A three-dimensional (3D) numerical two-phase flow model based on solving unsteady Reynolds-averaged Navier–Stokes (URANS) equations has been used to simulate breaking waves and steep waves past a vertical cylinder on a 1:10 slope. The volume of fluid (VOF) method is employed to capture the free surface and the k–ω shear–stress transport (k–ω SST) turbulence model is used to simulate the turbulence effects. Mesh and time-step refinement studies have been conducted. The numerical results of wave forces on the structure are compared with the experimental data (Irschik et al., 2004, “Breaking Wave Loads on a Slender Pile in Shallow Water,” Coastal Engineering, Vol. 4, World Scientific, Singapore, pp. 568–581) to validate the numerical model, and the numerical results are in good agreement with the measured data. The wave forces on the structure at different Keulegan–Carpenter (KC) numbers are discussed in terms of the slamming force. The secondary load cycles are observed after the wave front past the structure. The dynamic pressure and velocity distribution, as well as the characteristics of the vortices around the structure at four important time instants, are studied.

References

References
1.
Christensen
,
E. D.
,
Bredmose
,
H.
, and
Hansen
,
E. A.
,
2005
, “
Extreme Wave Forces and Wave Run-Up on Offshore Wind Turbine Foundations
,”
Copenhagen Offshore Wind Conference
, Copenhagen, Denmark, Oct. 26–28, pp.
1
10
.https://www.researchgate.net/publication/242394446_Extreme_wave_forces_and_wave_run-up_on_offshore_wind-_turbine_foundations
2.
Clauss
,
G. F.
,
Schmittner
,
C. E.
, and
Stück
,
R.
,
2005
, “
Numerical Wave Tank: Simulation of Extreme Waves for the Investigation of Structural Responses
,”
ASME
Paper No. OMAE2005-67048.
3.
Yang
,
C.
,
Löhner
,
R.
, and
Lu
,
H.
,
2006
, “
An Unstructured-Grid Based Volume-of-Fluid Method for Extreme Wave and Freely-Floating Structure Interactions
,”
J. Hydrodyn.
,
18
(
S1
), pp.
405
412
.
4.
Mo
,
W.
,
Irschik
,
K.
,
Oumeraci
,
H.
, and
Liu
,
P. L.-F.
,
2007
, “
A 3D Numerical Model for Computing Non-Breaking Wave Forces on Slender Piles
,”
J. Eng. Math.
,
58
(
1–4
), pp.
19
30
.
5.
Bredmose
,
H.
, and
Jacobsen
,
N. G.
,
2010
, “
Breaking Wave Impacts on Offshore Wind Turbine Foundations: Focused Wave Groups and CFD
,”
ASME
Paper No. OMAE2010-20368.
6.
Pakozdi
,
C.
,
Kendon
,
T. E.
, and
Stansberg
,
C.-T.
,
2011
, “
Breaking Wave Impact on a Platform Column: An Introductory CFD Study
,”
ASME
Paper No. OMAE2011-49976.
7.
Jacobsen
,
N. G.
,
Fuhrman
,
D. R.
, and
Fredsøe
,
J.
,
2012
, “
A Wave Generation Toolbox for the Open-Source CFD Library: Openfoam®
,”
Int. J. Numer. Methods Fluids
,
70
(
9
), pp.
1073
1088
.
8.
Hildebrandt
,
A.
, and
Schlurmann
,
T.
,
2012
, “
Breaking Wave Kinematics, Local Pressures, and Forces on a Tripod Structure
,”
Coastal Eng. Proc.
,
1
(
33
), p.
71
.
9.
Choi
,
S. J.
,
Lee
,
K. H.
, and
Gudmestad
,
O. T.
,
2015
, “
The Effect of Dynamic Amplification Due to a Structure's Vibration on Breaking Wave Impact
,”
Ocean Eng.
,
96
, pp.
8
20
.
10.
Kamath
,
A.
,
Chella
,
M. A.
,
Bihs
,
H.
, and
Arntsen
,
Ø. A.
,
2016
, “
Breaking Wave Interaction With a Vertical Cylinder and the Effect of Breaker Location
,”
Ocean Eng.
,
128
, pp.
105
115
.
11.
Jose
,
J.
, and
Choi
,
S.-J.
,
2017
, “
Estimation of Slamming Coefficients on Local Members of Offshore Wind Turbine Foundation (Jacket Type) Under Plunging Breaker
,”
Int. J. Nav. Archit. Ocean Eng.
,
9
(
6
), pp.
624
640
.
12.
Liu
,
S.
,
Jose
,
J.
