Acta Mechanica

, Volume 229, Issue 9, pp 3613–3627 | Cite as

Flow past a rotating circular cylinder with superhydrophobic surfaces

  • Q. Ren
  • Y. L. Xiong
  • D. Yang
  • J. Duan
Original Paper


Superhydrophobic surfaces (SHSs) are widely reported and applied to modify flow features. In this work, the two-dimensional flows past a rotating circular cylinder with SHSs are studied to explore its effect. The present numerical simulations take SHSs into account by alternating shear-free and no-slip boundary conditions with different gas fraction (GF) for non-dimensional rotation rates of \(0\le \alpha \le 6\) at \({ Re}=100\). Numerical results indicate that SHSs can obviously modify the critical rotation rates of vortex shedding, frequency of vortex shedding, force acting on the cylinder as well as the instantaneous and mean velocities near the cylinder. Moreover, such variation exhibits diverse behaviors in different flow regimes. For instance, both drag enhancement and drag reduction are found in the presence of SHSs. For the rotation rate corresponding to a vortex shedding regime, the drag of cylinder is reduced by SHSs. On the contrary, SHSs enhance the drag of cylinder in the steady regime. SHSs play different roles in different flow regimes so that the first critical rotation rate decreases monotonically with the increase of GF, while the second and the third critical rotation rates increase monotonically with increasing GF. The effect of SHSs in such flow could have some potential application.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.



