Skip to main content
SpringerLink
Log in

On the wavy flow past a weakly submerged horizontal circular cylinder at low Keulegan–Carpenter numbers

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

Abstract

The interaction of regular waves with a weakly submerged horizontal circular cylinder at Keulegan–Carpenter KC numbers up to 2.5 is studied by means of numerical simulations, solving the two-phase flow Navier–Stokes equations with the Finite Volume method and the Volume of Fluid interface capturing method. Experimental data from laboratory tests conducted in the past by one of the authors are used as reference data. The study is focused on the surface wave transformation, on the flow field in the near region and on the loads on the cylinder. The interest is driven on the spectral content of the transmitted waves at higher order frequencies and on the non-linear features of the wave reflected by the cylinder. The flow field in the near-body region is analyzed in terms of vortex onset, development and detachment, and correlating pressure pulses with the vorticity field at the cylinder surface. Inviscid flow simulations are carried out too, to evince the origin of higher order terms either from the free surface or from the viscous terms in the momentum equations. The steady streaming around the cylinder is analyzed, including its variability along the cylinder surface and its relationship with the vortex cores generated at the body surface.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18

Similar content being viewed by others

References

  1. Chaplin JR (1984) Mass transport around a horizontal cylinder beneath waves. J Fluid Mech 140:175–187

    Article  Google Scholar 

  2. Chaplin JR (1984) Nonlinear forces on a horizontal cylinder beneath waves. J Fluid Mech 147:449–464

    Article  Google Scholar 

  3. Chaplin JR (1988) Loading on a cylinder in uniform oscillatory flow: Part I—Planar oscillatory flow. Appl Ocean Res 10:120–128

    Article  Google Scholar 

  4. Chaplin JR (1992) Orbital flow around a circular cylinder. Part 1. Steady streaming in non-uniform conditions. J Fluid Mech 237:395–411

    Article  MATH  Google Scholar 

  5. Chaplin JR (1993) Orbital flow around a circular cylinder. Part 2. Attached flow at larger amplitudes. J Fluid Mech 246:397–418

    Article  MATH  Google Scholar 

  6. Chaplin JR (2001) Non-Linear Wave Interactions with a Submerged Horizontal Cylinder. In: Proceedings of the Eleventh (2001) International Offshore and Polar Engineering Conference, vol III, pp 272–279

  7. Chiu H (1973) Diffraction of water waves by a submerged circular cylinder. In: College of Engineering Rep. N A 73-4, University of California, Berkeley, CA

  8. Clement A (1995) Coupling of two absorbing boundary conditions for 2d time-domain simulations of free surface gravity waves. J Computat Phys 126:139–151

    Article  MATH  Google Scholar 

  9. Contento G (1995) A numerical wave tank for the free floating body problem. In: Proceedings of the 10th Workshop on Water Waves and Floating Bodies, Oxford, UK, pp 57–60

  10. Contento G, Casole S (1995) On the generation and propagation of waves in 2D numerical wave tanks. In: Proceedings of the 5th International Offshore and Polar Engineering Conference, vol III, pp 10–18

  11. Contento G, Codiglia R (2001) Non linear free surface induced pressure on a submerged horizontal circular cylinder at low Keulegan-Carpenters numbers. Appl Ocean Res 23:175–185

    Article  Google Scholar 

  12. Dean WR (1948) On the reflection of surface waves by a submerged circular cylinder. Proc Camb Phil Soc 483–491

  13. Dean RG, Dalrymple RN (1984) Water Wave Mechanics for Engineers and Scientists. World Scientific Advanced Series on Ocean Engineering, Prentice Hall Inc., Englewood Cliffs NJ

  14. Grue J (1992) Nonlinear water waves at a submerged obstacle or bottom topography. J Fluid Mech 244:455–476

    Article  Google Scholar 

  15. Grue J, Granlund K (1988) Impact of nonlinearity upon waves travelling over a submerged cylinder. In: Proceedings of the 3rd Workshop on Water Waves and Floating Bodies, Woods Hole, M.A. Dept. of Ocean Engineering, Mass. Inst of Technology, pp 57–60

  16. Haller G (2005) An objective definition of a vortex. J Fluid Mech 525:1–26

    Article  MathSciNet  MATH  Google Scholar 

  17. Higuera P, Lara LJ, Losada IJ (2013) Realistic wave generation and active wave absorption for Navier-Stokes models application to OpenFOAM. Coast Eng 71:102–118

    Article  Google Scholar 

  18. Hirt CW, Nichols BD (1981) Volume of fluid (VOF) method for the dynamics of free boundaries. J Comput Phys 39:201–225

    Article  MATH  Google Scholar 

  19. Hunt J, Wray A, Moin P (1988) Eddies, strem, and convergent zones in turbulent flows. Center Turbulence Res Report CTR-S88

  20. Jacobsen NG, Fuhrman DR, Fredsøe J (2012) A wave generation toolbox for the open-source CFD library: OpenFOAM. Int J Num Methods Fluids 70(9):1073–1088

