Skip to main content
Log in

High-reynolds number flow around coated symmetrical hydrofoil: effect of streamwise slip on drag force and vortex structures

  • Original article
  • Published:
Journal of Marine Science and Technology Aims and scope Submit manuscript

Abstract

Effects of slip on the flow around a symmetrical hydrofoil with a blunt trailing-edge are numerically investigated at Reynolds numbers of \(Re=5 \times {10^6}\), \(12.5 \times {10^6}\) and \(25 \times {10^6}\) based on the free-stream velocity and chord length. The simulations are performed by applying a two-dimensional Unsteady Reynolds–Averaged Navier–Stokes (URANS) approach and SST k–ω turbulence model. Furthermore, the Navier boundary condition with different slip lengths (\({L_{\text{s}}}=\;{\text{2}},{\text{ 35 and 7}}0\) µm) is employed on the surfaces. The results indicate that the Ls has a considerable effect on the integral parameters and a moderate influence on the wake flow structure. As such, a massive drag reduction (up to 47%) is observed, and an increase of Ls causes the increase of both frictional and pressure drag reduction rate. It is shown that a noticeable drag reduction can be achieved when the non-dimensional slip length is larger than one. The increment of slip length also leads to increase the amplitude of force fluctuations and frequency of vortex shedding; besides, the strength of vortex structures and the turbulence intensities are augmented.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

References

  1. Kim J (1999) Active control of turbulent boundary layers for drag reduction. Lect Notes Phys 529:142–152

    Article  MATH  Google Scholar 

  2. Sohankar A, Khodadadi M, Rangraz E (2015) Control of fluid flow and heat transfer around a square cylinder by uniform suction and blowing at low Reynolds numbers. Comput Fluids 109:155–167

    Article  MathSciNet  MATH  Google Scholar 

  3. McCormick ME, Bhattacharyya R (1973) Drag reduction of a submersible hull by electrolysis. Naval Eng J 85:11–16

    Article  Google Scholar 

  4. Catalanoy P, Wang M, Iaccarino G, Sbalzariniz IF, Koumoutsakos P (2002) Optimization of cylinder flow control via actuator with zero net mass flux, Center of Turbulence Research. In: Proceedings of the summer program

  5. Shao X, Lin J, Tao W, Yulin L (2002) Experimental research on drag reduction by polymer additives in a turbulent pipe flow. Can J Chem Eng 80:293–298

    Article  Google Scholar 

  6. Daniello RJ, Waterhouse NE, Rothstein JP (2009) Drag reduction in turbulent flows over superhydrophobic surfaces. Phys Fluids 21:085103

    Article  MATH  Google Scholar 

  7. Goldstein S, Council AR (1965) Modern developments in fluid dynamics (an account of theory and experiment relating to boundary layers, turbulent motion, and wakes). Dover, New York

    Google Scholar 

  8. Choi C-H, Johan K, Westin A, Breuer KS (2003) Apparent slip flows in hydrophilic and hydrophobic microchannels. Phys Fluids 15(10):2897–2902

    Article  MATH  Google Scholar 

  9. Thompson PA, Troian SM (1997) A general boundary condition for liquid flow at solid surfaces. Nature 389(25):360–362

    Article  Google Scholar 

  10. Priezjev NV (2007) Rate-dependent slip boundary conditions for simple fluids. Phys Rev E 75:051605

    Article  Google Scholar 

  11. Min T, Kim J (2004) Effects of hydrophobic surface on skin-friction drag. Phys Fluids 16(7):55–58

    Article  MATH  Google Scholar 

  12. You D, Moin P (2007) Effects of hydrophobic surfaces on the drag and lift of a circular cylinder. Phys Fluids 19:081701

    Article  MATH  Google Scholar 

  13. Nouri MN, Sekhavat S, Mofidi A (2012) Drag reduction in a turbulent channel flow with hydrophobic wall. J Hydrodyn 24(3):458–466

    Article  Google Scholar 

  14. Khosh Aghdam S, Ricco P (2016) Laminar and turbulent flows over hydrophobic surfaces with shear-dependent slip length. Phys Fluids 28:035109

    Article  Google Scholar 

  15. Ou J, Perot B, Rothstein JP (2004) Laminar drag reduction in microchannel using ultra hydrophobic surfaces. Phys Fluids 16:4635–4643

    Article  MATH  Google Scholar 

  16. Fukagata K, Kasagi N, Koumoutsakos P (2006) A theoretical prediction of friction drag reduction in turbulent flow by superhydrophobic surfaces. Phys Fluids 18(5):051703

    Article  Google Scholar 

  17. Nouri NM, Rastan MR, Sekhavat S (2016) Numerical method to predict slip length in turbulent channel flow. J Appl Fluid Mech 9(2):719–728

    Article  Google Scholar 

  18. Li L, Yuan MS (2011) Modeling of drag reduction in turbulent channel flow with hydrophobic walls by FVM method and weakly-compressible flow equations. Acta Mech Sin 27(2):200–207

    Article  MATH  Google Scholar 

  19. Nouri MN, Saadat Bakhsh M, Sekhavat S (2013) Analysis of shear rate effects on drag reduction in turbulent channel flow with superhydrophobic wall. J Hydrodyn 25(6):944–953.

