Korea-Australia Rheology Journal

The Korean Society of Rheology (한국유변학회)
권호 표지

Effect of viscoelasticity on two-dimensional laminar vortex shedding in flow past a rotating cylinder

  • Kim, Ju-Min (Department of Chemical Engineering, Ajou University) ;
  • Ahn, Kyung-Hyun (School of Chemical and Biological Engineering, Seoul National University) ;
  • Lee, Seung-Jong (School of Chemical and Biological Engineering, Seoul National University)
  • Published : 2009.03.31
Download PDF
⟨ Previous Next ⟩

Abstract

In this work, we numerically investigate the effect of viscoelasticity on 2D laminar vortex dynamics in flows past a single rotating cylinder for rotational rates $0{\leq}{\alpha}{\leq}5$ (the rotational rate ex is defined by the ratio of the circumferential rotating velocity to free stream velocity) at Re=100, in which the vortex shedding has been predicted to occur in literature for Newtonian fluids. The objective of the present research is to develop a promising technique to fully suppress the vortex shedding past a bluff body by rotating a cylinder and controlling fluid elasticity. The predicted vortex dynamics with the present method is consistent with the previous works for Newtonian flows past a rotating cylinder. We also verified our method by comparing our data with the literature in the case of viscoelastic flow past a non-rotating cylinder. For $0{\leq}{\alpha}{\leq}1.8$, the frequency of vortex shedding slightly decreases but the fluctuation of drag and lift coefficient significantly decreases with increasing fluid elasticity. We observe that the vortex shedding of viscoelastic flow disappears at lower ${\alpha}$ than the Newtonian case. At ${\alpha}$=5, the relationship between the frequency of vortex shedding and Weissenberg number (Wi) is predicted to be non-monotonic and have a minimum around Wi=0.25. The vortex shedding finally disappears over critical Wi number. The present results suggest that the vortex shedding in the flow around a rotating cylinder can be more effectively suppressed for viscoelastic fluids than Newtonian fluids.

