Hostname: page-component-745bb68f8f-g4j75 Total loading time: 0 Render date: 2025-01-08T22:05:11.500Z Has data issue: false hasContentIssue false
  • English
  • Français

Effects of viscoelasticity in the high Reynolds number cylinder wake

Published online by Cambridge University Press:  16 January 2012

David Richter ,
Gianluca Iaccarino  and
Eric S. G. Shaqfeh
David Richter
Affiliation:
Department of Mechanical Engineering, Stanford University, CA 94305, USA
Gianluca Iaccarino
Affiliation:
Department of Mechanical Engineering, Stanford University, CA 94305, USA
Eric S. G. Shaqfeh*
Affiliation:
Department of Mechanical Engineering, Stanford University, CA 94305, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

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.

JFM classification

Instability: Instability Non-Newtonian Flows: Viscoelasticity Wakes/Jets: Wakes
Type
Papers
Information
Journal of Fluid Mechanics , Volume 693 , 25 February 2012 , pp. 297 - 318
Copyright
Copyright © Cambridge University Press 2012

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

1. Azaiez, J. & Homsy, G. 1994a Linear stability of free shear flow of viscoelastic liquids. J. Fluid Mech. 268, 37–69.Google Scholar
2. Azaiez, J. & Homsy, G. 1994b Numerical simulation of non-Newtonian free shear flows at high Reynolds numbers. J. Non-Newtonian Fluid Mech. 52, 333–374.Google Scholar
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.Google Scholar
4. Bergins, C., Nowak, M. & Urban, M. 2001 The flow of a dilute cationic surfactant solution past a circular cylinder. Exp. Fluids 30, 410–417.Google Scholar
5. Bloor, M. S. 1964 The transition to turbulence in the wake of a circular cylinder. J. Fluid Mech. 19, 290–304.CrossRefGoogle Scholar
6. Cadot, O. & Kumar, S. 2000 Experimental characterization of viscoelastic effects on two- and three-dimensional shear instabilities. J. Fluid Mech. 416, 151–172.CrossRefGoogle Scholar
7. Chahine, G. L., Frederick, G. F. & Bateman, R. D. 1993 Propeller tip vortex cavitation suppression using selective polymer injection. J. Fluids Engng 115, 497–503.Google Scholar
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, 143–176.Google Scholar
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, 177–193.CrossRefGoogle Scholar
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, 55–68.Google Scholar
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, 153–162.CrossRefGoogle Scholar
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, 433–468.CrossRefGoogle Scholar
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), 1016–1027.CrossRefGoogle Scholar
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), 311–329.CrossRefGoogle Scholar
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, 271–280.CrossRefGoogle Scholar
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, 13–23.Google Scholar
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, 582–586.CrossRefGoogle Scholar
18. Kato, H. & Mizuno, Y. 1983 An experimental investigation of viscoelastic flow past a circular cylinder. Bull. Japan Soc. Mech. Engineers 26 (214), 529–536.Google Scholar
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, 281–299.CrossRefGoogle Scholar
20. Kravchenko, A. 1998 B-spline methods and zonal grids for numerical simulations of turbulent flows. PhD thesis, Stanford University.CrossRefGoogle Scholar
21. Kravchenko, A. & Moin, P. 2000 Numerical studies of flow over a circular cylinder at . Phys. Fluids 12 (2), 403–417.Google Scholar
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, 249–276.CrossRefGoogle Scholar
23. Ma, X., Karamanos, G. S. & Karniadakis, G. E. 2000 Dynamics and low-dimensionality of a turbulent near wake. J. Fluid Mech. 410, 29–65.Google Scholar
24. Ma, X., Symeonidis, V. & Karniadakis, G. 2003 A spectral vanishing viscosity method for stabilizing viscoelastic flows. J. Non-Newtonian Fluid Mech. 115, 125–155.Google Scholar
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), 49–57.Google Scholar
26. Ong, L. & Wallace, J. 1996 The velocity field of the turbulent very near wake of a circular cylinder. Exp. Fluids 20, 441–453.CrossRefGoogle Scholar
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), 1–14.Google Scholar
28. Prasad, A. & Williamson, C. H. K. 1997 The instability of the shear layer separating from a bluff body. J. Fluid Mech. 333, 375–402.Google Scholar
29. Rai, M. 2008 Towards direct numerical simulations of turbulent wakes. In 46th AIAA Aerospace Sciences Meeting and Exhibit. Paper 2008-0544.Google Scholar
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, 375–404.CrossRefGoogle Scholar
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, 415–442.Google Scholar
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, 554–565.Google Scholar
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. 303–310. Ellis Horwood.Google Scholar
34. Roshko, A. 1954 On the development of turbulent wakes from vortex streets. NACA Report 1191.Google Scholar
35. Sarpkaya, T., Rainey, P. & Kell, R. 1973 Flow of dilute polymer solutions about circular cylinders. J. Fluid Mech. 57, 177–208.Google Scholar
36. Sausset, F., Cadot, O. & Kumar, S. 2004 Experimental observation of frequency doubling in a viscoelastic mixing layer. C. R. Mechanique 332, 1001–1006.Google Scholar
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), 3470–3482.CrossRefGoogle Scholar
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), 743–755.CrossRefGoogle Scholar
39. Williamson, C. H. K. 1996a Three-dimensional wake transition. J. Fluid Mech. 328, 345–407.Google Scholar
40. Williamson, C. H. K. 1996b Vortex dynamics in the cylinder wake. Annu. Rev. Fluid Mech. 28, 477–539.Google Scholar
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.Google Scholar
42. Yakushiji, R. 2009 Mechanism of tip vortex cavitation suppression. PhD thesis, University of Michigan.Google Scholar
43. Yu, Z. & Phan-Thien, N. 2004 Three-dimensional roll-up of a viscoelastic mixing layer. J. Fluid Mech. 500, 29–53.Google Scholar