  1. 1.
    Mittal, S., Kumar, B.: Flow past a rotating cylinder. J. Fluid Mech. 476, 303–334 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Rao, A., Radi, A., Leontini, J.S., Thompson, M.C.: A review of rotating cylinder wake transitions. J. Fluids Struct. 53, 2–14 (2015)CrossRefGoogle Scholar
  3. 3.
    Tokumaru, P.T., Dimotakis, P.E.: Rotary oscillation control of cylinder wake. J. Fluid Mech. 224, 77–90 (1991)CrossRefGoogle Scholar
  4. 4.
    Kang, S., Choi, H., Lee, S.: Laminar flow past a rotating circular cylinder. Phys. Fluids 11, 3312 (1999)CrossRefzbMATHGoogle Scholar
  5. 5.
    Kumar, S., Cantu, C., Gonzalez, B.: Flow past a rotating cylinder at low and high rotation rates. J. Fluids Eng. 133(4), 041201 (2011)CrossRefGoogle Scholar
  6. 6.
    Prandtl, L.: The Magnus effect and windpowered ships. Naturwissenschaften 13, 93–108 (1925)CrossRefGoogle Scholar
  7. 7.
    Díaz, F., Gavaldà, J., Kawall, J.G., Keffer, J.F., Giralt, F.: Vortex shedding from a spinning cylinder. Phys. Fluids 26, 3454–3460 (1983)CrossRefGoogle Scholar
  8. 8.
    Chew, Y.T., Cheng, M., Luo, S.C.: A numerical study of flow past a rotating circular cylinder using a hybrid vortex scheme. J. Fluid Mech. 299, 35–71 (1995)CrossRefzbMATHGoogle Scholar
  9. 9.
    Degani, A.T., Walker, J.D.A., Smith, F.T.: Unsteady separation past moving surfaces. J. Fluid Mech. 375, 1–38 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Stojković, D., Breuer, M., Durst, F.: Effect of high rotation rates on the laminar flow around a circular cylinder. Phys. Fluids 14, 3160–3178 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Stojković, D., Schön, P., Breuer, M., Durst, F.: On the new vortex shedding mode past a rotating circular cylinder. Phys. Fluids 15, 1257–1260 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Akoury, R.E.L., Braza, M., Perrin, R., Harran, G., Hoaraau, Y.: The three-dimensional transition in the flow around a rotating cylinder. J. Fluid Mech. 607, 1–11 (2008)CrossRefzbMATHGoogle Scholar
  13. 13.
    Pralits, J.O., Brandt, L., Giannetti, F.: Instability and sensitivity of the flow around a rotating circular cylinder. J. Fluid Mech. 650, 513–536 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Pralits, J.O., Giannetti, F., Brandt, L.: Three-dimensional instability of the flow around a rotating circular cylinder. J. Fluid Mech. 730, 5–18 (2013)CrossRefzbMATHGoogle Scholar
  15. 15.
    Kimura, T., Tsutahara, M.: Wake of a rotating circular cylinder. AIAA J. 30, 555–556 (1991)CrossRefzbMATHGoogle Scholar
  16. 16.
    Jaminet, J.F., Van Atta, C.W.: Experiments on vortex shedding from rotating circular cylinders. AIAA J. 7, 1817–1819 (1969)CrossRefGoogle Scholar
  17. 17.
    Hu, G.H., Sun, D.J., Yin, X.Y., Tong, B.G.: Hopf bifurcation in wakes behind a rotating and translating circular cylinder. Phys. Fluids 8, 1972–1974 (1996)CrossRefzbMATHGoogle Scholar
  18. 18.
    Rothstein, J.P.: Slip on superhydrophobic surfaces. Annu. Rev. Fluid Mech. 42, 89–109 (2010)CrossRefGoogle Scholar
  19. 19.
    Voronov, S.R., Papavassiliou, D.V.: Review of fluid slip over superhydrophobic surface and its dependence on the contact angle. Ind. Eng. Chem. Res. 47, 2455–2477 (2008)CrossRefGoogle Scholar
  20. 20.
    Min, T., Kim, J.: Effects of hydrophobic surface on skin-friction drag. Phys. Fluids 16, L55–58 (2004)CrossRefzbMATHGoogle Scholar
  21. 21.
    Martell, M.B., Rothstein, J.P., Perot, J.B.: An analysis of superhydrophobic turbulent drag reduction mechanism using direct numerical simulation. Phys. Fluids 22, 065102 (2010)CrossRefzbMATHGoogle Scholar
  22. 22.
    Martell, M.B., Perot, J.B., Rothstein, J.P.: Direct numerical simulations of turbulent flows over superhydrophobic surfaces. J. Fluid Mech. 620, 31–41 (2009)CrossRefzbMATHGoogle Scholar
  23. 23.
    Park, H., Park, H., Kim, J.: A numerical study of the effects of superhydrophobic surface on skin-friction drag in turbulent channel flow. Phys. Fluids 25, 110815 (2013)CrossRefGoogle Scholar
  24. 24.
    Lee, C., Choi, C.H., Kim, C.J.: Structured surfaces for a giant liquid slip. Phys. Rev. Lett. 101, 064501 (2008)CrossRefGoogle Scholar
  25. 25.
    You, D., Moin, P.: Effects of hydrophobic surfaces on the drag and lift of a circular cylinder. Phys. Fluids 19, 081701 (2007)CrossRefzbMATHGoogle Scholar
  26. 26.
