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Effects of viscoelasticity in the high Reynolds number cylinder wake

  • David Richter (a1), Gianluca Iaccarino (a1) and Eric S. G. Shaqfeh (a1)


At , Newtonian flow past a circular cylinder exhibits a wake and detached shear layers which have transitioned to turbulence. It is the goal of the present study to investigate the effects which viscoelasticity has on this state and to identify the mechanisms responsible for wake stabilization. It is found through numerical simulations (employing the FENE-P rheological model) that viscoelasticity greatly reduces the amount of turbulence in the wake, reverting it back to a state which qualitatively appears similar to the Newtonian mode B instability which occurs at lower . By focusing on the separated shear layers, it is found that viscoelasticity suppresses the formation of the Kelvin–Helmholtz instability which dominates for Newtonian flows, consistent with previous studies of viscoelastic free shear layers. Through this shear layer stabilization, the viscoelastic far wake is then subject to the same instability mechanisms which dominate for Newtonian flows, but at far lower Reynolds numbers.


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1. Azaiez, J. & Homsy, G. 1994a Linear stability of free shear flow of viscoelastic liquids. J. Fluid Mech. 268, 3769.
2. Azaiez, J. & Homsy, G. 1994b Numerical simulation of non-Newtonian free shear flows at high Reynolds numbers. J. Non-Newtonian Fluid Mech. 52, 333374.
3. Beaudan, P. & Moin, P. 1994 Numerical experiments on the flow past a circular cylinder at sub-critical Reynolds number. Tech. Rep. TF-62. Stanford University, Stanford, CA, 94305.
4. Bergins, C., Nowak, M. & Urban, M. 2001 The flow of a dilute cationic surfactant solution past a circular cylinder. Exp. Fluids 30, 410417.
5. Bloor, M. S. 1964 The transition to turbulence in the wake of a circular cylinder. J. Fluid Mech. 19, 290304.
6. Cadot, O. & Kumar, S. 2000 Experimental characterization of viscoelastic effects on two- and three-dimensional shear instabilities. J. Fluid Mech. 416, 151172.
7. Chahine, G. L., Frederick, G. F. & Bateman, R. D. 1993 Propeller tip vortex cavitation suppression using selective polymer injection. J. Fluids Engng 115, 497503.
8. Coelho, P. & Pinho, F. 2003a Vortex shedding in cylinder flow of shear-thinning fluids. Part I. Identification and demarcation of flow regimes. J. Non-Newtonian Fluid Mech. 110, 143176.
9. Coelho, P. & Pinho, F. 2003b Vortex shedding in cylinder flow of shear-thinning fluids. Part II. Flow characteristics. J. Non-Newtonian Fluid Mech. 110, 177193.
10. Coelho, P. M. & Pinho, F. T. 2004 Vortex shedding in cylinder flow of shear-thinning fluids. Part III. Pressure measurements. J. Non-Newtonian Fluid Mech. 121, 5568.
11. Dimitropoulos, C. D., Dubief, Y., Shaqfeh, E. S. G. & Moin, P. 2006 Direct numerical simulation of polymer-induced drag reduction in turbulent boundary layer flow of inhomogeneous polymer solutions. J. Fluid Mech. 566, 153162.
12. Dimitropoulos, C., Sureshkumar, R. & Beris, A. 1998 Direct numerical simulation of viscoelastic turbulent channel flow exhibiting drag reduction: effect of the variation of rheological parameters. J. Non-Newtonian Fluid Mech. 79, 433468.
13. Dimitropoulos, C., Sureshkumar, R., Beris, A. & Handler, R. 2001 Budgets of Reynolds stress, kinetic energy and streamwise enstrophy in viscoelastic turbulent channel flow. Phys. Fluids 13 (4), 10161027.
14. Dubief, Y., Terrapon, V. E., White, C. M., Shaqfeh, E. S. G., Moin, P. & Lele, S. K. 2005 New answers on the interaction between polymers and vortices in turbulent flows. Flow Turbul. Combust. 74 (4), 311329.
15. Dubief, Y., White, C. M., Terrapon, V. E., Shaqfeh, E. S. G., Moin, P. & Lele, S. K. 2004 On the coherent drag-reducing and turbulence-enhancing behaviour of polymers in wall flows. J. Fluid Mech. 514, 271280.
