopalan, S., Antonia, R.A.: Flow around a circular cylinder—structure of the near wake shear layer. Exp. Fluids 38, 393–402 (2005)

    Article  Google Scholar 

  29. Reynolds, W.C., Hussain, A.K.M.F.: The mechanics of an organized wave in turbulent shear flow. Part 3. Theoretical models and comparisons with experiments. J. Fluid Mech. 54, 263–288 (1972)

    Article  Google Scholar 

  30. Saha, A.K., Muralidhar, K., Biswas, G.: Experimental study of flow past a square cylinder at high Reynolds numbers. Exp. Fluids 29, 553–563 (2000)

    Article  Google Scholar 

  31. Thompson, M.C., Hourigan, K.: The shear-layer instability of a circular cylinder wake. Phys. Fluids 17, 021,702 (2005)

    MathSciNet  Google Scholar 

  32. Thompson, M.C., Hourigan, K., Ryan, K., Sheard, G.J.: Wake transition of two-dimensional cylinders and axisymmetric bluff bodies. J. Fluids Struct. 22, 793–806 (2006)

    Article  Google Scholar 

  33. Yao, Y.F., Thomas, T.G., Sandham, N.D., Williams, J.J.R.: Direct numerical simulation of turbulent flow over a rectangular trailing edge. Theor. Comput. Fluid Dyn. 14, 337–358 (2001)

    Article  MATH  Google Scholar 

  34. Zdravkovich, M.M.: Flow Around Circular Cylinders Volume 1: Fundamentals. Oxford University Press (1997)

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  1. Vagesh D. Narasimhamurthy

    Present address: GexCon AS, P.O. Box 6015, Postterminalen, 5892, Bergen, Norway

Authors and Affiliations

  1. Fluids Engineering Division, Department of Energy and Process Engineering, Norwegian University of Science and Technology (NTNU), 7491, Trondheim, Norway

    Vagesh D. Narasimhamurthy & Helge I. Andersson

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  1. Vagesh D. Narasimhamurthy
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  2. Helge I. Andersson
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Correspondence to Vagesh D. Narasimhamurthy.

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Narasimhamurthy, V.D., Andersson, H.I. Statistical Flow Properties in the Turbulent Wake of a Tapered Flat Plate Placed Normal to the Free-stream. Flow Turbulence Combust 91, 805–826 (2013). https://doi.org/10.1007/s10494-013-9478-4

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  • DOI: https://doi.org/10.1007/s10494-013-9478-4

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