    Article  Google Scholar 

  20. Jia-peng Z, Xiang-dang DU, Xiu-hua SHI (2007) Experimental research on friction-reduction with superhydrophobic surfaces. J Mar Sci Appl 6(3):58–61

    Article  Google Scholar 

  21. Jeffs K, Maynes D, Webb BW (2010) Prediction of turbulent channel flow with superhydrophobic walls consisting of micro-ribs and cavities oriented parallel to the flow direction. Int J Heat Mass Transf 53(4):786–796

    Article  MATH  Google Scholar 

  22. Martell MB, Perot JB, Rothstein JP (2009) Direct numerical simulations of turbulent flows over superhydrophobic surfaces. J Fluid Mech 620:3

    Article  MATH  Google Scholar 

  23. Brian RK, Gruncell ND, Sandham G McHale (2013) Simulations of laminar flow past a superhydrophobic sphere with drag reduction and separation delay. Phys Fluids 25:043601

    Article  Google Scholar 

  24. Blake WK (1975) Periodic and random excitation of streamlined structures by trailing edge flows. In: Proceedings of the fourth biennial symposium on turbulence in liquids, Rolla, MO, USA

  25. Yao Z, Wang F, Dreyer M, Farhat M (2014) Effect of trailing edge shape on hydrodynamic damping for a hydrofoil. J Fluids Struct 51:189–198

    Article  Google Scholar 

  26. Zobeiri A, Ausoni P, Avellan F, Farhat M (2012) How oblique trailing edge of a hydrofoil reduces the vortex-induced vibration. J Fluids Struct 32:78–89

    Article  Google Scholar 

  27. Thomareis N, Papadakis G (2017) Effect of trailing edge shape on the separated flow characteristics around an airfoil at low Reynolds number: a numerical study. Phys Fluids 29:014101

    Article  Google Scholar 

  28. Do T, Chen L, Tu J (2010) Numerical study of turbulent trailing-edge flows with base cavity effects using URANS. J Fluids Struct 26:1155–1173

    Article  Google Scholar 

  29. FLUENT (V 6.4) and GAMBIT (V 2.1.6) User’s guides (2007). Fluent Inc., Lebanon

  30. Menter F (1994) Two-equation eddy viscosity turbulence models for engineering applications. AIAA J 32:1598–1605

    Article  Google Scholar 

  31. Wilcox DC (1994) Simulation of transition with a two-equation turbulence model. AIAA J 32:247–255

    Article  MATH  Google Scholar 

  32. Wilcox DC (2006) Turbulence modeling for CFD, 3rd edn. DCW Industries Inc., California, pp 124–128

    Google Scholar 

  33. Rastan MR, Sohankar A, Alam MM (2017) Low-Reynolds-number flow around a wall-mounted square cylinder: flow structures and onset of vortex shedding. Phys Fluids 29:103601

    Article  Google Scholar 

  34. Hao PF, Wong C, Yao ZH, Zhu KQ (2009) Laminar drag reduction in hydrophobic microchannels. Chem Eng Technol 32(6):912–918

    Article  Google Scholar 

  35. Sohankar A, Norberg C, Davidson L (1998) Low-Reynolds number flow around a square cylinder at incidence: study of blockage, onset of vortex shedding and outlet boundary condition. Int J Numer Methods Fluids 26:39–56

    Article  MATH  Google Scholar 

  36. Metzger MM, Klewicki JC (2001) A comparative study of near-wall turbulence in high and low Reynolds number boundary layers. Phys Fluids 13:692–701

    Article  MATH  Google Scholar 

  37. Park H, Park H, Kim J (2013) A numerical study of the effects of superhydrophobic surface on skin-friction drag in turbulent channel flow. Phys Fluids 25:110815

    Article  Google Scholar 

  38. Rastegari A, Akhavan R (2015) On the mechanism of turbulent drag reduction with super-hydrophobic surfaces. J Fluid Mech 773(R4):1–14

    MathSciNet  Google Scholar 

  39. Huang H, Liu M, Gu H, Li X, Wu X, Sun F (2018) Effect of the slip length on the flow over a hydrophobic circular cylinder. Fluid Dyn Res. https://doi.org/10.1088/1873-7005/aaab9b (in press)

    MathSciNet  Google Scholar 

  40. Ding L, Bernitsas MM, Kim ES (2013) 2-D URANS vs. experiments of flow induced motions of two circular cylinders in tandem with passive turbulence control for 30,000 < Re < 105,000. Ocean Eng 72:429–440

    Article  Google Scholar 

  41. Jeong J, Hussain F (1995) On the identification of a vortex. J Fluid Mech 285:69–94

    Article  MathSciNet  MATH  Google Scholar 

  42. Aboueian J, Sohankar A (2017) Identification of flow regimes around two staggered square cylinders by a numerical study. Theor Comput Fluid Dyn 31:295–315

    Article  Google Scholar 

  43. Hunt JCR, Wray AA, Moin P (1988) Eddies, stream, and convergence zones in turbulent flows. In: Cent. Turbul. Res Rep CTR-S88, pp. 193–208

Download references

Acknowledgements

The authors would like to thank the Islamic Azad University- East Tehran Branch, Iran for providing computing facilities and fund. The first author also gratefully acknowledges Dr. Danielle Moreau for her significant and constructive contribution to the presented work.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to S. Sekhavat.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Rastan, M.R., Foshat, S. & Sekhavat, S. High-reynolds number flow around coated symmetrical hydrofoil: effect of streamwise slip on drag force and vortex structures. J Mar Sci Technol 24, 500–511 (2019). https://doi.org/10.1007/s00773-018-0570-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00773-018-0570-2

Keywords

Navigation