16. Fruman, D. H., Pichon, T. & Cerrutti, P. 1995 Effect of a drag-reducing polymer solution ejection on tip vortex cavitation. J. Mar. Sci. Technol. 1, 1323.
17. Hibberd, M., Kwade, M. & Scharf, R. 1982 Influence of drag reducing additives on the structure of turbulence in a mixing layer. Rheol. Acta 21, 582586.
18. Kato, H. & Mizuno, Y. 1983 An experimental investigation of viscoelastic flow past a circular cylinder. Bull. Japan Soc. Mech. Engineers 26 (214), 529536.
19. Kim, K., Li, C., Sureshkumar, R., Balachandar, S. & Adrian, R. 2007 Effects of polymer stresses on eddy structures in drag-reduced turbulent channel flow. J. Fluid Mech. 584, 281299.
20. Kravchenko, A. 1998 B-spline methods and zonal grids for numerical simulations of turbulent flows. PhD thesis, Stanford University.
21. Kravchenko, A. & Moin, P. 2000 Numerical studies of flow over a circular cylinder at . Phys. Fluids 12 (2), 403417.
22. Kumar, S. & Homsy, G. 1999 Direct numerical simulation of hydrodynamic instabilities in two- and three-dimensional viscoelastic free shear layers. J. Non-Newtonian Fluid Mech. 83, 249276.
23. Ma, X., Karamanos, G. S. & Karniadakis, G. E. 2000 Dynamics and low-dimensionality of a turbulent near wake. J. Fluid Mech. 410, 2965.
24. Ma, X., Symeonidis, V. & Karniadakis, G. 2003 A spectral vanishing viscosity method for stabilizing viscoelastic flows. J. Non-Newtonian Fluid Mech. 115, 125155.
25. Ogata, S., Osano, Y. & Watanabe, K. 2006 Effect of surfactant solutions on the drag and the flow pattern of a circular cylinder. AIChE J. 52 (1), 4957.
26. Ong, L. & Wallace, J. 1996 The velocity field of the turbulent very near wake of a circular cylinder. Exp. Fluids 20, 441453.
27. 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 (8), 114.
28. Prasad, A. & Williamson, C. H. K. 1997 The instability of the shear layer separating from a bluff body. J. Fluid Mech. 333, 375402.
29. Rai, M. 2008 Towards direct numerical simulations of turbulent wakes. In 46th AIAA Aerospace Sciences Meeting and Exhibit. Paper 2008-0544.
30. 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.
31. Richter, D., Iaccarino, G. & Shaqfeh, E. S. G. 2010 Simulations of three-dimensional viscoelastic flows past a circular cylinder at moderate Reynolds numbers. J. Fluid Mech. 651, 415442.
32. Richter, D., Shaqfeh, E. S. G. & Iaccarino, G. 2011 Floquet stability analysis of viscoelastic flow over a cylinder. J. Non-Newtonian Fluid Mech. 166, 554565.
33. Riediger, S. 1989 Influence of drag reducing additives on a plane mixing layer. In Drag Reduction in Fluid Flows (ed. Sellin, R. H. J. & Moses, R. J. ), pp. 303310. Ellis Horwood.
34. Roshko, A. 1954 On the development of turbulent wakes from vortex streets. NACA Report 1191.
35. Sarpkaya, T., Rainey, P. & Kell, R. 1973 Flow of dilute polymer solutions about circular cylinders. J. Fluid Mech. 57, 177208.
36. Sausset, F., Cadot, O. & Kumar, S. 2004 Experimental observation of frequency doubling in a viscoelastic mixing layer. C. R. Mechanique 332, 10011006.
37. Stone, P., Roy, A., Larson, R., Waleffe, F. & Graham, M. 2004 Polymer drag reduction in exact coherent structures of plane shear flow. Phys. Fluids 16 (9), 34703482.
38. Sureshkumar, R., Beris, A. N. & Handler, R. A. 1997 Direct numerical simulation of the turbulent channel flow of a polymer solution. Phys. Fluids 9 (3), 743755.
39. Williamson, C. H. K. 1996a Three-dimensional wake transition. J. Fluid Mech. 328, 345407.
40. Williamson, C. H. K. 1996b Vortex dynamics in the cylinder wake. Annu. Rev. Fluid Mech. 28, 477539.
41. Xi, L. & Graham, M. D. 2010 Active and hibernating turbulence in minimal channel flow of Newtonian and polymeric fluids. Phys. Rev. Lett. 104, 218301.
42. Yakushiji, R. 2009 Mechanism of tip vortex cavitation suppression. PhD thesis, University of Michigan.
43. Yu, Z. & Phan-Thien, N. 2004 Three-dimensional roll-up of a viscoelastic mixing layer. J. Fluid Mech. 500, 2953.
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