    Behr, M., Hastreiter, D., Mittal, S., Tezduyar, T.E.: Incompressible flow past a circular cylinder: dependence of the computed flow field on the location of the lateral boundaries. Comput. Methods Appl. Mech. Eng. 123, 309–316 (1995)CrossRefGoogle Scholar
  27. 27.
    Tezduyar, T.E., Shih, R.: Numerical experiments on downstream boundary of flow past cylinder. J. Eng. Mech. 117, 854–871 (1991)CrossRefGoogle Scholar
  28. 28.
    Behr, M., Liou, J., Shih, R., Tezduyar, T.E.: Vorticity-stream function formulation of unsteady incompressible flow past a cylinder: sensitivity of the computed flow field to the location of the outflow boundary. Int. J. Numer. Methods Fluids 12, 323–342 (1991)CrossRefGoogle Scholar
  29. 29.
    Bhattacharyya, S.K., Maiti, D.K.: Vortex shedding suppression for laminar flow past a square cylinder near a plane wall: a two-dimensional analysis. Acta Mech. 184, 15–31 (2006)CrossRefzbMATHGoogle Scholar
  30. 30.
    Park, J., Kwon, K., Choi, H.: Numerical solutions of flow past a circular cylinder at Reynolds numbers up to 160. KSME Int. J. 12, 1200–1205 (1988)CrossRefGoogle Scholar
  31. 31.
    Tritton, D.J.: Experiments on the flow past a circular cylinder at low Reynolds numbers. J. Fluid Mech. 6(4), 547–567 (1959)CrossRefzbMATHGoogle Scholar
  32. 32.
    Li, J., Chambarel, A., Donneaud, M.: Numerical study of laminar flow past one and two circular cylinders. Comput. Fluids 19(2), 155–170 (1991)CrossRefzbMATHGoogle Scholar
  33. 33.
    Norberg, C.: An experimental investigation of flow around a circular cylinder: influence of aspect ratio. J. Fluid Mech. 258, 287–316 (1994)CrossRefGoogle Scholar
  34. 34.
    Sharman, B., Lien, F.S., Davidson, L., Norberg, C.: Numerical predictions of low Reynolds number flow over two tandem circular cylinders. Int. J. Numer. Methods Fluids 47, 423–447 (2005)CrossRefzbMATHGoogle Scholar
  35. 35.
    Braza, M., Persillon, H.: Physical analysis of the transition to turbulence in the wake of a circular cylinder by three-dimensional Navier–Stokes simulation. J. Fluid Mech. 365, 23–88 (1988)zbMATHGoogle Scholar
  36. 36.
    Badr, H.M., Dennis, S.C.R., Young, P.J.S.: Steady and unsteady flow past a rotating circular cylinder at low Reynolds numbers. Comput. Fluids 17, 579–609 (1989)CrossRefzbMATHGoogle Scholar
  37. 37.
    Tang, T., Ingham, D.B.: On steady flow past a rotating circular cylinder at Reynolds numbers 60 and 100. Comput. Fluids 19, 217–230 (1991)CrossRefzbMATHGoogle Scholar
  38. 38.
    Xiong, Y.L., Bruneau, C.H., Yang, D.: Numerical study on viscoelastic fluid flow past a rigid body. Appl. Math. Model. 42, 188–208 (2017)MathSciNetCrossRefGoogle Scholar
  39. 39.
    Xiong, Y.L., Bruneau, C.H., Kellay, H.: A numerical study of two dimensional flows past a bluff body for dilute polymer solutions. J. Non-Newton. Fluid Mech. 196, 8–26 (2013)CrossRefGoogle Scholar
  40. 40.
    Xiong, Y.L., Bruneau, C.H., Kellay, H.: Direct numerical simulations of 2D channel flows in the presence of polymers. Europhys. Lett. 95, 640003 (2011)CrossRefGoogle Scholar
  41. 41.
    Williamson, C.H.K.: Vortex dynamics in the cylinder wake. Annu. Rev. Fluid Mech. 28, 477–539 (1996)MathSciNetCrossRefGoogle Scholar
  42. 42.
    Xiong, Y.L., Yang, D.: Influence of slip on the three-dimensional instability of flow past an elongated superhydrophobic bluff body. J. Fluid Mech. 814, 69–94 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  43. 43.
    Bailey, S.C.C., Kopp, G.A., Martinuzzi, R.J.: Vortex shedding from a square cylinder near a wall. J. Turbul. 3, 1–18 (2003)Google Scholar
  44. 44.
    Dol, S.S., Kopp, G.A., Martinuzzi, R.J.: The suppression of periodic vortex shedding from a rotating circular cylinder. J. Wind Eng. Ind. Aerodyn. 96, 1164–1184 (2008)CrossRefGoogle Scholar
  45. 45.
    Muralidhar, P., Ferrer, N., Daniello, R., Rothstein, J.P.: Influence of slip on the flow past superhydrophobic circular cylinders. J. Fluid Mech. 680, 459–476 (2011)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MechanicsHuazhong University of Science and Technology (HUST)WuhanChina
  2. 2.Hubei Key Laboratory of Engineering Structural Analysis and Safety AssessmentWuhanChina
  3. 3.School of Naval Architecture and Ocean EngineeringHuazhong University of Science and Technology (HUST)WuhanChina

Personalised recommendations