    Article  MathSciNet  Google Scholar 

  21. Longuet-Higgins MS (1970) Steady currents induced by oscillations around islands. J Fluid Mech 42:701–720

    Article  MATH  Google Scholar 

  22. Lupieri G, Contento G (2015) Numerical simulations of 2-D steady and unsteady breaking waves. Ocean Eng 106:298–316

    Article  Google Scholar 

  23. Lupieri G, Contento G (2016) A numerical study on the viscous effects of waves travelling past a weakly submerged cylinder. To appear on Brodogradnja/Shipbuilding 67(4):61–79

  24. Lupieri G, Puzzer T, Contento G (2014) Numerical study of the wave-wave interaction by viscous flow simulation with OpenFoam. The \(21^{th}\) Symposium Theory and Practice of Shipbuilding SORTA, Baška, Island of Krk, Croatia

  25. Morison JR, O’Brien MP, Johnson JW, Schaaf SA (1950) The force exerted by surface waves on piles. Petrol Trans (Am Inst Min Eng) 189:149–154

    Google Scholar 

  26. Ogilvie TF (1963) First and second order forces on a cylinder submerged under a free surface. J Fluid Mech 16:451–472

    Article  MathSciNet  MATH  Google Scholar 

  27. Specialist Committee on CFD in Marine Hydrodynamics (2014) Proceedings—Volume II. \(27^{th}\) International Towing Tank Conference (ITTC), Copenhagen

  28. OpenFOAM (2012) OpenFoam user guide. OpenCFD Ltd

  29. Oshkai P, Rockwell D (1999) Free surface wave interaction with a horizontal cylinder. J Fluids Struct 13:935–954

    Article  Google Scholar 

  30. Otsuka K, Ikeda Y (1996) Estimation of inertia forces on a horizontal circular cylinder in regular and irregular waves at low Keulegan-Carpenter numbers. Appl Ocean Res 18:145–156

    Article  Google Scholar 

  31. Riley N (1971) Stirring of a viscous fluid. Z Angew Math Phys 22:645–653

    Article  MATH  Google Scholar 

  32. Riley N (1978) Circular oscillations of a cylinder in a viscous fluid. Z Angew Math Phys 29:439–449

    Article  MATH  Google Scholar 

  33. Riley N, Yan B (1996) Inviscid fluid flow around a submerged circular cylinder induced by free-surface travelling waves. J Eng Math 30:587–601

    Article  MathSciNet  MATH  Google Scholar 

  34. Rusche H (2002) Computational fluid dynamics of dispersed two—phase flows at high phase fractions. Imperial College of Science, Technology and Medicine, London

  35. Schønberg T, Chaplin JR (2001) Computation of Non-Linear Wave Reflections and Transmissions from a Submerged Horizontal Cylinder. In: Proceedings of the Eleventh (2001) International Offshore and Polar Engineering Conference, vol III, pp 280–287

  36. Stansby PK (1993) Forces on a circular cylinder in elliptical orbital flows at low Keulegan-Carpenter numbers. Appl Ocean Res 15:281–292

    Article  Google Scholar 

  37. Stansby PK, Smith PA (1991) Viscous forces on a circular cylinder in orbital flow at low Keulegan-Carpenter numbers. J Fluid Mech 229:159–171

    Article  MATH  Google Scholar 

  38. Swan C (2014) Group discussion on wave quality in wave basins and accurate models for the design wave kinematics. \(27^{th}\) International Towing Tank Conference (ITTC), Copenhagen

  39. Tsai WT, Yue DKT (1996) Computation of non linear free-surface flows. Annu Rev Fluid Mech 28:249–278

    Article  Google Scholar 

  40. Vada T (1987) A numerical solution of the second-order wave-diffraction problem for a submerged cylinder of arbitrary shape. J Fluid Mech 174:23–37

    Article  MATH  Google Scholar 

  41. Wu GX, Eatock Taylor R (1990) The second order diffraction force on a horizontal cylinder in finite water depth. Appl Ocean Res 12:106–111

    Article  Google Scholar 

  42. Yeung RW, Vaidhyanathan M (1992) Non-linear interaction of water waves with submerged obstacles. Int J Num Methods Fluids 14:1111–1130

    Article  MATH  Google Scholar 

  43. Zhang C, Shen L, Yue DKP (1999) The mechanism of vortex connection at a free surface. J Fluid Mech 384:207–241

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

The Programma Attuativo Regionale del Fondo per lo Sviluppo e la Coesione (PAR FSC 2007-2013) Linea d’Azione 3.1.2 is acknowledged for providing the financial support of the OpenViewSHIP Project.

Author information

Authors and Affiliations

  1. Department of Engineering and Architecture, University of Trieste, via Valerio, 10, 34127, Trieste, Italy

    Guido Lupieri & Giorgio Contento

Authors
  1. Guido Lupieri
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Giorgio Contento
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Guido Lupieri.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lupieri, G., Contento, G. On the wavy flow past a weakly submerged horizontal circular cylinder at low Keulegan–Carpenter numbers. J Mar Sci Technol 22, 673–693 (2017). https://doi.org/10.1007/s00773-017-0445-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00773-017-0445-y

Keywords

Search

Navigation