,
Ong
,
M. C.
, and
Gudmestad
,
O. T.
,
2019
, “
Characteristics of Higher-Harmonic Breaking Wave Forces and Secondary Load Cycles on a Single Vertical Circular Cylinder at Different Froude Numbers
,”
Mar. Struct.
,
64
, pp.
54
77
.
13.
Nielsen
,
P.
,
2009
,
Coastal and Estuarine Processes
, Vol.
29
,
World Scientific Publishing Company
, Singapore.
14.
Dütsch
,
H.
,
Durst
,
F.
,
Becker
,
S.
, and
Lienhart
,
H.
,
1998
, “
Low-Reynolds-Number Flow Around an Oscillating Circular Cylinder at Low Keulegan–Carpenter Numbers
,”
J. Fluid Mech.
,
360
, pp.
249
271
.
15.
Irschik
,
K.
,
Sparboom
,
U.
, and
Oumeraci
,
H.
,
2004
, “
Breaking Wave Loads on a Slender Pile in Shallow Water
,” Coastal Engineering, Vol. 4, World Scientific, Singapore, pp.
568
581
.
16.
Brown
,
S.
,
Greaves
,
D.
,
Magar
,
V.
, and
Conley
,
D.
,
2016
, “
Evaluation of Turbulence Closure Models Under Spilling and Plunging Breakers in the Surf Zone
,”
Coastal Eng.
,
114
, pp.
177
193
.
17.
Devolder
,
B.
,
Troch
,
P.
, and
Rauwoens
,
P.
,
2018
, “
Performance of a Buoyancy-Modified k-ω and k-ω Sst Turbulence Model for Simulating Wave Breaking Under Regular Waves Using OpenFOAM®
,”
Coastal Eng.
,
138
, pp.
49
65
.
18.
Menter
,
F. R.
,
1994
, “
Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications
,”
AIAA J.
,
32
(
8
), pp.
1598
1605
.
19.
Wilcox
,
D.
,
1988
, “
Reassessment of the Scale-Determining Equation for Advanced Turbulence Models
,”
AIAA J.
,
26
(
11
), pp.
1299
1310
.
20.
Mohammadi
,
B.
, and
Pironneau
,
O.
,
1993
,
Analysis of the k-Epsilon Turbulence Model
,
Wiley
, Hoboken, NJ.
21.
Berberović
,
E. V.
,
Hinsberg
,
N. P.
,
Jakirlić
,
S.
,
Roisman
,
I. V.
, and
Tropea
,
C.
,
2009
, “
Drop Impact Onto a Liquid Layer of Finite Thickness: Dynamics of the Cavity Evolution
,”
Phys. Rev. E
,
79
(
3
), p.
0363061
.
22.
Seng
,
S.
,
2012
, “
Slamming and Whipping Analysis of Ships
,” Ph.D. thesis, Delhi Technological University, Delhi, India.
23.
Mayer
,
S.
,
Garapon
,
A.
, and
Sørensen
,
L.
,
1998
, “
A Fractional Step Method for Unsteady Free-Surface Flow With Applications to Non-Linear Wave Dynamics
,”
Int. J. Numer. Methods Fluids
,
28
(
2
), pp.
293
315
.
24.
Versteeg
,
H. K.
, and
Malalasekera
,
W.
,
2007
,
An Introduction to Computational Fluid Dynamics: The Finite Volume Method
,
Pearson Education
, London.
25.
Holzmann
,
T.
,
2017
,
Mathematics, Numerics, Derivations and OpenFOAM®
, Holzmann CFD, Loeben, Germany.
26.
Holthuijsen
,
L. H.
,
2010
,
Waves in Oceanic and Coastal Waters
,
Cambridge University Press
,
Cambridge, UK
.
27.
Koh
,
R. C.
, and
Le Méhauté
,
B.
,
1966
, “
Wave Shoaling
,”
J. Geophys. Res.
,
71
(
8
), pp.
2005
2012
.
28.
Grue
,
J.
,
Bjørshol
,
G.
, and
Strand
,
Ø.
,
1993
,
Higher Harmonic Wave Exciting Forces on a Vertical Cylinder
, (Mechanics and Applied Mathematics), University of Oslo Library, Oslo, Norway.
29.
Chaplin
,
J.
,
Rainey
,
R.
, and
Yemm
,
R.
,
1997
, “
Ringing of a Vertical Cylinder in Waves
,”
J. Fluid Mech.
,
350
, pp.
119
147
.
30.
Harrower
,
M.
, and
Brewer
,
C. A.
,
2003
, “
ColorBrewer.org: An Online Tool for Selecting Colour Schemes for Maps
,”
Cartographic J.
,
40
(
1
), pp.
27
37
.
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