Keywords

References

  1. Alves, M. A., F. T. Pinho and P. J. Oliveira, 2001, The flow of viscoelastic fluids past a cylinder: finite-volume high-resolution methods, J Non-Newtonian Fluid Mech. 97, 207-232 https://doi.org/10.1016/S0377-0257(00)00198-1
  2. Brooks, A. N. and T. J. R. Hughes, 1982, Streamline upwind/ Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations, Comput. Mrthods Appl. Mech. Eng. 32, 199-259 https://doi.org/10.1016/0045-7825(82)90071-8
  3. Cadot, O. and M. Lebey, 1999, Phys. Fluids 11, 494-496 https://doi.org/10.1063/1.869864
  4. Cadot, O. and S. Kumar, 2000, J Fluid Mech. 416, 151-172 https://doi.org/10.1017/S0022112000008818
  5. Caola A. E., Y. L. Joo, R. C. Armstrong and R. A. Brown, 2001, Highly parallel time integration of viscoelastic flows, J Non-Newtonian Fluid Mech. 100, 191-216 https://doi.org/10.1016/S0377-0257(01)00136-7
  6. Carew, E. O. A., P. Townsend and M. F. Webster, 1993, A taylorpetrov- galerkin algorithm for viscoelastic flow, J Non-Newtonian Fluid Mech. 50, 253-287 https://doi.org/10.1016/0377-0257(93)80034-9
  7. Deville, M. O., P. F. Fischer and E. H. Mund, 2002, High-order methods for incompressible fluid flow, Cambridge University Press, Cambridge, UK
  8. Dimitropoulos, C. D., R. Sureshkumar and A. N. Beris, 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 https://doi.org/10.1016/S0377-0257(98)00115-3
  9. Fan, Y. and M. J. Crochet, 1995, High-order finite element methods for steady viscoelastic flows, J Non-Newtonian Fluid Mech. 57, 283-311 https://doi.org/10.1016/0377-0257(94)01338-I
  10. Graham, M. D., 2003, Interfacial hoop stress and instability of viscoelastic free surface flows, Physics Fluids 15, 1702-1710 https://doi.org/10.1063/1.1568340
  11. Groisman, A. and V. Steinberg, 2000, Elastic turbulence in a polymer solution flow, Nature 405, 53-55 https://doi.org/10.1038/35011019
  12. Kang, S., H. Choi and S. Lee, 1999, Laminar flow past a rotating circular cylinder, Phys. Fluids 11, 3312-3321 https://doi.org/10.1063/1.870190
  13. Kang, S., 2006, Laminar flow over a steadily rotating circular cylinder under the influence of uniform shear, Phys. Fluids 18, 047106 https://doi.org/10.1063/1.2189293
  14. Kirn, J. M., C. Kim, K. H. Ahn and S. J. Lee, 2004, An efficient iterative solver and high-resolution computations of the Oldroyd-B fluid flow past a confined cylinder, J Non-Newtonian Fluid Mech. 123(2-3), 161-173 https://doi.org/10.1016/j.jnnfm.2004.08.003
  15. Lilek Z., S. Muzaferija, M. PeriE and V. Seidl, 1997, Computation of unsteady flows using nonmatching blocks of structured grids, Numer. Heat Transf B 32, 403-418 https://doi.org/10.1080/10407799708915016
  16. McKinley, G H., R. C. Armstrong and R. A. Brown, 1993, The wake instability in viscoelastic flow past confined circular cylinders, Phil. Trans. Roy. Soc. Lond. A 344, 265-304 https://doi.org/10.1098/rsta.1993.0091
  17. McKinley, G. H., P. Pakdel and A. Oztekin, 1996, Rheological and geometric scaling of purely elastic instabilities, J Non-Newtonian Fluid Mech. 67, 19-47 https://doi.org/10.1016/S0377-0257(96)01453-X
  18. Min, T., J. Y. Yoo and H. Choi, 2001, Effect of spatial discretization schemes on numerical solutions of viscoelastic fluid flows, J Non-Newtonian Fluid Mech. 100, 27-47 https://doi.org/10.1016/S0377-0257(01)00128-8
  19. Min, T., J. Y. Yoo and H. Choi, 2003, Maximum drag reduction in a turbulent channel flow by polymer additives, J Fluid Mech. 492, 91-100 https://doi.org/10.1017/S0022112003005597
  20. Nigen, S. and K. Walters, 2002, Viscoelastic contraction flows: comparison of axisymmetric and planar configurations, J Non-Newtonian Fluid Mech. 102, 343-359 https://doi.org/10.1016/S0377-0257(01)00186-0
  21. Oliveira, P. J., 2001 , Method for time-dependent simulations of viscoelastic flows: vortex shedding behind cylinder, J Non-Newtonian Fluid Mech. 101, 113-137 https://doi.org/10.1016/S0377-0257(01)00146-X
  22. Oliveira, P. J. and A. I. P. Miranda, 2005, A numerical study of steady and unsteady viscoelastic flow past bounded cylinders, J Non-Newtonian Fluid Mech. 127, 51-66 https://doi.org/10.1016/j.jnnfm.2005.02.003
  23. Papanastasiou, T. C., N. Malamataris and K. Ellwood, 1992, A new outflow boundary condition, Int. J Numer. Methods Fluids 14, 587-608 https://doi.org/10.1002/fld.1650140506
  24. Park, J., K. Kwon and H. Choi, 1998, Numerical solutions of flow past ,a circular cylinder at Reynolds number up to 160, KSME Int. J 12, 1200-1205
  25. Park, S. J. and S. J. Lee, 1999, On the use ofthe open boundary condition method in the numerical simulation of nonisothermal viscoelastic flow, J. Non-Newtonian Fluid Mech. 87(2-3), 197-214 https://doi.org/10.1016/S0377-0257(99)00064-6
  26. Rothstein, J. P. and G. H. McKinly, 1999, Extensional flow of a polystyrene Boger fluid through a 4:1:4 axisymmetric contraction/expansion, J. Non- Newtonian Fluid Mech. 86, 61-88 https://doi.org/10.1016/S0377-0257(98)00202-X
  27. Sahin, M. and R. G. Owens, 2004, On the effect of viscoelasticity on two-dimentional vortex dynamics in the cylinder wake, J Non-Newtonian Fluid Mech. 123, 121-139 https://doi.org/10.1016/j.jnnfm.2004.08.002
  28. Saramito, P. and J. M. Piau, 1994, Flow characteristics of viscoelastic fluids in an abrupt contraction by using numerical modeling, J. Non-Newtonian Fluid Mech. 52, 263-288 https://doi.org/10.1016/0377-0257(94)80055-3
  29. Spiegelberg H. and G. H. McKinley, 1996, Stress relaxation and elastic decohesion of viscoelastic polymer solutions in extensional flow, J. Non-Newtonian Fluid Mech. 67, 49-76 https://doi.org/10.1016/S0377-0257(96)01475-9
  30. Stojkovic, D., M. Breuer and F. Durst, 2002, Effect of high rotation rates on the laminar flow around a circular cylinder, Phys Fluids 14(9), 3160-3178 https://doi.org/10.1063/1.1492811
  31. Stojkovic, D., P. Schon, M. Breuer and F. Durst, 2003, On thε new vortex shedding mode past a rotating circular cylinder, Phys. Fluids 15(5), 1257-1260 https://doi.org/10.1063/1.1562940
  32. Sunwoo, G. B , S. J. Park, S. J. Lee, K. H. Ahn and S. J. LEE， 2001, Numerical simulation of three-dimensional viscoelastic flow using the open boundary condition method in coextrusion process, J Non-Newtonian Fluid Mech. 99(2-3), 125-144 https://doi.org/10.1016/S0377-0257(01)00115-X
  33. Surεshkwnar, R., A. N. Beris and R. A. Handler, 1997, Direct numerical simulation of the turbulent channel flow of a polymer solution, Phys. Fluids 9(3), 743-755 https://doi.org/10.1063/1.869229
  34. Usui, H., T. Shibata and Y. Sano, 1980, J Chem. Eng. Jpn. 13, 77-79 https://doi.org/10.1252/jcej.13.77
  35. van der Vorst, H. A., 1992, Bi-CGSTAB: A fast and smoothly converging variant of Bi-CG for the solution of non-symmetric linear systems, SIAM J Sci. Stat. Comput. 12, 631-634
  36. Williamson, C. H. K., 1996, Vortex dynamics in the cylinder wake, Annu. Rev. Fluid Mech. 28, 477-539 https://doi.org/10.1146/annurev.fl.28.010196.002401